Related papers: Calculation of two Belyi pairs
Deterministic extraction of Bell pairs from a finite number of partially entangled pairs is discussed. We derive the maximum number of Bell pairs that can be obtained with probability 1 by local operations and classical communication. It is…
Versions of Bailey's lemma which change the base from q to q^2 or q^3 are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities. We also prove Melzer's conjectures for the Fermionic forms of the…
We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at non-positive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as…
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…
We construct an operational calculus supported on the algebraic operational calculus introduced by Bengochea and Verde. With this operational calculus we study the solution of certain Bessel type equations.
We propose a new approach towards approximating the density-to-pair-density map based on copula theory from statistics. We extend the copula theory to multi-dimensional marginals, and deduce that one can describe any (exact or approximate)…
Two non-interacting qubits are coupled to an environment. Both coupling and environment are represented by random matrix ensembles. The initial state of the pair is a Bell state, though we also consider arbitrary pure states. Decoherence of…
Derivations of two Bell's inequalities are given in a form appropriate to the interpretation of experimental data for explicit determination of all the correlations. They are arithmetic identities independent of statistical reasoning and…
Let $X$ be a smooth projective Calabi-Yau variety and $L$ a Koszul line bundle on $X$. We show that for Betti numbers of a maximal Cohen-Macaulay module over the homogeneous coordinate ring $A$ of $X$ there are formulas similar to the…
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…
We use decoupling theory to estimate the number of solutions for quadratic and cubic Parsell--Vinogradov systems in two dimensions.
In this paper we study some algebraic properties of hypergraphs, in particula their Betti numbers. We define some different types of complete hypergraphs, which to the best of our knowledge, are not previously considered in the literature.…
We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights $w_0,w_1$ are local Muckenhoupt weights in the sense of Rychkov. As a first step we calculate the Calder\'on products of associated sequence…
We provide some new conditions under which the graded Betti numbers of a monomial ideal can be computed in terms of the graded Betti numbers of smaller ideals, thus complementing Eliahou and Kervaire's splitting approach. As applications,…
In this paper, we study linear differential equations arising from Bessel polynomials and their applications. From these linear differential equations, we give some new and explicit identities for Bessel polynomials.
We suggest an effective procedure to calculate numerical invariants for rank two bundles over blown-up surfaces. We study the moduli spaces M_j of bundles on the blown-up plane splitting over the exceptional divisor as O(j)+O(-j). We use…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
In this paper we offer some new identities associated with mock theta functions and establish new Bailey pairs related to indefinite quadratic forms. We believe our proof is instructive use of changing base of Bailey pairs, and offers new…
Following the pioneering work of H. Reiss [1], we provide a covariant calculation of the charged scalar particle pair production. The calculation is facilitated by the use of two-dimensional Bessel functions and light-font coordinates.
This paper is a rigorous study of two dual pairs of momentum maps arising in the context of fluid equations whose configuration Lie group is the group of automorphism of a trivial principal bundle, generically called here non-abelian…