Multiple hypothesis testing is concerned with maintaining low the number of false positives when testing several hypotheses simultaneously, while achieving a number of false negatives as small as possible. Procedures should be distribution free and robust with respect to known or possibly unknown dependence. This thesis is related to modern approaches. After a review of the most recent developments, we prove robustness of certain procedures under weak dependence. We then propose a new class of procedures and estimators for the proportion of false null hypotheses, i.e., the strength of the simoultaneous signal. In order to develop our findings, we provide probability inequalities and related tools under dependence. We show a pletora of...

ISBN: 978-3-6390-9627-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Presented is a new computer-aided multispectral image processing method which is used in 3 spatial dimensions and 1 spectral dimension where the dynamic, contrast enhanced magnetic resonance parameter maps derived from voxelwise model-fitting represent the spectral dimension. The method is based on co-occurrence analysis using a 3-dimensional window of observation which introduces an automated identification of suspicious lesions. The co-occurrence analysis defines 21 different statistical features, a subset of which were input to a neural network classifier where the assessments of the voxelwise majority of a group of radiologist readings were used as the gold standard. The voxelwise true positive fraction (TPF) and false positive...

ISBN: 978-3-6391-3248-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles!In mathematics, the multiplicity of a member of a multiset is how many memberships in the multiset it has. For example, the term is used to refer to the number of times a given polynomial equation has a root at a given point. The common reason to consider notions of multiplicity is to count correctly, without specifying exceptions (for example, double roots counted twice). Hence the expression counted with (sometimes implicit) multiplicity. When mathematicians wish to ignore multiplicity they will refer to the number of distinct elements of a set. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-1724-4
Издательство: Книга по требованию
Дата выхода: июль 2011

ISBN: 978-5-5100-2890-4

High Quality Content by WIKIPEDIA articles! The number n is called the degree of the root. A root of degree 2 is called a square root, a root of degree 3 is called a cube root, a root of degree 4 is called a fourth root, and so forth. In general, a root of degree n is called an nth root. An unresolved root, especially one using the radical symbol, is often referred to as a surd. Roots are particularly important in the theory of infinite series, where the root test determines the radius of convergence of a power series. Roots can also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in higher mathematics. Much of Galois theory is concerned with determining which algebraic numbers can...

ISBN: 978-6-1311-3240-7
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, an n-ary group (also n-group, polyadic group or multiary group) is a generalization of a group to a set G with a n-ary operation instead of a binary operation. The axioms for an n-ary group are defined in such a way as to reduce to those of a group in the case n = 2.The easiest axiom to generalize is the associative law. Ternary associativity is (abc)de = a(bcd)e = ab(cde), i.e. the string abcde with any three adjacent elements bracketed. n-ary associativity is a string of length n+(n-1) with any n adjacent elements bracketed. A set G with a closed n-ary operation is an n-ary groupoid. If the operation is associative then it is an n-ary semigroup. Данное издание...

ISBN: 978-6-1305-0905-7
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Rubik's cube is the original and most well-known of the three-dimensional sequential move puzzles. There have been many virtual implementations of this puzzle in software. It is a natural extension to create sequential move puzzles in more than three dimensions. Although no such puzzle could ever be physically constructed, the rules of how they operate are quite rigorously defined mathematically and are analogous to the rules found in three-dimensional geometry. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1303-3428-4
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, an n-dimensional space is a topological space whose dimension is n (where n is a fixed natural number). The archetypical example is n-dimensional Euclidean space, which describes Euclidean geometry in n dimensions. Many familiar geometric objects can be generalized to any number of dimensions. For example, the two-dimensional triangle and the three-dimensional tetrahedron can be seen as specific instances of the n-dimensional simplex. Also, the circle and the sphere can be seen as specific instances of the n-dimensional hypersphere. More generally, an n-dimensional manifold is a space that locally looks like n-dimensional Euclidean space, but whose global structure may be...

ISBN: 978-6-1303-3436-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to arbitrary dimension. For any natural number n, an n-sphere of radius r is defined as the set of points in (n + 1)-dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number. It is an n-dimensional manifold in Euclidean (n + 1)-space. In particular, a 0-sphere is a pair of points on a line, a 1-sphere is a circle in the plane, and a 2-sphere is an ordinary sphere in three-dimensional space. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1303-3440-6
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Norman Eustace Cameron was born in New Amsterdam, Guyana. He attended Queen's CollegeQueen's College in Georgetown, and in 1921 won the Guyana Scholarship, achieving First Class Honours at the Oxford and Cambridge Higher Examination, with five distinctions in Latin, French, English, Mathematics and Religious Knowledge, placing him first among candidates from Barbados and Guyana. At the University of Cambridge, he continued to excel in Mathematics. taking first class honours in Part 1 of the Mathematical TriposCambridge Mathematical Tripos in 1923, and graduating Senior Optime in 1925. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1312-6214-2
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. N.E.W.S is a 2003 instrumental jazz fusion/funk album by Prince containing four tracks of fourteen minutes duration each. Recorded at Prince's Paisley Park Studios over a single day, the album was initially available through Prince's NPG Music Club website on May 26, 2003 before becoming widely commercially available on July 22. The album can be seen as a modern incarnation of Madhouse, but this time as a Prince release. Original Madhouse member Eric Leeds lends his talents, as well as The New Power Generation members John Blackwell, Rhonda Smith and Renato Neto. The album is reportedly the lowest selling Prince...

ISBN: 978-6-1312-6201-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Nabors Industries Ltd. (NYSE: NBR) founded in 1968 as Anglo Energy, Ltd. (former AMEX symbol: AEL), and currently based in Hamilton, Bermuda, is an S Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1329-2221-2
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Greek geographer Strabo of Amaseia, in Geography 16.1–.6, writes: "In Babylon a settlement is set apart for the local philosophers, the Chaldaeans, as they are called, who are concerned mostly with astronomy; but some of these, who are not approved of by the others, profess to be writers of horoscopes. (There is also a tribe of the Chaldaeans, and a territory inhabited by them, in the neighborhood of the Arabs and of the Persian Gulf, as it is called.) There are also several tribes of the Chaldaean astronomers. For example, some are called Orcheni [those from Uruk], others Borsippeni [those from Borsippa], and several others by different names, as though divided into different sects which...

ISBN: 978-6-1329-2276-2
Издательство: Книга по требованию
Дата выхода: июль 2011

In mathematics, in the area of complex analysis, Nachbin's theorem (named after Leopoldo Nachbin) is commonly used to establish a bound on the growth rates for an analytic function. This article will provide a brief review of growth rates, including the idea of a function of exponential type. Classification of growth rates based on type help provide a finer tool than big O or Landau notation, since a number of theorems about the analytic structure of the bounded function and its integral transforms can be stated. In particular, Nachbin's theorem may be used to give the domain of convergence of the generalized Borel transform, given below. The theorem is named in honour of the Brazilian mathematician Leopoldo Nachbin. Данное...

ISBN: 978-6-1329-2960-0
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Nachman Aronszajn (1907–1980) was a Polish American mathematician of Jewish descent. Aronszajn's main field of study and expertise was mathematical analysis. He also contributed to mathematical logic. He received his Ph.D. from the University of Warsaw, in 1930, in Poland. Stefan Mazurkiewicz was his thesis advisor. He also received a Ph.D. from Paris University, in 1935; this time Maurice Frechet was his thesis advisor. He joined the University of Kansas in 1951, where he retired in 1977. He was a Summerfield Distinguished Scholar from 1964 to his death. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1311-5567-3
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Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! Nada holds a BSc in Mathematics and Computing, a Graduate Diploma in Management Sciences and a Masters Degree in Public Administration at the University of Canberra (Australia), and has earned her PhD in Management at the University of Western Sydney - Nepean (Australia). Nada has undertaken consulting work for a number of international organisations in Scandinavia and Europe, as well as in the Middle East and North Africa, and for several UK Government departments and the Canadian Federal Government. Her clients in the private sector have included Alliance Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1329-7112-8
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Nagata conjecture on curves governs the minimal degree required for a plane algebraic curve to pass though a collection of very general points with prescribed multiplicity. Nagata arrived at the conjecture via work on the 14th problem of Hilbert, which asks whether the invariant ring of a linear group action on the polynomial ring k[x_1, ldots x_n] over some field k is finitely generated. Nagata published the conjecture in a 1959 paper in the American Journal of Mathematics, in which he presented a counterexample to Hilbert's 14th problem. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1312-9652-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Nagata conjecture on curves governs the minimal degree required for a plane algebraic curve to pass though a collection of very general points with prescribed multiplicity. Nagata arrived at the conjecture via work on the 14th problem of Hilbert, which asks whether the invariant ring of a linear group action on the polynomial ring over some field k is finitely generated. Nagata published the conjecture in a 1959 paper in the American Journal of Mathematics, in which he presented a counterexample to Hilbert's 14th problem. Данное издание не является...

ISBN: 978-6-1331-6207-5
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In geometry, the Nagel point is a point associated with any triangle. In the plane of a triangle ABC with side lengths a = |BC|, b = |CA|, and c = |AB|, let TA, TB, and TC be the points in which the A-excircle meets line BC, the B-excircle meets line CA, and C-excircle meets line AB, respectively. The lines ATA, BTB, CTC concur in the Nagel point N of triangle ABC. The Nagel point is named after Christian Heinrich von Nagel, a nineteenth century German mathematician, who wrote about it in 1836. Another construction of the point TA is to start at A and trace around triangle ABC half its perimeter, and similarly...

ISBN: 978-6-1312-9670-3
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations. In more technical language, they define an algebraic curve, algebraic surface, or more general object, and ask about the lattice points on it. The word Diophantine refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into...

ISBN: 978-6-1331-7428-3
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In mathematics, the Nagell–Lutz theorem is a result in the diophantine geometry of elliptic curves, which describes rational torsion points on elliptic curves over the integers. Suppose that the equation y^2 = x^3 + ax^2 + bx + c defines a non-singular cubic curve with integer coefficients a, b, c, and let D be the discriminant of the cubic polynomial on the right side: D = -4a^3c + a^2b^2 + 18abc - 4b^3 - 27c^2. If P = (x,y) is a rational point of finite order on C, for the elliptic curve group law, Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1312-9683-3
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Nahm equations are a system of ordinary differential equations introduced by Werner Nahm in the context of the Nahm transform – an alternative to Ward's twistor construction of monopoles. The Nahm equations are formally analogous to the algebraic equations in the ADHM construction of instantons, where finite order matrices are replaced by differential operators. Deep study of the Nahm equations was carried out by Nigel Hitchin and Simon Donaldson. Conceptually, the equations arise in the process of infinite-dimensional hyperkahler reduction. Among their many applications we can mention: Hitchin's...

ISBN: 978-6-1332-6758-9
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! The Nahm equations are a system of ordinary differential equations introduced by Werner Nahm in the context of the Nahm transform – an alternative to Ward's twistor construction of monopoles. The Nahm equations are formally analogous to the algebraic equations in the ADHM construction of instantons, where finite order matrices are replaced by differential operators.Deep study of the Nahm equations was carried out by Nigel Hitchin and Simon Donaldson. Conceptually, the equations arise in the process of infinite-dimensional hyperkahler reduction. Among their many applications we can mention: Hitchin's construction of monopoles, where this approach is critical for establishing nonsingularity of...

ISBN: 978-6-1312-9687-1
Издательство: Книга по требованию
Дата выхода: июль 2011

High Quality Content by WIKIPEDIA articles! In operator theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It can be viewed as a consequence of Stinespring's dilation theorem.In the mathematical literature, one may also find other results that bear Naimark's name. Let X be a compact Hausdorff space, H be a Hilbert space, and L(H) the Banach space of bounded operators on H. A mapping E from the Borel -algebra on X to L(H) is called a operator-valued measure if it is weakly countably additive, that is, for any disjoint sequence of Borel sets {Bi}, we have langle E (cup _i B_i) x, y rangle = sum_i langle E (B_i) x, y rangle, langle E (cup _i B_i) x, y rangle = sum_i langle E (B_i) x, y...

ISBN: 978-6-1312-9706-9
Издательство: Книга по требованию
Дата выхода: июль 2011

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to...

ISBN: 978-6-1333-0766-7
Издательство: Книга по требованию
Дата выхода: июль 2011