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ophy of science enjoyed great popularity for some years if his criterion is construed as an answer to the question the positivists were asking it turns out to fail in exactly parallel ways negative existential claims there are no unicorns and positive universals all ravens are black can be falsified but positive existential and negative universal claims cannot logical positivists response to the first criticism is that logical positivism like all other philosophies of science is a philosophy of science not an axiomatic system that can prove its own consistency see g del s incompleteness theorem secondly a theory of language and mathematical logic were created to answer what it really means to say things like all ravens are black a response to the second criticism was provided by a j ayer in language truth and logic in which he sets out the distinction between strong and weak verification a proposition is said to be verifiable in the strong sense of the term if and only if its truth could be conclusively estab |
lished by experience ayer one nine four six five zero it is this sense of verifiable that causes the problem of verification with negative existential claims and positive universal claims however the weak sense of verification states that a proposition is verifiable if it is possible for experience to render it probable ibid after establishing this distinction ayer goes on to claim that no proposition other than a tautology can possibly be anything more than a probable hypothesis ayer one nine four six five one and therefore can only be subject to weak verification this defence was controversial among logical positivists some of whom stuck to strong verification and claimed that general propositions were indeed nonsense subsequent philosophy of science tends to make use of the better aspects of both of these approaches work by w v o quine and thomas kuhn has convinced many that it is not possible to provide a strict criterion for good or bad scientific method outside of the science we already have but even th |
is sentiment was not unknown to the logical positivists otto neurath famously compared science to a boat which we must rebuild on the open sea see also kurt g del rudolf carnap moritz schlick otto neurath david stove sociological positivism external links http www philosophypages com hy six q htm logik der forschung in one nine three four the philosophy of logical positivism references edmonds david wittgenstein s poker isbn zero zero six six two one two four four eight ayer a j language truth and logic isbn zero four eight six two zero zero one zero eight neurath otto and carnap r et al one nine three eight international encyclopedia of unified science u chicago press chicago philosophical movements philosophy of language epistemology philosophy of science a lorentz transformation lt is a linear transformation that preserves the spacetime interval between any two events in minkowski space while leaving the origin fixed the transformation describes how space and time coordinates are related as measured by obs |
ervers in different inertial reference frames poincar one nine zero five named them after the dutch physicist and mathematician hendrik lorentz one eight five three one nine two eight they form the mathematical basis for albert einstein s theory of special relativity the lorentz transformations remove contradictions between the theories of electromagnetism and classical mechanics they were derived by larmor one eight nine seven and lorentz one eight nine nine one nine zero four in one nine zero five einstein derived them under the assumptions of lorentz covariance and the constancy of the speed of light in any inertial reference frame in a given coordinate system x a the spacetime interval between two events a and b with coordinates t one x one y one z one and t two x two y two z two respectively is given by s two t two t one two x two x one two y two y one two z two z one two and is an invariant x a x a x a x a i e eta x ax b eta x c x d where eta is the minkowski metric eta begin one when c a zero the trans |
formation is a lorentz transformation taking the determinant of the first equation gives det lambda a b pm one lorentz transformations with det lambda a b one are called proper lorentz transformations and consist of spatial rotations and boosts those with det lambda a b one are called improper lorentz transformations and consist of discrete space and time reflections a quantity invariant under lorentz transformations is known as a lorentz scalar lorentz transformation for frames in standard configuration given two observers s and s each using a cartesian coordinate system to measure space and time intervals t x y z and t x y z assume that the coordinate systems are oriented so that s moves with constant speed v relative to s along the common x x axis with the y and y axes parallel and similarly for the z and z axes also assume that their origins meet at the common time t t zero then the frames are said to be in standard configuration sc the lorentz transformation for frames in sc can be shown to be t gamma le |
ft t frac right x gamma x v t y y z z where gamma equiv frac is called the lorentz factor or gamma factor and c is the speed of light in a vacuum this lorentz transformation is called a boost in the x direction and is often expressed in matrix form as begin c t x y z end begin gamma x x vt y z which incorporated relativity of simultaneity local time and time dilation for voigt clocks ran slower by the factor gamma two which is greater than the now accepted value of gamma predicted by larmor one eight nine seven note that voigt equations have a length expansion in the transverse direction voigt derived these transformations as those which would make the speed of light the same in all reference frames lorentz believed voigt s transformations were equivalent to his apparently not seeing the significance of the different time dilation and wrote in a paper which to my regret has escaped my notice all these years voigt has applied a transformation equivalent to the lorentz treansformation the idea of the transforma |
tions used above might therefore have been borrowed form voigt and the proof that it does not alter the form of the equations for the free ether is contained in his paper lorentz one nine one three in a similar vein larmor and lorentz who believed the luminiferous aether hypothesis were seeking the transformations under which maxwell s equations were invariant when transformed from the ether to a moving frame henri poincar in one nine zero zero attributed the invention of local time to lorentz and showed how lorentz s first version of it which applies to invariant clock rates arose when clocks were sychronised by exchanging light signals which were assumed to travel at the same speed against and with the motion of the reference frame see relativity of simultaneity larmor s one eight nine seven and lorentz s one eight nine nine one nine zero four final equations were not in the modern notation and form but were algebraically equivalent to those published one nine zero five by henri poincar the french mathemati |
cian who revised the form to make the four equations into the coherent self consistent whole we know today both larmor and lorentz discovered that the transformation preserved maxwell s equations paul langevin one nine one one said of the transformation it is the great merit of h a lorentz to have seen that the fundamental equations of electromagnetism admit a group of transformations which enables them to have the same form when one passes from one frame of reference to another this new transformation has the most profound implications for the transformations of space and time see also carroll group electromagnetic field galilean transformation principle of relativity special relativity external links nothing but relativity there are many ways to derive the lorentz transformation without invoking einstein s constancy of light postulate the path preferred in this paper restates a simple established approach the paradox of special relativity this webpage poses a problem the solution of which is the lorentz tra |
nsformation which is presented graphically in its next page a note on relativity before einstein brit journal philos science three seven two three two three four one nine eight six a brief discussion of the work of voigt larmor and lorentz warp special relativity simulator a computer program demonstrating the lorentz transformations on everyday objects a history of special relativity including a discussion of the independent derivations of the lorentz transformations by voigt and larmor references ernst a and hsu j p two zero zero one first proposal of the universal speed of light by voigt one eight eight seven chinese journal of physics three nine three two one one two three zero langevin p one nine one one l evolution of l espace et du temps scientia x three one five four larmor j one eight nine seven dynamical theory of the electric and luminiferous medium philosophical transactions of the royal society one nine zero two zero five three zero zero larmor j one nine zero zero aether and matter cambridge univ |
ersity press lorentz h a one eight nine nine simplified theory of electrical and optical phenomena in moving systems proc acad science amsterdam i four two seven four three lorentz h a one nine zero four electromagnetic phenomena in a system moving with any velocity less than that of light proc acad science amsterdam iv six six nine seven eight lorentz h a one nine one three the theory of electrons book poincar h one nine zero five sur la dynamque de l electron comptes rendues one four zero one five zero four zero eight voigt w one eight eight seven ueber das doppler sche princip nachrichten von der k niglicher gesellschaft den wissenschaft zu g ttingen two four one five one special relativity equations this article is about the aether as a hypothesis in physics for other uses see aether disambiguation the luminiferous aether it was hypothesised that the earth moves through a medium of aether that carries light in the late one nine th century luminiferous aether light bearing aether was the term used to descr |
ibe a medium for the propagation of light later theories including special relativity were formulated without the ether concept and today the aether is considered to be an obsolete scientific theory the word aether stems via latin from the greek from a root meaning to kindle burn shine which signified the substance thought in ancient times to fill the upper regions of space beyond the clouds the history of light and aether see also timeline of luminiferous aether isaac newton had assumed that light was made up of numerous small particles in order to explain features such as its ability to travel in straight lines and reflect off surfaces this theory was known to have its problems although it explained reflection well its explanation of refraction and diffraction was less pleasing in order to explain refraction in fact newton s opticks one seven zero four postulated an aethereal medium transmitting vibrations faster than light by which light when overtaken is put into fits of easy reflexion and easy transmissi |
on causing refraction and diffraction newton believed that these vibrations were related to things like heat radiation saying is not the heat of the warm room convey d through the vacuum by the vibrations of a much subtiler medium than air which after the air was drawn out remained in the vacuum and is not this medium the same with that medium by which light is refracted and reflected and by whose vibrations light communicates heat to bodies and is put into fits of easy reflexion and easy transmission the modern understanding of course is that heat radiation is light but newton considered them two different phenomena believing heat vibrations to be excited when a ray of light falls upon the surface of any pellucid body he wrote that i do not know what this aether is but that if it consists of particles then they must be exceedingly smaller than those of air or even than those of light the exceeding smallness of its particles may contribute to the greatness of the force by which those particles may recede from |
one another and thereby make that medium exceedingly more rare and elastick than air and by consequence exceedingly less able to resist the motions of projectiles and exceedingly more able to press upon gross bodies by endeavoring to expand itself christiaan huygens prior to newton had hypothesized that light itself was a wave propagating through an aether but newton rejected this idea the main reason for his rejection stemmed from the fact that both men could apparently only envision light to be a longitudinal wave like sound and other mechanical waves in gases and fluids however longitudinal waves by necessity have only one form for a given propagation direction rather than two polarizations as in a transverse wave and thus they were unable to explain the phenomenon of birefringence where two polarizations of light are refracted differently by a crystal instead newton preferred to imagine non spherical particles or corpuscles of light with different sides that give rise to birefringence a further reason wh |
y newton rejected light as waves in a medium however was because such a medium would have to extend everywhere in space and would thereby disturb and retard the motions of those great bodies the planets and comets and thus as it light s medium is of no use and hinders the operation of nature and makes her languish so there is no evidence for its existence and therefore it ought to be rejected in one seven two zero james bradley carried out a series of experiments attempting to measure stellar parallax although he failed to detect any parallax thereby placing a lower limit on the distance to stars he discovered another effect stellar aberration an effect which depends not on position as in parallax but on speed he noticed that the apparent position of the star changed as the earth moved around its orbit bradley explained this effect in the context of newton s corpuscular theory of light by showing that the aberration angle was given by simple vector addition of the earth s orbital velocity and the velocity of |
the corpuscles of light just as vertically falling raindrops strike a moving object at an angle knowing the earth s velocity and the aberration angle this enabled him to estimate the speed of light to explain stellar aberration in the context of an ether based theory of light was regarded as more problematic because it requires that the ether be stationary even as the earth moves through it precisely the problem that led newton to reject a wave model in the first place however a century later young and fresnel revived the wave theory of light when they pointed out that light could be a transverse wave rather than a longitudinal wave the polarization of a transverse wave like newton s sides of light could explain birefringence and in the wake of a series of experiments on diffraction the particle model of newton was finally abandoned physicists still assumed however that like mechanical waves light waves required a medium for propagation and thus required huygens idea of an aether gas permeating all space howe |
ver a transverse wave apparently required the propagating medium to behave as a solid as opposed to a gas or fluid the idea of a solid that did not interact with other matter seemed a bit odd and augustin louis cauchy suggested that perhaps there was some sort of dragging or entrainment but this made the aberration measurements difficult to understand he also suggested that the absence of longitudinal waves suggested that the aether had negative compressibility but george green pointed out that such a fluid would be unstable george gabriel stokes became a champion of the entrainment interpretation developing a model in which the aether might be by analogy with pine pitch rigid at very high frequencies and fluid at lower speeds thus the earth could move through it fairly freely but it would be rigid enough to support light later maxwell s equations showed that light is an electromagnetic wave maxwell s equations required that all electromagnetic waves in vacuum propagate at a fixed speed c as this can only occ |
ur in one reference frame in newtonian physics see galilean newtonian relativity the aether was hypothesized as the absolute and unique frame of reference in which maxwell s equations hold that is the aether must be still universally otherwise c would vary from place to place maxwell himself proposed several mechanical models of aether based on wheels and gears and george fitzgerald even constructed a working model of one of them these models were non trivial especially because they had to agree with the fact that the electromagnetic waves are transverse but never longitudinal nevertheless by this point the mechanical qualities of the aether had become more and more magical it had to be a fluid in order to fill space but one that was millions of times more rigid than steel in order to support the high frequencies of light waves it also had to be massless and and without viscosity otherwise it would visibly effect the orbits of planets additionally it appeared it had to be completely transparent non dispersive |
incompressible and continuous at a very small scale contemporary scientists were aware of the problems but aether theory was so entrenched in physical law by this point that it was simply assumed to exist in one nine zero eight oliver lodge gave a speech in behalf of lord rayleigh to the royal institution on this topic in which he outlined its physical properties and then attempted to offer reasons why they were not impossible nevertheless he was also aware of the criticisms and quoted lord salisbury as saying that aether is little more than a nominative case of the verb to undulate others criticized it as an english invention although rayleigh jokingly corrected them to state it was actually an invention of the royal institution by the early two zero th century aether theory was in trouble a series of increasingly complex experiments had been carried out in the late one eight zero zero s to try to detect the motion of earth through the aether and had failed to do so a range of proposed aether dragging theor |
ies could explain the null result but these were more complex and tended to use arbitrary looking coefficients and physical assumptions lorentz and fitzgerald offered a more elegant solution to how the motion of an absolute aether could be undetectable length contraction but if their equations were correct the new special theory of relativity one nine zero five could generate the same mathematics without referring to an aether at all aether fell to occam s razor aether and classical mechanics the key difficulty with the aether hypothesis arose from the juxtaposition of the two well established theories of newtonian dynamics and maxwell s electromagnetism under a galilean transformation the equations of newtonian dynamics are invariant whereas those of electromagnetism are not basically this means that while physics should remain the same in non accelerated experiments light would not follow the same rules because it is travelling in the universal aether frame some effect caused by this difference should be de |
tectable a simple example concerns the model on which aether was originally built sound the speed of propagation for mechanical waves the speed of sound is defined by the mechanical properties of the medium for instance if one is in an airliner you can still carry on a conversation with the person beside you because the sound of your words are travelling along with the air inside the aircraft this effect is basic to all newtonian dynamics which says that everything from sound to the trajectory of a thrown baseball should all remain the same in the aircraft as sitting still on the earth this is the basis of the galilean transformation and the concept of frame of reference but the same was not true for light since maxwell s mathematics demanded a single universal speed for the propagation of light based not on local conditions but two measured properties that were assumed to be the same throughout the universe if these numbers did change there should be noticable effects in the sky stars in different directions |
would have different colors for instance certainly they would remain constant within a small volume inside the aircraft in our example for instance which implies that light would not follow along with the aircraft or the earth in a fashion similar to sound nor could light change media for instance using the atmosphere while near the earth it had already been demonstrated that if this were so the sky would be colored in different directions as the light moved from the still medium of the aether to the moving medium of the earth s atmosphere causing diffraction thus at any point there should be one special coordinate system at rest relative to the aether maxwell noted in the late one eight seven zero s that detecting motion relative to this aether should be easy enough light travelling along with the motion of the earth would have a different speed than light travelling backward as they would both be moving against the unmoving aether even if the aether had an overall universal flow changes in position during |
the day night cycle or over the span of seasons should allow the drift to be detected experiments numerous experiments were carried out in the late one eight zero zero s to test for this aether wind effect but most were open to dispute due to low accuracy measurements on the speed of propagation were so inaccurate that comparing two speeds to look for a difference was essentially impossible the famous michelson morley experiment instead compared the source light with itself after being sent in different directions looking for changes in phase in a manner that could be measured with extremely high accuracy the publication of their result in one eight eight seven the null result was the first clear demonstration that something was seriously wrong with the absolute aether concept a series of experiments using similar but increasingly sophisticated apparatus all returned the null result as well a conceptually different experiment that also attempted to detect the motion of the aether was the one nine zero three t |
routon noble experiment which like michelson morley obtained a null result it is important to understand what null result means in this context it does not mean there was no motion detected it means that the results produced by the experiment were not compatible with the assumptions used to devise it in this case the mm experiment showed a small positive velocity causing a movement of the fringing pattern of about zero zero one of a fringe however it was too small to demonstrate the expected aether wind effect due to the earth s seasonally varying velocity which would have required a shift of zero four of a fringe and the error was enough that the value may have indeed been zero more modern experiments have since reduced the possible value to a number very close to zero about one zero one five these aether wind experiments led to its abandonment by some scientists and to a flurry of efforts to save aether by assigning it ever more complex properties by others of particular interest was the possibility of aeth |
er entrainment or aether drag which would lower the magnitude of the measurement perhaps enough to explain mmx results however as noted earlier aether dragging already had problems of its own notably aberration a more direct measurement was made in the hamar experiment which ran a complete mm experiment with one of the legs placed between two massive lead blocks if the aether was dragged by mass then this experiment would have been able to detect the drag caused by the lead but again the null result was found similar experiments by hoek placed one leg in a heavy vat of water the theory was again modified this time to suggest that the entrainment only worked for very large masses or those masses with large magnetic fields this too was shown to be incorrect when oliver joseph lodge noted no such effect around other planets another completely different attempt to save absolute aether was made in the lorentz fitzgerald contraction hypothesis which posited that everything was affected by travel through the aether |
in this theory the reason the michelson morley experiment failed was that it contracted in length in the direction of travel that is the light was being affected in the natural manner by its travel though the aether as predicted but so was the experiment itself cancelling out any difference when measured even lorentz was not very happy with this suggestion although it did neatly solve the problem later this idea received additional support from the kennedy thorndike experiment in one nine three two as kennedy and thorndike concluded that both a lorentz contraction as well as time dilation occur thus confiming special relativity another experiment purporting to show effects of an aether was fizeau s one eight five one experimental confirmation of fresnel s one eight one eight prediction that a medium with refractive index n moving with a velocity v would increase the speed of light traveling through the medium in the same direction as v from c n to frac left one frac right v that is movement adds only a fracti |
on of the medium s velocity to the light predicted by fresnel in order to make snell s law work in all frames of reference consistent with stellar aberration this was initially interpreted to mean that the medium drags the aether along with a portion of the medium s velocity but that understanding was rejected after wilhelm veltmann demonstrated that the index n in fresnel s formula depended upon the wavelength of light so that the aether could not be moving at a wavelength independent speed with the advent of special relativity fresnel s equation was shown by laue in one nine zero seven to be an approximation valid for v much smaller than c for the correct relativistic formula to add the velocities v medium and c n rest frame frac approx frac left one frac right v o left frac right variations on these themes continued for the next three zero years positive results were reported by several of the key researchers including additional experiments by michelson morley and dayton miller miller reported positive re |
sults on several occasions but of a magnitude that required further modifications to the drag or contraction theories during the one nine two zero s a slew of increasingly accurate experiments returned the null result and the positives were generally attributed to experimental errors other positive results included sagnac in one nine one three and the michelson gale pearson experiment in one nine two five this effect that is known as sagnac effect is nowadays used in optical gyroscopes and shows that rotation is similarly absolute for light as it is for pendulums end of aether aether theory was dealt another blow when the galilean transformation and newtonian dynamics were both modified by albert einstein s special theory of relativity giving the mathematics of lorentzian electrodynamics a new non aether context like most major shifts in scientific thought the move away from aether theory did not happen immediately but as experimental evidence built up and as older scientists left the field and their places w |
ere taken by the young the concept lost adherents einstein based his special theory on lorentz s earlier work but instead of suggesting that the mechanical properties of objects changed with their constant velocity motion through an aether he took the somewhat more radical step of suggesting that the math was a general transformation and that the galilean transformation was a special case that worked only at the low speeds we had studied up to that time by applying the transformation to all inertial frames of reference he demonstrated that physics remained invariant as it had with the galilean transformation but that light was now invariant as well with the development of special relativity the need to account for a single universal frame had disappeared and aether went along with it for einstein but not for lorentz the transformation also implied something much more radical that the concept of position in space or time was not absolute but could differ depending on the observer s location and speed this oddn |
ess of einstein s interpretation led to special relativity being considered highly questionable for some time all of this left the problem of light propagation through a vacuum however in another paper published the same month einstein also made several observations on a then thorny problem the photoelectric effect in this work he demonstrated that light can be considered as particles that have a wave like nature particles obviously do not need a medium to travel and thus neither did light this was the first step that would lead to the full development of quantum mechanics in which the wave like nature and the particle like nature of light are both considered to be simplifications of what is really happening continuing adherents most current physicists do not see a need to have a medium for light to propagate the combination of relativity and quantum mechanics seems to render the concept unnecessary however this doesn t mean it doesn t exist just that it doesn t have to and there remain a number of problems i |
n modern physics that would be simplified with such a concept a few physicists like dayton miller and edward morley continued research on the aether for some time and occasionally researchers still explore these concepts while it is not difficult to create aether theories consistent with the michelson morley experiment it is much harder to remain consistent with all of the related experiments of modern physics any new theory of aether must be consistent with all of the experiments testing phenomena of special relativity general relativity relativistic quantum mechanics and so on although the vast majority of modern physicists reject all aether based theories the intuitive appeal of a causal background for relativistic effects cannot be denied in a paper of one nine five eight g builder concluded that the observable effects of absolute accelerations and of absolute velocites must be described to iteraction of bodies and physical systems with some absolute inertial system interaction of bodies and physical syst |
ems with the universe cannot be described in terms of mach s hypothesis since this is untenable there is therefore no alternative to the ether hypothesis in agreement with this professor sherwin wrote in one nine six zero one is led therefore to the conclusion that clocks having a velocity in an inertial frame are literally slowed down by the speed itself it is this very deduction which makes the generally accepted prediction regarding the clock paradox unacceptable to dingle but which has led both ives and builder to consider interpretations of special relativity in which an ether plays an important role at least from the philosophical point of view a number of new ether concepts have been proposed in recent years for example in a controversial quantum approach to gravity called loop quantum gravity spacetime is filled with a structure called the spin foam much like aether it picks a privileged reference frame and is therefore incompatible with lorentz invariance a symmetry of special theory of relativity it |
s existence therefore potentially disagrees with the michelson morley like experiments maurizio consoli of the italian national institute of nuclear physics in catania sicily argues in physics letters a vol three three three p three five five that any michelson morley type of experiment carried out in a vacuum will show no difference in the speed of light even if there is an aether electroweak theory and quantum field theory suggest that light could appear to move at different speeds in different directions in a medium such as a dense gas the speed of light would be sensitive to motion relative to an ether and the refractive index of the medium consoli and evelina costanzo propose an experiment with laser light passing through cavities filled with a relatively dense gas with the earth passing through an ether wind light would travel faster in one direction than in the perpendicular direction this would fit with predictions by lorentz whose theory for light predict equivalent results to those of the special th |
eory of relativity only in a vacuum some adherents of modern geocentrism claim that the michelson morley experiment proves that the earth is stationary which in turn causes them to explain the universe in terms of an aether or firmament aether conceptions aether theories aether classical element aether and general relativity aether drag hypothesis see also history of special relativity list of fringe theories in physics preferred frame references banesh hoffman relativity and its roots freeman new york one nine eight three michael janssen one nine th century ether theory einstein for everyone course at umn two zero zero one isaac newton opticks one seven zero four republished one nine five two dover new york with commentary by bernard cohen albert einstein and edmund whittaker j larmour a dynamical theory of the luminiferous medium transactions of the royal society one eight eight five eight six albert einstein ether and the theory of relativity one nine two zero republished in sidelights on relativity dover |
ny one nine two two albert einstein ideas and opinions pp two eight one three six two isbn zero five one seven eight eight four four zero two langevin p one nine one one l volution de l espace et du temps scientia x p three one g builder ether and relativity australian journal of physics one one one nine five eight p two seven nine p dirac is there an ether nature one six eight one nine five one p nine zero six h ives the measurement of velocity with atomic clocks science vol nine one one nine four zero p six five h a lorentz the principle of relativity for uniform translations one nine one zero one nine one two lectures on theoretical physics vol iii one nine three one authorised translation of the dutch version of one nine two two g sagnac e bouty the luminiferous ether demonstrated by the effect of the relative motion of the ether in an interferometer in uniform rotation in french comptes rendus paris one five seven one nine one three p seven zero eight seven one zero c sherwin some recent experimental tes |
ts of the clock paradox physical review one two zero no one one nine six zero p one seven two one aether s comeback in contemporary physics an essay by adrian sfarti external links what is the experimental basis of special relativity includes a lengthy list of aether experiments among others the ether of space lord rayleigh s address modern scientific theories of the ancient aether a categorised compendium of articles relating to the emergence of scientific theories that reference the aether or quantum foam of space ether and the theory of relativity albert einstein s one nine two zero inaguration address at the university of leyden actually delivered on two seven october one nine two zero history of physics aether theories history of ideas obsolete scientific theories lame official logo lame is an open source mp three that is mpeg one audio layer three audio compression application lame is a recursive acronym for l ame a in t an m p three e ncoder although the current version is a stand alone encoder see bel |
ow as of two zero zero four consensus is that lame produces the highest quality mp three files for bitrates one two eight kb s in a public listening test early in two zero zero four lame mp three files were the most identical one two eight kb s mp three files compared to the uncompressed original audio legal issues lame endured some legal difficulties regarding fraunhofer s patent on certain key algorithms involved in mp three encoding including and foreign counterparts these patents were intended to prevent anyone from being able to create an mp three encoder without paying licensing fees to fraunhofer something that is difficult to enforce for an open source program whose users live in dozens of countries many of which do not recognize patents on algorithms lame front end at one time lame was simply a set of patches against the iso demonstration source which is distributed separately hence the ain t an encoder name that iso code had a restrictive license but was available without charge however in may two z |
ero zero zero the lame project reimplemented the last of the iso source code and thus lame is now a totally new implementation available under the lgpl license compiling recent versions of lame no longer requires the iso source code lame developers however state that since their code is only released in source form source code is considered as speech which may contain descriptions of patented technology descriptions of patents are in the public domain the lame software is licensed under the gnu lesser general public license lgpl in november two zero zero five there were reports that the extended copy protection software included on some sony compact discs includes portions of the lame library without complying with the terms of the lgpl lame compatible systems grip a front end for use with gnome linux lamedrop yet another easy to use front end for use of lame in windows similar to oggdrop razorlame formerly razorblade a microsoft windows front end user interface for the commandline lame encoder executable win |
lame another front end for windows zortam mp three media studio another front end for windows exact audio copy eac windows audio grabber for cd rom drives which can make use of lame lame gui besweet gui another front end for windows itunes lame a front end that integrates lame with itunes on mac os x jripper a java based frontend for lame which includes windows binaries also works on linux based systems see also mp three list of codecs vorbis audio data compression external links lame website lame win three two macos x linux bsd solaris etc binaries historical lame versions lame source tarballs lame mp three info tag revision one specifications lame at hydrogenaudio wiki hydrogenaudio forums audio codecs free multimedia codecs containers and splitters lucille ball lucille d sir e ball august six one nine one one april two six one nine eight nine was an american actress comedian and star of i love lucy a b grade movie star of the one nine three zero s and one nine four zero s she later achieved tremendous succ |
ess as a television actress and became one of the most popular stars in american history early life and career she was born on august one nine one one in the small town of celoron a suburb of jamestown new york to henry durrell ball and desiree dede eve hunt during her late teens she was fired from an ice cream shop because she kept forgetting to put bananas in banana splits her father was a telephone lineman for the bell company while her mother was often described as a lively and energetic young woman her father s job required frequent transfers and within three years after her birth lucille had moved from jamestown to anaconda montana and then to wyandotte michigan while dede ball was pregnant with her second child frederick henry ball contracted typhoid fever and died in february one nine one five after her father passed away ball and her brother fred were raised by her working mother and grandparents her grandfather fred hunt was an eccentric socialist who enjoyed the theater he frequently took the famil |
y to local vaudeville shows and encouraged young lucy to take part in both her own and school plays at the age of fifteen lucy dropped out of high school in one nine two five after a romance with a local bad boy johnny devito ball decided to enroll in the john murray anderson school for the dramatic arts with her mother s approval there the shy girl was outshined by another pupil bette davis ball went home a few weeks later when drama coaches told her that she had no future at all as a performer two years later she witnessed the accidental shooting of a friend of her brother s warner erikson who found himself in the path of a two two caliber rifle shot severing his spinal cord her grandfather was sued and prosecuted and lost the family home she moved back to new york city in one nine three zero to become an actress and had some success as a fashion model for designer hattie carnegie and as the chesterfield girl she began her performing career on broadway using the stage name dianne belmont and was hired by th |
eatre impresario earl carroll but then quickly fired from his earl carroll s vanities she was let go again from the shubert brothers production of stepping stones but did manage an uncredited walk on role in one nine three three s thru a keyhole but then moved to hollywood to appear in films she appeared in many small movie roles in the one nine three zero s as a contract player for rko including one movie with the marx brothers and another with the three stooges she switched to mgm in the one nine four zero s but never achieved great success in films she was known in many hollywood circles as queen of the bs a title previously held by fay wray starring in a number of b movies such as one nine three nine s five came back macdonald carey was designated as her king in one nine four zero ball met cuban bandleader desi arnaz while filming the film version of the rodgers and hart stage hit too many girls the two hit it off immediately and eloped the same year to much press attention when arnaz was drafted to the u |
nited states army in one nine four two he cheated on ball arnaz ended up being classified for limited service due to a knee injury as a result arnaz stayed in los angeles organizing and performing uso shows for wounded gis being brought back from the pacific ball filed for a divorce in one nine four four however shortly after ball obtained an interlocutory decree she got together with desi again in one nine four eight lucille was cast as liz cugat later cooper a wacky wife in my favorite husband a radio program for cbs the program was successful and cbs asked her to develop it as a television program she agreed but insisted on working with arnaz this show eventually became i love lucy cbs was initially not impressed with the pilot episode produced by the couple s desilu productions company so the arnazes toured the road in a vaudeville act with lucille as the zany housewife wanting to get in arnaz s show the tour was a smash and cbs put the show on their lineup in one nine five three she was subpoenaed by the |
house committee on un american activities due to her having registered to vote in the communist party in one nine three six at her socialist grandfather s insistence per fbi foia released documents in response to these accusations desi quipped the only thing red about lucy is her hair and even that s not legitimate lucy survived this unpleasant encounter with the huac and named no names lucy made friends in hollywood not very many perhaps but life long including ginger rogers mary wickes and vivian vance her longtime costar on several series ironically all were childless wickes never married but lucy s instincts were always more professional and connubial than maternal which explained her strained relations with her children and even grandchildren especially lucie arnaz her daughter who after her mother s death called her controlling i love lucy lucille ball as lucy vivian vance as ethel on an episode of i love lucy lucy and ethel try to speed it up a little the i love lucy show was not only a star vehicle f |
or lucille ball but a way for her to try to salvage her marriage to desi arnaz which had become badly strained in part by the fact that each had a hectic performing schedule which often kept them apart along the way she created a very early television sitcom although the format had existed for decades in radio and in fact other tv sitcoms predated her show and was among the first stars to film before a live audience from a production aspect the use of actual film as opposed to the inferior quality kinescope of other tv shows of the time made the show far more visually appealing the initial decision to use film was driven by the performers desire to stay in los angeles sponsor philip morris didn t want to show kinescopes to the major markets on the east coast so lucy and desi agreed to take a pay cut to finance filming in return cbs relinquished the show rights back to desilu after broadcast not realizing they were giving away a valuable and durable asset desilu made many millions of dollars on ill rebroadcast |
s through syndication lucy and desi also hired legendary czech cameraman karl freund as their director of photography freund had worked for f w murnau and fritz lang shot part of metropolis had directed a number of hollywood films himself and knew his business for lucy freund developed the three camera setup which became the standard way of shooting situation comedies shooting long shots medium shots and close ups on a comedy in front of a live audience demanded discipline technique and close choreography among other non standard techniques used in filming the show cans of paint in shades ranging from white to medium gray were kept on set to paint out innappropriate shadows and disguise lighting flaws on july one seven one nine five one just one month shy of her four zero th birthday and after several miscarriages ball gave birth to her first child lucie desiree arnaz a year and a half later ball gave birth to her second child desiderio alberto arnaz iv i love lucy was in full swing by this time and neither b |
all nor arnaz wanted to take a hiatus for the pregnancy they planned to write the pregnancy into the show s story line so that lucy ricardo would have her baby around the same time the arnazes own child was born however the network balked declaring you cannot show a pregnant woman on television they also declared that the word pregnant could not be uttered over the airwaves ball and arnaz consulted a priest a rabbi and a minister about the appropriateness of their plans and all three said that none of it was in any way offensive finally the network compromised the pregnancy could be worked into the scripts but the word pregnant was still taboo instead the euphemism expecting was substituted which made for additional laughs as arnaz deliberately mispronounced it as spectin the birth made the first cover of tv guide the same year however these blessings could not alleviate the pressures on the marriage by the end of the one nine five zero s the desilu company had gotten much bigger and desi was beginning to dri |
nk more heavily on may four one nine six zero a few weeks after filming the final episode of the lucy desi comedy hour the couple divorced one of television s greatest marriages had come to an end however until his death in one nine eight six arnaz would remain friends with ball the following year ball married comedian gary morton a borscht belt stand up comic thirteen years her junior morton told interviewers at the time that he never saw lucy on tv since he worked nights ball immediately installed morton in her production company teaching him the television business and eventually promoting him to producer morton also played occasional bit parts on ball s various series after buying out her ex husband s share of the studio ball functioned as studio head following i love lucy ball appeared in the broadway musical wildcat which was unsuccessful and cost her a lot of money she made a few more movies including yours mine and ours and mame and two more successful sitcoms the lucy show one nine six two six eight |
which costarred vance and gale gordon and here s lucy one nine six eight seven four which also featured gordon as well as her real life children lucie arnaz and desi arnaz jr during the mid one nine eight zero s she attempted to resurrect her television career while a one nine eight five dramatic made for tv film about an elderly homeless woman stone pillow was well received her one nine eight six sitcom life with lucy which also costarred gale gordon was a critical and commercial flop and was canceled less than two months into its run the failure of her series was said to have sent ball into a serious depression and other than a few miscellaneous awards show appearances she was absent from the public eye for the final three years of her life lucille ball died on april two six one nine eight nine of a ruptured aorta at the age of seven seven and was cremated her remains were initially interred in the forest lawn hollywood hills cemetery in los angeles california but were later moved by her children desi arnaz |
jr and lucie arnaz to the lake view cemetery in jamestown new york lucille mcgillicuddy considered by professional clowns to be one of their own lucille ball s clown character was lucy ricardo nee lucille mcgillicuddy an instantly recognizable clown moniker lucy ricardo was a friendly ambitious and somewhat na ve housewife constantly getting into trouble of one kind or another the setup of the show provided ample opportunities for ball to display her skills at clowning and physical comedy she is regarded as one of the best in the history of film and television at physical schtick in the course of the television series lucy shared the screen with numerous famous clowns prominent among these were red skelton and harpo marx clown shtick on i love lucy lucy tries to get into the act a recurring and almost omnipresent theme on the show was that talentless plain old lucy the housewife dearly desired a chance to perform as anything a dancer showgirl clown singing cowboy or in any role the real joke here is that luc |
ille ball aside from being regarded as beautiful was also quite talented in a variety of performance arts as well as being a ground breaking television director perhaps the best example of this gag is when lucy shows up unannounced at ricky s club toting a clown modified cello and pretending to be a musician asking to speak with risky riskerdoo ricky ricardo this classic includes lucy winding the cello s tuning peg as if it were a watch to the accompaniment of ratcheting sounds and shooting the cello s bow at ricky s backside lucy in the candy factory speeeeeeed it up a little lucy and ethel attempt to get jobs for which they are demonstrably unprepared the classic candy gobbling scene in this episode is an american cultural icon the mirror gag now a classic improvisational acting exercise with harpo marx in which lucy dressed as harpo marx encounters the real harpo while hiding in the kitchen doorway perplexed at what he sees he confronts his reflection and lucy is forced to mimic his every move this scene w |
as based upon the famous mirror scene in duck soup the stranger with a kind face aka slowly i turned or niagara falls in which a veteran clown introduces lucy ricardo to some basics of the clown art and is schooled in this classic and at that time quite familiar vaudevillian routine complete with seltzer bottles a familiar clown prop and slapstick vita meata vege min do you poop out at parties are you unpopular well the answer to all your troubles is in this little bottle and it s so tasty too mrs ricardo as a slick television huckster pitching a foul tasting and alcoholic concoction the substance was actually apple butter of which the actress quite enjoyed the taste the gag being that aside from tasting bad and having a name which only a clown would embrace the product contained alcohol in large quantities and in numerous repeated rehearsals prior to the live spot lucy gradually and inexorably becomes half crocked with the inevitable hilarious result made only the more funny by the alliterative tongue twisti |
ng product name and pitch do you pop out at parties are you un poop ular well the answer to all your troubles is in this bittle lottle lucy tries to meet the famous star another recurring theme many popular stars were eager to appear on the show and hilarity ensues in countless episodes as a result of the character lucy s obsession with fame and the famous the cousin ernie story arc lucy receives a letter informing her that her best friend s roommate s cousin s middle boy of whom she has never heard is coming to visit from bent fork tennessee cousin ernie played by tennessee ernie ford is a stereotypical country boy in the big city in awe of the sophistication as he perceives it of his new hosts cousin ernie and the citizens of bent fork and its environs are encountered again during the course of the show s life the singing jailbreak this episode is part of the hollywood story arc ricky lucy fred and ethel participate in a square dance called by cousin ernie to escape a bent fork tennessee jail in the course |
of which the sheriff and his two rubenesque daughters are tied up with a handy piece of rope lucy gives a feminine kick into the officer s groin ricky lucy fred and ethel make their escape to continue their cross country venture filmography lucille ball the bowery one nine three three broadway through a keyhole one nine three three blood money one nine three three roman scandals one nine three three moulin rouge one nine three four nana one nine three four hold that girl one nine three four bottoms up one nine three four the affairs of cellini one nine three four murder at the vanities one nine three four bulldog drummond strikes back one nine three four pefectly mismated one nine three four short subject kid millions one nine three four men of the night one nine three four broadway bill one nine three four jealousy one nine three four three little pigskins one nine three four short subject fugitive lady one nine three four behind the evidence one nine three five his old flame one nine three five short subjec |
t carnival one nine three five the whole town s talking one nine three five roberta one nine three five i ll love you always one nine three five a night at the biltmore bowl one nine three five short subject old man rhythm one nine three five top hat one nine three five the three musketeers one nine three five i dream too much one nine three five chatterbox one nine three six muss em up one nine three six follow the fleet one nine three six the farmer in the dell one nine three six bunker bean one nine three six dummy ache one nine three six short subject swing it one nine three six short subject so and sew one nine three six short subject one live ghost one nine three six short subject winterset one nine three six that girl from paris one nine three six don t tell the wife one nine three seven there goes my girl one nine three seven scenes deleted stage door one nine three seven joy of living one nine three eight go chase yourself one nine three eight having wonderful time one nine three eight the affairs of |
annabel one nine three eight room service one nine three eight annabel takes a tour one nine three eight next time i marry one nine three eight beauty for the asking one nine three nine twelve crowded hours one nine three nine panama lady one nine three nine five came back one nine three nine that s right you re wrong one nine three nine the marines fly high one nine four zero you can t fool your wife one nine four zero dance girl dance one nine four zero too many girls one nine four zero a girl a guy and a gob one nine four one look who s laughing one nine four one valley of the sun one nine four two the big street one nine four two seven days leave one nine four two best foot forward one nine four three du barry was a lady one nine four three thousands cheer one nine four three meet the people one nine four four without love one nine four five abbott and costello in hollywood one nine four five cameo ziegfeld follies one nine four six the dark corner one nine four six two smart people one nine four six lov |
er come back one nine four six easy to wed one nine four six lured one nine four seven her husband s affairs one nine four seven sorrowful jones one nine four nine miss grant takes richmond one nine four nine easy living one nine four nine a woman of distinction one nine five zero cameo fancy pants one nine five zero the fuller brush girl one nine five zero the magic carpet one nine five one i love lucy one nine five three unreleased a movie which includes a handful of ill episodes with actors playing audience members it has rare footage of desi arnaz warming up the audience and introducing the cast the film was finally shown at the two zero zero two lucy desi convention the long long trailer one nine five four forever darling one nine five six the facts of life one nine six zero critic s choice one nine six three all about people one nine six seven short subject narrator a guide for the married man one nine six seven yours mine and ours one nine six eight mame one nine seven four television work i love lucy |
one nine five one one nine five seven the lucy desi comedy hour one nine five seven one nine six zero the lucy show one nine six two one nine six eight the danny kaye show with lucille ball one nine six two danny kaye mr and mrs one nine six four lucy in london one nine six six carol two one nine six seven here s lucy one nine six eight one nine seven four happy anniversary and goodbye one nine seven four lucy gets lucky one nine seven five a lucille ball special starring lucille ball and jackie gleason one nine seven five cbs salutes lucy the first two five years one nine seven six what now catherine curtis one nine seven six lucy calls the president one nine seven seven lucy comes to nashville one nine seven eight lucy moves to nbc one nine eight zero stone pillow one nine eight five life with lucy one nine eight six canceled after one two episodes were filmed only eight ever aired roman scandals one nine three three radio my favorite husband one nine four eight one nine five one notes her cousin suzan ball |
wife of actor richard long was an actress for several years before dying of cancer aged two one lucille ball and desi arnaz founded desilu productions there is a lucy desi museum honoring lucille ball and desi arnaz in jamestown new york there are also lucille ball museums located in the universal studios hollywood and universal studios florida theme parks in the summer of two zero zero five lucille ball was voted america s most beloved deceased star books love lucy one nine nine seven isbn zero four two five one seven seven three one nine external links the long live lucy message board lucille ball at classic actresses classic movies one nine three nine one nine six nine lucille ball the lucy lounge the lucy shows find a grave lucille desiree ball lucille ball at the internet broadway database everything lucy one nine one one births one nine eight nine deaths people from new york people from jamestown new york american film actors american female singers american television actors english americans entertai |
ners who died in their seven zero s hollywood walk of fame presidential medal of freedom recipients gay icons leszek miller leszek miller born three july one nine four six was prime minister of poland from september two zero zero one to may two two zero zero four miller was born in yrard w in central poland he joined the ruling polish united workers party party in one nine six nine until one nine seven zero he worked as an electrician in a linen textile factory in yrard w in one nine seven seven he graduated from a higher school of political sciences wy sza szko a nauk spo ecznych from to one nine seven seven one nine eight two he worked in the regional committee of puwp in skierniewice in one nine eight eight he became secretary of puwp at voivodship level and the following year he was briefly a member of the party s politburo after the dissolution of the communist party from one nine eight nine to one nine nine three miller was secretary general of sdrp he became a member of the sejm in one nine nine one he |
was minister of labor in waldemar pawlak s government and minister of internal affairs in the governments of jozef oleksy and w odzimierz cimoszewicz he became sld party leader in december one nine nine nine and served in this position until march two zero zero four he became prime minister of poland in september two zero zero one on march two six two zero zero four he announced his resignation as prime minister effective may two the day after poland became a member of european union his government encountered problems and unpopularity because of high unemployment possible spending cuts corruption scandals most notably the lew rywin affair and miller s support for u s president george w bush particularly the american led war against iraq in two zero zero three in april two zero zero four miller s former treasury minister wies aw kaczmarek now in a splinter socialist party called socjaldemokracja polska accused him of illegally using counter intelligence services for political reasons those allegations are cu |
rrently being investigated by a special house inquiry commission pkn orlen investigation commission miller s government involved polish troops in the invasion and occupation of iraq the government also completed the negotiations for poland to join the european union still a member of polish sejm the lower house of the parliament in the spring of two zero zero five he took a leave from sejm to work on a paper at the woodrow wilson center in washington d c one nine four six births living people prime ministers of poland in linear algebra a basis is a minimum set of vectors that when combined can address every vector in a given space more precisely a basis of a vector space is a set of linearly independent vectors that span the whole space definition let b be a subset of a vector space v a linear combination is a finite sum of the form a one v one cdots a n v n where the v k are different vectors from b and the a k are scalars the vectors in b are linearly independent if the only linear combinations adding up to |
the zero vector have a one cdots a n zero the set b is a generating set if every vector in v is a linear combination of vectors in b finally b is a basis if it is a generating set of linearly independent vectors properties again b denotes a subset of a vector space v then b is a basis if and only if any of the following equivalent conditions is met b is a minimal generating set of v i e it is a generating set but no proper subset of b is b is a maximal set of linearly independent vectors i e it is a linearly independent set but no other linearly independent set contains it as a proper subset every vector in v can be expressed as a linear combination of vectors in b in a unique way one can prove that every vector space has a basis for spaces that cannot be finitely generated zorn s lemma is needed for the proof all bases of a vector space have the same cardinality number of elements called the dimension of the vector space the latter result is known as the dimension theorem and requires the ultrafilter lemma |
a strictly weaker form of choice examples consider r two the vector space of all co ordinates a b where both a and b are real numbers then a very natural and simple basis is simply the vectors e one one zero and e two zero one suppose that v a b is a vector in r two then v a one zero b zero one but any two linearly independent vectors like one one and one two will also form a basis of r two see the section proving that a set is a basis further down more generally the vectors e one e two e n are linearly independent and generate r n therefore they form a basis for r n and the dimension of r n is n this basis is called the standard basis let v be the real vector space generated by the functions e t and e two t these two functions are linearly independent so they form a basis for v let rx denote the vector space of real polynomials then one x x two is a basis of rx the dimension of rx is therefore equal to aleph zero basis extension between any linearly independent set and any generating set there is a basis mor |
e formally if l is a linearly independent set in the vector space v and g is a generating set of v containing l then there exists a basis of v that contains l and is contained in g in particular taking g v any linearly independent set l can be extended to form a basis of v these extensions are not unique proving that a set is a basis as an easy example let us show that the vectors one one and one two form a basis for r two the following proof methods require increasing amounts of sophistication and decreasing amounts of effort by brute force we have to prove that these two vectors are linearly independent and that they generate r two part i to prove that they are linearly independent suppose that there are numbers a b such that a one one b one two zero zero then a b a two b zero zero and a b zero and a two b zero subtracting the first equation from the second we obtain three b zero so b zero and from the first equation then a zero part ii to prove that these two vectors generate r two we have to let a b be an |
arbitrary element of r two and show that there exist numbers x y such that x one one y one two a b then we have to solve the equations x y a x two y b subtracting the first equation from the second we get three y b a and then y b a three and finally x y a b a three a by the dimension theorem since one two is clearly not a multiple of one one and since one one is not the zero vector these two vectors are linearly independent since the dimension of r two is two the two vectors already form a basis of r two without needing any extension by the invertible matrix theorem simply compute the determinant det begin one first or second coordinate which makes sense only if an ordering is specified for the basis for finite dimensional vector spaces one typically indexes a basis by the first n integers suppose v is an n dimensional vector space over a field f a choice of an ordered basis for v is equivalent to a choice of a linear isomorphism from the coordinate space f n with its standard basis to v to see this let a f |
n v be a linear isomorphism define an ordered basis for v by v i a e i for one i n where is the standard basis for f n conversely given any ordered basis for v define a linear map a f n v by a x sum n x i v i it is not hard to check that a is an isomorphism thus ordered bases for v are in one one correspondence with linear isomorphisms f n v related notions the phrase hamel basis is sometimes used to refer to a basis as defined above in which the fact that all linear combinations are finite is crucial a set b is a hamel basis of a vector space v if every member of v is a linear combination of just finitely many members of b in hilbert spaces and other banach spaces there is a need to work with linear combinations of infinitely many vectors in an infinite dimensional hilbert space a set of vectors orthogonal to each other can never span the whole space via their finite linear combinations what is called an orthonormal basis is a set of mutually orthogonal unit vectors that span the space via sometimes infinite |
linear combinations except in the finite dimensional case this concept is not purely algebraic and is distinct from a hamel basis it is also more generally useful an orthonormal basis of an infinite dimensional hilbert space is therefore not a hamel basis in topological vector spaces quite generally one may define infinite sums infinite series and express elements of the space as certain infinite linear combinations of other elements to keep clear the distinction of bases using finite and infinite combination the former ones are called hamel bases and the latter ones schauder bases if the context requires it the corresponding dimensions are also known as hamel dimension and schauder dimension example in the study of fourier series one learns that the functions are an orthonormal basis of the set of all complex valued functions that are quadratically integrable on the interval zero two i e functions f satisfying int zero left f x right two dx these functions are linearly independent and every function that is |
quadratically integrable on that interval is an infinite linear combination of them that means that lim int zero left left a zero sum n a k cos kx b k sin kx right f x right two dx zero for suitable coefficients a k b k but most quadratically integrable functions cannot be represented as finite linear combinations of these basis functions which therefore do not comprise a hamel basis every hamel basis of this space is much bigger than this merely countably infinite set of functions hamel bases of spaces of this kind are of little if any interest orthonormal bases of these spaces are important to fourier analysis see also linear algebra linear combination linear algebra linear algebra is the branch of mathematics concerned with the study of vectors vector spaces also called linear spaces linear transformations and systems of linear equations in finite dimensions vector spaces are a central theme in modern mathematics thus linear algebra is widely used in both abstract algebra and functional analysis linear al |
gebra also has a concrete representation in analytic geometry and it is generalized in operator theory it has extensive applications in the natural sciences and the social sciences since nonlinear models can often be approximated by a linear model history the history of modern linear algebra dates back to the years one eight four three and one eight four four in one eight four three william rowan hamilton from whom the term vector stems discovered the quaternions in one eight four four hermann grassmann published his book die lineale ausdehnungslehre see references arthur cayley introduced two two matrices one of the most fundamental linear algebraic ideas in one eight five seven elementary introduction linear algebra had its beginnings in the study of vectors in cartesian two space and three space a vector here is a directed line segment characterized by both its magnitude represented by length and its direction vectors can be used to represent physical entities such as forces and they can be added and multi |
plied with scalars thus forming the first example of a real vector space modern linear algebra has been extended to consider spaces of arbitrary or infinite dimension a vector space of dimension n is called an n space most of the useful results from two and three space can be extended to these higher dimensional spaces although many people cannot easily visualize vectors in n space such vectors or n tuples are useful in representing data since vectors as n tuples are ordered lists of n components it is possible to summarize and manipulate data efficiently in this framework for example in economics one can create and use say eight dimensional vectors or eight tuples to represent the gross national product of eight countries one can decide to display the gnp of eight countries for a particular year where the countries order is specified for example united states united kingdom france germany spain india japan australia by using a vector v one v two v three v four v five v six v seven v eight where each country |
s gnp is in its respective position a vector space or linear space as a purely abstract concept about which we prove theorems is part of abstract algebra and well integrated into this field some striking examples of this are the group of invertible linear maps or matrices and the ring of linear maps of a vector space linear algebra also plays an important part in analysis notably in the description of higher order derivatives in vector analysis and the study of tensor products and alternating maps a vector space is defined over a field such as the field of real numbers or the field of complex numbers linear operators take elements from a linear space to another or to itself in a manner that is compatible with the addition and scalar multiplication given on the vector space s the set of all such transformations is itself a vector space if a basis for a vector space is fixed every linear transform can be represented by a table of numbers called a matrix the detailed study of the properties of and algorithms act |
ing on matrices including determinants and eigenvectors is considered to be part of linear algebra one can say quite simply that the linear problems of mathematics those that exhibit linearity in their behaviour are those most likely to be solved for example differential calculus does a great deal with linear approximation to functions the difference from nonlinear problems is very important in practice the general method of finding a linear way to look at a problem expressing this in terms of linear algebra and solving it if need be by matrix calculations is one of the most generally applicable in mathematics some useful theorems every linear space has a basis this statement is logically equivalent to the axiom of choice a non zero matrix a with n rows and n columns is invertible if there exists a matrix b that satisfies ab ba i where i is the identity matrix a matrix is invertible if and only if its determinant is different from zero a matrix is invertible if and only if the linear transformation represente |
d by the matrix is an isomorphism see also invertible matrix for other equivalent statements a matrix is positive semidefinite if and only if each of its eigenvalues is greater than or equal to zero a matrix is positive definite if and only if each of its eigenvalues is greater than zero the spectral theorem regarding diagonal matrices generalization and related topics since linear algebra is a successful theory its methods have been developed in other parts of mathematics in module theory one replaces the field of scalars by a ring in multilinear algebra one deals with the several variables problem of mappings linear in each of a number of different variables inevitably leading to the tensor concept in the spectral theory of operators control of infinite dimensional matrices is gained by applying mathematical analysis in a theory that is not purely algebraic in all these cases the technical difficulties are much greater see also list of linear algebra topics important publications in linear algebra reference |
s beezer rob a first course in linear algebra licensed under gfdl fearnley sander desmond hermann grassmann and the creation of linear algebra american mathematical monthly eight six one nine seven nine pp eight zero nine eight one seven grassmann hermann die lineale ausdehnungslehre ein neuer zweig der mathematik dargestellt und durch anwendungen auf die brigen zweige der mathematik wie auch auf die statik mechanik die lehre vom magnetismus und die krystallonomie erl utert o wigand leipzig one eight four four external links linear algebra by jim hefferon an online textbook mit linear algebra lectures videos from mit opencourseware free to everyone linear algebra toolkit linear algebra workbench multiply and invert matrices solve systems eigenvalues etc linear algebra on mathworld linear algebra overview and notation summary on planetmath linear algebra by elmer g wiens interactive web pages for vectors matrices linear equations etc linear algebra solved problems interactive forums for discussion of linear al |
gebra problems from the lowest up to the hardest level putnam elements of abstract and linear algebra free book from edwin h connell linear algebra venus in furs redirects here for other uses see venus in furs disambiguation book cover for venus in furs leopold ritter von sacher masoch january two seven one eight three six march nine one eight nine five writer and journalist was born in lemberg austria hungary now l viv ukraine he was the son of the police director in lemberg and charlotte von masoch a ukrainian lady of noble birth he started learning german at age one two during his life sacher masoch was well known as a man of letters who was seen by some as a potential successor to goethe he was a utopian thinker who espoused socialist and humanist ideals in his fiction and non fiction he associated with the artistic elite of middle europe but was frequently in debt venus in furs he planned to write a series of six novels under the collective title the heritage of cain only the first two were ever complete |
d of which venus in furs is the most famous venus im pelz is the original title in german this novel tells of a man severin so infatuated with a woman wanda that he requests to be treated as her slave and encourages her to treat him in progressively more degrading ways severin describes his feelings during these experiences as suprasensuality at the end of the book severin ceases to desire to submit stating that men should dominate women until the time when women are equal to men in education and civil rightss an ending that can be viewed as both misogynist and feminist the novel expressed sacher masoch s fantasies and fetishes especially for dominant women wearing fur which strongly influenced his other works he did his best to live out with his mistresses and wives he pressured his first wife aurora r melin into living out the experience of the book against her preferences however he wasn t excited about his family life got a divorce and married his assistant he died in frankfurt am main germany influence t |
he term masochism was coined by the one nine th century psychiatrist krafft ebing with sacher masoch and his writings in mind sacher masoch was not pleased with this development the novel has been adapted for film three times in one nine six seven in one nine six nine and in one nine nine four the one nine nine four film was directed by maartje seyferth and victor e nieuwenhuijs and received an award at the one nine nine four international film festival of saint petersburg russia the lyrics of the velvet underground song venus in furs refer to this book in the one nine nine eight todd haynes film velvet goldmine main character brian slade s backing band is called venus in furs notes see also sadism and masochism in fiction the story of o paraphilia external links the complete text of venus in furs from project gutenberg leopold von sacher masoch leopold von sacher masoch article from human sexuality an encyclopedia one eight three six births one eight nine five deaths bdsm erotic fiction austrian nobility aus |
trian writers negative litography stone and positive print of a map of munich lithography is a method for printing on a smooth surface it can be used to print text or artwork onto paper or another suitable material it can also refer to a method of manufacturing semiconductor and mems devices printing the principle litography press for printing maps in munich in lithography the entire print block comes in contact with the paper sheet and a chemical process confines the ink to the desired image on the block this contrasts with relief printing where the ink is carried on a raised image and intaglio where it lies in the grooves of an incised image because the print block is flat rather than relief lithography is described as a planographic print process the chemical process lithography works because of the repulsion of oil and water the image is drawn on the surface of the print block with an oil based medium the range of oil based mediums is endless but the dexterity of the image relies on the lipid content of t |
he material being used its ability to withstand water and acid following the placement of the image is the application of an acid emulsified with gum arabic the function of this emulsion is to create a salt layer directly around the image area the salt layer seeps into the pores of the stone completely enveloping the original image this process is called etching using lithographic turpentine the printer then removes the greasy drawing material leaving only the salt layer it is this salt layer which holds the skeleton of the image s original form when printing the stone or plate is kept wet with water naturally the water is attracted to the layer of salt created by the acid wash ink that bears a high lipid content is then rolled over the surface the water repells the grease in the ink and the only place for it to go is the cavity left by the original drawing material when the cavity is sufficiently full the stone and paper are run through a press which applies even pressure over the surface transferring the in |
k to the paper and off the stone the early process an example of lithography one nine zero two original size three three two four cm sea anemones from ernst haeckel s kunstformen der natur artforms of nature of one nine zero four lithography was invented by alois senefelder in bohemia in one seven nine eight and it was the first new printing process since the invention of relief printing in the fifteenth century in the early days of lithography a smooth piece of limestone was used hence the name lithography lithos is the ancient greek word for stone after the oil based image was put on the surface acid burned the image onto the surface gum arabic a water soluble solution was then applied sticking only to the non oily surface and sealing it during printing water adhered to the gum arabic surfaces and avoided the oily parts while the oily ink used for printing did the opposite within a few years of its invention the lithographic process was used to create multi color printed images a process known by the middle |
of the one nine th century as chromolithography a separate stone was used for each colour and a print went through the press separately for each stone the main challenge was of course to keep the images aligned in register this method lent itself to images consisting of large areas of flat colour and led to the characteristic poster designs of this period many fine works of chromolithographic printing were produced in america and europe the modern process modern high volume lithography is used to produce posters books newspapers packaging credit cards decorated cds just about any smooth mass produced item with print on in this form of lithography which depends on photographic processes flexible aluminum or plastic printing plates are used in place of stone tablets modern printing plates have a brushed or roughened texture and are covered with a photosensitive emulsion a photographic negative of the desired image is placed in contact with the emulsion and the plate is exposed to light after development the em |
ulsion shows a reverse of the negative image which is thus a duplicate of the original positive image the plate is then chemically treated so the positive image is receptive to printing inks the plate is affixed to a drum on a printing press rollers apply water which covers the blank portions of the plate and ink which adheres to the positive image areas such as the type and photographs on a newspaper page if this image were directly transferred to paper it would create a positive image but the paper would become too wet instead the plate rolls against a drum covered with a rubber blanket which squeezes away the water and picks up the ink the paper rolls across the blanket drum and the image is transferred to the paper because the image is first transferred or offset to the rubber drum this reproduction method is known as offset lithography or offset printing many innovations and technical refinements have been made in printing process and presses over the years including the development of presses with multi |
ple units each containing one printing plate that can print multi color images in one pass on both sides of the sheet and presses that accommodate continuous rolls webs of paper known as web presses another innovation was the continuous dampening system first introduced by dahlgren this increased control over the water flow to the plate and allowed for better ink and water balance current dampening systems include a delta effect which slows the roller in contact with the plate thus creating a sweeping movement over the ink image to clean impurities know as hickies the advent of desktop publishing made it possible for type and images to be manipulated easily on personal computers for eventual printing on desktop or commercial presses the development of digital imagesetters enabled print shops to produce negatives for platemaking directly from digital input skipping the intermediate step of photographing an actual page layout the development of the digital platesetter in the late twentieth century eliminated fi |
lm negatives altogether by exposing printing plates directly from digital input a process known as computer to plate printing semiconductor lithography main article photolithography semiconductor lithography was developed for use in manufacturing microchips it is also used in mems applications as it is one of the best methods currently in use for manufacturing devices on scales much smaller than a micrometer although silicon lithographic technology is most advanced other materials are also used the emerging technology of a maskless lithography process and nanoimprint lithography for the semiconductor is also being used lithography as an artistic medium during the first twenty five years of the nineteenth century the practice of lithography was predominantly restricted to cheap reproductions of paintings and drawings however around one eight two five the french artists ingres g ricault and delacroix embraced the process as a way to avoid the problems inherent in wood block and copper engraving namely the near |
necessity of middlemen like draughtsmen who transferred the image to the wood or copper plate and engravers who carved the image out of the plate the advantage to lithography for an artist s point of view was that he or she could draw or paint directly onto the lithographic material and avoid entirely the intermediate steps and craftsmen involved in engraving therefore an artist s drawing and a lithographic print made from it were nearly identical no reworking or transfer to another medium was necessary it also afforded at the time the most complete range of line color from white to black goya s lithographs the bulls of bordeaux one eight two eight and delacroix s illustrations to goethe s faust were the groundbreaking artist s lithographs that sparked a flood of mostly french artists who dabbled in lithography including prud hon cezanne manet and of course its greatest practitioner daumier whose prints began to appear in the one eight three zero s for the first time in history an artist was able to send out |
into the world his or her own drawing not in unique specimen but in editions each impression had all their personality skill and genius with no recourse to intermediary persons and technological steps see delacroix s faust lithographs at the davison art center wesleyan university see goya s lithographs at la biblioteca nacional de espa a see also printing letterpress printing block printing chromolithography flexography intaglio color printing offset printing rotogravure typography further reading ivins william jr prints and visual communication cambridge harvard university press one nine five three isbn zero two six two five nine zero zero two six external links museum of modern art information on printing techniques and examples of prints the invention of lithography by alois senefelder eng trans one nine one one a searchable facsimile at the university of georgia libraries djvu layered pdf format search what s lithography printing related articles and resources printing printmaking icd nine systemic lupus |
erythematosus sle or lupus is a chronic potentially debilitating or fatal autoimmune disease in which the immune system attacks the body s cells and tissue resulting in inflammation and tissue damage sle can affect any part of the body but most often harms the kidneys lupus nephritis heart joints rheumatological skin lungs blood vessels and brain nervous system lupus is treatable though there is currently two zero zero six no cure for it the standard treatment for decades has been a limited group of drugs primarily corticosteroids and chemotherapy drugs research into more modern treatments has recently begun and is accelerated by genetic discoveries especially mapping of the human genome sle is known as the great imitator symptoms often mimic other illnesses and because they come and go unpredictably diagnosis can be elusive with patients sometimes suffering unexplained symptoms and untreated sle for years increased awareness and education about lupus since the one nine six zero s has helped many more patient |
s get an accurate diagnosis and made it possible to estimate the number of people with lupus lupus was previously believed to be a rare disease in the united states alone an estimated two seven zero zero zero zero to one five million people have lupus making it more common than cystic fibrosis or cerebral palsy world wide a conservative estimate states that over five million people have lupus sle was called lupus latin for wolf perhaps due to a crude similarity between the facial rash that some lupus patients develop and a wolf s face although various explanations exist etiology the exact cause of the disease is unknown and there is no consensus on whether it is a single condition or a group of related diseases sle is a chronic inflammatory disease believed to be a type iii hypersensitivity serum sickness response which is characterised by the body s production of antibodies against the nuclear components of its own cells there are three mechanisms by which lupus is thought to develop genetic predisposition e |
nvironmental causes and drug reaction drug induced lupus genetics the first mechanism may arise genetically research indicates that sle may have a genetic link several genes need to be affected for lupus to occur and the most important genes are located on chromosome six these genes may occur randomly or be a result of heredity additionally people with sle have an altered runx one binding site which may be either cause or contributor or both to the condition altered binding sites for runx one have also been found in people with psoriasis and rheumatoid arthritis environmental causes the second mechanism may be owing to environmental factors these factors can not only exacerbate existing lupus conditions but can trigger the initial onset they include certain medications such as some antidepressants and antibiotics extreme stress exposure to sunlight hormones and infections some researchers have sought to find a connection between certain infectious agents viruses and bacteria but no pathogen can be consistentl |
y linked to the disease non sle forms of lupus there are two other forms of lupus discoid lupus and drug induced lupus discoid lupus is limited to skin symptoms and is diagnosed via biopsy of skin rash on the face neck or scalp often an anti nuclear antibody ana test for discoid patients is negative or a low titre positive about one zero of discoid lupus patients eventually develop sle drug induced lupus is a reversible condition that usually occurs in patients being treated for a long term illness drug induced lupus mimics systemic lupus however symptoms of drug induced lupus generally disappear once a patient is taken off of the medication which triggered the episode there are about four zero medications currently in use that can cause this condition though the most common drugs are procainamide hydralazine and quinidine pathophysiology abnormalities in apoptosis apoptosis is increased in monocytes and keratinocytes expression of fas by b cells and t cells is increased there are correlations between the apo |
ptotic rates of lymphocytes and disease activity tingible body macrophages tbms are large phagocytic cells in the germinal centers of secondary lymph nodes they express cd six eight protein these cells normally engulf b cells which have undergone apoptosis after somatic hypermutation in some patients with sle significantly fewer tbms can be found and these cells rarely contain material from apoptotic b cells also uningested apoptotic nuclei can be found outside of tbms this material may present a threat to the tolerization of b cells and t cells dendritic cells in the germinal center may endocytose such antigenic material and present it to t cells activating them also apoptotic chromatin and nuclei may attach to the surfaces of follicular dendritic cells and make this material available for activating other b cells which may have randomly acquired self specificity through somatic hypermutation complement pathway sle is associated with defects in lectins and the classical complement pathway signs and symptoms |
common initial and chronic complaints are fever malaise joint pains myalgias and fatigue because they are so often seen with other diseases these signs and symptoms are not part of the diagnostic criteria for sle when occurring in conjunction with other signs and symptoms however they are considered suggestive dermatological manifestations as many as three zero of patients present with some dermatological symptoms and six five suffer such symptoms at some point with three zero to five zero suffering from the classic malar or butterfly rash associated with the disease patients may present with discoid lupus thick red scaly patches on the skin alopecia mouth nasal and vaginal ulcers and lesions on the skin are also possible manifestations musculoskeletal manifestations patients most often seek medical attention for joint pain with small joints of the hand and wrist usually affected although any joint is at risk unlike rheumatoid arthritis sle arthropathy is not usually destructive of bone however deformities ca |
used by the disease may become irreversible in as many as two zero of patients hematological manifestations anemia and iron deficiency may develop in as many as half of patients low platelet and white blood cell counts may be due to the disease or a side effect of pharmacological treatment cardiac manifestations patients may present with inflammation of various parts of the heart pericarditis myocarditis and endocarditis the endocarditis of sle is characteristically non infective libman sacks endocarditis and involves either the mitral valve or the tricuspid valve atherosclerosis also tends to occur more often and advance more rapidly in sle patients than in the general population asanuma et al two zero zero three bevra two zero zero three roman et al two zero zero three pulmonary manifestations lung and plura inflammation can cause pleuritis pleural effusion lupus pneumonitis chronic diffuse interstitial lung disease pulmonary hypertension pulmonary emboli pulmonary hemorrhage renal involvement painless hema |
turia or proteinuria may often be the only presenting renal symptom acute or chronic renal impairment may develop with lupus nephritis leading to acute or end stage renal failure because of early recognition and management of sle end stage renal failure occurs in less than five of patients neurological manifestations about one zero of patients may present with seizures or psychosis a third may test positive for abnormalities in the cerebrospinal fluid t cell abnormalities abnormalities in t cell signaling are associated with sle including deficiency in cd four five phosphatase increased expression of cd four zero ligand also associated with sle is increased expression of fc ri which replaces the tcr chain which is deficient in some sle patients other abnormalities include increased and sustained calcium levels in t cells moderate increase of inositol triphosphate reduction in pkc phosphorylation reduction in ras map kinase signalling and deficiencies in protein kinase a i activity diagnosis some physicians ma |
ke a diagnosis on the basis of the acr classification criteria see below the criteria however were established mainly for use in scientific research i e inclusion in randomised controlled trials and patients may have lupus despite never meeting the criteria antinuclear antibody testing and anti extractable nuclear antigen anti ena form the mainstay of serologic testing for lupus antiphospholipid antibodies occur more often in sle and can predispose for thrombosis more specific is the anti smith antibody other tests routinely performed in suspected sle are complement system levels low levels suggest consumption by the immune system electrolytes and renal function disturbed if the kidney is involved liver enzymes and a full blood count diagnostic criteria the american college of rheumatology acr has established eleven criteria in one nine eight two which were revised in one nine nine seven as a classificatory instrument to operationalise the definition of sle in clinical trials they were not intended to be used |
to diagnose individual patients and do not do well in that capacity a patient must present with four of the eleven criteria either simultaneously or serially during a given period of observation to be classified as having sle for the purposes of inclusion in clinical trials malar rash rash on cheeks discoid lupus red scaly patches on skin which cause scarring photosensitivity adverse reaction to sunlight mouth ulcers arthritis more than zero five g per day protein in urine or cellular casts seen in urine under a microscope seizures or psychosis pleuritis inflammation of the membrane around the lungs or pericarditis inflammation of the membrane around the heart hemolytic anemia low red blood cell count leukopenia low white blood cell count lymphopenia low lymphocyte count or thrombocytopenia low platelet count anti dna antibody anti sm antibody or false positive serological test for syphilis or antiphospholipid antibody positivity positive fluorescence antinuclear antibody test positive ana some patients may |
have sle without four criteria and sle is associated with manifestations other than those listed in the criteria dr graham r v hughes an authority on lupus in the uk has published alternative criteria to diagnose sle in one nine eight two a useful mnemonic for these one one criteria is soap brain md s erositis eight o ral ulcers four a rthritis five p hotosensitivity three b lood changes nine r enal involvement proteinuria or casts six a na one one i mmunological changes one zero n eurological signs seizures frank psychosis seven m alar rash one d iscoid rash two treatment current treatment sle is a chronic disease with no cure there are however some medications such as corticosteroids and immunosuppressants which can control the disease and prevent flares flares are typically treated with steroids with dmards disease modifying antirheumatic drugs to suppress the disease process reduce steroid needs and prevent flares dmards commonly in use are the antimalarials e g hydroxychloroquine and azathioprine cycloph |
osphamide is used for severe nephritis or other organ damaging complications patients who require steroids frequently may develop obesity diabetes and osteoporosis hence steroids are avoided where possible measures such as avoiding sunlight to prevent problems due to photosensitivity may also have some effect treatment research other immunosuppressants and autologous stem cell transplants are under investigation epidemiology although sle can occur in anyone at any age it is most common in women of childbearing age it affects one in four zero zero zero people in the united states with women suffering five to fifteen times more often than men the disease appears to be more prevalent in women of african asian hispanic and native american origin but this may be due to socioeconomic factors people with relatives who suffer from sle rheumatoid arthritis or thrombotic thrombocytopenic purpura are at a slightly higher risk than the general population a person with a parent or sibling with the condition has a one zero |
chance of developing the condition only five of children born to a parent with lupus will develop the condition prognosis in the one nine five zero s most patients diagnosed with sle lived fewer than five years advances in diagnosis and treatment have improved survival to the point where over nine zero of patients now survive for more than ten years and many can live relatively asymptomatically the most common cause of death is infection due to immunosuppression as a result of medications used to manage the disease prognosis is normally worse for men and children than for women and if symptoms are present after age six zero the disease tends to run a more benign course research lupus research has dramatically increased in recent years the largest research funding organization in the united states as of two zero zero six is the alliance for lupus research history the source of the name lupus is unclear all explanations originate with the characteristic butterfly shaped malar rash that the disease classically |
exhibits across the nose and cheeks in various accounts some doctors thought the rash resembled a wolf pattern in other accounts doctors thought that the rash which was often more severe in earlier centuries created lesions that resembled wolf bites or scratches stranger still is the account that the term lupus didn t come from latin at all but from the term for a french style of mask which women reportedly wore to conceal the rash on their faces the history of lupus erythematosus can be divided into three periods the classical neoclassical and modern the classical period began when the disease was first recognised in the middle ages and saw the description of the dermatological manifestation of the disorder the term lupus is attributed to the twelfth century physician rogerius who used it to describe the classic malar rash the neoclassical period was heralded by moritz kaposi s recognition in one eight seven two of the systemic manifestations of the disease the modern period began in one nine four eight with |
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