We observe that the classical Faulhaber’s theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+b, a+2b, . . . , a+nb is a polynomial in na+ n(n + 1)b/2. While this assertion can be deduced from the original Fauhalber’s theorem, we give an alternative formula in terms of the Bernoulli polynomials. Moreover, b...

OBJECTIVE To examine the factor structure of the 144-item Chinese version of the Temperament and Character Inventory (TCI) and its association with age and gender in a large non-clinical population. METHOD We recruited 1966 non-clinical participants in China who completed the TCI Chinese version. They were randomly divided into two independent samples. One sample (n=983) was used for explorat...

We use the generating function approach to derive simple expressions for factorial moments of distance distribution over Reed-Solomon codes. obtain better upper bounds error term a counting formula given by Li and Wan, which gives nontrivial estimates on number polynomials finite fields with prescribed leading coefficients linear factors. This improvement leads new results classification deep h...

For each infinite series of the classical Lie groups of type B, C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the corresponding flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynom...

In a number of practical scenarios, such as video conferencing and visual human/computer interaction, objects that belong to a well defined class are segmented, normalized, and encoded, after which they are stored and/or transmitted, and subsequently reconstructed. The Karhunen-Loève Transform (KLT) optimally concentrates the signal power in a relatively small number of uncorrelated coefficient...

In this text we introduce and analyze families of symmetric functions arising as partition for colored fermionic vertex models associated with the quantized affine Lie superalgebra $U_q \big ( \widehat {\mathfrak {sl}} (1 | n) )$. We establish various combinatorial results these functions, which include following. apply fusion procedure to fundamental $R$-matrix )$ obtain an explicit family wei...

We present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual ...

A permutation σ of a multiset is called Stirling permutation if σ(s) ≥ σ(i) as soon as σ(i) = σ(j) and i < s < j. In our paper we study Stirling polynomials that arise in the generating function for descent statistics on Stirling permutations of any multiset. We develop generalizations of the classical Stirling numbers and present their combinatorial interpretations. Particularly, we apply the ...

in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.