Báo cáo toán học: "Grothendieck bialgebras, Partition lattices, and symmetric functions in noncommutative variables" doc

... non-commuting variables) corresponding to the disjoint union of X and Y , together with the total order obtained from X and Y placing all Y after all X.(Thatis,x<yfor all x in X and all y in Y ... ρ m,n forms an inverse system in the category of graded algebras. Let NCSym be its inverse limit in this category. We call NCSym the algebra of symmetric functions in an in n...

Ngày tải lên: 07/08/2014, 13:21

... vector is defined by the corresponding column a i in the mixing matrix A. Following this interpretation of Equation 1, Llinares and Igual EURASIP Journal on Advances in Signal Processing 2011, 2011:134 http://asp.eurasipjournals.com/content/2011/1/134 Page ... of the signals and the way they are mixed before obtaining the multidimensional recording. One of the most common types of pri...

Ngày tải lên: 20/06/2014, 21:20

... Uniformly Starlike and Convex Functions Defined by Certain Integral Operator Maslina Darus 1 ,AiniJanteng 2 , and Suzeini Abdul Halim 2 1 School of Mathematical Sciences, Faculty of Sciences and Technology, University ... corresponding subclasses of uniformly convex functions are also obtained. 1. Introduction Let S denote the class of functions f which are analytic and univalent...

Ngày tải lên: 06/08/2014, 05:20

... generated by the elementary symmetric functions e n , and also by the complete symmetric functions h n . The generating functions E(t) and H(t) for these symmetric functions are related by E(t) ... Geissinger, Hopf algebras of symmetric functions and class functions, in Combi- natoire et repr´esentation du groupe sym´etrique (Strasbourg, 1976), Springer Lecture Note...

Ngày tải lên: 07/08/2014, 21:20

... variation in D and strain e with mean diameter, revealing the increase in magnetic anisotropic energy with increasing particle size. b Schematic plots for negative strain (e \0), and c positive strain ... a closed d shell and a single s electron. Finite-size effects play a dominant role in determining the magnetic properties. A decrease in size can lead to unusual ferromagnetic...

Ngày tải lên: 22/06/2014, 00:20

... continuous non-self-intersecting curve connecting the embedding of its end vertices. The interiors of the embedding of the edges are pairwise disjoint and the interiors of the curves embedding ... order, else according to the natural order. 3. All the remaining arcs orient in ¯ D in the same way as in D. Note that relevant edges are oriented in the same way in both D and ¯ D. th...

Ngày tải lên: 07/08/2014, 06:23

... mock theta functions. He separated these 17 functions into three classes. First containing 4 functions of order 3, second containing 10 functions of order 5 and the third containg 3 functions ... function for partitions into odd parts without gaps [5]. We in this paper use n-color partitions (also called partitions with n copies of n and studied first by Agarwal and Andrews i...

Ngày tải lên: 07/08/2014, 08:20

... combinatorial proof. I have been informed that A. Sills, A. J. Yee, and C. Boulet have independently found such proofs in addition to further results. References [1] G.E. Andrews, The Theory of Partitions, ... (10) We conclude with some open questions. 2 The Main Theorem We begin with some preliminaries about partitions and their conjugates. For a given partition π with parts each  N...

Ngày tải lên: 07/08/2014, 08:22

... is obtained using entropy considerations (and in particular, Shearer’s Lemma). ∗ This work was begun while the author was a member of the Institute for Advanced Study, Einstein Drive, Princeton, ... Z W Ising,β,h (K d,d ) N 2d ≤  2 2d e βd 2  N 2d (2) =2 N exp  βdN 2  . (3) In (2) we are using that there are 2 2d possible configurations on K d,d and that each has weight at most e βd...

Ngày tải lên: 07/08/2014, 13:21

... occurring in the second components of elements of J  , and that the parts of π contained in J  are those obtained by listing the remaining such numbers in increasing order, chopping that list into ... concatenating the elements of I 0 (in increasing order) followed by the elements of I 1 (in increasing order), I 2 (in increasing order), and so on up to I  n d  , where the...

Ngày tải lên: 07/08/2014, 13:21