High Quality Content by WIKIPEDIA articles! In geometry, the Steinmetz solid is the solid body generated by the intersection of two or three cylinders of equal radius at right angles. It is named after Charles Proteus Steinmetz, though these solids were known long before Steinmetz studied them. If two cylinders are intersected, the overlap is called a bicylinder or mouhefanggai. If three cylinders are intersected, then the overlap is called a tricylinder.The surface area is 16r2. The ratio of tfrac{r}{3} between surface area and volume holds more generally for a large family of shapes circumscribed around a sphere, including spheres themselves, cylinders, cubes, and both types of Steinmetz solid (Apostol and Mnatsakanian 2006). The...

ISBN: 978-6-1312-5417-8
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High Quality Content by WIKIPEDIA articles! In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design. A Steiner system with parameters l, m, n, written S(l,m,n), is an n-element set S together with a set of m-element subsets of S (called blocks) with the property that each l-element subset of S is contained in exactly one block. A Steiner system with parameters l, m, n is often called simply "an S(l,m,n)". An S(2,3,n) is called a Steiner triple system, and its blocks are called triples. The number of triples is n(n-1)/6. We can define a multiplication on a Steiner triple system by setting aa = a for all a in S, and ab = c if {a,b,c} is a triple. This makes S into an idempotent commutative...

ISBN: 978-6-1304-9547-3
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High Quality Content by WIKIPEDIA articles! Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its application to statistical inference — in particular, its application to James–Stein estimation and empirical Bayes methods.Suppose X is a normally distributed random variable with expectation ? and variance ?2. Further suppose g is a function for which the two expectations E( g(X) (X ? ?) ) and E( g ?(X) ) both exist (the existence of the expectation of any random variable is equivalent to the finiteness of the expectation of its absolute value). Данное издание не является оригинальным. Книга печатается по...

ISBN: 978-6-1312-5057-6
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High Quality Content by WIKIPEDIA articles! Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, their combined estimator is more accurate (has lower expected mean-squared error) than any method that handles the parameters separately. This is surprising since the parameters and the measurements might be totally unrelated. The phenomenon is named after its discoverer, Charles Stein. Let be a vector consisting of n >= 3 unknown parameters. To estimate these parameters, a single measurement Xi is performed for each parameter i, resulting in a vector X of length n. Suppose the measurements are independent, identically...

ISBN: 978-6-1312-5050-7
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High Quality Content by WIKIPEDIA articles! In mathematics, a Stein manifold in the theory of several complex variables and complex manifolds is a complex submanifold of the vector space of n complex dimensions. The name is for Karl Stein.Numerous further characterizations of such manifolds exist, in particular capturing the property of their having "many" holomorphic functions taking values in the complex numbers. See for example Cartan's theorems A and B, relating to sheaf cohomology. The initial impetus was to have a description of the properties of the domain of definition of the (maximal) analytic continuation of an analytic function. In the GAGA set of analogies, Stein manifolds correspond to affine varieties. Stein manifolds are...

ISBN: 978-6-1312-5007-1
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High Quality Content by WIKIPEDIA articles! Steinhaus theorem is a theorem in real analysis, first proved by H. Steinhaus, concerning the difference set of a set of positive measure.Steinhaus was born in Jas?o, Austria-Hungary (now in Poland) to a Jewish family, and received his Ph.D. from Gottingen University. He was a professor at the Universities of Lwow (1920–41) and Wroc?aw (1945–61), the University of Notre Dame (Indiana, USA, 1961–62), and the University of Sussex (1966), and a corresponding member of PAU (the Polish Academy of Learning) from 1945 and PAN (the Polish Academy of Sciences) from 1952, and of many international scientific societies and science academies. Данное издание не является...

ISBN: 978-6-1312-5377-5
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High Quality Content by WIKIPEDIA articles! In mathematics, the Steinberg representation, or Steinberg module, denoted by St, is a particular linear representation of a group of Lie type over a finite field of characteristic p, of degree equal to the largest power of p dividing the order of the group. These representations were discovered by Robert Steinberg (1957). Most finite simple groups have exactly one Steinberg representation. A few have more than one because they are groups of Lie type in more than one way, and sporadic and most alternating groups have no Steinberg representation. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1312-5334-8
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High Quality Content by WIKIPEDIA articles! In statistics, Stein's unbiased risk estimate (SURE) is an unbiased estimator of the mean-squared error of a given estimator, in a deterministic estimation scenario. In other words, it provides an indication of the accuracy of a given estimator. This is important since, in deterministic estimation, the true mean-squared error of an estimator generally depends on the value of the unknown parameter, and thus cannot be determined completely. The technique is named after its discoverer, Charles Stein. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения...

ISBN: 978-6-1312-5081-1
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High Quality Content by WIKIPEDIA articles! Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric. It was introduced by Charles Stein, who first published it 1972, to obtain a bound between the distribution of a sum of m-dependent sequence of random variables and a standard normal distribution in the Kolmogorov (uniform) metric and hence to prove not only a central limit theorem, but also bounds on the rates of convergence for the given metric. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после...

ISBN: 978-6-1312-5070-5
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High Quality Content by WIKIPEDIA articles! In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the 3-vertex-connected planar graphs. That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs. Steinitz's theorem is named after Ernst Steinitz, who proved it in 1922. Branko Grunbaum has called this theorem “the most important and deepest known result on 3-polytopes.” Данное издание не...

ISBN: 978-6-1312-5407-9
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High Quality Content by WIKIPEDIA articles! In geometry, a Steiner chain is a set of n circles, all of which are tangent to two given non-intersecting circles (blue and red in Figure 1), where n is finite and each circle in the chain is tangent to the previous and next circles in the chain. In the usual closed Steiner chains, the first and last (nth) circles are also tangent to each other; by contrast, in open Steiner chains, they need not be. The given circles ? and ? do not intersect, but otherwise are unconstrained; the smaller circle may lie completely inside or outside of the larger circle. If these cases, the centers of Steiner-chain circles lie on an ellipse or a hyperbola, respectively. Данное издание не...

ISBN: 978-6-1312-5356-0
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm is an algorithm that generates permutations by transposing elements.The algorithm is set up with the idea that only one set of neighbors needs to swap positions and that there need only be one swap to generate the next permutation. To accommodate this, there needs to be an extra data element added: direction of mobility (ie direction of the swap). This direction is either left or right, but is initialized to the left.An integer is said to be mobile if, in the direction of its mobility, the nearest integer is less than the current integer....

ISBN: 978-6-1312-5385-0
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High Quality Content by WIKIPEDIA articles! Stencil jumping, at times called stencil walking, is an algorithm to locate the grid element enclosing a given point for any structured mesh. In simple words, given a point and a structured mesh, this algorithm will help locate the grid element that will enclose the given point. This algorithm finds extensive use in Computational Fluid Dynamics (CFD) in terms of holecutting and interpolation when two meshes lie one inside the other. The other variations of the problem would be something like this: Given a place, at which latitude and longitude does it lie? The brute force algorithm would find the distance of the point from every mesh point and see which is smallest. Another approach would be to...

ISBN: 978-6-1312-1183-6
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High Quality Content by WIKIPEDIA articles! In mathematics, especially the areas of numerical analysis concentrating on the numerical solution of partial differential equations, a stencil is a geometric arrangement of a nodal group that relate to the point of interest by using a numerical approximation routine. Stencils are the basis for many algorithms to numerically solve partial differential equations (PDE). Two examples of stencils are the five-point stencil and the Crank–Nicolson method stencil. Stencils are classified into two categories: compact and non-compact, the difference being the layers from the point of interest that are also used for calculation. Данное издание не является...

ISBN: 978-6-1312-1166-9
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High Quality Content by WIKIPEDIA articles! In mathematics, Stengle's Positivstellensatz characterizes polynomials which are positive on a given semialgebraic set over the real numbers, or more generally, any real-closed field. It can be thought of as an ordered analogue of Hilbert's Nullstellensatz. It was discovered by Gilbert Stengle. In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. For example, x2 ? 4x + 7 is a polynomial, but x2 ? 4/x + 7x3/2 is not, because its second term involves division by the variable x and because its third term...

ISBN: 978-6-1312-1190-4
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High Quality Content by WIKIPEDIA articles! In mathematics, a function on the real numbers is called a step function (or staircase function) if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. A constant function is a trivial example of a step function. Then there is only one interval, A_0=mathbb R. The Heaviside function H(x) is an important step function. It is the mathematical concept behind some test signals, such as those used to determine the step response of a dynamical system. The rectangular function, the next simplest step function. The rectangular function, the normalized boxcar function,...

ISBN: 978-6-1304-9227-4
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High Quality Content by WIKIPEDIA articles! The steradian is the SI unit of solid angle. It is used to describe two-dimensional angular spans in three-dimensional space, analogous to the way in which the radian describes angles in a plane. The name is derived from the Greek stereos for "solid" and the Latin radius for "ray, beam". The steradian, like the radian, is dimensionless because 1 sr = m2·m?2 = 1. It is useful, however, to distinguish between dimensionless quantities of different nature, so in practice the symbol "sr" is used where appropriate, rather than the derived unit "1" or no unit at all. For example, radiant intensity can be measured in watts per steradian (W·sr?1). Данное издание не является...

ISBN: 978-6-1312-1215-4
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High Quality Content by WIKIPEDIA articles! Calculating the steric number of a molecule's central atom is a vital step in figuring out its geometry. On the molecule SF4, for example, the central sulfur atom has four ligands about it, calculated by considering sulfur's coordination number. In addition to the four ligands, sulfur also has one remaining lone pair (expanded octet does not apply in this compound). Thus, the steric number is 5. Comparing a central atom's steric number to the number of ligands (not counting lone pairs) allows one to figure out the geometry of that central atom. Данное издание не является оригинальным. Книга печатается по технологии...

ISBN: 978-6-1310-7413-4
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High Quality Content by WIKIPEDIA articles! In number theory, the Stern–Brocot tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. The Stern–Brocot tree was discovered independently by Moritz Stern (1858) and Achille Brocot (1861). Stern was a German number theorist; Brocot was a French clockmaker who used the Stern–Brocot tree to design systems of gears with a gear ratio close to some desired value by finding a ratio of smooth numbers near that value. The root of the Stern–Brocot tree corresponds to the number 1. The parent-child relation between numbers in the Stern–Brocot tree may be defined in terms of continued fractions or mediants, and a path in the tree from the root to any other...

ISBN: 978-6-1312-1231-4
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Steve Shnider is professor of mathematics at Bar Ilan University. He received a PhD in Mathematics from Harvard University in 1972, under Shlomo Sternberg. His main interests are in the differential geometry of fiber bundles; algebraic methods in the theory of deformation of geometric structures; symplectic geometry; supersymmetry; operads; and Hopf algebras. Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.

ISBN: 978-6-1311-8463-5
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High Quality Content by WIKIPEDIA articles! In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four twists, or as the (5,?1,?1) pretzel knot. The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper at the end of a rope. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted loop. Данное издание не является оригинальным. Книга печатается...

ISBN: 978-6-1312-1262-8
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High Quality Content by WIKIPEDIA articles! Steven J. Wiebe is an algebra teacher at Finn Hill Junior High, a school in Kirkland, Washington. A competitive gamer, Wiebe was the first person to achieve over a million points in the arcade game Donkey Kong with a score of 1,006,600 on July 4, 2004. He is one of the primary subjects of the 2007 documentary The King of Kong: A Fistful of Quarters. He regained the world record from Billy Mitchell on September 20, 2010 with a score of 1,064,500 points. Wiebe was interviewed about the documentary The King of Kong: A Fistful of Quarters on the The Late Late Show with Craig Ferguson and on G4's Attack of the Show. He also voiced his own cartoon character on Code Monkeys in the episode "The Great...

ISBN: 978-6-1339-7346-6
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High Quality Content by WIKIPEDIA articles! 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 reality." Данное издание не является оригинальным....

ISBN: 978-6-1312-5188-7
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High Quality Content by WIKIPEDIA articles! In mathematics, the Stiefel manifold Vk(Rn) is the set of all orthonormal k-frames in Rn. That is, it is the set of ordered k-tuples of orthonormal vectors in Rn. Likewise one can define the complex Stiefel manifold Vk(Cn) of orthonormal k-frames in Cn and the quaternionic Stiefel manifold Vk(Hn) of orthonormal k-frames in Hn. More generally, the construction applies to any real, complex, or quaternionic inner product space. In some contexts, a non-compact Stiefel manifold is defined as the set of all linearly independent k-frames in Rn, Cn, or Hn; this is topologically equivalent, as the compact Stiefel manifold is a deformation retract of the non-compact one, by Gram–Schmidt. Statements...

ISBN: 978-6-1305-1557-7
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High Quality Content by WIKIPEDIA articles! 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 reality." Данное издание не является оригинальным....

ISBN: 978-6-1312-5193-1
Издательство: Книга по требованию
Дата выхода: июль 2011