Explicit formula

One of the important consequences of the mere existence of this formula is the following. Suppose that g is the Lie algebra of a Lie group G. Then the local structure of G near the identity, i.e. the rule for the product of two elements of G suﬃciently closed to the identity is determined by its Lie algebra g. Indeed, the exponential map is locally a diﬀeomorphism from a neighborhood of the origin in g onto a neighborhood W of the identity, and if U ⊂ W is a (possibly smaller) neighborhood of the identity such that U · U ⊂ W, the the product of a...
198p tiramisu0908 25102012 26 7 Download

To the memory of Rodica Simion The goals of this paper are twofold. First, we prove, for an arbitrary ﬁnite root system Φ, the periodicity conjecture of Al. B. Zamolodchikov [24] that concerns Y systems, a particular class of functional relations playing an important role in the theory of thermodynamic Bethe ansatz. Algebraically, Y systems can be viewed as families of rational functions deﬁned by certain birational recurrences formulated in terms of the root system Φ.
43p tuanloccuoi 04012013 18 5 Download

We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer conﬁgurations) on a weighted, bipartite, doubly periodic graph G embedded in the plane. We derive explicit formulas for the surface tension and local Gibbs measure probabilities of these models. The answers involve a certain plane algebraic curve, which is the spectral curve of the Kasteleyn operator of the graph. For example, the surface tension is the Legendre dual of the Ronkin function of the spectral curve.
39p noel_noel 17012013 20 5 Download

Introduction In 1903 Voronoi [42] postulated the existence of explicit formulas for sums of the form (1.1) n≥1 an f (n) , for any “arithmetically interesting” sequence of coeﬃcients (an )n≥1 and every f in a large class of test functions, including characteristic functions of bounded intervals. He actually established such a formula when an = d(n) is the number of positive divisors of n [43]. He also asserted a formula for (1.2) an = #{(a, b) ∈ Z2  Q(a, b) = n} , where Q denotes a positive deﬁnite integral quadratic form [44]; ...
67p noel_noel 17012013 19 5 Download

BOUNDARY VALUE PROBLEMS FOR ANALYTIC FUNCTIONS IN THE CLASS OF CAUCHYTYPE INTEGRALS WITH DENSITY IN
BOUNDARY VALUE PROBLEMS FOR ANALYTIC FUNCTIONS IN THE CLASS OF CAUCHYTYPE INTEGRALS WITH DENSITY IN L p(·) (Γ) V. KOKILASHVILI, V. PAATASHVILI, AND S. SAMKO Received 9 July 2004 We study the Riemann boundary value problem Φ+ (t) = G(t)Φ− (t) + g(t), for analytic functions in the class of analytic functions represented by the Cauchytype integrals with density in the spaces L p(·) (Γ) with variable exponent. We consider both the case when the coeﬃcient G is piecewise continuous and the case when it may be of a more general nature, admitting its oscillation.
29p sting12 10032012 15 4 Download

The Chebyshev polynomial of degree n is denoted Tn (x), and is given by the explicit formula This may look trigonometric at ﬁrst glance (and there is in fact a close relation between the Chebyshev polynomials and the discrete Fourier transform); however (5.8.1) can
6p babyuni 17082010 34 3 Download

We present explicit formulas representations of the real diamond Lie algebra obtained from the normal polarization on Korbits. From this we have list irreducible unitary representations of the real diamond Lie group that is coincide with the representations via Fedosov deformation quantisation. Here the computations are more simple for use starproduct.
9p tuanlocmuido 19122012 10 2 Download

Selecting Cells by Reference Chọn các ô theo tham chiếu If a cell contains a formula, Excel defines the cell’s precedents as those cells that the formula refers to. For example, if cell A4 contains the formula = SUM(A1:A3), cells A1, A2, and A3 are the precedents of A4. A direct precedent is a cell referred to explicitly in the formula. In the preceding example, A1, A2, and A3 are direct precedents of A4. An indirect precedent is a cell referred to by a precedent. For example, if cell A1 contains the formula = B3*2, cell B3 is an indirect...
10p yesno123 16092011 79 50 Download

This chapter gives an overview of some properties of the storage occupancy process in a buffer fed with ``fractional Brownian traf®c,'' a Gaussian selfsimilar process. This model, called here ``fractional Brownian storage,'' is the logically simplest longrangedependent (LRD) storage system having strictly selfsimilar input variation. The impact of the selfsimilarity parameter H can be very clearly illustrated with this model.
14p vaseline 30082010 35 9 Download

The purpose of this paper is to give an explicit local formula for the diﬀerence of two natural versions of equivariant analytic torsion in de Rham theory. This diﬀerence is the sum of the integral of a ChernSimons current and of a new invariant, the V invariant of an odd dimensional manifold equipped with an action of a compact Lie group.
165p tuanloccuoi 04012013 20 5 Download

We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and G˚ ardingGindikin fractional integrals associated to the cone of positive deﬁnite matrices. By using this connection, we obtain Abeltype representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with Lp spaces.
36p tuanloccuoi 04012013 22 5 Download