Related papers: On the evaluation of Matsubara sums
We consider Vinberg $\theta$-groups associated to a cyclic quiver on $r$ nodes. Let $K$ be the product of general linear groups associated to the nodes, acting naturally on $V = \oplus \text{Hom}(V_i, V_{i+1})$. We study the harmonic…
The partition function of a factor graph can sometimes be accurately estimated by Monte Carlo methods. In this paper, such methods are extended to factor graphs with negative and complex factors.
Multiple zeta-star values are variants of multiple zeta values which allow equality in the definition. Similar to the theory of continued fractions, every real number which is greater than $1$ can be realized as an unique infinite multiple…
The double graph of a graph $G$ is defined as $\mathcal{D}[G]$ = $G \times T_2$, where \(T_2\) is the total graph with 2 vertices and $\times$ stands for the Kronecker product of graphs. In this paper, sufficient conditions for double…
In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…
The sum-essential graph $ \mathcal{S}_R(M) $ of a left $R$-module $M$ is a graph whose vertices are all nontrivial submodules of $M$ and two distinct submodules are adjacent iff their sum is an essential submodule of $M$. Properties of the…
We construct an extension of the Kontsevich integral of knots to knotted trivalent graphs, which commutes with orientation switches, edge deletions, edge unzips, and connected sums. In 1997 Murakami and Ohtsuki [MO] first constructed such…
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain…
Multiple actions of the monodromy matrix elements onto off-shell Bethe vectors in the $\mathfrak{gl}(m|n)$-invariant quantum integrable models are calculated. These actions are used to describe recursions for the highest coefficients in the…
In [Ok] Okounkov studies a specific $q$-analogue of multiple zeta values and makes some conjectures on their algebraic structure. In this note we compare Okounkovs $q$-analogues to the generating function for multiple divisor sums defined…
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
A multivariate interpolation formula (MVIF) over finite fields is presented by using the proposed Kronecker delta function. The MVIF can be applied to yield polynomial relations over the base field among homogeneous symmetric rational…
Let $F_n$ and $L_n$ be the Fibonacci and Lucas numbers, respectively. Four corresponding zeta functions in $s$ are defined by \[\zeta_F(s) \,:=\, \sum_{n=1}^{\infty} \frac{1}{F_n^s}\,,\quad \zeta_F^*(s) \,:=\,\sum_{n=1}^{\infty}…
We give a generalization of the geometric estimate used by Hart and the second author in their 2008 work on sums and products in finite fields. Their result concerned level sets of non-degenerate bilinear forms over finite fields, while in…
Let $G=(V, E)$ be a connected finite graph, $h$ be a positive function on $V$ and $\lambda _{1}(V)$ be the first non-zero eigenvalue of $-\Delta$. For any given finite measure $\mu$ on $V$, define functionals \begin{eqnarray*} J_{ \beta…
A sum rule is an identity connecting the entropy of a measure with coefficients involved in the construction of its orthogonal polynomials (Jacobi coefficients). Our paper is an extension of Gamboa, Nagel and Rouault (2016), where we have…
We will show in this paper that if $\lambda$ is very close to 1, then $$I(M,\lambda,m)= \sup_{u\in H^{1,n}_0(M) ,\int_M|\nabla u|^ndV=1}\int_\Omega (e^{\alpha_n |u|^\frac{n}{n-1}}-\lambda\sum\limits_{k=1}^m\frac{|\alpha_nu^\frac{n}{n-1}|^k}…
Given $n$ positive integers $a_1,a_2,\dots,a_n$, and a positive integer right hand side $\beta$, we consider the feasibility version of the subset sum problem which is the problem of determining whether a subset of $a_1,a_2,\dots,a_n$ adds…
Let $X$ be a smooth projective variety. The Iitaka dimension of a divisor $D$ is an important invariant, but it does not only depend on the numerical class of $D$. However, there are several definitions of ``numerical Iitaka dimension'',…
Let M be a factor of type II_\infty or II_1 having separable predual and let M-bar be the algebra of affiliated \tau-measureable operators. We characterize the commutator space [I,J] for sub-(M,M)-bimodules I and J of M-bar.