Abstract About two dozens of exactly solvable Markov chains on one-dimensional finite and semi-infinite integer lattices are constructed in terms convolutions orthogonality measures the Krawtchouk, Hahn, Meixner, Charlier, q-Hahn, q-Meixner little q-Jacobi polynomials. By construction, stationary probability distributions, complete sets eigenvalues eigenvectors provided by polynomials measures. A...

Let Q be a positive definite integral quadratic form in ti variables, with the additional property that the adjoint form Q' is also integral. Using the functional equation of the Epstein zeta function, we obtain a symmetric functional equation of the ¿-function of Q with a primitive character to mod q (additive or multiplicative) defined by £io(2(x))C(x)-ï. Re(s) > nl2> where the summation exte...

Enumeration of derangements in the symmetric group $\mathfrak{S}_n$ is classical. Extensions enumerative results to hyperoctahedral $B_n$ are combinatorially sound. That even-signed permutation $D_n$ remains largely unexplored. Let $d_n^D(q) = \sum_{\sigma \in \mathcal{D}_n^D} q^{\operatorname{maj}(\sigma)}$ be generating function by their major indices. We study this work properties $d_n^D(q)$...

We consider the following problem in the paper of Kim et al. 2010 : “Find Witt’s formula for Carlitz’s type q-Euler numbers.” We give Witt’s formula for Carlitz’s type q-Euler numbers, which is an answer to the above problem. Moreover, we obtain a new p-adic q-l-function lp,q s, χ for Dirichlet’s character χ, with the property that lp,q −n, χ En,χn,q − χn p p nqEn,χn,qp for n 0, 1, . . . using ...

tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Our aim in this paper is to discover special symmetric properties for twisted q-Genocchi polynomials. We are going to find a symmetric identity for twisted q-Genocchi zeta function. From property of the twis...

Suppose we have a concatenated code where the outer code is an [N,K,D]Q code, and the inner code is an [n, k, d]q code, with Q = q. In section 4 we will see that the concatenated code is actually an [Nn,Kk, Dd]q code, but for now we will show the weaker property that it is an [Nn,Kk, Dd/2]q. Consider the näıve decoding procedure which uses the inner decoding scheme on each received symbol, then...

Let q be an odd number and Sq,0(n) the difference between the number of k < n, k ≡ 0 mod q, with an even binary digit sum and the corresponding number of k < n, k ≡ 0 mod q, with an odd binary digit sum. A remarkable theorem of Newman says that S3,0(n) > 0 for all n. In this paper it is proved that the same assertion holds if q is divisible by 3 or q = 4N + 1. On the other hand, it is shown tha...

The Gaussian matrix model is known to deform the $q,t$-matrix model. We consider further deformation elliptic $q,t$ by properly deforming density as well Vandermonde factor. Properties of an associated basis symmetric functions that provide property $\sim {\rm char}$ in deformed case are discussed.

Assume T is superstable, Φ(x) is a formula over ∅, Q = Φ(M∗) is countable and KQ = {M : M is countable and Φ(M) = Q}. We investigate models in KQ assuming KQ has the prime model property. We prove some corollaries on the number of models inKQ. We show an example of an ω-stable T and Q with KQ having exactly 3 models. First we fix the general set-up. Throughout, T is a countable complete theory ...

We construct infinite Galois extensions $L$ of $\mathbb {Q}$ that satisfy the Northcott property on elements small height, and where this can be deduced solely from local behavior at different prime numbers. also give examples which have finite degree all numbers do not property.