Henry (unit)

The henry (symbol: H) is the SI derived unit of electrical inductance. If a current of 1 ampere flowing through a coil produces flux linkage of 1 weber turn, that coil has a self inductance of 1 henry. The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.
Definition.
The inductance of an electric circuit is one henry when an electric current that is changing at one ampere per second results in an electromotive force of one volt across the inductor:
where "V"("t") denotes the resulting voltage across the circuit, "I"("t") is the current through the circuit, and "L" is the inductance of the circuit.
The henry is a derived unit based on four of the seven base units of the International System of Units: kilogram (kg), metre (m), second (s), and ampere (A).
Expressed in combinations of SI units, the henry is:
where: , , , , , , , , , , , , , Hz = hertz
Use.
The International System of Units (SI) specifies to write the symbol of a unit named for a person with an initial capital letter, while the name is not capitalized in sentence text, except when any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.
The United States National Institute of Standards and Technology recommends users writing in English to use the plural as "henries".
Applications.
The inductance of a coil depends on its size, the number of turns, and the permeability of the material within and surrounding the coil. Formulas can be used to calculate the inductance of many common arrangements of conductors, such as parallel wires, or a solenoid. A small air-core coil used for broadcast AM radio tuning might have an inductance of a few tens of microhenries. A large motor winding with many turns around an iron core may have an inductance of scores or hundreds of henries. The physical size of an inductance is also related to its current carrying and voltage withstand ratings.


Ljubov Rebane

Ljubov A. Rebane (née Chagalova) (September 6, 1929 Leningrad – June 13, 1991 Tallinn) was an Estonian physicist. She graduated from Leningrad University in 1952 and received a PhD in Physics and Mathematics in 1961 from the same university.
She received the USSR State Prize (Russian: Госуда́рственная пре́мия СССР) in 1986, together with Rein Avarmaa, Anšel Gorohhovski, Roman Personov, Boris Harlamov, Jevgeni Alšits, Ljudmila Bõkovskaja, Vladimir Maslov, Jaak Kikas and Konstantin Solovjov, for the cycle of articles "High-spectral-resolution spectroscopy and for the persistent spectral hole burning of molecules and solids" (Russian: Авармаа, Рейн Арнольдович, зав. сектором, Гороховский, Аншель Александрович, Кикас, Яак Вернерович, ст. н. с., Альшиц, Евгений Иосифович, Быковская, Людмила Анатольевна, мл. н. с. Института физики АН ЭССР; Маслов, Владимир Григорьевич, ст. н. с. ГОИ имени С. И. Вавилова; Ребане, Любовь Александровна, ст. н. с. ИХБФАН ЭССР; Соловьёв, Константин Николаевич, зав. лабораторией Института физики АН БССР, — за цикл работ «Фотовыжигание стабильных спектральных провалов и гелективная спектроскопия сложных молекул» (1972—1984)).
Family.
She married the physicist Karl Rebane. Their children Aleksander and Inna Rebane both became physicists themselves.


Kron Stone


WM Recordings

WM Recordings is a Heerlen, the Netherlands based record label founded in 2004, by Marco Kalnenek, who was also involved with Comfort Stand Recordings.
Kalnenek also is the webmaster of Weirdomusic.com, a website nominated for a Webby Award in 2004.
WM Recordings focuses on music that is, in their own words, "a little different".
They do not specialize in one style, but release anything from free jazz to experimental soundscapes, world music and other styles that are often neglected by other netlabels.
In 2007, WM Recordings started adding commercial releases to their catalog. These are available from most major download stores.
August 2008 saw the release of their first physical CD: "Handle With Care - Might Panic" by Danish band Panicphobia.


976 Benjamina

976 Benjamina ("prov. designation:" "or" ) is a dark background asteroid from the outer regions of the asteroid belt, approximately in diameter. It was discovered on 27 March 1922, by Russian-French astronomer Benjamin Jekhowsky at the Algiers Observatory in North Africa. The large X/D-type asteroid has a rotation period of 9.7 hours and is likely regular in shape. It was named after the discoverer's son.
Orbit and classification.
"Benjamina" is a non-family asteroid of the main belt's background population when applying the hierarchical clustering method to its proper orbital elements. It orbits the Sun in the outer main-belt at a distance of 2.9–3.5 AU once every 5 years and 9 months (2,092 days; semi-major axis of 3.2 AU). Its orbit has an eccentricity of 0.10 and an inclination of 8° with respect to the ecliptic.
The asteroid was first observed as () at Heidelberg Observatory on 8 January 1910. The body's observation arc begins at the Crimean Simeiz Observatory in September 1930, more than 7 years after its official discovery observation at Algiers Observatory in March 1922.
Naming.
This minor planet was named after Benjamin Jekhowsky Jr., son of discoverer Benjamin Jekhowsky. The was mentioned in "The Names of the Minor Planets" by Paul Herget in 1955 ().
Physical characteristics.
In the Tholen classification, and based on a noisy spectra (:), "Benjamina" is an X-type asteroid, somewhat similar to that of a dark D-type (XD), which are common in the outer asteroid belt and among the Jupiter trojan population.
Rotation period and pole.
In September 2004, a rotational lightcurve of "Benjamina" was obtained from photometric observations by French amateur astronomer Laurent Bernasconi. Lightcurve analysis gave a well-defined rotation period of hours with a brightness variation of magnitude (). Follow-up observation by his college René Roy in March 2018, determined a concurring period of hours but with a much higher amplitude of magnitude (). The objects first lightcurve was obtained by Colin Bembrick at Mount Tarana Observatory in Australia in March 2003. It showed a period of hours with an amplitude of magnitude (). The overall amplitude suggest a rather regular shape with a ratio of 0.86 for the length of the a and b axes.
In 2018, Czech astronomers Josef Ďurech and Josef Hanuš published a modeled lightcurve using photometric data from the "Gaia" probe's second data release. It showed a sidereal period of hours, and gave a spin axis at (354.0°, 80.0°) in ecliptic coordinates (λ, β).
Diameter and albedo.
According to the surveys carried out by the Japanese Akari satellite, the Infrared Astronomical Satellite IRAS, and the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer (WISE), "Benjamina" measures , and kilometers in diameter with an albedo of its surface of , and , respectively. Additional measurements by the WISE telescope were published giving a mean-diameter as low as , and as high as .
The "Collaborative Asteroid Lightcurve Link" adopts the result from IRAS, that is, an albedo of 0.0559 and a diameter of 80.53 kilometers based on an absolute magnitude of 9.22.
The asteroid had been observed in 7 stellar occultation events since 2003. On 19 July 2003 the mag. 5.7 star HIP 88816 was occulted by the asteroid, and was observed at 11 stations; 1 in Argentina, 3 in New Zealand, and 7 in Australia. From these observations, the best-fit ellipse measures 85.2 x 56.2 +/-12.4 kilometres.


2430 Bruce Helin

2430 Bruce Helin ("prov. designation": ) is a stony Phocaea asteroid and slow rotator from the inner regions of the asteroid belt. It was discovered by American astronomers Eleanor Helin and Eugene Shoemaker at the U.S. Palomar Observatory in California, on 8 November 1977. It was later named after Bruce Helin, son of the first discoverer. The S-type asteroid (Sl) has an exceptionally long rotation period of 128 hours and measures approximately in diameter.
Orbit and classification.
"Bruce Helin" is a member of the Phocaea family (). It orbits the Sun in the inner main-belt at a distance of 1.9–2.9 AU once every 3 years and 8 months (1,326 days). Its orbit has an eccentricity of 0.21 and an inclination of 23° with respect to the ecliptic. It was first observed at at Heidelberg Observatory in 1908. The body's observation arc begins with a precovery taken at Crimea–Nauchnij in 1976, or one year prior to its official discovery observation at Palomar.
Naming.
This minor planet was named after Bruce Helin, son of the first discover Eleanor Helin, in an expression of gratitude for "the many years he tolerated his mother's preoccupation with extraterrestrial objects". The discoverer has also honoured her daughter-in-law and wife of Bruce, Nancy Coker Helin, by the minor planet 4222 Nancita. The official was published by the Minor Planet Center on 13 October 1981 ().
Physical characteristics.
In the Tholen classification, "Bruce Helin" is a common, stony S-type asteroid, while in the Bus–Binzel SMASS taxonomy, it is an Sl-subtype, which transitions from the S-type to the uncommon L-type asteroid.
Rotation period.
The first rotational lightcurve of "Bruce Helin" was obtained from photometric observations by Czech astronomer Petr Pravec in September 2006. The lightcurve showed a rotation period of hours with a brightness variation of 0.60 in magnitude (). Later observations rendered a similar rotation period of 129.75 and hours, respectively ().
Diameter and albedo.
According to the surveys carried out by the Japanese Akari satellite and NASA's Wide-field Infrared Survey Explorer with its NEOWISE mission, "Bruce Helin" measures 11.8 and 12.5 kilometers in diameter, and its surface has an albedo of 0.18 and 0.24, respectively. The "Collaborative Asteroid Lightcurve Link" (CALL) assumes an albedo of 0.23 and calculates a diameter of 12.1 kilometers with an absolute magnitude of 11.8.


Bernard Ziegler

Bernard Ziegler (12 March 1933 – 4 May 2021) was a French pilot and engineer, who served in Airbus as senior vice president for engineering, well known for his evangelical zeal for the application of the fly-by-wire system in the Airbuses. He was the son of Airbus founder Henri Ziegler.
Biography.
Bernard Ziegler was born in Boulogne sur Seine, France. He was educated in the École Polytechnique (1954), as an engineer and École de l'Air (1955), for his pilot training and military commission. Ziegler began his career as a fighter pilot in the French air force. He saw action in the Algerian War and was decorated twice. Principal medals and decorations received include the Officier de l’Ordre National du Mérite, Médaille de l'Aéronautique, Croix de la Valeur Militaire and Officier de la Légion d'honneur.
In August 1961 the Vallee Blanche Aerial Tramway was badly damaged when an aeroplane of the French Air Force piloted by Bernard Ziegler tore its hauling cable. Three cars crashed and six people were killed.
He continued his studies in École nationale supérieure de l'aéronautique et de l'espace (Supaéro) (1961) and was later posted to École du personnel navigant d'essais et de réception (EPNER), the French Air Force test pilot establishment in 1964. He was the chief test pilot for the Dassault Mirage G in 1968. At Airbus, his career spans from chief test pilot (1972), to senior vice president for flight and support and then, to senior vice president for engineering. As a test pilot, he flew the first flights of the Airbus A300, A310, A320 and the A340.
Bernard Ziegler was the most influential figure in developing the cockpit design and fly-by-wire control system for the Airbus airliners. He proposed that numerous technological innovations be applied to Airbus aircraft; for example, using composites, twin-engine configuration for the A300, fly-by-wire and many others. He was the guiding force in the creation of the flight envelope protection, incorporated in the Airbus flight-control software. This innovation allows the pilot to apply the maximum control forces considered necessary, while preventing inadvertent inputs that could place the aircraft outside the safety margin. This feature is considered by many to be highly beneficial in avoiding unusual altitudes in flight and in safely maximizing the effectiveness of evasive maneuvers in response to GPWS warnings.
For his efforts in advancing the fly-by-wire cause, he was honoured by the Flight Safety Foundation in 1998. He retired from Airbus after 25 years of service in 1997.


Random variate

In the mathematical fields of probability and statistics, a random variate is a particular outcome of a random variable: the random variates which are other outcomes of the same random variable might have different values.
A random deviate or simply deviate is the difference of random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution.
Random variates are used when simulating processes driven by random influences (stochastic processes). In modern applications, such simulations would derive random variates corresponding to any given probability distribution from computer procedures designed to create random variates corresponding to a uniform distribution, where these procedures would actually provide values chosen from a uniform distribution of pseudorandom numbers.
Procedures to generate random variates corresponding to a given distribution are known as procedures for "random variate generation" or pseudo-random number sampling.
In probability theory, a random variable is a measurable function from a probability space to a measurable space of values that the variable can take on. In that context, those values are also known as random variates or random deviates, and this represents a wider meaning than just that associated with pseudorandom numbers.
Definition.
Devroye defines a random variate generation algorithm (for real numbers) as follows:
The distinction between "random variable" and "random variate" is subtle and is not always made in the literature. It is useful when one wants to distinguish between a random variable itself with an associated probability distribution on the one hand, and random draws from that probability distribution on the other, in particular when those draws are ultimately derived by floating-point arithmetic from a pseudo-random sequence.
Practical aspects.
For the generation of uniform random variates, see Random number generation.
For the generation of non-uniform random variates, see Pseudo-random number sampling.


List of presidents of the New York Stock Exchange

This is a list of presidents of the New York Stock Exchange.


Mode Records

Mode Records is an American record label in New York City that concentrates on contemporary classical music and other forms of avant-garde music. The label was founded by Brian Brandt in 1984, with a goal of releasing music composed by John Cage.
Composers featured include John Cage, Morton Feldman, Iannis Xenakis, Giacinto Scelsi, and Harry Partch. Performers include Steve Lacy, Aki Takahashi, Martine Joste, the Arditti Quartet, and Gerry Hemingway. The label also has a commitment to younger composers with releases featuring Jason Eckardt, Joshua Fineberg, and Lei Liang.
An earlier unrelated Mode Records existed for a short time in the 1950s and was involved West Coast jazz. It is now controlled by VSOP.


Marcia Gumpertz

Marcia Lynn Gumpertz is an American statistician known for her research on agricultural statistics, spatial analysis, the design of experiments, and plant disease epidemiology. She has also studied employment issues for women and members of underrepresented minorities in science and technology. She is a professor of statistics at North Carolina State University.
Education and career.
Gumpertz earned a bachelor's degree in philosophy from the University of California, Berkeley in 1973, and a master's degree in statistics from Oregon State University in 1979. She completed her Ph.D. at North Carolina State University in 1989. Her dissertation, "Simple Estimators for the Linear Random Coefficient Regression Model and the Nonlinear Model with Variance Components", was jointly supervised by Sastry Pantula and John Rawlings.
She worked as a scientist for Northrop Services Inc., in Oregon, from 1980 to 1984, doing research for the Environmental Protection Agency, and joined the North Carolina State University on completing her doctorate in 1989. At North Carolina State University, she has also served as assistant vice provost for faculty diversity.
Book.
With Francis G. Giesbrecht, Gumpertz is the co-author of the book "Planning, Construction, and Statistical Analysis of Comparative Experiments" (Wiley, 2004).
Recognition.
Gumpertz was president of Mu Sigma Rho, the US national statistics honor society, for 2004–2006. She was elected as a Fellow of the American Statistical Association in 2006, and given the Distinguished Achievement Award of the American Statistical Association Section on Statistics and the Environment in 2008.


203 Pompeja

Pompeja (minor planet designation: 203 Pompeja) is a quite large main-belt asteroid.
It was discovered by C. H. F. Peters on September 25, 1879, in Clinton, New York, and named after Pompeii, the Roman town destroyed in volcanic eruption in AD 79.
Based upon Photometric observations taken during 2011, it has a synodic rotation period of 24.052 ± 0.001 h, with a peak-to-peak amplitude of 0.10 ± 0.01 in magnitude. Because the rotation period nearly matches that of the Earth, it required coordinated observations from multiple observatories at widely spaced latitudes to produce a complete light curve.


Hypodorian mode

The Hypodorian mode, a musical term literally meaning 'below Dorian', derives its name from a "tonos" or octave species of ancient Greece which, in its diatonic genus, is built from a tetrachord consisting (in rising direction) of a semitone followed by two whole tones. The rising scale for the octave is a single tone followed by two conjoint tetrachords of this type. This is roughly the same as playing all the white notes of a piano from A to A: A | B C D E | (E) F G A. Although this scale in medieval theory was employed in Dorian and Hypodorian, from the mid-sixteenth century and in modern music theory they came to be known as the Aeolian and Hypoaeolian modes.
The term Hypodorian came to be used to describe the second mode of Western church music. This mode is the plagal counterpart of the authentic first mode, which was also called "Dorian". The ecclesiastical Hypodorian mode was defined in two ways: (1) as the diatonic octave species from A to A, divided at the mode final D and composed of a lower tetrachord of tone–semitone–tone, ending on D, plus a pentachord tone–semitone–tone–tone continuing from D, and (2) as a mode whose final was D and whose ambitus was G–B (that is, with B below the final and B above it). In addition, the note F, corresponding to the reciting note or "tenor" of the second psalm tone, was regarded as an important secondary center.


Test of Russian as a Foreign Language

The Test of Russian as a Foreign Language (TORFL) ( or ) is a contemporary test of Russian language for foreign citizens compliant with the best European quality standards.
Levels.
Levels of the Test of Russian as a Foreign Language are matched to the Common European Framework of Reference for Languages: Learning, Teaching, Assessment (CEFR).
The TORFL test consists of 6 different levels:
The Testing Center of the Herzen State Pedagogical University conducts testing in accordance with the Federal Law of the Russian Federation № 115 from the 25th of June 2002. On the legal status of the foreign citizens in the Russian Federation and the order of the Ministry of Education and Science of the Russian Federation № 1156 from the 28th of August 2014. On the approval of the form and procedure of the examination in Russian language, history of Russia and fundamentals of legislation of the Russian Federation and requirements on the minimum level of knowledge requisite for the stated exam.
Test Content.
The Test of Russian as a Foreign Language comprises 5 parts examining language competences: writing, vocabulary/grammar, reading, listening and speaking.
Usually the exam is held over a period of 2 days. On the first day candidates take the "Writing", "Vocabulary/Grammar" and “Reading" parts, on the second day – "Listening" and "Speaking" parts. The TORFL test assesses foreign citizens' skills to express various communicative intentions in the writing form using correct words and phrases, to understand different types of written information in Russian, to comprehend information in Russian given aurally, to participate in dialogues and to produce the monologue according to the proposed subject.
The question papers for the TORFL test are compiled by the experts of each educational organization authorized to run the Test, e.g. Herzen University question papers are compiled by Herzen University experts, Moscow State University question papers are compiled by MSU experts and so on.
Procedure of issuing certificates.
After successfully passing a test, a foreign citizen receives the TORFL certificate confirming the person's level of language competence in Russian as a foreign language. The form and procedure of issuing the TORFL certificates are determined by the Order of the Ministry of education and science of the Russian Federation of 25 April 2014 No. 412.
This Order states that the 10 days is the maximum period for issuing a certificate, but the testing organizations seek to do this faster. For example, Herzen University issues a TORFL certificate on the next day after exam.
Testing Centres.
By the Order of the Ministry of education and science of the Russian Federation of 20 February 2018 No. 130 the list of educational organizations conducting testing of Russian as a foreign language includes 13 educational organizations, for example: Herzen University, Moscow State University, Pskov State University, St. Petersburg State University, RUDN University, Pushkin State Russian Language Institute.
These Universities are the only organizations authorized to conduct the TORFL test. However, they can outsource the provision of technical support to other organizations in various regions of Russia and in overseas countries. By that SPbU cooperates with more than 50 organizations around the world.
The full lists of test centres where the TORFL test is conducted can be found on the Universities’ websites.


Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is described informally as a variable whose values depend on outcomes of a random phenomenon. The formal mathematical treatment of random variables is a topic in probability theory. In that context, a random variable is understood as a measurable function defined on a probability space that maps from the sample space to the real numbers.
A random variable's possible values might represent the possible outcomes of a yet-to-be-performed experiment, or the possible outcomes of a past experiment whose already-existing value is uncertain (for example, because of imprecise measurements or quantum uncertainty). They may also conceptually represent either the results of an "objectively" random process (such as rolling a die) or the "subjective" randomness that results from incomplete knowledge of a quantity. The meaning of the probabilities assigned to the potential values of a random variable is not part of probability theory itself, but is instead related to philosophical arguments over the interpretation of probability. The mathematics works the same regardless of the particular interpretation in use.
As a function, a random variable is required to be measurable, which allows for probabilities to be assigned to sets of its potential values. It is common that the outcomes depend on some physical variables that are not predictable. For example, when tossing a fair coin, the final outcome of heads or tails depends on the uncertain physical conditions, so the outcome being observed is uncertain. The coin could get caught in a crack in the floor, but such a possibility is excluded from consideration.
The domain of a random variable is called a "sample space," defined as the set of possible outcomes of a non-deterministic event. For example, in the event of a coin toss, only two possible outcomes are possible: heads or tails.
A random variable has a probability distribution, which specifies the probability of Borel subsets of its range. Random variables can be discrete, that is, taking any of a specified finite or countable list of values (having a countable range), endowed with a probability mass function that is characteristic of the random variable's probability distribution; or continuous, taking any numerical value in an interval or collection of intervals (having an uncountable range), via a probability density function that is characteristic of the random variable's probability distribution; or a mixture of both.
Two random variables with the same probability distribution can still differ in terms of their associations with, or independence from, other random variables. The realizations of a random variable, that is, the results of randomly choosing values according to the variable's probability distribution function, are called random variates.
Although the idea was originally introduced by Christiaan Huygens, the first person to think systematically in terms of random variables was Pafnuty Chebyshev.
Definition.
A random variable formula_1 is a measurable function formula_2 from a set of possible outcomes formula_3 to a measurable space formula_4. The technical axiomatic definition requires formula_5 to be a sample space of a probability triple formula_6 (see the measure-theoretic definition). A random variable is often denoted by capital roman letters such as formula_1, formula_8, formula_9, formula_10.
The probability that formula_1 takes on a value in a measurable set formula_12 is written as
Standard case.
In many cases, formula_1 is real-valued, i.e. formula_15. In some contexts, the term random element (see extensions) is used to denote a random variable not of this form.
When the image (or range) of formula_1 is countable, the random variable is called a discrete random variable and its distribution is a discrete probability distribution, i.e. can be described by a probability mass function that assigns a probability to each value in the image of formula_1. If the image is uncountably infinite (usually an interval) then formula_1 is called a continuous random variable. In the special case that it is absolutely continuous, its distribution can be described by a probability density function, which assigns probabilities to intervals; in particular, each individual point must necessarily have probability zero for an absolutely continuous random variable. Not all continuous random variables are absolutely continuous, a mixture distribution is one such counterexample; such random variables cannot be described by a probability density or a probability mass function.
Any random variable can be described by its cumulative distribution function, which describes the probability that the random variable will be less than or equal to a certain value.
Extensions.
The term "random variable" in statistics is traditionally limited to the real-valued case (formula_19). In this case, the structure of the real numbers makes it possible to define quantities such as the expected value and variance of a random variable, its cumulative distribution function, and the moments of its distribution.
However, the definition above is valid for any measurable space formula_20 of values. Thus one can consider random elements of other sets formula_20, such as random boolean values, categorical values, complex numbers, vectors, matrices, sequences, trees, sets, shapes, manifolds, and functions. One may then specifically refer to a "random variable of type formula_20", or an "formula_20-valued random variable".
This more general concept of a random element is particularly useful in disciplines such as graph theory, machine learning, natural language processing, and other fields in discrete mathematics and computer science, where one is often interested in modeling the random variation of non-numerical data structures. In some cases, it is nonetheless convenient to represent each element of formula_20, using one or more real numbers. In this case, a random element may optionally be represented as a vector of real-valued random variables (all defined on the same underlying probability space formula_5, which allows the different random variables to covary). For example:
Distribution functions.
If a random variable formula_38 defined on the probability space formula_6 is given, we can ask questions like "How likely is it that the value of formula_1 is equal to 2?". This is the same as the probability of the event formula_41 which is often written as formula_42 or formula_43 for short.
Recording all these probabilities of output ranges of a real-valued random variable formula_1 yields the probability distribution of formula_1. The probability distribution "forgets" about the particular probability space used to define formula_1 and only records the probabilities of various values of formula_1. Such a probability distribution can always be captured by its cumulative distribution function
and sometimes also using a probability density function, formula_49. In measure-theoretic terms, we use the random variable formula_1 to "push-forward" the measure formula_51 on formula_5 to a measure formula_49 on formula_54.
The underlying probability space formula_5 is a technical device used to guarantee the existence of random variables, sometimes to construct them, and to define notions such as correlation and dependence or independence based on a joint distribution of two or more random variables on the same probability space. In practice, one often disposes of the space formula_5 altogether and just puts a measure on formula_54 that assigns measure 1 to the whole real line, i.e., one works with probability distributions instead of random variables. See the article on quantile functions for fuller development.
Examples.
Discrete random variable.
In an experiment a person may be chosen at random, and one random variable may be the person's height. Mathematically, the random variable is interpreted as a function which maps the person to the person's height. Associated with the random variable is a probability distribution that allows the computation of the probability that the height is in any subset of possible values, such as the probability that the height is between 180 and 190 cm, or the probability that the height is either less than 150 or more than 200 cm.
Another random variable may be the person's number of children; this is a discrete random variable with non-negative integer values. It allows the computation of probabilities for individual integer values – the probability mass function (PMF) – or for sets of values, including infinite sets. For example, the event of interest may be "an even number of children". For both finite and infinite event sets, their probabilities can be found by adding up the PMFs of the elements; that is, the probability of an even number of children is the infinite sum formula_58.
In examples such as these, the sample space is often suppressed, since it is mathematically hard to describe, and the possible values of the random variables are then treated as a sample space. But when two random variables are measured on the same sample space of outcomes, such as the height and number of children being computed on the same random persons, it is easier to track their relationship if it is acknowledged that both height and number of children come from the same random person, for example so that questions of whether such random variables are correlated or not can be posed.
If formula_59 are countable sets of real numbers, formula_60 and formula_61, then formula_62 is a discrete distribution function. Here formula_63 for formula_64, formula_65 for formula_66. Taking for instance an enumeration of all rational numbers as formula_67, one gets a discrete distribution function that is not a step function or piecewise constant.
Coin toss.
The possible outcomes for one coin toss can be described by the sample space formula_68. We can introduce a real-valued random variable formula_8 that models a $1 payoff for a successful bet on heads as follows:
If the coin is a fair coin, "Y" has a probability mass function formula_71 given by:
Dice roll.
A random variable can also be used to describe the process of rolling dice and the possible outcomes. The most obvious representation for the two-dice case is to take the set of pairs of numbers "n"1 and "n"2 from {1, 2, 3, 4, 5, 6} (representing the numbers on the two dice) as the sample space. The total number rolled (the sum of the numbers in each pair) is then a random variable "X" given by the function that maps the pair to the sum:
and (if the dice are fair) has a probability mass function "ƒ""X" given by:
Continuous random variable.
Formally, a continuous random variable is a random variable whose cumulative distribution function is continuous everywhere. There are no "gaps", which would correspond to numbers which have a finite probability of occurring. Instead, continuous random variables almost never take an exact prescribed value "c" (formally, formula_75) but there is a positive probability that its value will lie in particular intervals which can be arbitrarily small. Continuous random variables usually admit probability density functions (PDF), which characterize their CDF and probability measures;
such distributions are also called absolutely continuous; but some continuous distributions are singular, or mixes of an absolutely continuous part and a singular part.
An example of a continuous random variable would be one based on a spinner that can choose a horizontal direction. Then the values taken by the random variable are directions. We could represent these directions by North, West, East, South, Southeast, etc. However, it is commonly more convenient to map the sample space to a random variable which takes values which are real numbers. This can be done, for example, by mapping a direction to a bearing in degrees clockwise from North. The random variable then takes values which are real numbers from the interval [0, 360), with all parts of the range being "equally likely". In this case, X = the angle spun. Any real number has probability zero of being selected, but a positive probability can be assigned to any "range" of values. For example, the probability of choosing a number in [0, 180] is . Instead of speaking of a probability mass function, we say that the probability "density" of X is 1/360. The probability of a subset of [0, 360) can be calculated by multiplying the measure of the set by 1/360. In general, the probability of a set for a given continuous random variable can be calculated by integrating the density over the given set.
More formally, given any interval formula_76, a random variable formula_77 is called a "continuous uniform random variable" (CURV) if the probability that it takes a value in a subinterval depends only on the length of the subinterval. This implies that the probability of formula_78 falling in any subinterval formula_79 is proportional to the length of the subinterval, that is, if , one has
formula_80
where the last equality results from the unitarity axiom of probability. The probability density function of a CURV formula_81 is given by the indicator function of its interval of support normalized by the interval's length: formula_82Of particular interest is the uniform distribution on the unit interval formula_83. Samples of any desired probability distribution formula_84 can be generated by calculating the quantile function of formula_84 on a randomly-generated number distributed uniformly on the unit interval. This exploits properties of cumulative distribution functions, which are a unifying framework for all random variables.
Mixed type.
A mixed random variable is a random variable whose cumulative distribution function is neither piecewise-constant (a discrete random variable) nor everywhere-continuous. It can be realized as the sum of a discrete random variable and a continuous random variable; in which case the will be the weighted average of the CDFs of the component variables.
An example of a random variable of mixed type would be based on an experiment where a coin is flipped and the spinner is spun only if the result of the coin toss is heads. If the result is tails, X = −1; otherwise X = the value of the spinner as in the preceding example. There is a probability of that this random variable will have the value −1. Other ranges of values would have half the probabilities of the last example.
Most generally, every probability distribution on the real line is a mixture of discrete part, singular part, and an absolutely continuous part; see . The discrete part is concentrated on a countable set, but this set may be dense (like the set of all rational numbers).
Measure-theoretic definition.
The most formal, axiomatic definition of a random variable involves measure theory. Continuous random variables are defined in terms of sets of numbers, along with functions that map such sets to probabilities. Because of various difficulties (e.g. the Banach–Tarski paradox) that arise if such sets are insufficiently constrained, it is necessary to introduce what is termed a sigma-algebra to constrain the possible sets over which probabilities can be defined. Normally, a particular such sigma-algebra is used, the Borel σ-algebra, which allows for probabilities to be defined over any sets that can be derived either directly from continuous intervals of numbers or by a finite or countably infinite number of unions and/or intersections of such intervals.
The measure-theoretic definition is as follows.
Let formula_86 be a probability space and formula_87 a measurable space. Then an formula_87-valued random variable is a measurable function formula_89, which means that, for every subset formula_90, its preimage formula_91 where formula_92. This definition enables us to measure any subset formula_93 in the target space by looking at its preimage, which by assumption is measurable.
In more intuitive terms, a member of formula_5 is a possible outcome, a member of formula_95 is a measurable subset of possible outcomes, the function formula_51 gives the probability of each such measurable subset, formula_20 represents the set of values that the random variable can take (such as the set of real numbers), and a member of formula_98 is a "well-behaved" (measurable) subset of formula_20 (those for which the probability may be determined). The random variable is then a function from any outcome to a quantity, such that the outcomes leading to any useful subset of quantities for the random variable have a well-defined probability.
When formula_20 is a topological space, then the most common choice for the σ-algebra formula_98 is the Borel σ-algebra formula_102, which is the σ-algebra generated by the collection of all open sets in formula_20. In such case the formula_87-valued random variable is called an formula_20-valued random variable. Moreover, when the space formula_20 is the real line formula_54, then such a real-valued random variable is called simply a random variable.
Real-valued random variables.
In this case the observation space is the set of real numbers. Recall, formula_86 is the probability space. For a real observation space, the function formula_109 is a real-valued random variable if
This definition is a special case of the above because the set formula_111 generates the Borel σ-algebra on the set of real numbers, and it suffices to check measurability on any generating set. Here we can prove measurability on this generating set by using the fact that formula_112.
Moments.
The probability distribution of a random variable is often characterised by a small number of parameters, which also have a practical interpretation. For example, it is often enough to know what its "average value" is. This is captured by the mathematical concept of expected value of a random variable, denoted formula_113, and also called the first moment. In general, formula_114 is not equal to formula_115. Once the "average value" is known, one could then ask how far from this average value the values of formula_1 typically are, a question that is answered by the variance and standard deviation of a random variable. formula_113 can be viewed intuitively as an average obtained from an infinite population, the members of which are particular evaluations of formula_1.
Mathematically, this is known as the (generalised) problem of moments: for a given class of random variables formula_1, find a collection formula_120 of functions such that the expectation values formula_121 fully characterise the distribution of the random variable formula_1.
Moments can only be defined for real-valued functions of random variables (or complex-valued, etc.). If the random variable is itself real-valued, then moments of the variable itself can be taken, which are equivalent to moments of the identity function formula_123 of the random variable. However, even for non-real-valued random variables, moments can be taken of real-valued functions of those variables. For example, for a categorical random variable "X" that can take on the nominal values "red", "blue" or "green", the real-valued function formula_124 can be constructed; this uses the Iverson bracket, and has the value 1 if formula_1 has the value "green", 0 otherwise. Then, the expected value and other moments of this function can be determined.
Functions of random variables.
A new random variable "Y" can be defined by applying a real Borel measurable function formula_126 to the outcomes of a real-valued random variable formula_1. That is, formula_128. The cumulative distribution function of formula_8 is then
If function formula_131 is invertible (i.e., formula_132 exists, where formula_133 is formula_131's inverse function) and is either increasing or decreasing, then the previous relation can be extended to obtain
With the same hypotheses of invertibility of formula_131, assuming also differentiability, the relation between the probability density functions can be found by differentiating both sides of the above expression with respect to formula_137, in order to obtain
If there is no invertibility of formula_131 but each formula_137 admits at most a countable number of roots (i.e., a finite, or countably infinite, number of formula_141 such that formula_142) then the previous relation between the probability density functions can be generalized with
where formula_144, according to the inverse function theorem. The formulas for densities do not demand formula_131 to be increasing.
In the measure-theoretic, axiomatic approach to probability, if a random variable formula_1 on formula_5 and a Borel measurable function formula_126, then formula_149 is also a random variable on formula_5, since the composition of measurable functions is also measurable. (However, this is not necessarily true if formula_131 is Lebesgue measurable.) The same procedure that allowed one to go from a probability space formula_152 to formula_153 can be used to obtain the distribution of formula_8.
Example 1.
Let formula_1 be a real-valued, continuous random variable and let formula_156.
If formula_158, then formula_159, so
If formula_161, then
so
Example 2.
Suppose formula_1 is a random variable with a cumulative distribution
where formula_166 is a fixed parameter. Consider the random variable formula_167 Then,
The last expression can be calculated in terms of the cumulative distribution of formula_169 so
which is the cumulative distribution function (CDF) of an exponential distribution.
Example 3.
Suppose formula_1 is a random variable with a standard normal distribution, whose density is
Consider the random variable formula_173 We can find the density using the above formula for a change of variables:
In this case the change is not monotonic, because every value of formula_8 has two corresponding values of formula_1 (one positive and negative). However, because of symmetry, both halves will transform identically, i.e.,
The inverse transformation is
and its derivative is
Then,
This is a chi-squared distribution with one degree of freedom.
Example 4.
Suppose formula_1 is a random variable with a normal distribution, whose density is
Consider the random variable formula_173 We can find the density using the above formula for a change of variables:
In this case the change is not monotonic, because every value of formula_8 has two corresponding values of formula_1 (one positive and negative). Differently from the previous example, in this case however, there is no symmetry and we have to compute the two distinct terms:
The inverse transformation is
and its derivative is
Then,
This is a noncentral chi-squared distribution with one degree of freedom.
Equivalence of random variables.
There are several different senses in which random variables can be considered to be equivalent. Two random variables can be equal, equal almost surely, or equal in distribution.
In increasing order of strength, the precise definition of these notions of equivalence is given below.
Equality in distribution.
If the sample space is a subset of the real line, random variables "X" and "Y" are "equal in distribution" (denoted formula_191) if they have the same distribution functions:
To be equal in distribution, random variables need not be defined on the same probability space. Two random variables having equal moment generating functions have the same distribution. This provides, for example, a useful method of checking equality of certain functions of independent, identically distributed (IID) random variables. However, the moment generating function exists only for distributions that have a defined Laplace transform.
Almost sure equality.
Two random variables "X" and "Y" are "equal almost surely" (denoted formula_193) if, and only if, the probability that they are different is zero:
For all practical purposes in probability theory, this notion of equivalence is as strong as actual equality. It is associated to the following distance:
where "ess sup" represents the essential supremum in the sense of measure theory.
Equality.
Finally, the two random variables "X" and "Y" are "equal" if they are equal as functions on their measurable space:
This notion is typically the least useful in probability theory because in practice and in theory, the underlying measure space of the experiment is rarely explicitly characterized or even characterizable.
Convergence.
A significant theme in mathematical statistics consists of obtaining convergence results for certain sequences of random variables; for instance the law of large numbers and the central limit theorem.
There are various senses in which a sequence formula_197 of random variables can converge to a random variable formula_1. These are explained in the article on convergence of random variables.


Wegberg-Wildenrath Test and Validation Centre

The Wegberg-Wildenrath Test and Validation Centre () is a railway test centre owned by Siemens Mobility near Wildenrath in North Rhine-Westphalia, Germany.
History.
The centre is located on the site of the former RAF Wildenrath British military airfield. After the airfield closed in 1992, it was taken over by Siemens who opened the test and validation centre in June 1997. By 2007, the railway test tracks had taken over considerable areas of the airfield, with all but the western threshold and overrun of the runway obliterated. The north-east dispersal is completely taken over by sidings, workshops and loops. Of the southern dispersals, the central and eastern are bisected by the main railway oval test track.
There are ovals of track for testing trains, and various electrification systems. The test track is connected to the rest of the German railway network by the German portion of the Iron Rhine freight railway, branching off near Wegberg.
Testing.
As well as Siemens the test tracks are also used by competitors such as Stadler, Alstom and Bombardier Transportation.
There are standard gauge and metre gauge tracks. The facility is used for technical acceptance tests and approvals of locomotives, rolling stock and trams under operating conditions, and personnel training. It has been equipped for trials with Galileo.


Test equipment

Test equipment is a general term describing equipment used in many fields. Types of test equipment include:
Electrical and electronic test equipment.
Electronic test equipment.
Electronic test equipment is used to create signals and capture responses from electronic devices, to prove proper operation or trace faults. Types of electronic test equipment include:


3090 Tjossem


Transient grating spectroscopy

Transient grating spectroscopy is an optical technique used to measure quasiparticle propagation. It can track changes in metallic materials as they are irradiated.


Hierarchical INTegration

Hierarchical INTegration, or HINT for short, is a computer benchmark that ranks a computer system as a whole (i.e. the entire computer instead of individual components). It measures the full range of performance, mostly based on the amount of work a computer can perform over time. A system with a very fast processor would likely be rated poorly if the buses were very poor compared to those of another system that had both an average processor and average buses. For example, in the past, Macintosh computers with relatively slow processor speeds (800 MHz) used to perform better than x86 based systems with processors running at nearly 2 GHz.
HINT is known for being almost immune to artificial optimization and can be used by many computers ranging from a calculator to a supercomputer. It was developed at the U.S. Department of Energy's Ames Laboratory and is licensed under the terms of the GNU General Public License.
HINT is intended to be "scalable" to run on any size computer, from small serial systems to highly parallel supercomputers.
The person using the HINT benchmark can use any floating-point or integer type.
HINT benchmark results have been published comparing a variety of parallel and uniprocessor systems.
A related tool ANALYTIC HINT can be used as a design tool to estimate the benefits of using more memory, a faster processor, or improved communications (bus speed) within the system.


Type 97 Chi-Ni medium tank

The Experimental Medium Tank Chi-Ni (試製中戦車 チニ "Shisei-chū-sensha chini") was a prototype Japanese medium tank. Initially proposed as a low-cost alternative to the Type 97 Chi-Ha medium tank, it was eventually passed over by its competitor.
History and development.
In 1935 news had reached Japan of the United Kingdom's development of a new tank, the A6 medium tank. A multi-turreted design that mounted a 47 mm tank gun and was capable of reaching speeds of 50 km/h. In comparison, Japan's tank force had not undergone any significant changes in tactics or organization in six years. The country's widely fielded medium tank, the Type 89 I-Go, while popular with troops and tank crews had begun to show its age, attempts to update the design with the Type 89B I-Go Otsu were made in 1934, but no fundamentally new design was undertaken. In comparison, the A6 was seen as having superior offensive and defence capabilities over the Type 89 I-Go. Britain's new tank design, along with reports from Manchuria of the Type 89's inability to keep up with other motorized vehicles–given its inadequate 25 km/h top speed–brought about plans for a replacement.
Tank designers recommended research on a new tank design, a medium tank capable of going 35 km/h and weighing 15 tons with offensive and defensive abilities greater than the Type 89 I-Go. The Chief-of-Staff Operations was not enthusiastic for the project as it was peace-time and the military had a limited budget. The army thus issued peace time requirements for a new tank design. Rather than focusing on performance improvements, the Chief-of-Staff Operations made a lighter weight the main requirement in order to lower production costs. The finalised requirements were for a lighter weight tank that was capable of going 35 km/h, and armed with a 57 mm main gun. The Engineering Department believed that it was highly regrettable that their efforts would be devoted solely to weight reduction, so instead, two concurrent projects were built. The first plan was for a lower-weight, low-cost medium tank that was to be made by the Osaka Army Arsenal, which would become the Chi-Ni. The second plan was contracted to Mitsubishi Heavy Industries for a higher performance medium tank, which would become the Chi-Ha.
Design.
The initial design requirements for the two prototypes were:
The Chi-Ni was envisioned as a smaller, lighter alternative to the Chi-Ha, a medium tank closer to the original Chief-of-Staff Operations preference for more "lightly armored infantry support vehicles". The hull was of a monocoque design and welding was used more extensively than previous tanks. This was unlike previous Japanese tanks, which were all riveted around a framework. The Chi-Ni also shared the same bell crank scissors suspension as the Chi-Ha that would continue to be used by later Japanese tanks until the end of the Second World War. The hull was designed with a streamlined silhouette to protect from shell damage. The crew of the Chi-Ni, unlike the Chi-Ha was only made up of three men, with the tank commander acting as both a gunner and loader in the small, single-man turret. The turret did not have room for any coaxial machine gun. The driver was seated in the hull on the left hand side, with the third crew member, a machine gunner, was seated to right of the driver. The tank was initially planned to be armed with the Type 89 I-Gos Type 90 57 mm gun, but a new tank gun was being designed at the time to replace the lower velocity gun. This improved tank gun was the Type 97 57 mm tank gun. A single, forward firing, 7.7×58mm Arisaka Type 97 machine gun was mounted in the hull. The diameter of the turret ring for both tanks was made as large as possible to allow for any future up-gunning of the tanks. The tank was powered by a Mitsubishi 135 hp diesel engine. There are also documents stating that the Chi-Ni was tested with a 120 hp Mitsubishi A6120VDe air-cooled diesel engine from a Type 95 Ha-Go. The Chi-Ni was equipped with a 'tadpole tail', a tail extension attached to the back of the tank to allow it to better cross trenches. Both prototypes were completed and tested in early 1937.
Production.
During the time of the Chi-Ni and Chi-Ha trials, the China Incident occurred on 7 July 1937, sparking a war with China. With the out-break of hostilities the peacetime budgetary limitations were removed and the more capable and expensive Mitsubishi Chi-Ha model was accepted as the new Type 97 medium tank by the army. The Type 97 Chi-Ha would go on to be the most numerically important Japanese medium tank of the Second World War. Only a single Chi-Ni prototype was built. Even though the Chi-Ni was passed over in favour of the Chi-Ha, several individuals in the Japanese military, such as Japanese Army tank designer Lieutenant General Tomio Hara, believed that there was still potential in the design and the tank could be reused in the future as a light tank.


Direct analysis in real time

In mass spectrometry, direct analysis in real time (DART) is an ion source that produces electronically or vibronically excited-state species from gases such as helium, argon, or nitrogen that ionize atmospheric molecules or dopant molecules. The ions generated from atmospheric or dopant molecules undergo ion-molecule reactions with the sample molecules to produce analyte ions. Analytes with low ionization energy may be ionized directly. The DART ionization process can produce positive or negative ions depending on the potential applied to the exit electrode.
This ionization can occur for species desorbed directly from surfaces such as currency, tablets, bodily fluids (blood, saliva and urine), polymers, glass, plant leaves, fruits & vegetables, clothing, and living organisms. DART is applied for rapid analysis of a wide variety of samples at atmospheric pressure and in the open laboratory environment. It does not need a specific sample preparation, so it can be used for the analysis of solid, liquid and gaseous samples in their native state.
With the aid of DART, exact mass measurements can be done rapidly with high-resolution mass spectrometers. DART mass spectrometry has been used in pharmaceutical applications, forensic studies, quality control, and environmental studies.
History.
DART resulted from conversations between Laramee and Cody about the development of an atmospheric pressure ion source to replace the radioactive sources in handheld chemical weapons detectors.DART was developed in late 2002 to early 2003 by Cody and Laramee as a new atmospheric pressure ionization process, and a US patent application was filed in April 2003. Although the development of DART actually predated the desorption electrospray ionization (DESI) ion source, the initial DART publication did not appear until shortly after the DESI publication, and both ion sources were publicly introduced in back-to-back presentations by R. G. Cooks and R. B. Cody at the January 2005 ASMS Sanibel Conference. DESI and DART are considered as pioneer techniques in the field of ambient ionization, since they operate in the open laboratory environment and do not require sample pretreatment. In contrast to the liquid spray used by DESI, the ionizing gas from the DART ion source contains a dry stream containing excited state species.
Principle of operation.
Ionization process.
Formation of metastable species.
As the gas (M) enters the ion source, an electric potential in the range of +1 to +5 kV is applied to generate a glow discharge. The glow discharge plasma contains and short-lived energetic species including electrons, ions, and excimers. Ion/electron recombination leads to the formation of long-lived excited-state neutral atoms or molecules (metastable species, M*) in the flowing afterglow region. The DART gas can be heated from room temperature (RT) to 550 °C to facilitate desorption of analyte molecules. Heating is optional but may be necessary depending on the surface or chemical being analyzed. The heated stream of gaseous metastable species passes through a porous exit electrode that is biased to a positive or negative potential in the range 0 to 530V. When biased to a positive potential, the exit electrode acts to remove electrons and negative ions formed by Penning ionization from the gas stream to prevent ion/electron recombination and ion loss. If the exit electrode is biased to a negative potential, electrons can be generated directly from the electrode material by surface Penning ionization. An insulator cap at the terminal end of the ion source protects the operator from harm.
DART can be used for the analysis of solid, liquid or gaseous samples. Liquids are typically analyzed by dipping an object (such as a glass rod) into the liquid sample and then presenting it to the DART ion source. Vapors are introduced directly into the DART gas stream.
Positive ion formation.
Once the metastable carrier gas atoms (M*) released from the source, they initiate Penning ionization of nitrogen, atmospheric water and other gaseous species. Although some compounds can be ionized directly by Penning ionization, the most common positive-ion formation mechanism for DART involves ionization of atmospheric water.
Although the exact ion formation mechanism is not clear, water can be ionized directly by Penning ionization. Another proposal is that water is ionized by the same mechanism that has been proposed for atmospheric pressure chemical ionization
Ionized water can undergo further ion-molecule reactions to form protonated water clusters ().
The stream of protonated water clusters acts as a secondary ionizing species and generates analytes ions by chemical ionization mechanisms at atmospheric pressure. Here protonation, deprotonation, direct charge transfer and adduct ion formation may occur.
Negative ion formation.
In negative-ion mode, the potential of the exit grid electrode can be set to negative potentials. Penning electrons undergo electron capture with atmospheric oxygen to produce O2−. The O2− will produce radical anions. Several reactions are possible, depending on the analyte.
The negative ion sensitivity of DART gases varies with the efficiency in forming electrons by Penning ionization, which means that the negative ion sensitivity increases with the internal energy of the metastable species, for example nitrogenᐸneonᐸhelium.
Instrumentation.
Source to analyzer interface.
Analyte ions are formed at ambient pressure during Penning and chemical ionization. The mass spectrometry analysis, however, takes place at high vacuum condition. Therefore ions entering the mass spectrometer, first go through a source - to - analyzer interface (vacuum interface), which was designed in order to bridge the atmospheric pressure region to the mass spectrometer vacuum. It also minimizes spectrometer contamination.
In the original JEOL atmospheric pressure interface used for DART, ions are directed to the ion guide through (outer) і and (inner) іі skimmer orifices by applying a slight potential difference between them: orifice і : 20 V and orifice іі : 5 V. The alignment of the two orifices is staggered to trap neutral contamination and protect the high-vacuum region. Charged species (ions) are guided to the second orifice through an intermediate cylindrical electrode ("ring lens"), but neutral molecules travel in a straight pathway and are thus blocked from entering the ion guide. The neutral contamination is then removed by the pump.
The DART source can be operated in surface desorption mode or transmission mode. In the ordinary surface desorption mode, the sample is positioned in a way, which enables the reactive DART reagent ion stream to flow on to the surface while allowing the flow of desorbed analyte ions into interface. Therefore this mode requires that the gas stream grazes the sample surface and does not block gas flow to the mass spectrometer sampling orifice. In contrast, transmission mode DART (tm-DART) uses a custom-made sample holder and introduces the sample at a fixed geometry.
Coupling with separation techniques.
DART can be combined with many separation techniques. Thin-layer chromatography (TLC) plates have been analyzed by positioning them directly in the DART gas stream. Gas chromatography has been carried out by coupling gas chromatography columns directly into the DART gas stream through a heated interface. Eluate from a high-pressure liquid chromatograph (HPLC) can be also introduced to the reaction zone of the DART source and analyze. DART can be coupled with capillary electrophoresis (CE) and the eluate of CE is guided to the mass spectrometer through the DART ion source.
Mass spectra.
In positive ion mode, DART produces predominantly protonated molecules [M+H]+ and in negative-ion mode deprotonated molecules [M-H]−. Both negative and positive modes of DART provides relatively simple mass spectra. Depending on the type of analyte, other species may be formed, such as multiple charged adducts. DART categorized under soft ionization technique. Fragmentation can be rarely observed for some molecules.
Use of DART compared to traditional methods minimizes sample amount, sample preparation, eliminates extraction steps, decreases limit of detection and analysis time. Also it provides a broad range sensitivity, simultaneous determination of multi-drug analytes and sufficient mass accuracy for formulation determination.
The DART ion source is a kind of gas-phase ionization, and it requires some sort of volatility of the analyte to support thermally assisted desorption of analyte ions. This limits the size range of the molecules that can be analyzed by DART i.e. "m/z 50" to 1200. DART-MS is capable of semi-quantitative and quantitative analysis. To accelerate sample release from the surface, the DART gas stream is usually heated to temperature in the range 100-500 °C and this operation can be employed for temperature-dependent analysis.
Applications.
DART is being applied in many fields, including the fragrance industry, pharmaceutical industry, foods and spices, forensic science and health, materials analysis, etc.
In forensic science, DART is used for analysis of explosives, warfare agents, drugs, inks and sexual assault evidence. In clinical and pharmaceutical sector, DART is utilized for body fluid analysis such as blood, plasma, urine etc. and study traditional medicines. Also DART can detect composition in medicine in a tablet form as per there is no need for sample preparation such as crushing or extracting.
In food industry, DART assures the quality and authenticity assessment of food. It is also used in the analysis of mycotoxins in beverages, semi-quantitative analysis of caffeine, monitoring heat accelerated decomposition of vegetable oils and many other food safety analysis. In the manufacturing industry, to determine the deposition and release of a fragrance on surfaces such as fabric and hair and dyes in textiles, DART is often utilized.
DART is used in environmental analysis. For example, analysis of organic UV filters in water, contaminants in soil, petroleum products and aerosols etc. DART also plays an important role in biological studies. It enables studying chemical profiles of plants and organisms.


Marco Papiro

Marco Papiro is a Swiss-Italian experimental musician, electronic music producer, sound artist and graphic designer born in Basel, Switzerland
Biography.
Classically trained from early age, he played violin, synthesizer and bass guitar in several bands before creating and releasing his own self-produced music as Papiro. His influences are numerous and audible: drone, minimal, folk from all times and places, psychedelic, contemporary classical, industrial – but also easy listening, pop and even new age music. His compositions are generally instrumental, meditative and hypnotic, but at times also bizarre and humorous. Papiro is a multi-instrumentalist with a fondness for synthesizers from the pre-programmable era – the EMS VCS3, the Moog Sonic Six, the Roland Jupiter 4 and the Serge Modular among others.
Marco Papiro has collaborated with various musicians such as Mani Neumeier, Hans Koch or Gyða Valtýsdóttir, and has been a „sound carrier“ for Damo Suzuki on several occasions. He is also a regular guest with Swiss garage-psych band Roy & the Devil's Motorcycle. In 2005 he founded the noise band Mir, together with Daniel Buess and Michael Zaugg (later also Marlon McNeill and Yanik Soland). Until Daniel Buess' death in 2016, the band played over a hundred shows in Europe, Brazil and Japan. As a producer he has initiated the re-release of "Herzschlag Erde / Verdunkelt die Sinne" and "Die singende Sternlaterne / Folklore des Weltalls 1982" by Swiss underground musician and outsider artist "Die Welttraumforscher", of whom he is a big admirer.
Papiro is also active as an unorthodox DJ. Together with Markus Stähli of Roy & the Devil's Motorcycle they host a monthly night were they expand their eclectic sets by using various speeds, additional instruments, prepared tapes and effects.
Marco Papiro has studied graphic design at the Basel School of Design from 1995 to 1999. As a graphic designer Marco Papiro is mostly known for the posters and album covers he has created for related artists such as Sun Araw, Spacemen 3 / Spectrum(with Peter Kember aka Sonic Boom), Panda Bear, Z'EV, Antoine Chessex, Oren Ambarchi and many others. He teaches at the Basel School of Design since 2006.


Sagami Trough

The also Sagami Trench, Sagami Megathrust, or Sagami Subduction Zone is a long trough, which is the surface expression of the convergent plate boundary where the Philippine Sea Plate is being subducted under the Okhotsk Plate. It stretches from the Boso Triple Junction in the east, where it meets the Japan Trench, to Sagami Bay in the west, where it meets the Nankai Trough. It runs north of the Izu Islands chain and the Izu–Bonin–Mariana Arc (IBM).
Megathrust earthquakes associated with the Sagami Trough, known as Kantō earthquakes, are a major threat to Tokyo and the Kantō Region because of the proximity to a population center (with over 36 million living in Tokyo's metro area, with a total of 43 million living in the Kanto Region) and the magnitude the Sagami Trough can create.
Earthquakes.
The Sagami Trough megathrust generated the 1703 Genroku earthquake, which was the greatest rupture along the trough in the last thousand years, and the 1855 (Ansei) and 1923 (Great Kanto or Taisho) earthquakes.


Woof (label)

Woof Records is a British independent record label founded by English musicians Tim Hodgkinson and Bill Gilonis in London in 1980.
Background.
Tim Hodgkinson and Bill Gilonis began experimenting with tape collages in 1979 and recorded "I Do – I Do – I Don't – I Don't", an 18-minute collection of songs. Hodgkinson and Gilonis then created Woof Records to release the title on a 7-inch EP in 1980. They continued to release titles on the label, subject to the restriction that at least one of them had to play on, engineer, or produce each record. Between 1980 and 1994, 15 titles were released on the label.


List of longest ring roads

Here are the list some of the longest ring roads in the world.


G-sharp major

G-sharp major is a theoretical key based on the musical note G, consisting of the pitches G, A, B, C, D, E and F. Its key signature has six sharps and one double sharp.
Its relative minor is E-sharp minor (usually replaced by F minor), its parallel minor is G-sharp minor, and its enharmonic equivalent is A-flat major.
The G-sharp major scale is:
\override Score.TimeSignature #'stencil = ##f
\relative c" {
 \clef treble \key gis \major \time 7/4 gis4 ais bis cis dis eis fisis gis fisis eis dis cis bis ais gis2
</score>
Although G-sharp major is usually notated as the enharmonic key of A-flat major, because A-flat major has only four flats as opposed to G-sharp major's eight sharps (including the F), it does appear as a secondary key area in several works in sharp keys, most notably in the Prelude and Fugue in C-sharp major from Johann Sebastian Bach's "The Well-Tempered Clavier", Book 1. The G-sharp minor prelude (and, in some editions, the fugue) from the same set ends with a Picardy third, on a G-sharp major chord.
G-sharp major is tonicised briefly in several of Frédéric Chopin's nocturnes in C-sharp minor. A section in the second movement of Chopin's Piano Concerto No. 1 is in G-sharp major, although the key signature has four sharps. The end of the exposition of the second movement Charles-Valentin Alkan's "Grande sonate 'Les quatre âges"', subtitled "Quasi-Faust", is in G-sharp major, albeit written with a six-sharp key signature (the movement opens in D-sharp minor and ends in F-sharp major).
The final pages of "A World Requiem" by John Foulds are written in G-sharp major with its correct key signature shown in the vocal score including the F. The key signature is shown as in the LilyPond example with the scale above, starting with the C and ending at the F.


4396 Gressmann


766 Moguntia

766 Moguntia is a minor planet orbiting the Sun. It is named after Mainz, ancient "Moguntiacum".


Outlier

In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set. An outlier can cause serious problems in statistical analyses.
Outliers can occur by chance in any distribution, but they often indicate either measurement error or that the population has a heavy-tailed distribution. In the former case one wishes to discard them or use statistics that are robust to outliers, while in the latter case they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a mixture model.
In most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable. This can be due to incidental systematic error or flaws in the theory that generated an assumed family of probability distributions, or it may be that some observations are far from the center of the data. Outlier points can therefore indicate faulty data, erroneous procedures, or areas where a certain theory might not be valid. However, in large samples, a small number of outliers is to be expected (and not due to any anomalous condition).
Outliers, being the most extreme observations, may include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum are not always outliers because they may not be unusually far from other observations.
Naive interpretation of statistics derived from data sets that include outliers may be misleading. For example, if one is calculating the average temperature of 10 objects in a room, and nine of them are between 20 and 25 degrees Celsius, but an oven is at 175 °C, the median of the data will be between 20 and 25 °C but the mean temperature will be between 35.5 and 40 °C. In this case, the median better reflects the temperature of a randomly sampled object (but not the temperature in the room) than the mean; naively interpreting the mean as "a typical sample", equivalent to the median, is incorrect. As illustrated in this case, outliers may indicate data points that belong to a different population than the rest of the sample set.
Estimators capable of coping with outliers are said to be robust: the median is a robust statistic of central tendency, while the mean is not. However, the mean is generally a more precise estimator.
Occurrence and causes.
In the case of normally distributed data, the three sigma rule means that roughly 1 in 22 observations will differ by twice the standard deviation or more from the mean, and 1 in 370 will deviate by three times the standard deviation. In a sample of 1000 observations, the presence of up to five observations deviating from the mean by more than three times the standard deviation is within the range of what can be expected, being less than twice the expected number and hence within 1 standard deviation of the expected number – see Poisson distribution – and not indicate an anomaly. If the sample size is only 100, however, just three such outliers are already reason for concern, being more than 11 times the expected number.
In general, if the nature of the population distribution is known "a priori", it is possible to test if the number of outliers deviate significantly from what can be expected: for a given cutoff (so samples fall beyond the cutoff with probability "p") of a given distribution, the number of outliers will follow a binomial distribution with parameter "p", which can generally be well-approximated by the Poisson distribution with λ = "pn". Thus if one takes a normal distribution with cutoff 3 standard deviations from the mean, "p" is approximately 0.3%, and thus for 1000 trials one can approximate the number of samples whose deviation exceeds 3 sigmas by a Poisson distribution with λ = 3.
Causes.
Outliers can have many anomalous causes. A physical apparatus for taking measurements may have suffered a transient malfunction. There may have been an error in data transmission or transcription. Outliers arise due to changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. A sample may have been contaminated with elements from outside the population being examined. Alternatively, an outlier could be the result of a flaw in the assumed theory, calling for further investigation by the researcher. Additionally, the pathological appearance of outliers of a certain form appears in a variety of datasets, indicating that the causative mechanism for the data might differ at the extreme end (King effect).
Definitions and detection.
There is no rigid mathematical definition of what constitutes an outlier; determining whether or not an observation is an outlier is ultimately a subjective exercise. There are various methods of outlier detection. Some are graphical such as normal probability plots. Others are model-based. Box plots are a hybrid.
Model-based methods which are commonly used for identification assume that the data are from a normal distribution, and identify observations which are deemed "unlikely" based on mean and standard deviation:
Peirce's criterion.
It is proposed to determine in a series of formula_1 observations the limit of error, beyond which all observations involving so great an error may be rejected, provided there are as many as formula_2 such observations. The principle upon which it is proposed to solve this problem is, that the proposed observations should be rejected when the probability of the system of errors obtained by retaining them is less than that of the system of errors obtained by their rejection multiplied by the probability of making so many, and no more, abnormal observations. (Quoted in the editorial note on page 516 to Peirce (1982 edition) from "A Manual of Astronomy" 2:558 by Chauvenet.)
Tukey's fences.
Other methods flag observations based on measures such as the interquartile range. For example, if formula_3 and formula_4 are the lower and upper quartiles respectively, then one could define an outlier to be any observation outside the range:
for some nonnegative constant formula_6.
John Tukey proposed this test, where formula_7 indicates an "outlier", and formula_8 indicates data that is "far out".
In anomaly detection.
In various domains such as, but not limited to, statistics, signal processing, finance, econometrics, manufacturing, networking and data mining, the task of "anomaly detection" may take other approaches. Some of these may be distance-based and density-based such as Local Outlier Factor (LOF). Some approaches may use the distance to the k-nearest neighbors to label observations as outliers or non-outliers.
Modified Thompson Tau test.
The modified Thompson Tau test is a method used to determine if an outlier exists in a data set. The strength of this method lies in the fact that it takes into account a data set's standard deviation, average and provides a statistically determined rejection zone; thus providing an objective method to determine if a data point is an outlier.
How it works:
First, a data set's average is determined. Next the absolute deviation between each data point and the average are determined. Thirdly, a rejection region is determined using the formula:
where formula_10 is the critical value from the Student distribution with "n"-2 degrees of freedom, "n" is the sample size, and s is the sample standard deviation.
To determine if a value is an outlier:
Calculate formula_11.
If "δ" > Rejection Region, the data point is an outlier.
If "δ" ≤ Rejection Region, the data point is not an outlier.
The modified Thompson Tau test is used to find one outlier at a time (largest value of "δ" is removed if it is an outlier). Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
Some work has also examined outliers for nominal (or categorical) data. In the context of a set of examples (or instances) in a data set, instance hardness measures the probability that an instance will be misclassified ( formula_12 where is the assigned class label and represent the input attribute value for an instance in the training set ). Ideally, instance hardness would be calculated by summing over the set of all possible hypotheses :
Practically, this formulation is unfeasible as is potentially infinite and calculating formula_14 is unknown for many algorithms. Thus, instance hardness can be approximated using a diverse subset formula_15:
where formula_17 is the hypothesis induced by learning algorithm formula_18 trained on training set with hyperparameters formula_19. Instance hardness provides a continuous value for determining if an instance is an outlier instance.
Working with outliers.
The choice of how to deal with an outlier should depend on the cause. Some estimators are highly sensitive to outliers, notably estimation of covariance matrices.
Retention.
Even when a normal distribution model is appropriate to the data being analyzed, outliers are expected for large sample sizes and should not automatically be discarded if that is the case. The application should use a classification algorithm that is robust to outliers to model data with naturally occurring outlier points.
Exclusion.
Deletion of outlier data is a controversial practice frowned upon by many scientists and science instructors; while mathematical criteria provide an objective and quantitative method for data rejection, they do not make the practice more scientifically or methodologically sound, especially in small sets or where a normal distribution cannot be assumed. Rejection of outliers is more acceptable in areas of practice where the underlying model of the process being measured and the usual distribution of measurement error are confidently known. An outlier resulting from an instrument reading error may be excluded but it is desirable that the reading is at least verified.
The two common approaches to exclude outliers are truncation (or trimming) and Winsorising. Trimming discards the outliers whereas Winsorising replaces the outliers with the nearest "nonsuspect" data. Exclusion can also be a consequence of the measurement process, such as when an experiment is not entirely capable of measuring such extreme values, resulting in censored data.
In regression problems, an alternative approach may be to only exclude points which exhibit a large degree of influence on the estimated coefficients, using a measure such as Cook's distance.
If a data point (or points) is excluded from the data analysis, this should be clearly stated on any subsequent report.
Non-normal distributions.
The possibility should be considered that the underlying distribution of the data is not approximately normal, having "fat tails". For instance, when sampling from a Cauchy distribution, the sample variance increases with the sample size, the sample mean fails to converge as the sample size increases, and outliers are expected at far larger rates than for a normal distribution. Even a slight difference in the fatness of the tails can make a large difference in the expected number of extreme values.
Set-membership uncertainties.
A set membership approach considers that the uncertainty corresponding to the "i"th measurement of an unknown random vector "x" is represented by a set "X"i (instead of a probability density function). If no outliers occur, "x" should belong to the intersection of all "X"i's. When outliers occur, this intersection could be empty, and we should relax a small number of the sets "X"i (as small as possible) in order to avoid any inconsistency. This can be done using the notion of "q"-relaxed intersection. As illustrated by the figure, the "q"-relaxed intersection corresponds to the set of all "x" which belong to all sets except "q" of them. Sets "X"i that do not intersect the "q"-relaxed intersection could be suspected to be outliers.
Alternative models.
In cases where the cause of the outliers is known, it may be possible to incorporate this effect into the model structure, for example by using a hierarchical Bayes model, or a mixture model.


Philippine units of measurement

A number of units of measurement were used in the Philippines to measure various quantities including mass, area, and capacity. The metric system has been compulsory in the country since 1860, during the late Spanish colonial period. A mixture of Spanish units and indigenous units were used alongside American units in the 1900s.
Mass.
Measurements of Mass
Area.
Measurements of Area
Volume.
Measurements of Volume:


All fourths tuning

Among alternative tunings for the guitar, all-fourths tuning is a regular tuning. In contrast, the standard tuning has one irregularity—a major third between the third and second strings—while having perfect fourths between the other successive strings. The standard tuning's irregular major-third is replaced by a perfect fourth in all-fourths tuning, which has the open notes E2-A2-D3-G3-C4-F4.
Among regular tunings, this all-fourths tuning best approximates the standard tuning.
In all guitar tunings, the higher-octave version of a chord can be found by translating a chord by twelve frets higher along the fretboard. In every regular tuning, for example in all-fourths tuning, chords and intervals can be moved also "diagonally". For all-fourths tuning, all twelve major chords (in the first or open positions) are generated by two chords, the open F major chord and the D major chord. The regularity of chord-patterns reduces the number of finger positions that need to be memorized. Jazz musician Stanley Jordan plays guitar in all-fourths tuning; he has stated that all-fourths tuning "simplifies the fingerboard, making it logical".
Among all regular tunings, all-fourths tuning E-A-D-G-C-F is the best approximation of standard tuning, which is more popular. An advantage of standard tuning is that it has many six-string chords, unlike all-fourths tuning. All-fourths tuning is traditionally used for the bass guitar; it is also used for the "bajo sexto".
Allan Holdsworth stated that if he were to learn the guitar again he would tune it in all-fourths.
Relation with all-fifths tuning.
All-fourths tuning is closely related to all-fifths tuning.
All-fourths tuning is based on the perfect fourth (five semitones), and all-fifths tuning is based on the perfect fifth (seven semitones). The perfect-fifth and perfect-fourth intervals are inversions of one another, and the chords of all-fourth and all-fifths are paired as inverted chords. Consequently, chord charts for all-fifths tunings may be used for left-handed all-fourths tuning.


Wilfried von Engelhardt

Wilfried Baron von Engelhardt (11 September 1928, Liebenberg – 24 January 2015, Linz, Austria) was Chief Test Pilot of MBB, first flight of Bölkow Bo 46 and Bo 105. Fellow SETP. Member of the French Académie de l'air et de l'espace.
Life.
Wilfried “Fred” Baron von Engelhardt was born in the Castle of Liebenberg (north of Berlin, Germany) as the great-grandson of Fürst Philip zu Eulenburg. Through his step-father, C.A. von Schoenbeck, who flew as a pilot in WW I in the famous squadron of the „Red Baron“ and who was later the Commander of the German Flight Test Center in Rechlin, Fred early on developed a passion for aviation. Young Fred often met with famous German pilots - Hanna Reitsch and Ernst Udet to name a few. While his step-father frequently piloted a Fieseler Fi 156 Storch and would sometimes land on the Castle's estate, Fred got attached to helicopters. Back then helicopters were in their infancy. The rotorcraft aerodynamics, not well understood these days, the much more complex mechanism as such and the versatility of helicopters attracted him more than fixed wing aircraft.
Nevertheless, Fred started out fixed wing. At age 16 he was trained as a glider pilot – the first step towards a seat in a fighter aircraft of the German Luftwaffe. Fred was trained on SG38 and Grunay Baby. He earned his wings in the “Kranich”. By October 1944 he held the A,B and C-privileges in his Glider license.
Towards the end of the WWII he continued training and was supposed to fly the Heinkel He 162 “Volksjäger”. However, events turned. The lack of aviation fuel in the last days of the war forced Fred to stay out of the Heinkel.
His family had to flee to Austria after the war had ended and Fred earned his high school diploma in Linz in 1947. He would definitely have opted for an aerospace program; however; the Allies banned courses on aeronautical engineering at German and Austrian universities. Fred completed a training to become hotel manager instead.
At the time his step-father had the German dealership for Hiller Helicopters. Fred moved to Paris, was taught French at Sorbonne and eventually became an aircraft mechanic. This likely was the most important step towards his professional career as a test pilot.
From 1955 to 1956 Fred then worked as an aircraft mechanic in the Netherlands. It was a small enterprise and he lived on a very small salary. In return, he was allowed to fly the Hiller 12B and eventually became the first commercial helicopter pilot in the Netherlands and Germany. His log book shows his first flight in a Hiller H12B, registration PH-NFL, on August 2, 1954 (Fred had flown fixed wing aircraft before, mainly gliders and – not official - his step-father's “Fieseler Storch”. When starting official fixed wing flight training his flight instructor would let him solo after only 20 minutes of dual instruction).
Fred progressed to flight instructor in 1956 in Paris and earned his living as a flight instructor, for both civilian and military pilots, flying Bell 47 and Djinn helicopters until 1960.
Looking at his flight log the next step in his career brought him to Dutch New-Guinea. He worked there as an operational helicopter pilot from September 26, 1961 to August 3, 1962. In these days Fred worked for S.G.O.N.N.G., flying the Aloutte II to remote locations in a remote part of the world.
Because of his technical background Fred was invited to join the newly created group around Ludwig Bölkow. His mentor was the engineer Hans Derschmidt, a member of the Bölkow group who developed a swept rotor system with variable sweep and who recommended Engelhardt to the company owner Mr. Boelkow (“he is not only a pilot – he also has some solid understanding of helicopter technology”). Boelkow was in need for a test pilot for his Bo 46 project (the Bo 46 employed a novice rotor concept with variable sweep main rotor blades so to achieve higher speeds in forward flight. After his inventor this rotor system is named “Derschmidt Rotor”).
Fred went to Test Pilot School in Istres. In his spare time on weekends he tested French helicopters as a volunteer and graduated as best of class on July 1, 1966 with test pilot certificate No 31. He served as the Chief Test pilot at MBB from 1962 to 1973.
After his career as a test pilot Fred worked as Head of Sales, then Head of Customer Training. This position took him into many parts of the world, among other, Africa and Middle East and he would now pass on his knowledge to younger pilots.
First flights.
Wilfried “Fred” von Engelhardt's First Flights:
Achievements.
Together with Sigi Hoffmann, Fred was the first holder of an instrument rating for helicopters in Germany.
Fred has held SETP functions in the European part of the society in the past. Despite of his high age he showed great interest in the activities of the society.
Last flights.
Wilfried “Fred” von Engelhardt's Last Flights
After his retirement Wilfried dedicated himself to helping people, in particular those who were disabled. He was an active member in Church and developed and supported an S.O.S Kinderdorf for homeless children. Fred took courses in theology at Linz University and completed an education as a medical professional in Traditional Chinese Medicine. He was very active in the field of anthropology as well.


6233 Kimura


Variable pathlength cell

A variable pathlength cell is a sample holder used for ultraviolet–visible spectroscopy or infrared spectroscopy that has a path length that can be varied to change the absorbance without changing the sample concentration.
Equations.
The Beer-Lambert law states that there is a logarithmic dependence between the transmission (or transmissivity), T, of light through a substance and the product of the absorption coefficient of the substance, α, and the distance the light travels through the material (i.e. the path length), ℓ. The absorption coefficient can, in turn, be written as a product of either a molar absorptivity of the absorber, ε, and the concentration c of absorbing species in the material, or an absorption cross section, σ, and the (number) density N of absorbers. (see Beer Lambert Law link for full derivation)
Spectroscopy with a variable pathlength cell takes advantage of Beer-Lambert law to determine concentrations of various solutions. By knowing the molar absorbtivity of the material and varying the path length, absorption can be plotted as a function of path length. See sample plot to the right:
By taking a linear regression of the linear plot above an expression relating Absorbance, A, slope, m, pathlength and concentration can be derived.
A linear equation of two variables can be derived,
by equating in terms of units we get,
Since the slope of the line is in units of Abs/Pathlength, slope can be expressed as,
by inserting into Beer’s Law we get,
This is the slope spectroscopy equation.
Applications.
Variable pathlength techniques can be applied in any situation where Beer’s law can be applied. It provides an analytical method that averages out minor variations in sample preparation consistency. It also provides a means to calculate concentrations without calibrations curves or serial dilution of samples.
Variable pathlength absorption spectroscopy is typically used when highly reproducible data is a necessity. This can be in the fields of medicine, biotechnology, pharmacology, and drug discovery. It is particularly useful in the protein purification stage of biotechnology where accurate concentrations of various proteins are required or in crystallography.
Determining the relative ratio of protein to DNA is common practice and can be calculated by finding the slope at the corresponding absorption peaks and taking their ratio. This method is used to find the purity of a sample containing these two types of molecule.
Experimental methods.
In ultraviolet-visible spectroscopy or spectroscopy in general a 1 cm pathlength cuvette is used to measure samples. The cuvette is filled with sample, light is passed through the sample and intensity readings are taken. The slope spectroscopy technique can be applied using the same methods as in absorption spectroscopy. With the advent of accurate linear stages, variable pathlength absorption spectroscopy is easily applied experimentally.
Other experimental methods include using ratios of slopes to build extinction coefficient spectra. This is possible because application of slope spectroscopy allows the scientist to keep concentration levels constant and vary path lengths.
Background subtraction.
Variable pathlength absorption spectroscopy uses a determined slope to calculate concentration. As stated above this is a product of the molar absorbtivity and the concentration. Since the actual absorbance value is taken at many data points at equal intervals, background subtraction is generally unnecessary. The image on the right is a linear plot showing both the background corrected data and the raw data.
This shows that the absorbance values on the plot are offset by an equal amount and the slope of the two plots are equal. Thus, the concentration calculated from the two plots is equal. Other scalar components that contribute to the absorbance of a given sample like contaminants on the cuvette or a different cuvette material also are averaged out during the slope measurement.
The technique is also applicable for in line measurements for TFF and chromatography applications.


3730 Hurban