In earlier work we proposed a generating function that encodes the Jordan block spectrum of integrable Hypereclectic spin chain, related to one-loop dilatation operator dynamical fishnet quantum field theory. We significantly improve expressions for these functions, rendering them much more explicit and elegant. particular, treat case full chain without imposing any cyclicity constraints on sta...

Given that r and s are natural numbers and X ∼ Binomial(r, q) and Y ∼ Binomial(s, p) are independent random variables where q, p ∈ (0, 1), we prove that the likelihood ratio of the convolution Z = X + Y is decreasing, increasing, or constant when q < p, q > p or q = p, respectively. © 2009 Elsevier B.V. All rights reserved.

the main aim of this paper is to introduce three classes $h^0_{p,q}$, $h^1_{p,q}$ and $th^*_p$ of $p$-harmonic mappings and discuss the properties of mappings in these classes. first, we discuss the starlikeness and convexity of mappings in $h^0_{p,q}$ and $h^1_{p,q}$. then establish the covering theorem for mappings in $h^1_{p,q}$. finally, we determine the extreme points of the class $th^*_{p}$.

1. The q-disease A symptom of the q-disease|that scourge since Euler's times|is that those aaicted feel compelled to retrace steps taken long ago by their masters. For instance, when last counted 4], there were 53 proofs of the Rogers{Ramanujan identities. Other popular identities, such as the q-binomial theorem, Euler's pentagonal number theorem, Jacobi's triple product identity, and Ramanujan...

We present new proofs and generalizations of unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of representations of Sn. Other applications of this approach include strict unimodality of the diagonal q-binomial coefficients and unimodality of certa...

We consider Kemp’s q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of classical convergence properties. From the results about distributions, we deduce some new convergence results for (q-)Krawtchouk and q-Charlier polynomials. Besides...

In this paper, we apply a general family of basic (or q-) polynomials with double q-binomial coefficients as well some homogeneous q-operators in order to construct several q-difference equations involving seven variables. We derive the Rogers type and extended formulas Srivastava-Agarwal-type bilinear generating functions for q-polynomials, which generalize Cigler polynomials. also class mixed...

In this paper, we develop the theory of a p, q-analogue of the binomial coefficients. Some properties and identities parallel to those of the usual and q-binomial coefficients will be established including the triangular, vertical, and the horizontal recurrence relations, horizontal generating function, and the orthogonality and inverse relations. The construction and derivation of these result...