Joseph Gallian

Joseph A. Gallian (born January 5, 1942) is an American mathematician, the Morse Alumni Distinguished University Professor of Teaching in the Department of Mathematics and Statistics at the University of Minnesota Duluth.
Professional career.
Gallian completed his Ph.D. thesis, entitled "Two-Step Centralizers in Finite p-Groups", at the University of Notre Dame in 1971 under the supervision of Karl Kronstein. He has been a professor at the University of Minnesota Duluth since 1972. In addition to teaching math classes, he taught a humanities course called "The Lives and Music of the Beatles" for 33 years and a liberal arts course on math and sports.
Gallian has authored or edited six books (Contemporary Abstract Algebra, Cengage; For All Practical Purposes, W.H. Freeman (coauthor); Principles and Practices of Mathematics, Springer-Verlag; Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, Editor, American Mathematical Society; Proceedings of the Conference on Promoting Undergraduate Research in Mathematics (editor), American Mathematical Society; Mathematics and Sports, Mathematical Association of America) and over 100 articles. He earned media attention in 1991 when he determined the methods used by Minnesota and many other states for assigning drivers' license numbers.
Between 1977 and 2019, Gallian ran forty Research Experience for Undergraduates (REU) programs at the University of Minnesota Duluth. The program has been funded by the University of Minnesota Duluth grants from the National Science Foundation (40+ years) and the National Security Agency (30+ years). It is one of the oldest and longest running REUs in the country. As of the end of 2019, the program has had 254 undergraduate participants and has produced more than 240 publications in mainstream professional journals. More than 150 Duluth REU students have received a PhD degree.
Gallian served a 2-year term as the President of the Mathematical Association of America starting in January 2007. In addition, he was co-director of Project NExT from 1998 to 2012, Associate Editor of MAA OnLine since 1997, a member of the advisory board of "Math Horizons" from 1993 to 2013, and a member of the editorial board of the American Mathematical Monthly for 15 years.
In September of 2019, the Department of Mathematics and Statistics at University of Minnesota Duluth in aggregate, including Prof. Gallian, was found "hostile and offensive to a reasonable woman" after an investigation by the Office of Equal Opportunity and Affirmative Action. As of April of 2021, multiple women have submitted their resignations due to continued hostility in the department and its effects on their health. A link to the public summary can be found here or requested through the University of Minnesota.
Awards and honors.
Gallian has won both the Allendoerfer and Evans awards for exposition from the Mathematical Association of America (MAA) and was the Pólya lecturer for the MAA from 1999 to 2001.
His excellence in teaching earned him the Haimo Award for distinguished teaching from the MAA in 1993 and he was the Carnegie Foundation for the Advancement of Teaching Minnesota Professor of the Year in 2003.
In 2019 he received the MAA's Mary P. Dolciani Award for making a distinguished contribution to the mathematical education of K-16 students in the United States or Canada.
In 2011 he received the MAA's Yueh-Gin Gung and Dr. Charles Y. Hu Distinguished Service to Mathematics Award.
In 2000, Gallian was named by a Duluth newspaper as one of the "100 Great Duluthians of the 20th Century".
In 2013 he became a fellow of the American Mathematical Society.


K-finite

In mathematics, a K-finite function is a type of generalized trigonometric polynomial. Here "K" is some compact group, and the generalization is from the circle group "T".
From an abstract point of view, the characterization of trigonometric polynomials amongst other functions "F", in the harmonic analysis of the circle, is that for functions "F" in any of the typical function spaces, "F" is a trigonometric polynomial if and only if its Fourier coefficients
vanish for |"n"| large enough, and that this in turn is equivalent to the statement that all the translates
by a fixed angle θ lie in a finite-dimensional subspace. One implication here is trivial, and the other, starting from a finite-dimensional invariant subspace, follows from complete reducibility of representations of "T".
From this formulation, the general definition can be seen: for a representation ρ of "K" on a vector space "V", a "K"-finite vector "v" in "V" is one for which the
for "k" in "K" span a finite-dimensional subspace. The union of all finite-dimension "K"-invariant subspaces is itself a subspace, and "K"-invariant, and consists of all the "K"-finite vectors. When all "v" are "K"-finite, the representation ρ itself is called "K"-finite.
References.
Lectures on Lie Groups and Lie Algebras by Roger Carter, Graeme Segal and Ian Macdonald


Essential dimension

In mathematics, essential dimension is an invariant defined for certain algebraic structures such as algebraic groups and quadratic forms. It was introduced by J. Buhler and Z. Reichstein
and in its most generality defined by A. Merkurjev.
Basically, essential dimension measures the complexity of algebraic structures via their fields of definition. For example, a quadratic form q : V → K over a field K, where V is a K-vector space, is said to be defined over a subfield L of K if there exists a K-basis e1...,en of V such that q can be expressed in the form formula_1 with all coefficients aij belonging to L. If K has characteristic different from 2, every quadratic form is diagonalizable. Therefore, q has a field of definition generated by n elements. Technically, one always works over a (fixed) base field k and the fields K and L in consideration are supposed to contain k. The essential dimension of q is then defined as the least transcendence degree over k of a subfield L of K over which q is defined.
Formal definition.
Fix an arbitrary field k and let "Fields/k" denote the category of finitely generated field extensions of k with inclusions as morphisms. Consider a (covariant) functor F : Fields/k → Set.
For a field extension K/k and an element "a" of F(K/k) a "field of definition of a" is an intermediate field K/L/k such that "a" is contained in the image of the map F(L/k) → F(K/k) induced by the inclusion of L in K.
The "essential dimension of a", denoted by "ed(a)", is the least transcendence degree (over k) of a field of definition for "a". The essential dimension of the functor F, denoted by "ed(F)", is the supremum of "ed(a)" taken over all elements "a" of F(K/k) and objects K/k of Fields/k.


Inner product space

In mathematics, an inner product space or a Hausdorff pre-Hilbert space is a vector space with a binary operation called an inner product. This operation associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors, often denoted using angle brackets (as in formula_1). Inner products allow the rigorous introduction of intuitive geometrical notions, such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors (zero inner product). Inner product spaces generalize Euclidean spaces (in which the inner product is the dot product, also known as the scalar product) to vector spaces of any (possibly infinite) dimension, and are studied in functional analysis. Inner product spaces over the field of complex numbers are sometimes referred to as unitary spaces. The first usage of the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898.
An inner product naturally induces an associated norm, (|"x"| and |"y"| are the norms of and , in the picture), which canonically makes every inner product space into a normed vector space. If this normed space is also a Banach space then the inner product space is called a Hilbert space. If an inner product space is not a Hilbert space then it can be "extended" to a Hilbert space , called a completion. Explicitly, this means that is linearly and isometrically embedded onto a dense vector subspace of and that the inner product on is the unique continuous extension of the original inner product .
Definition.
In this article, the field of scalars denoted is either the field of real numbers formula_2 or the field of complex numbers formula_3.
Formally, an inner product space is a vector space over the field together with a map
called an inner product that satisfies the following conditions (1), (2), and (3) for all vectors and all scalars :
The above three conditions are the defining properties of an inner product, which is why an inner product is sometimes (equivalently) defined as being a .
An inner product can equivalently be defined as a positive-definite sesquilinear form.
Assuming (1) holds, condition (3) will hold if and only if both conditions (4) and (5) below hold:
Conditions (1) through (5) are satisfied by every inner product.
Elementary properties.
Positive-definiteness and linearity, respectively, ensure that:
Conjugate symmetry implies that is real for all , because
Conjugate symmetry and linearity in the first variable imply
that is, conjugate linearity in the second argument. So, an inner product is a sesquilinear form.
This important generalization of the familiar square expansion follows:
These properties, constituents of the above linearity in the first and second argument:
are otherwise known as .
In the case of formula_10 conjugate-symmetry reduces to symmetry, and sesquilinearity reduces to bilinearity. Hence an inner product on a real vector space is a . That is,
and the binomial expansion becomes:
Alternative definitions, notations and remarks.
A common special case of the inner product, the scalar product or dot product, is written with a centered dot formula_13
Some authors, especially in physics and matrix algebra, prefer to define the inner product and the sesquilinear form with linearity in the second argument rather than the first. Then the first argument becomes conjugate linear, rather than the second. In those disciplines, we would write the inner product formula_14 as (the bra–ket notation of quantum mechanics), respectively (dot product as a case of the convention of forming the matrix product , as the dot products of rows of with columns of ). Here, the kets and columns are identified with the vectors of , and the bras and rows with the linear functionals (covectors) of the dual space , with conjugacy associated with duality. This reverse order is now occasionally followed in the more abstract literature, taking to be conjugate linear in rather than . A few instead find a middle ground by recognizing both and as distinct notations—differing only in which argument is conjugate linear.
There are various technical reasons why it is necessary to restrict the base field to formula_2 and formula_3 in the definition. Briefly, the base field has to contain an ordered subfield in order for non-negativity to make sense, and therefore has to have characteristic equal to (since any ordered field has to have such characteristic). This immediately excludes finite fields. The basefield has to have additional structure, such as a distinguished automorphism. More generally, any quadratically closed subfield of formula_2 or formula_3 will suffice for this purpose (e.g., algebraic numbers, constructible numbers). However, in the cases where it is a proper subfield (i.e., neither formula_2 nor formula_3), even finite-dimensional inner product spaces will fail to be metrically complete. In contrast, all finite-dimensional inner product spaces over formula_2 or formula_22 such as those used in quantum computation, are automatically metrically complete (and hence Hilbert spaces).
In some cases, one needs to consider non-negative sesquilinear forms. This means that formula_23 is only required to be non-negative. Treatment for these cases are illustrated below.
Some examples.
Real numbers.
A simple example is the real numbers with the standard multiplication as the inner product
Euclidean vector space.
More generally, the real -space formula_25 with the dot product is an inner product space, an example of a Euclidean vector space.
where is the transpose of .
Complex coordinate space.
The general form of an inner product on formula_27 is known as the Hermitian form and is given by
where is any Hermitian positive-definite matrix and is the conjugate transpose of . For the real case, this corresponds to the dot product of the results of directionally-different scaling of the two vectors, with positive scale factors and orthogonal directions of scaling. It is a weighted-sum version of the dot product with positive weights—up to an orthogonal transformation.
Hilbert space.
The article on Hilbert spaces has several examples of inner product spaces, wherein the metric induced by the inner product yields a complete metric space. An example of an inner product space which induces an incomplete metric is the space formula_29 of continuous complex valued functions formula_30 and formula_31 on the interval formula_32 The inner product is
This space is not complete; consider for example, for the interval the sequence of continuous "step" functions, , defined by:
This sequence is a Cauchy sequence for the norm induced by the preceding inner product, which does not converge to a function.
Random variables.
For real random variables and , the expected value of their product
is an inner product. In this case, if and only if (i.e., almost surely). This definition of expectation as inner product can be extended to random vectors as well.
Real matrices.
For real square matrices of the same size, with transpose as conjugation
is an inner product.
Vector spaces with forms.
On an inner product space, or more generally a vector space with a nondegenerate form (hence an isomorphism ), vectors can be sent to covectors (in coordinates, via transpose), so that one can take the inner product and outer product of two vectors—not simply of a vector and a covector.
Norm.
Inner product spaces are normed vector spaces for the norm defined by
As for every normed vector space, an inner product space is a metric space, for the distance defined by
The axioms of the inner product guarantee that the map above forms a norm, which will have the following properties.
Real and complex parts of inner products.
Suppose that formula_39 is an inner product on (so it is antilinear in its second argument). The polarization identity shows that the real part of the inner product is
If formula_41 is a real vector space then
formula_42
and the imaginary part (also called the ) of formula_39 is always .
Assume for the rest of this section that is a complex vector space.
The polarization identity for complex vector spaces shows that
The map defined by formula_45 for all formula_46 satisfies the axioms of the inner product except that it is antilinear in its , rather than its second, argument. The real part of both formula_47 and formula_14 are equal to formula_49 but the inner products differ in their complex part:
The last equality is similar to the formula expressing a linear functional in terms of its real part.
Let formula_51 denote formula_41 considered as a vector space over the real numbers rather than complex numbers.
The real part of the complex inner product formula_14 is the map formula_54 which necessarily forms a real inner product on the real vector space formula_55 Every inner product on a real vector space is symmetric and bilinear.
For example, if formula_56 with inner product formula_57 where formula_41 is a vector space over the field formula_22 then formula_60 is a vector space over formula_2 and formula_62 is the dot product formula_63 where formula_64 is identified with the point formula_65 (and similarly for formula_66). Also, had formula_14 been instead defined to be the symmetric map formula_68 (rather than the usual antisymmetric map formula_69) then its real part formula_62 would be the dot product.
The next examples show that although real and complex inner products have many properties and results in common, they are not entirely interchangeable.
For instance, if formula_71 then formula_72 but the next example shows that the converse is in general true.
Given any formula_73 the vector formula_74 (which is the vector formula_75 rotated by 90°) belongs to formula_41 and so also belongs to formula_51 (although scalar multiplication of formula_75 by is not defined in formula_79 it is still true that the vector in formula_41 denoted by formula_74 is an element of formula_51). For the complex inner product, formula_83 whereas for the real inner product the value is always formula_84
If formula_56 has the inner product mentioned above, then the map formula_86 defined by formula_87 is a non-zero linear map (linear for both formula_41 and formula_51) that denotes rotation by 90° in the plane. This map satisfies formula_90 for all vectors formula_91 where had this inner product been complex instead of real, then this would have been enough to conclude that this linear map formula_92 is identically formula_93 (i.e. that formula_94), which rotation is certainly not. In contrast, for all non-zero formula_73 the map formula_92 satisfies formula_97
Orthonormal sequences.
Let be a finite dimensional inner product space of dimension . Recall that every basis of consists of exactly linearly independent vectors. Using the Gram–Schmidt process we may start with an arbitrary basis and transform it into an orthonormal basis. That is, into a basis in which all the elements are orthogonal and have unit norm. In symbols, a basis is orthonormal if for every and for each .
This definition of orthonormal basis generalizes to the case of infinite-dimensional inner product spaces in the following way. Let be any inner product space. Then a collection
is a for if the subspace of generated by finite linear combinations of elements of is dense in (in the norm induced by the inner product). We say that is an for if it is a basis and
if and for all .
Using an infinite-dimensional analog of the Gram-Schmidt process one may show:
Theorem. Any separable inner product space has an orthonormal basis.
Using the Hausdorff maximal principle and the fact that in a complete inner product space orthogonal projection onto linear subspaces is well-defined, one may also show that
Theorem. Any complete inner product space has an orthonormal basis.
The two previous theorems raise the question of whether all inner product spaces have an orthonormal basis. The answer, it turns out is negative. This is a non-trivial result, and is proved below. The following proof is taken from Halmos's "A Hilbert Space Problem Book" (see the references).
Parseval's identity leads immediately to the following theorem:
Theorem. Let be a separable inner product space and an orthonormal basis of . Then the map
is an isometric linear map with a dense image.
This theorem can be regarded as an abstract form of Fourier series, in which an arbitrary orthonormal basis plays the role of the sequence of trigonometric polynomials. Note that the underlying index set can be taken to be any countable set (and in fact any set whatsoever, provided is defined appropriately, as is explained in the article Hilbert space). In particular, we obtain the following result in the theory of Fourier series:
Theorem. Let be the inner product space . Then the sequence (indexed on set of all integers) of continuous functions
is an orthonormal basis of the space with the inner product. The mapping
is an isometric linear map with dense image.
Orthogonality of the sequence follows immediately from the fact that if , then
Normality of the sequence is by design, that is, the coefficients are so chosen so that the norm comes out to 1. Finally the fact that the sequence has a dense algebraic span, in the , follows from the fact that the sequence has a dense algebraic span, this time in the space of continuous periodic functions on with the uniform norm. This is the content of the Weierstrass theorem on the uniform density of trigonometric polynomials.
Operators on inner product spaces.
Several types of linear maps from an inner product space to an inner product space are of relevance:
From the point of view of inner product space theory, there is no need to distinguish between two spaces which are isometrically isomorphic. The spectral theorem provides a canonical form for symmetric, unitary and more generally normal operators on finite dimensional inner product spaces. A generalization of the spectral theorem holds for continuous normal operators in Hilbert spaces.
Generalizations.
Any of the axioms of an inner product may be weakened, yielding generalized notions. The generalizations that are closest to inner products occur where bilinearity and conjugate symmetry are retained, but positive-definiteness is weakened.
Degenerate inner products.
If is a vector space and a semi-definite sesquilinear form, then the function:
makes sense and satisfies all the properties of norm except that does not imply (such a functional is then called a semi-norm). We can produce an inner product space by considering the quotient }. The sesquilinear form factors through .
This construction is used in numerous contexts. The Gelfand–Naimark–Segal construction is a particularly important example of the use of this technique. Another example is the representation of semi-definite kernels on arbitrary sets.
Nondegenerate conjugate symmetric forms.
Alternatively, one may require that the pairing be a nondegenerate form, meaning that for all non-zero there exists some such that , though need not equal ; in other words, the induced map to the dual space is injective. This generalization is important in differential geometry: a manifold whose tangent spaces have an inner product is a Riemannian manifold, while if this is related to nondegenerate conjugate symmetric form the manifold is a pseudo-Riemannian manifold. By Sylvester's law of inertia, just as every inner product is similar to the dot product with positive weights on a set of vectors, every nondegenerate conjugate symmetric form is similar to the dot product with weights on a set of vectors, and the number of positive and negative weights are called respectively the positive index and negative index. Product of vectors in Minkowski space is an example of indefinite inner product, although, technically speaking, it is not an inner product according to the standard definition above. Minkowski space has four dimensions and indices 3 and 1 (assignment of "+" and "−" to them differs depending on conventions).
Purely algebraic statements (ones that do not use positivity) usually only rely on the nondegeneracy (the injective homomorphism ) and thus hold more generally.
Related products.
The term "inner product" is opposed to outer product, which is a slightly more general opposite. Simply, in coordinates, the inner product is the product of a with an vector, yielding a 1 × 1 matrix (a scalar), while the outer product is the product of an vector with a covector, yielding an matrix. Note that the outer product is defined for different dimensions, while the inner product requires the same dimension. If the dimensions are the same, then the inner product is the of the outer product (trace only being properly defined for square matrices). In an informal summary: "inner is horizontal times vertical and shrinks down, outer is vertical times horizontal and expands out".
More abstractly, the outer product is the bilinear map sending a vector and a covector to a rank 1 linear transformation (simple tensor of type (1, 1)), while the inner product is the bilinear evaluation map given by evaluating a covector on a vector; the order of the domain vector spaces here reflects the covector/vector distinction.
The inner product and outer product should not be confused with the interior product and exterior product, which are instead operations on vector fields and differential forms, or more generally on the exterior algebra.
As a further complication, in geometric algebra the inner product and the (Grassmann) product are combined in the geometric product (the Clifford product in a Clifford algebra) – the inner product sends two vectors (1-vectors) to a scalar (a 0-vector), while the exterior product sends two vectors to a bivector (2-vector) – and in this context the exterior product is usually called the (alternatively, ). The inner product is more correctly called a product in this context, as the nondegenerate quadratic form in question need not be positive definite (need not be an inner product).


End (category theory)

In category theory, an end of a functor formula_1 is a universal extranatural transformation from an object "e" of X to "S".
More explicitly, this is a pair formula_2, where "e" is an object of X and formula_3 is an extranatural transformation such that for every extranatural transformation formula_4 there exists a unique morphism formula_5
of X with formula_6
for every object "a" of C.
By abuse of language the object "e" is often called the "end" of the functor "S" (forgetting formula_7) and is written
Characterization as limit: If X is complete and C is small, the end can be described as the equalizer in the diagram
where the first morphism being equalized is induced by formula_10 and the second is induced by formula_11.
Coend.
The definition of the coend of a functor formula_12 is the dual of the definition of an end.
Thus, a coend of "S" consists of a pair formula_13, where "d" is an object of X and formula_14
is an extranatural transformation, such that for every extranatural transformation formula_15 there exists a unique morphism
formula_16 of X with formula_17 for every object "a" of C.
The "coend" "d" of the functor "S" is written
Characterization as colimit: Dually, if X is cocomplete and C is small, then the coend can be described as the coequalizer in the diagram


List of polynomial topics

This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.


Network operator matrix

Network operator matrix (NOM) is a representation of mathematical expressions in computer memory.
NOM is a new approach to the problem of automatic search of mathematical equations. The researcher defines the sets of operations, variables and parameters. The computer program generates a number of mathematical equations that satisfy given restrictions. Then the optimization algorithm finds the structure of appropriate mathematical expression and its parameters.
Network operator is a directed graph that corresponds to some mathematical expressions. Every source nodes of the graph are variables or constants of mathematical expression, inner nodes correspond to binary operations and edges correspond to unary operations. The calculation’s result of mathematical expression is kept in the last sink node.
Example.
Consider the following mathematical expression
The graph for Expression (), is presented in Fig. 1.
On the edges we place unary operations
formula_1

formula_2

formula_3

formula_4
In the inner and sink nodes we place binary operations

formula_5

formula_6
Expression 1 can be presented in the PC memory as a NOM
Any mathematical expression can be presented as a network operator matrix.

To calculate the mathematical expression by the network operator matrix the node vector is used.

Each component of node vector corresponds to the nodes of the network operator graph. Initially each component is equal to the argument for the given node or the unit element of binary operation.

For addition and multiplication the number of operation equals its unit element. For addition it is 0, for multiplication it is 1.
The node vector for the given example

formula_8

The calculation by matrix formula_9 is performed for nonzero nondiagonal elements formula_10 by

formula_11
Follow the rows of the matrix.

For the Row 1 we have formula_12, that is formula_13, formula_14, formula_15.
Take arguments from formula_8
formula_17, formula_18 then

formula_19

Further in Row 1 we have formula_20

formula_21

formula_22

formula_23.

As a result after Row 1 we have formula_24.

For the Row 2 we have
formula_25

formula_26

then follow the rows
formula_27

formula_28
formula_29

formula_30
formula_31

formula_32
formula_33

formula_34
formula_35

formula_36.
Josue Ortega

Josue Ortega is a lecturer in economics at Queen's University Belfast. He is the author of a controversial article that suggests that the emergence of online dating has caused an increase in the number of interracial marriages in the US. Ortega's findings have been covered by international media, including "Forbes", "the Times", "New Scientist", "Business Insider" and the "MIT Technology Review". Ortega has been interviewed by "Thinking Allowed" at BBC Radio 4.
Ortega obtained his PhD at the University of Glasgow under the supervision of Professor Hervé Moulin. He received the Catherine Richards prize by the UK Institute for Mathematics and its Applications in 2016. He sits in the editorial board of Palgrave Communications and has published his research in the Journal of Mathematical Economics, the Proceedings of the ACM Conference on Economics and Computation, Economics Letters and .


Petri Kuljuntausta

Petri Kuljuntausta is a Finnish composer, musician, sound artist and author of three books on electronic music and sound art. Since the 1990s he has belonged to a new generation of composers in Finland interested in experimental and electronic music.
Career.
Kuljuntausta has composed digital music for experimental films, video art, visual art and dance projects, and made media and sound installations in museums, galleries and concert halls. His works has been performed in many European countries, Australia, Mexico and the USA, and he has made recordings for various labels in Australia, Colombia, England, Estonia, Finland, France, Germany, India, Sweden and the USA. In 2004 Star's End and Inner Space radio shows selected Kuljuntausta's "Momentum" as one of the most significant CD releases of the year. In 2005 he won an award, The Finnish State Prize for Art, from the Finnish government as a distinguished national artist. NPS, the Nederlandse Programma Stichting (Dutch broadcasting foundation), and Yleisradio (Finnish Broadcasting Company) has produced extensive artistic profiles on Kuljuntausta.
Kuljuntausta is famous for music composed of sounds both natural and extraordinary. In close collaboration with natural scientists, he has composed underwater installations from underwater materials and made music out of whale calls and the sounds of the Northern Lights. In many ways Kuljuntausta's art is based on good knowledge of tradition. Environmental sounds, live electronic music, improvisation and collaborations with Media Artists has influenced him as a composer.
One of his many challenging composition projects is "Northern Lights Live", which is based on soundscapes of the Northern Lights and audio feedback. The work was commissioned by the ISEA2004 (Inter-Society for the Electronic Arts) festival, 12th Symposium on Electronic Arts. "Northern Lights Live" is a vivid collaboration in the field between art and science, recycling original nature recordings of the phenomena as well as processed aurora borealis sounds. A forty-five-minute-long continuous audio-visual dialogue between nature's own soundscapes and their digitally altered, urban noise-art substitutes were created on stage.<ref name="http://www.aureobel.com">http://www.aureobel.com</ref> In collaboration with zoomusicologist Dario Martinelli, Kuljuntausta released in 2008 a CD entitled "Zoosphere. A Musical Encryptation of Animal Sounds", which is entirely based on animal sounds, like the sounds of birds, whales, wolves, shrimps. Kuljuntausta has also composed extensive body of works in the style of Minimalist music. Since mid-1990s he has developed new composition technique based on Phasing. Repetitive music could be heard especially in his film and video soundtracks.
In collaboration with visual artist and experimental film director Sami van Ingen Kuljuntausta has created media installations where the energy of light waves reveal audible sounds ("Wave Motion"), and the sound waves in water reveal moving light figures with the help of laser beams ("Waves & Patterns"). Soundscapes and environmental sounds are often present in his works. Another distinctive character in his music is the use of feedback noise. Kuljuntausta has developed his own electronic system to generate and control feedback sounds live.
The most extreme musical environment for Kuljuntausta's music is Saturn's moon Titan. When Cassini-Huygens spacecraft (Titan-IVB/Centaur) started its journey in 1997 from Kennedy Space Center, United States, his composition Charm of Sound was inside the Huygens probe of Cassini-Huygens spacecraft, stored on the CD-rom. When Huygens probe reached its destination on Friday January 14, 2005, Kuljuntausta's Charm of Sound landed on the ground of Titan after travelling seven years and four billion kilometres through Space.
Kuljuntausta has collaborated with composers and artists Morton Subotnick, Atau Tanaka, Richard Lerman, David Rothenberg, Robert Jürjendal, Markus Reuter, Pat Mastelotto, Chris Mann, Jim Nollman, Dario Martinelli, Al Margolis (If, Bwana), Helmut Lemke, Ocean-North, Juhani Liimatainen, Juhani Nuorvala, Hepa Halme, Jukka Orma, Markku Veijonsuo, Markus Fagerudd, Rihmasto, John Richardson, and VJ group Random Doctors, and he has produced and coordinated many album projects since late-1990s. In 2011 Kuljuntausta composed soundtrack for the film Five Fragments of the Extinct Empathy (directed by Anna Nykyri), the film was selected as the Best Short Documentary 2012 at the Hot Docs Canadian International Documentary Festival, Toronto. Two years earlier, in 2009, Kuljuntausta composed soundtrack for the film Water Cities (directed by Jaana Puhakka) which won the first prize at III. Istanbul International Architecture and Urban Films Festival in Istanbul, Turkey. He has also composed music for the films "Texas Scramble", "The Blow", "Days", and "Navigator", all directed by Sami van Ingen.
Kuljuntausta is the author of an 800-page history of Finnish electronic music, "On/Off. Eetteriäänistä sähkömusiikkiin" ("On/Off. From Ether Sounds To Electronic Music") (Kiasma and Like Publishing). With the book was released a CD compilation (compiled, restored and produced by Kuljuntausta), which contains the first Finnish electronic compositions from the years 1958-1963 first time on the CD.<ref name="http://www.like.fi">http://www.like.fi</ref>
In 2006, Kuljuntausta published his second book, "Äänen eXtreme" ("eXtreme Sound") (Like Publishing), on his own approach to music and sound. Together with the book was released a DVD, which was simply entitled as "Petri Kuljuntausta" (also known as "1994-2005", referring to the composition period of the disc), which contains almost nine hours of electronic music and sound works (42 works) composed and performed by Kuljuntausta. His third book, "First Wave" (Like Publishing), on Finnish electronic music was published in English in 2008.
Kuljuntausta is the founder of Charm of Sound association (Äänen Lumo), established in 1995 to support electronic music, experimental music and sound art, and the Finnish Society for Acoustic Ecology which was founded in 1999. Kuljuntausta was the founder and main editor of "..." ezine (electronic magazine, 1997–2001) and he also founded Charmlist emailing-list in 2001, both focused on distributing information on the activities on electronic music and sound art.
Radio programme.
During 1997-2005, Kuljuntausta produced a radio programme on electroacoustic music and sound art entitled Charmed Sounds (Lumottuja ääniä) for Yleisradio, Finnish Broadcasting Company. In 2000 Kuljuntausta worked at City University London, Department of Music / Composition (Electroacoustic), as a Visiting Scholar. During the visit he composed soundscape music from the sounds of London City. One of these works, "Vroom!!", was released on Hearing Place (Sound Art Exploring Place from Around the World), a CD published by Australian label Move Records.
Web sites.
In 2005, Kuljuntausta produced internet (media) albums of Atau Tanaka, Richard Lerman, If, Bwana (Al Margolis) and Petri Kuljuntausta for Aureobel internet publishing company. Since its start the label has worked as a distribution channel for experimental music and sound art. In 2008, Kuljuntausta worked as an artistic director of the Nightingala festival and invited composers and performers to create music from nightingale song. In 2009, Science Centre Heureka commissioned Kuljuntausta to compose 20th anniversary music for the Science Centre. The original opening music of Heureka was composed by Einojuhani Rautavaara in 1989. In 2012 Aalto university commissioned a work from Kuljuntausta for the university's opening ceremony. Kuljuntausta lecturers regularly on Sonic Art, Electronic Music, and Soundscape Art at the University of Art and Design Helsinki and Theatre Academy (Finland).
Discography.
Production.
Kuljuntausta has also produced and/or mastered (audio post-production) music and sound art works for CD releases at least from the following artists: Gordon Monahan, Francisco López, Jorge Haro, Disinformation, Charlie Morrow, Jimi Tenor, Incite/, Erkki Kurenniemi, Jukka Ruohomäki, Timo Hietala, Juhani Liimatainen, Jarmo Sermilä, Patrick Kosk, Hepa Halme, Nemesis, Juhani Nuorvala, Chris Mann, Urban Shepherds, Dario Martinelli, John Richardson, Jukka Ylitalo, Teemu Ontero, Inéz, Pekka Sirén, Jukka Mikkola, Tom Ahola, Agnieszka Waligórska, Vesa Lahti, Teemu Mäki, Kalev Tiits, Koray Tahiroglu, Shinji Kanki, Reijo Jyrkiäinen, Bengt Johansson, Henrik Otto Donner, Erkki Salmenhaara, Ilkka Kuusisto, Seppo Mustonen, Usko Meriläinen, Pehr Henrik Nordgren, Martti Vuorenjuuri, Veikko Eskolin, RANK Ensemble, Horst Quartet, Grey Park, Täydellisyys, Koelse, Umpio, Kheta Hotem, Tripolar, Gaia B, Alice Evermoore & Eavesdropper, Sami Klemola, Helena Gough, Jean-Marc Savic, Sinebag, Gintas K, Siri Austeen, Pekka Sassi, Olle Essvik, Goodiepal, Marja-Leena Sillanpää, Child of Klang, Åsa Maria Bengtsson, Ida Lundén, Lise-Lotte Norelius, Mikko Maasalo, Juhani Räisänen, Pink Twins, Juha Valkeapää, Pauli Apollo Ahopelto, Pessi Parviainen, Jakob Nordgren, Juan Kasari, Aleksi Keränen, Taito Kantomaa, Janne Jankeri, Jussi Österman, Jukka Rintamäki, Sebastian Lindberg, Sami Pennanen, Sound Meccano & Evgeniy Droomoff, Gas Of Latvia, Andres Lõo, Taavi Tulev, Lauri Dag-Tüür, Arturas Bumsteinas, Antanas Jasenka, Kaspars Groshevs, John Grzinich, Taavi Kerikmäe, Kiwa, Darius Čiuta, Raul Keller, Antireality & Bernurits, Astma, Lina Lapelyté, Martins Rokis, Raimundas Eimontas, Pekka ja Susiluoto, USO, Lau Nau, Tsembla.


Subharmonic (record label)

Subharmonic was an independent record label based in New York City. It primarily issued music with strong ambient and dub music influence. Its sub-label was Strata Records, which issued all its albums in an opaque black container. The label was founded in 1993 by music producers Bill Laswell, John Matarazzo and Robert Soares. A falling out with Matarazzo occurred during the mid-nineties, effectively ending the label's activities.


Quantum-optical spectroscopy

Quantum-optical spectroscopy is a quantum-optical generalization of laser spectroscopy where matter is excited and probed with a sequence of laser pulses.
Classically, such pulses are defined by their spectral and temporal shape as well as phase and amplitude of the electromagnetic field. Besides these properties of light, the phase-amplitude aspects have intrinsic quantum fluctuations that are of central interest in quantum optics. In ordinary laser spectroscopy, one utilizes only the classical aspects of laser pulses propagating through matter such as atoms or semiconductors. In quantum-optical spectroscopy, one additionally utilizes the quantum-optical fluctuations of light to enhance the spectroscopic capabilities by directly shaping and/or detecting the quantum fluctuations of light. Quantum-optical spectroscopy has applications in controlling and characterizing quantum dynamics of many-body states because one can directly access a large set of many-body states, which is not possible in classical spectroscopy .
Quantum-optical state injection.
A generic electromagnetic field can always be expressed in terms of a mode expansion where individual components form a complete set of modes. Such modes can be constructed with different methods and they can, e.g., be energy eigenstate, generic spatial modes, or temporal modes. Once these light mode are chosen, their effect on the quantized electromagnetic field can be described by Boson creation and annihilation operators
formula_1
and
formula_2
for photons, respectively. The quantum fluctuations of the light field can be uniquely defined by the photon correlations
formula_3
that contain the pure formula_4-particle correlations as defined with the cluster-expansion approach. Using the same second-quantization formalism for the matter being studied, typical electronic excitations in matter can be described by Fermion operators for electronic excitations and holes, i.e.~electronic vacancies left behind to the many-body ground state. The corresponding electron–hole excitations can be described by operators formula_5 and formula_6 that create and annihilate an electron–hole pair, respectively.
In several relevant cases, the light–matter interaction can be described using the dipole
interaction
formula_7
where the summation is implicitly taken over all possibilities to create an electron–hole pair (the formula_5 part) via a photon absorption (the formula_2 part); the Hamiltonian also contains the Hermitian conjugate (abbreviated as h.c.) of the terms that are explicitly written. The coupling strength between light and matter is defined by formula_10.
When the electron–hole pairs are excited resonantly with a single-mode light formula_2, the photon correlations are directly injected into the many-body correlations. More specifically, the fundamental form of the light–matter interaction inevitably leads to a correlation-transfer relation
formula_12
between photons and electron–hole excitations. Strictly speaking, this relation is valid before the onset of scattering induced by the Coulomb and phonon interactions in the solid. Therefore, it is desirable to use laser pulses that are faster than the dominant scattering processes. This regime is relatively easy to realize in present-day laser spectroscopy because lasers can already output femtosecond, or even attosecond, pulses with a high precision in controllability.
Realization.
Physically, the correlation-transfer relation means that one can "directly" inject desired
many-body states simply by adjusting the quantum fluctuations of the light pulse, as long as the light pulse is short enough. This opens a new possibility for studying properties of distinct many-body states, once the quantum-optical spectroscopy is realized through controlling the quantum fluctuations of light sources. For example, a coherent-state laser is described entirely by its single-particle expectation value formula_13. Therefore, such excitation directly injects property formula_14 that is polarization related to electron–hole transitions. To directly excite bound electron–hole pairs, i.e., excitons, described by a two-particle correlation formula_15, or a biexciton transition formula_16, one needs to have a source with formula_17 or formula_18 photon correlations, respectively.
To realize quantum-optical spectroscopy, high-intensity light sources with freely adjustable quantum statistics are needed which are currently not available. However, one can apply projective methods to access the quantum–optical response of matter from a set of classical measurements. Especially, the method presented in Ref. is robust in projecting quantum-optical responses of genuine many-body systems. This work has shown that one can indeed reveal and access many–body properties that remain hidden in classical spectroscopy. Therefore, the quantum-optical spectroscopy is ideally suited for characterizing and controlling complicated many-body states in several different systems, ranging from molecules to semiconductors.
Relation to semiconductor quantum optics.
Quantum-optical spectroscopy is an important approach in general semiconductor quantum optics. The capability to discriminate and control many-body states is certainly interesting in extended semiconductors such as quantum wells because a typical classical excitation indiscriminately detects contributions from multiple many-body configurations; With quantum-optical spectroscopy one can access and control a desired many-body state within an extended semiconductor. At the same time, the ideas of quantum-optical spectroscopy can also be useful when studying simpler systems such as quantum dots.
Quantum dots are a semiconductor equivalent to simple atomic systems where most of the first quantum-optical demonstrations have been measured. Since quantum dots are man-made, one can possibly customize them to produce new quantum-optical components for information technology. For example, in quantum-information science, one is often interested to have light sources that can output photons on demand or entangled photon pairs at specific frequencies. Such sources have already been demonstrated with quantum dots by controlling their photon emission with various schemes. In the same way, quantum-dot lasers may exhibit unusual changes in the conditional probability to emit a photon when already one photon is emitted; this effect can be measured in the so-called "g"2 correlation. One interesting possibility for quantum-optical spectroscopy is to pump quantum dots with quantum light to control their light emission more precisely.
Quantum-dot microcavity investigations have progressed rapidly ever since the experimental demonstration of vacuum Rabi splitting between a single dot and a cavity resonance. This regime can be understood on the basis of the Jaynes–Cummings model while the semiconductor aspects provide many new physical effects due to the electronic coupling with the lattice vibrations.
Nevertheless, the quantum Rabi splitting—stemming directly from the quantized light levels—remained elusive because many experiments were monitoring only the intensity of photoluminescence. Following the ideology of quantum-optical spectroscopy, Ref. predicted that quantum-Rabi splitting could be resolved in photon-correlation measurement even when it becomes smeared out in photoluminescence spectrum. This was experimentally demonstrated by measuring the so-called "g"2 correlations that quantify how regularly the photons are emitted by the quantum dot inside a microcavity.


English as a Second Language (Community)

"English as a Second Language" is the twenty-fourth and penultimate episode of the first season of the American comedy television series "Community". It aired in the United States on NBC on May 13, 2010. In the episode, a revelation from Señor Chang threatens the study group's Spanish credit, and Troy discovers his skill at plumbing. It received generally positive reviews.
Plot.
Señor Chang (Ken Jeong) privately reveals to Jeff (Joel McHale) that he, like Jeff, faked his credentials, and does not have a teaching degree. The conversation is inadvertently recorded by Annie (Alison Brie), who records all classes for taking notes. When Dean Pelton (Jim Rash) finds out, Chang is replaced by Dr. Escodera (Marlene Forte), who is stricter and will make the Spanish class take a harder final exam. The class worries they will not be able to pass the new exam. Meanwhile, Troy (Donald Glover) discovers he has a natural talent for fixing plumbing. A persistent maintenance worker (Jerry Minor) urges him to use his talent to become a plumber, but Troy turns down the offer in favor of his education.
As everyone faces the fact that they will have to retake Spanish, Jeff realizes that Annie was the one who turned in Chang, as she wanted to keep the group together by keeping them in a shared class. The rest of the study group shuns her as they try to cram for the exam. Abed (Danny Pudi) tries to encourage Troy to pursue plumbing, but Troy, misunderstanding, gets angry that Abed does not want him around.
As the exam is about to start, Shirley (Yvette Nicole Brown) gets a text from Annie, who explains she's trying to make things better with Chang. Worried about how Chang will react, the study group runs to his office, where Chang explains that getting fired was good for him and that Annie is helping him plan a new future. After taking the exam, Troy and Abed reconcile, and the group agrees to take anthropology next year.
In the end tag, the study group finds out they all passed the Spanish finals. It is then implied that Pierce (Chevy Chase) had slept with Dr. Escodera to ensure that the Spanish finals would be easy enough for everyone to pass.
Production.
The episode was written by Tim Hobert, his fifth writing credit for the show, and was directed by Gail Mancuso in her first credit for the show.
Cultural references.
The subplot where Troy discovers his skills as a plumber is inspired by the film "Good Will Hunting", with Abed's encouragement paralleling Ben Affleck's role in the film. However, the details are somewhat reversed in that Troy is being called to a trade instead of to further education. When chiding Annie for her actions, Jeff tells the group to picture her as Paul Giamatti and comments that the friends in Sisterhood of the Traveling Pants didn't do such things. After their exam, Abed likens Troy's understanding of the test to his grasp of "The Wire".
Reception.
In its original broadcast, the episode was watched by approximately 4.49 million Americans and achieved a 2.0/7 in the 18-49 demographic.
The episode received generally positive reviews, with many critics noting the challenges of following up the previous episode. Emily VanDerWerff of "The A.V. Club" gave the episode an A-, commenting that after "Modern Warfare," "pretty much anything Community did would seem like a disappointment" but that the episode mostly avoids that issue by "taking a hard left into the series master plot." She also noted that the episode "nicely dealt with the show's central conflicts without being too heavy-handed" and thought it "feels quite a bit like a season finale." Jonah Krakow of IGN gave the episode 7.5 out of 10, denoting a "good" episode. He wrote that it "felt like just another sitcom" and "really wasn't that bad, just weaker than usual," especially compared to the last few episodes. He also praised guest actors Dino Stamatopoulos and Jerry Minor for their roles. Alan Sepinwall of Uproxx called it "a more character-driven – but still very funny – episode," noting the "nice character duet for Annie and Jeff." Like VanDerWerff, he also noted the episode felt like a season finale, asking, "[W]hat exactly do Dan Harmon and company have up their sleeves for the actual finale?"


Violin plot

A violin plot is a method of plotting numeric data. It is similar to a box plot, with the addition of a rotated kernel density plot on each side.
Violin plots are similar to box plots, except that they also show the probability density of the data at different values, usually smoothed by a kernel density estimator. Typically a violin plot will include all the data that is in a box plot: a marker for the median of the data; a box or marker indicating the interquartile range; and possibly all sample points, if the number of samples is not too high.
Recently it was shown that the violin plot called Mirrored Density plot (MD plot) outperforms conventional violin plots in terms of the identification of interesting structures in data in the programming languages of R and Python. Violin plots are available as extensions to a number of software packages such as DataVisualization on CRAN and the md-plot package on PyPI.
A violin plot is more informative than a plain box plot. While a box plot only shows summary statistics such as mean/median and interquartile ranges, the violin plot shows the full distribution of the data. The difference is particularly useful when the data distribution is multimodal (more than one peak). In this case a violin plot shows the presence of different peaks, their position and relative amplitude.
Like box plots, violin plots are used to represent comparison of a variable distribution (or sample distribution) across different "categories" (for example, temperature distribution compared between day and night, or distribution of car prices compared across different car makers).
A violin plot can have multiple layers. For instance, the outer shape represents all possible results. The next layer inside might represent the values that occur 95% of the time. The next layer (if it exists) inside might represent the values that occur 50% of the time.
Although more informative than box plots, they are less popular. Because of their unpopularity, their meaning can be harder to grasp for many readers not familiar with the violin plot representation. In this case, a more accessible alternative can be plotting a series of stacked histograms or kernel density distributions.
Violin plots are available as extensions to a number of software packages, including the R packages vioplot, wvioplot, caroline, UsingR, lattice and ggplot2, the Stata add-on command vioplot, and the Python libraries matplotlib, Plotly, ROOT and Seaborn, a graph type in Origin, IGOR Pro,
Julia statistical plotting package StatsPlots.jl and DistributionChart in Mathematica.


Connie M. Borror

Connie M. Borror (September 16, 1966 – April 10, 2016) was an American statistician and industrial engineer interested in quality control and forensic toxicology. She was named the winner of the Shewhart Medal of the American Society for Quality shortly before her death, for "outstanding technical leadership in the field of modern quality control, especially through the development to its theory, principles, and techniques", and became the first woman to win the medal.
Education and career.
Borror was born in Granite City, Illinois.
She studied mathematics at Southern Illinois University Edwardsville, earning a bachelor's degree there in 1988 and a master's degree in 1992. She earned her Ph.D. in industrial engineering from Arizona State University in 1998, and returned to Arizona State as a faculty member in 2005. She was the editor of "Quality Engineering" from 2011 to 2013, and chaired the Section on Quality and Productivity of the American Statistical Association for 2008.
Books.
Borror was the author of
She was also the editor of "The Certified Quality Engineer Handbook" (3rd ed., American Society for Quality, 2009).
Awards and honors.
Borror became a Fellow of the American Statistical Association in 2011, and was also a fellow of the American Society for Quality. In 2015, Arizona State named her an ASU Foundation Professor. She won the Shewhart Medal in 2016.


Test of Adolescent and Adult Language

The Test of Adolescent and Adult Language: Third Edition (TOAL-3) is a standardized, norm-referenced assessment of receptive, written and expressive language. The TOAL-3 was published in 1994. The test used to help identify individuals who may have a language disorder, and to help determine in what area(s) the dysfunction lies. Though the test is commonly administered by a Speech and Language Pathologist (SLP), it can also be administered by anyone who has some training or practice administering language or psychology type tests, and has familiarized him/herself with the test and scoring procedures.
Components.
The TOAL-3 is composed of eight sub-tests examining expressive, receptive, and written capabilities in semantic (vocabulary) and syntactic (grammar) areas. It includes written portions of the sub-tests.
Validity.
The Examiner's Manual included in the testing materials provides detailed accounting of content, construct, and criterion validity for each sub-test, and the possible composites of those sub-tests. Test-retest reliability, inter-scorer, and internal reliability have been established using various measures. Results regarding this language assessment are consistent. However, when measuring language there can be many variables and much is left to examiner inference. Further assessment based on TOAL-3 results should not be undertaken unless one is a professional in a language area.
There has since been another revision, and the current version is the TOAL-4.


Alternative hypothesis

In statistical hypothesis testing, the alternative hypothesis is a position that states something is happening, a new theory is preferred instead of an old one (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc. However, the research hypothesis is sometimes consistent with the null hypothesis.
In statistics, alternative hypothesis is often denoted as Ha or H1. Hypotheses are formulated to compare in a statistical hypothesis test.
In the domain of inferential statistics two rival hypotheses can be compared by explanatory power and predictive power.
Example.
An example is where water quality in a stream has been observed over many years, and a test is made of the null hypothesis that "there is no change in quality between the first and second halves of the data", against the alternative hypothesis that "the quality is poorer in the second half of the record".
History.
The concept of an alternative hypothesis in testing was devised by Jerzy Neyman and Egon Pearson, and it is used in the Neyman–Pearson lemma. It forms a major component in modern statistical hypothesis testing. However it was not part of Ronald Fisher's formulation of statistical hypothesis testing, and he opposed its use. In Fisher's approach to testing, the central idea is to assess whether the observed dataset could have resulted from chance if the null hypothesis were assumed to hold, notionally without preconceptions about what other models might hold. Modern statistical hypothesis testing accommodates this type of test since the alternative hypothesis can be just the negation of the null hypothesis.
Types.
In the case of a scalar parameter, there are four principal types of alternative hypothesis:


Color triangle

A color triangle is an arrangement of colors within a triangle, based on the additive combination of three primary colors at its corners.
An additive color space defined by three primary colors has a chromaticity gamut that is a color triangle, when the amounts of the primaries are constrained to be nonnegative.
Before the theory of additive color was proposed by Thomas Young and further developed by James Clerk Maxwell and Hermann von Helmholtz, triangles were also used to organize colors, for example around a system of red, yellow, and blue primary colors.
After the development of the CIE system, color triangles were used as chromaticity diagrams, including briefly with the trilinear coordinates representing the chromaticity values. Since the sum of the three chromaticity values has a fixed value, it suffices to depict only two of the three values, using Cartesian co-ordinates. In the modern "x,y" diagram, the large triangle bounded by the imaginary primaries X, Y, and Z has corners (1,0), (0,1), and (0,0), respectively; color triangles with real primaries are often shown within this space.
Maxwell's disc.
Maxwell was intrigued by James David Forbes's use of color tops. By rapidly spinning the top, Forbes created the illusion of a single color that was a mixture of the primaries:
Maxwell took this a step further by using a circular scale around the rim with which to measure the ratios of the primaries, choosing vermilion (V), emerald (EG), and ultramarine (U).
Initially, he compared the color he observed on the spinning top with a paper of different color, in order to find a match. Later, he mounted a pair of papers, snow white (SW) and ivory black (Bk), in an inner circle, thereby creating shades of gray. By adjusting the ratio of primaries, he matched the observed gray of the inner wheel, for example:
formula_1
To determine the chromaticity of an arbitrary color, he replaced one of the primaries with a sample of the test color and adjusted the ratios until he found a match. For pale chrome (PC) he found formula_2. Next, he rearranged the equation to express the test color (PC, in this example) in terms of the primaries.
This would be the precursor to the color matching functions of the CIE 1931 color space, whose chromaticity diagram is shown above.


IOzone

IOzone is a file system benchmark utility. Originally made by William Norcott, further enhanced by Don Capps and others..
Source code is available from iozone.org. It does mmap() file I/O and uses POSIX Threads.
It won the 2007 Infoworld Bossie Awards for Best file I/O tool.
The Windows version of IOzone uses Cygwin. Builds are available for AIX, BSDI, HP-UX, IRIX, FreeBSD, Linux, OpenBSD, NetBSD, OSFV3, OSFV4, OSFV5, SCO OpenServer, Solaris, Mac OS X, Windows (95/98/Me/NT/2K/XP).
It is available as a test profile in the Phoronix Test Suite.


Argentine units of measurement

A number of different units of measurement were used in Argentina as its national system was derived from Spanish Castillian. The metric system was legally optional since 1863 and has been compulsory since 1887.
Pre-metric units.
A number of different units were used before 1887.
Length.
A number of different units were used to measure length. These units varied from one province or city to another. In the province of Buenos Aires, one vara (yard) was 0.8666 m. Some other units used in the province of Buenos Aires are given below:
1 línea (line) = vara
1 pulgada (inch) = vara
1 palma (palm) = vara
1 pié (foot) = vara
1 braza (fathom) = 2 vara
1 cuadra = 150 vara
1 legua (league) = 6000 vara.
Railway measures.
There were some other units used on the railways. One legua was equal to 600 varas (0.3231 mile). One milla was equal to 1.85 km (1.149 miles)
Mass.
Different units were used to measure mass. These units were vary from one province or city to another and, in the province of Buenos Aires, one libra (pound) was equal to 459.4 g while one "Libra de Farmacia" (apothecary pound) was equal to libra or 344.5 g. Some other units in the province of Buenos Aires are provided below:
1 lb (Argentine Confederation libra) = 1.0127142432 lb (US pound 1893) = 1.01271544757245 lb (Avoirdupois) = 0.45936 kg
1 grano (grain) = libra
1 adarme (dram) = libra
1 onza (ounce) = libra
1 arroba = 25 libra
1 quintal (hundredweight) = 100 libra
1 tonelada (ton) = 2000 libra.
The marco used for gold and silver was equal to 3544.4 grains.
Capacity.
Dry and liquid units were used for capacity. These units varied from one province or city to another.
Dry.
1 fanega = 137.1977 l
1 Cuartilla = Fanega
1 Tonelada = 7 Fanega
1 Lastre = 12 Fanega.
Liquid.
Units included:
1 Frasco (gallon) = 2.375 l
1 Octava (pint) = Frasco
1 Cuarta (quart) = Frasco
1 Baril (barrel) = 32 Frasco
1 Cuerta = 48 Frasco
1 Pipa = 192 Frasco.
Units after metric adoption.
Although theoretically the metric system was compulsory, a survey in 1920 revealed the widespread use of both traditional Spanish units and US customary units (particularly in trade with the USA).


743 Eugenisis

743 Eugenisis is a minor planet orbiting the Sun that was discovered by German astronomer Franz Kaiser in 1913.
Photometric observations of this asteroid collected during 2004 show a rotation period of 10.23 ± 0.01 hours with a brightness variation of 0.20 ± 0.02 magnitude.


Alpha-particle spectroscopy

Alpha spectrometry (also known as alpha(-particle) spectroscopy) is the quantitative study of the energy of alpha particles emitted by a radioactive nuclide that is an alpha emitter.
As emitted alpha particles are mono-energetic (i.e. not emitted with a spectrum of energies, such as beta decay) with energies often distinct to the decay they can be used to identify which radionuclide they originated from.
[For methods of gamma rays and beta particles, please see gamma spectroscopy and liquid scintillation counting respectively.]
Experimental methods.
Counting using a source in a metal disk.
It is common to place a drop of the test solution on a metal disk which is then dried out to give a uniform coating on the disk. This is then used as the test sample. If the thickness of the layer formed on the disk is too thick then the lines of the spectrum are broadened to lower energies. This is because some of the energy of the alpha particles is lost during their movement through the layer of active material.
Liquid scintillation.
An alternative method is to use internal liquid scintillation counting, where the sample is mixed with a scintillation cocktail. When the light emissions are then counted, some machines will record the amount of light energy per radioactive decay event. Due to the imperfections of the liquid scintillation method (such as a failure for all the photons to be detected, cloudy or coloured samples can be difficult to count) and the fact that random quenching can reduce the number of photons generated per radioactive decay, it is possible to get a broadening of the alpha spectra obtained through liquid scintillation. It is likely that these liquid scintillation spectra will be subject to a Gaussian broadening, rather than the distortion exhibited when the layer of an active material on a disk is too thick.
Alpha spectra.
From left to right the peaks are due to 209Po, 239Pu, 210Po and 241Am. The fact that isotopes such as 239Pu and 241Am have more than one alpha line indicates that the (daughter) nucleus can be in different discrete energy levels.
Calibration:
MCA does not work on energy, it works on voltage. To relate the energy to voltage one must calibrate the detection system. Here different alpha emitting sources of known energy were placed under the detector and the full energy peak is recorded.
Measurement of thickness of thin foils:
Energies of alpha particles from radioactive sources are measured before and after passing through the thin films. By measuring difference and using SRIM we can measure the thickness of thin foils.
Kinematics of alpha decay.
The decay energy, Q (also called the "Q-value of the reaction"), corresponds to a disappearance of mass.
For the alpha decay nuclear reaction: <chem>^{A}_{Z}P -> ^{(A-4)}_{(Z-2)}D + \alpha
</chem>, (where P is the parent nuclide and D the daughter).
formula_1, or to put in the more commonly used units: "Q" (MeV) = -931.5 Δ"M" (Da), (where Δ"M = ΣMproducts - ΣMreactants").
When the daughter nuclide and alpha particle formed are in their ground states (common for alpha decay), the total decay energy is divided between the two in kinetic energy (T):
formula_2
The size of T is dependent on the ratio of masses of the products and due to the conservation of momentum (the parent's momentum = 0 at the moment of decay) this can be calculated:
formula_3
formula_4 and formula_5, formula_6
formula_7
formula_8
 formula_9
The alpha particle, or 4He nucleus, is an especially strongly bound particle. This combined with the fact that the binding energy per nucleon has a maximum value near A=56 and systematically decreases for heavier nuclei, creates the situation that nuclei with A>150 have positive Qα-values for the emission of alpha particles.
For example, one of the heaviest naturally occurring isotopes, <chem>^238U -> ^234Th + ^4He
</chem> (ignoring charges):
Note that the decay energy will be divided between the alpha-particle and the heavy recoiling daughter so that the kinetic energy of the alpha particle (Tα) will be slightly less:
Tα = (234.043 601/238.050 788 2)4.2699 = 4.198 MeV, (note this is for the 238gU to 238gTh reaction, which in this case has the branching ratio of 79%). The kinetic energy of the recoiling 234Th daughter nucleus is TD = (mα/mP)Qα = (4.002 603 254 13/238.050 788 2)4.2699 = 0.0718 MeV or 71.8 keV, which whilst much smaller is still substantially bigger than that of chemical bonds (<10 eV) meaning the daughter nuclide will break away from whatever chemical environment the parent had been in.
The recoil energy is also the reason that alpha spectrometers, whilst run under reduced pressure, are not operated at too low a pressure so that the air helps stop the recoiling daughter from moving completely out of the original alpha-source and cause serious contamination problems if the daughters are themselves radioactive.
The Qα‐values generally increase with increasing atomic number but the variation in the mass surface due to shell effects can overwhelm the systematic increase. The sharp peaks near A=214 are due to the effects of the N=126 shell.


768 Struveana

768 Struveana is a minor planet orbiting the Sun. The asteroid was named jointly in honor of Baltic German astronomers Friedrich Georg Wilhelm von Struve, Otto Wilhelm von Struve and Karl Hermann Struve.


Walter Gordy

Walter Gordy, (April 20, 1909 – October 6, 1985) was an American physicist best known for his experimental work in microwave spectroscopy. His laboratory at Duke University became a center for research in this field, and he authored one of the definitive books on the field.
Career.
Gordy began college at Clarke Memorial Junior College in 1929. He enrolled in Mississippi College in 1930 and completed his bachelor's degree in 1932. He then began graduate work at the University of North Carolina where he received a M.A. in 1933 and a Ph.D. in 1935. Gordy's doctoral research in infrared spectroscopy was carried out under Earle K. Plyler.
From 1935 to 1941 Gordy taught at Mary Hardin-Baylor College where he was an associate professor of physics and mathematics. During this time he pursued his research interests, spectroscopic studies of hydrogen bonding, through summer research work at the University of North Carolina and The Ohio State University. In 1941, Gordy was awarded a National Research Fellowship for this work. He used the fellowship to move to the California Institute of Technology and work with Linus Pauling. The advent of World War II cut this fellowship short. In 1942 Gordy joined the MIT Radiation Laboratory where he worked on the development of microwave radar. Gordy's work with microwave technology during this time led him to focus his subsequent spectroscopic research efforts on microwave spectroscopy. He joined the physics department at Duke University in 1946 and established a research group centered on microwave and millimeter-wave spectroscopy. He achieved the university's highest rank, James B. Duke Professor, in 1958 and continued at Duke until his retirement in 1979.


Thunderstrike (Kevin Masterson)

Kevin Masterson is a fictional character appearing in American comic books published by Marvel Comics. The character was first introduced as a supporting character in "Thor" and appeared again in the spin-off series "Thunderstrike", as the son of Eric Masterson, the featured character of both series. Kevin Masterson was later re-introduced in the Marvel Comics 2 series "A-Next", as the superhero Thunderstrike, a theme which would be revisited in the Heroic Age of Marvel Comics in the eponymous limited series.
Publication history.
Kevin Masterson was created by Tom DeFalco and Ron Frenz, first appearing in "Thor" vol. 1 #392 in June 1988 as the son of the original hero known as Thunderstrike, Eric Masterson. He would continue to appear in a supporting role in "Thor" and spin-off series "Thunderstrike".
The character would be re-imagined in "What If" vol. 2 #105, appearing for the first time as a new version of Thunderstrike. An origin for Kevin Masterson as Thunderstrike would appear in the follow-up MC2 series "A-Next" #1, where he would continue to be featured, as part of the ensemble cast of characters. He would also appear in the MC2 series "Last Hero Standing" and sequel "Last Planet Standing"; as well as, the follow-up series "Avengers Next."
The use of Kevin Masterson as a legacy version of Thunderstrike was a theme revisited during the Heroic Age. It was announced that the character would return in a new five-issue miniseries by co-creators Tom DeFalco and Ron Frenz in November 2010. Promotionals leading into the event began in August depicting the mace stating "One will rise..." and "The World Still Needs Heroes." The first issues received generally positive reviews, lauding the premise, characterization and plotting. By series end the book was praised for plotting, dialogue, and characterization, with the contemporization of a classic character into timeless.
Thunderstrike appeared in "Fear Itself: The Home Front".
He is currently a member of the Asgardians of the Galaxy.
Fictional character biography.
MC2.
Kevin Masterson is granted the mace of his deceased father by Edwin Jarvis, the Avengers' butler, per his father's will. The mace is stolen from Kevin and even comes into the possession of Loki, who had created a spell to tap the dormant power within the mace. Kevin leaps into the midst of the spell, absorbing the mace and the magic it contains. He becomes his own version of Thunderstrike and a founding member of a new version of the Avengers.
As the series continues, Thunderstrike's biggest challenge comes when the Avengers travel to a dark parallel dimension, where he encounters a dark version of his father. The alternate Eric Masterson recognized Thunderstrike as Kevin, who learns that in this reality, he, not Eric, has died. The alternate Eric and Kevin bonded, and once the Avengers defeat the dark dimension's ruler, Kevin stays behind to be with his "father".
Kevin returns to his home reality, and rejoins the Avengers to aid in the battle with Seth. When Galactus destroys Asgard, Thunderstrike seemingly loses his powers in "Last Planet Standing". He is kidnapped by Ulik and Sylene, daughter of Loki, as part of a plan to restore Asgard; but Kevin Masterson struggles against his captors. Ultimately he is responsible for turning the tables on the villains. Thena, daughter of Thor, who had also taken part in the battle against her cousin, is able to restore Kevin's power, allowing him to become Thunderstrike once again.
"Thunderstrike" (limited series).
An embittered adolescent Kevin Masterson is featured in the "Thunderstrike" limited series. The character previously featured as an idealistic child is shown to have anger, behavioral problems, and disillusioned outlook on "spandex-covered glory hounds."
He is given his father's enchanted mace by Captain Steve Rogers; which to their mutual disappointment triggers no change in the character (although he does receive an open invitation to the Avengers Academy, in which he is later seen arriving on their New Campus in California.).
While on his way home, Kevin tries to save a mother and child from a rampaging Rhino and is transformed into a superhero. Kevin briefly battles the Rhino, and shortly after Kevin is defeated, he realizes that he is in his father's body. Mangog, a foe of Thor, resurfaces and threatens New York City. The young hero teams with Thor, to battle the monster. Kevin accepts his new identity as Thunderstrike, along with a new image, and continues his adventures under the mentorship of Brunnhilde the Valkyrie.
During the "Fear Itself" storyline, Thunderstrike ends up teleported onto a station in the middle of the Pacific Ocean with Amadeus Cho, X-23, Spider-Girl, and Power Man. They end up fighting a bunch of samurai Shark Men.
Kevin briefly appeared as part of the new class of students when the Avengers Academy moves to the former headquarters of the West Coast Avengers.
Powers and abilities.
MC2.
Kevin has the ability to change from his normal form into the superhuman Thunderstrike. As Thunderstrike, he has the powers contained within the mace of the same name. Thunderstrike is superhumanly strong and durable. He can generate explosive bursts of sonic force (his "thunderbolts") from his hands, and direct them as blasts of force, or focus the energy into his fists to deliver super-strong punches. Thunderstrike can direct his blasts downwards to launch himself into the air and, while he cannot fly, can propel himself to great distances. He even learned how to modulate the frequency of his sonic energies to shatter objects just by touching them, without harming nearby people.
"Thunderstrike" (limited series).
Kevin's demonstrated powers in the limited series are the same as his father's, including the reversion to his normal state if he is separated from Thunderstrike for over sixty seconds. He did not use the ability to fire energy blasts from the mace in the limited series. Thanks to tutoring by the valkyrie Brunnehilde, he is also capable of changing his appearance as Thunderstrike, finally choosing a form which is a modified version of his normal self.


Deviance (statistics)

In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals (RSS) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood. It plays an important role in exponential dispersion models and generalized linear models.
Definition.
The unit deviance formula_1 is a bivariate function that satisfies the following conditions:
The total deviance formula_4 of a model with predictions formula_5 of the observation formula_6 is the sum of its unit deviances: formula_7.
The (total) deviance for a model "M"0 with estimates formula_8, based on a dataset "y", may be constructed by its likelihood as:
Here formula_10 denotes the fitted values of the parameters in the model "M"0, while formula_11 denotes the fitted parameters for the "saturated model": both sets of fitted values are implicitly functions of the observations "y". Here, the saturated model is a model with a parameter for every observation so that the data are fitted exactly. This expression is simply 2 times the log-likelihood ratio of the full model compared to the reduced model. The deviance is used to compare two models – in particular in the case of generalized linear models (GLM) where it has a similar role to residual variance from ANOVA in linear models (RSS).
Suppose in the framework of the GLM, we have two nested models, "M1" and "M2". In particular, suppose that "M1" contains the parameters in "M2", and "k" additional parameters. Then, under the null hypothesis that "M2" is the true model, the difference between the deviances for the two models follows, based on Wilks' theorem, an approximate chi-squared distribution with "k"-degrees of freedom. This can be used for hypothesis testing on the deviance.
Some usage of the term "deviance" can be confusing. According to Collett:
Examples.
The unit deviance for the Poisson distribution is formula_14, the unit deviance for the Normal distribution is given by formula_15.


Tetratonic scale

A tetratonic scale is a musical scale or mode with four notes per octave. This is in contrast to a heptatonic (seven-note) scale such as the major scale and minor scale, or a dodecatonic (chromatic 12-note ) scale, both common in modern Western music. Tetratonic scales are not common in modern art music, and are generally associated with prehistoric music.
Distribution.
Native American music.
Tetratonic scales were common among the Plains Indians, though less common than the pentatonic scale. Amongst the Arapaho, Blackfoot, Crow, Omaha, Kiowa, Pawnee, and Sioux, as well as some Plateau tribes, especially the Flathead, the tetratonic and pentatonic scales used are anhemitonic (that is, they do not include semitones). Tetratonic scales have also been noted among the music of the Creek Indians, and in the Great Basin region among the Washo, Ute, Paiute, and Shoshone. In the Southwest, the Navajo people also largely used the pentatonic and tetratonic, occasionally also tritonic scales.
Inuit.
Tetratonic music was known among the Inuit, including the Greenlandic peoples.
Maori.
A 1969 study by ethnomusicologist Mervyn McLean noted that tetratonic scales were the second-most common type among the Maori tribes surveyed, accounting for 31% of scales used. The most common were tritonic (3-note) scales at 47%, while the third-most was ditonic (two-note) scales at 17%.
Oceania.
Tetratonic music was noted as common in Polynesia and Melanesia. On Guadalcanal in particular, anhemitonic pentatonic and tetratonic scales are the predominant types, although the minor second does nevertheless occasionally appear as a melodic interval. The most often used melodic intervals, however, are the major second, minor third, perfect fourth, perfect fifth, and octave.
Africa.
The main instrument in the Lobi area of Ghana is the xylophone, some of which are tuned to a tetratonic scale. In eastern Uganda, the Gwere use for their six-string harp (called "tongoli") a tetratonic scale in which all the intervals are nearly equal, which to Western ears sounds like a chain of minor thirds.
In South Africa, the San use a tetratonic scale approaching 5 equal temperament, but lacking the second step.
India.
Tetratonic, as well as tritonic scales, were commonly used by the tribal peoples of India, such as the Juang and Bhuyan of Orissa state.
Russia.
The music of the Volga-Finnic Cheremis (Mari people) of central Russia was primarily pentatonic, but used tetratonic scales 20% of the time.
Western Europe.
The second-earliest scales of Scandinavian, German, English, and Scottish folk music are believed to have been pentatonic, themselves developed from an earlier tetratonic scale. Tetratonic scales, along with pentatonic scales, account for 54% of songs in the traditional "joik" repertoire of the European Arctic Sami people, where the singing range extends to a tenth or eleventh.
The predominant style of traditional music from the Peloponnese region of Greece is a mixture of Christian, Albanian, and Vlach. It employs tetratonic, pentachordal, and pentatonic scales, around the notes of which microtonal ornamentation ("stolidia"/"psevtikes") occurs.
Art music.
A rare example of an art-music composition based entirely on a tetratonic scale is the early minimalist work "Reed Phase" (1966), by Steve Reich, which is based entirely on a single five-note cell, or "basic unit", repeated continually throughout the entire work. Because the note A occurs twice in this pattern, there are only four pitches in all.


Link prefetching

Link prefetching allows web browsers to pre-load resources. This speeds up both the loading and rendering of web pages. Prefetching was first introduced in HTML5.
Prefetching is accomplished through hints in web pages. These hints are used by the browser to prefetch links. Resources which can be prefetched include: JavaScript, CSS, image, audio, video, and web fonts. DNS names and TCP connections can also be hinted for prefetching.
Prefetching in HTML5.
There are two W3C standards covering prefetching for HTML5:
HTML5 methods for prefetch hints:
Issues and criticisms.
An issue inherent to indiscriminate link prefetching involves the misuse of "safe" HTTP methods. The HTTP GET and HEAD requests are said to be "safe", i.e., a user agent that issues one of these requests should expect that the request results in no change on the recipient server. However, it is common for website operators to use these requests outside of this constraint. Plain hyperlinks (which almost universally result in GET requests) are often used to implement logout functionality and account verification, e.g., when a user completes an account creation form, and an automated service sends a verification e-mail to the user's given e-mail address.
Similarly, it is entirely possible for a hosting service to provide a Web front end to manage files, including links that delete one or more files. Users who visit pages containing these types of links, (whilst using a browser which employs an indiscriminate link prefetcher), might find that they have been logged out or that their files have been deleted.
Additionally, there are a number of criticisms regarding the privacy and resource usage implications of link prefetching:
In the case of mobile devices or for users with a limited bandwidth allowance, prefetching may result in an unnecessary costly drain on limited bandwidth.
It is possible for implementations to prefetch links even when they are not specified as prefetch links.
In the case of prerendering, Google warns that improper use may result in the aforementioned increased bandwidth usage, slower loading of other links, and slightly stale content.


Nahang-class submarine

The Nahang () is an Iranian-made class of midget submarine designed for shallow water operations. Only one prototype of this class is known to be completed, although its characteristics have remained unclear.
History.
Iran had shown interest in midget submarines in the 1980s. According to the "Conway's All The World's Fighting Ships", Iran assembled a midget in Bandar Abbas that was completed in 1987 in an unsuccessful attempt. Iran reportedly purchased a second midget of another design from North Korea, delivered in 1988. It is alleged that by 1993, nine midget submarines –able to displace 76 tons surfaced and 90 tons submerged, with a top speed between and – were imported from North Korea.
Existence of "Nahang" was first known in April 2006. On 6 March 2006, Iranian state television announced that "Nahang 1" has been commissioned into the Southern Fleet. Later that year in late August, she participated in the third phase of Zarbat-e Zolfaghar wargame.
Two other submarines in the class were allegedly planned, but building further units is considered unlikely.
In April 2017, Bellingcat reported that for the first time in years, satellite imagery suggests "Nahang" had been deployed for a mission.
Description.
There is not much confidently known about characteristics of the class. According to "Jane's Fighting Ships", the class displaces when at the surface and while submerged. Alternate estimates for surfaced and submerged displacement are and respectively while the number given goes as high as .
"Jane's" mentions the approximate dimensions as for length, with a beam of and a draft of . and are top speeds reported for the submarine. "Nahang" is reportedly unarmed and not fitted with torpedoes, however there are contradicting reports suggesting it has a pair of 533mm torpedo tubes in drop collars and can carry and lay four MDM-6 or EM-52 naval mines. "Nahang" may be utilized as a mothership for swimmer delivery vehicles and a platform for special operations.
The submarine has no sonar on the report of "Jane's", but another account suggests that she is equipped with active/passive sonar on her bow. The machinery installed for propulsion is unknown. Other apparatus reportedly installed include a mast with electronic warfare support capabilities (similar to Russian-made 'Stop Light' type) and surface search and navigation radar.


Function (music)

In music, function (also referred to as harmonic function) is a term used to denote the relationship of a chord or a scale degree to a tonal centre. Two main theories of tonal functions exist today:
Both theories find part of their inspiration in the theories of Jean-Philippe Rameau, starting with his "Traité d'harmonie" of 1722. Even if the concept of harmonic function was not so named before 1893, it could be shown to exist, explicitly or implicitly, in many theories of harmony before that date. Early usages of the term in music (not necessarily in the sense implied here, or only vaguely so) include those by Fétis ("Traité complet de la théorie et de la pratique de l'harmonie", 1844), Durutte ("Esthétique musicale", 1855), Loquin ("Notions élémentaires d'harmonie moderne", 1862), etc.
The idea of function has been extended further and is sometimes used to translate Antique concepts, such as "dynamis" in Ancient Greece, or "qualitas" in medieval Latin.
Origins of the concept.
The concept of harmonic function originates in theories about just intonation. It was realized that three perfect major triads, distant from each other by a perfect fifth, produced the seven degrees of the major scale in one of the possible forms of just intonation: for instance, the triads F–A–C, C–E–G and G–B–D (subdominant, tonic, and dominant respectively) produce the seven notes of the major scale. These three triads were soon considered the most important chords of the major tonality, with the tonic in the center, the dominant above and the subdominant under.
This symmetric construction may have been one of the reasons why the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under [the tonic]". It also is one of the origins of the dualist theories which described not only the scale in just intonation as a symmetric construction, but also the minor tonality as an inversion of the major one. Dualist theories are documented from the 16th century onwards.
German functional theory.
The term 'functional harmony' derives from Hugo Riemann and, more particularly, from his "Harmony Simplified". Riemann's direct inspiration was Moritz Hauptmann's dialectic description of tonality. Riemann described three abstract functions: the tonic, the dominant (its upper fifth), and the subdominant (its lower fifth). He also considered the minor scale to be the inversion of the major scale, so that the dominant was the fifth above the tonic in major, but below the tonic in minor; the subdominant, similarly, was the fifth below the tonic (or the fourth above) in major, and the reverse in minor.
Despite the complexity of his theory, Riemann's ideas had huge impact, especially where German influence was strong. A good example in this regard are the textbooks by Hermann Grabner. More recent German theorists have abandoned the most complex aspect of Riemann's theory, the dualist conception of major and minor, and consider that the dominant is the fifth degree above the tonic, the subdominant the fourth degree, both in minor and in major.
In Diether de la Motte's version of the theory, the three tonal functions are denoted by the letters T, D and S, for Tonic, Dominant and Subdominant respectively; the letters are uppercase for functions in major (T, D, S), lowercase for functions in minor (t, d, s). Each of these functions can in principle be fulfilled by three chords: not only the main chord corresponding to the function, but also the chords a third lower or a third higher, as indicated by additional letters. An additional letter P or p indicates that the function is fulfilled by the relative (German "Parallel") of its main triad: for instance Tp for the minor relative of the major tonic (e.g., a minor for C major), tP for the major relative of the minor tonic (e.g. E major for c minor), etc. The other triad a third apart from the main one may be denoted by an additional G or g for "Gegenparallelklang" or "Gegenklang" ("counterrelative"), for instance tG for the major counterrelative of the minor tonic (e.g. A major for c minor).
The relation between triads a third apart resides in the fact that they differ from each other by one note only, the two other notes being common notes. In addition, within the diatonic scale, triads a third apart necessarily are of opposite mode. In the simplified theory where the functions in major and minor are on the same degrees of the scale, the possible functions of triads on degrees I to VII of the scale could be summarized as in the table below (degrees II in minor and VII in major, diminished fifths in the diatonic scale, are considered as chords without fundamental). Chords on III and VI may exert the same function as those a third above or a third below, but one of these two is less frequent than the other, as indicated by parentheses in the table.
In each case, the mode of the chord is denoted by the final letter: for instance, Sp for II in major indicates that II is the minor relative (p) of the major subdominant (S). The major VIth degree in minor is the only one where both functions, Sp (relative of the minor subdominant) and tG (counterparallel of the minor tonic), are equally plausible. Other signs (not discussed here) are used to denote altered chords, chords without fundamental, applied dominants, etc. Degree VII in harmonic sequence (e.g. I–IV–VII–III–VI–II–V–I) may at times be denoted by its roman numeral; in major, the sequence would then be denoted by T–S–VII–Dp–Tp–Sp–D–T.
As summarized by d'Indy (1903), who shared the conception of Riemann:
Viennese theory of the degrees.
The Viennese theory on the other hand, the "Theory of the degrees" ("Stufentheorie"), represented by Simon Sechter, Heinrich Schenker and Arnold Schoenberg among others, considers that each degree has its own function and refers to the tonal center through the cycle of fifths; it stresses harmonic progressions above chord quality. In music theory as it is commonly taught in the US, there are six or seven different functions, depending on whether degree VII is considered to possess an independent function.
Comparison of the terminologies.
The table below compares the English and German terminologies for the major scale. In English, the names of the scale degrees are also the names of their function, and they remain the same in major and in minor.
Note that ii, iii, and vi are lowercase: this indicates that they are minor chords; vii° indicates that this chord is a diminished triad.
Reviewing usage of harmonic theory in American publications, William Caplin writes:
Caplin further explains that there are two main types of pre-dominant harmonies, "those built above the fourth degree of the scale () in the bass voice and those derived from the dominant of the dominant (V/V)" (p. 10). The first type includes IV, II6 or II6, but also other positions of these, such as IV6 or II. The second type groups harmonies which feature the raised-fourth scale degree () functioning as the leading tone of the dominant: VII7/V, V6V, or the three varieties of augmented sixth chords.


College English Test

The College English Test (), better known as CET, is a national English as a foreign language test in the People's Republic of China. It examines the English proficiency of undergraduate and postgraduate students in China. It is meant to ensure that Chinese undergraduates and postgraduates reach the required English levels specified in the National College English Teaching Syllabuses (NCETS). This test has existed in China for 26 years and now 18 million people take it annually. It includes two levels: CET4 (非专业四级) and CET6 (非专业六级).
Another kind of national English as a foreign language test is Test for English Majors (), better known as TEM. It includes two levels — TEM4 (英语专业四级) and TEM8 (英语专业八级).
College English Test.
Generally, College English Test allows all non-English-major university students to attend.
Before 2005 reform.
Before the 2005 reform, the maximum score was 100 points. A test score higher than 85 is graded as "Excellent", and a test score higher than 60 but below 85 is graded as "Pass" in the certificate. This test was held nationally twice a year in summer and winter. The CET consisted of the non-English-specialized "Band 4" (CET4), in which certificate-holders have reached the English level of non-English major undergraduate students, and "Band 6" (CET6), in which the certificate-holders have reached the English level of non-English major postgraduates. The test included listening, reading and writing sections. The spoken test was optional.
2005 reform.
The CET was reformed in 2005. Several changes were made, including:
The CET-4 is mandatory for university students in China who are not English majors. It is also a prerequisite for a bachelor's degree. Many employers in China prefer applicants with CET-4 or even CET-6 certification.
Passing the CET is important for Chinese college students. Graduates may only be able to get a degree or a good job if they can pass the CET with a high score.
While the CET tests reading, writing and listening, it does have a separate test for speaking. The speaking test is held twice a year and only students with a CET Band-4 score higher than 550 or a CET Band-6 higher than 485 are eligible for the test.
Test for English Majors.
A similar but more rigorous test, the Test for English Majors (TEM), is mandatory for English majors, and it is generally only for English majors. For these students, passing the TEM-4 is a graduation requirement. The test should be taken by the end of the second academic or sophomore year. TEM-8 ("Band 8") is the highest level for English major students; it should be taken during the end of the last academic or senior year.
If an English-major student fails to pass the TEM-4 during his or her sophomore year, they may attempt to pass the TEM-8 during their senior year. Those failing the TEM-8 are only allowed one re-test (during the following year after they have graduated from college). A second failure results in disqualification lifelong.
Both TEM4 and TEM8 are only two qualifications for any students lifelong.
Social consequences.
Some Chinese researchers point out the positive social consequences of the CET as it has promoted the role of English teaching and learning at the tertiary level in China over its 20-year history. At the same time, other researchers challenge the CET by pointing out that the test does not assess communicative competence as the teaching syllabus requires. Before the recent reform of the CET, the large proportion of multiple choice questions made this test an efficient one, but possible sacrifices in accurately measuring English language ability remained a concern. Since the CET certificates had been one of the graduation requirements of undergraduates in the majority of Chinese universities for almost 20 years, test-oriented teaching was another severe problem. However, there have been changes made in the CET test content, format, and scoring systems are evidence of the endeavors to bring about positive washback of the test on English teaching and learning in China. It is the expectation of the CET committee that the test can reflect and catch up with the needs of rapid economic reform and the new open-door policy.
Exam score distributions.
Answering all questions incorrectly will result in 330, the lowest score a test taker can get in CET4. By contrast, receiving a score higher than 600 is usually regarded as "perfect" and that means the test taker has not only answered most multiple choice questions correctly but received a positive feedback on their performance in the writing section.