Related papers: A Closed Formula for the Product in Simple Integra…

The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the negative finiteness property, that is the set of finite $(-\beta)$-expansions is equal to…

Two methods can be used to calculate explicitly the Killing form on the Lie algebras. The first one is a direct calculation of the traces of the generators in a matrix representation of the algebra, and the second one is the usage of the…

In this paper, by use of matrix inversions, we establish a general $q$-expansion formula of arbitrary formal power series $F(z)$ with respect to the base $$\left\{z^n\frac{(az:q)_n}{(bz:q)_n}\bigg|n=0,1,2\cdots\right\}.$$ Some concrete…

We consider Exel's new construction of a crossed product of a C*-algebra A by an endomorphism \alpha. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be…

We treat the problem of normally ordering expressions involving the standard boson operators a, a* where [a,a*]=1. We show that a simple product formula for formal power series - essentially an extension of the Taylor expansion - leads to a…

We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. We show how to control this complexity using the arithmetic and geometry of algebraic curves.

In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion formula, and simple integrals, integral operators, some…

For an arbitrary positive integer $p$, Landen's formula is extended to express theta function with modulus $p\tau$ by $p$ product of theta functions with $\tau$, which is applied to several examples. Next it is shown that double product of…

We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is…

Let $(H,\alpha)$ be a monoidal Hom-Hopf algebra, and $(A,\beta)$ a Hom-algebra. In this paper we will introduce the crossed product $(A\#_{\sigma}H,\beta\otimes\alpha)$, which is a Hom-algebra. Then we will introduce the notions of cleft…

Given a partial action \alpha of a group G on an associative algebra A we consider the crossed product A x_\alpha G. Using the algebras of multipliers of ideals of A we prove that A x_\alpha G is associative, provided that all ideals of A…

Let $0 < \beta \leq \alpha < 1$ and $\kappa > 0$. I prove that there exists $\eta > 0$ such that the following holds for every pair of Borel sets $A,B \subset \mathbb{R}$ with $\dim_{\mathrm{H}} A = \alpha$ and $\dim_{\mathrm{H}} B =…

The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie…

In this paper we give a closed form expression for the Drinfeld modular polynomial $\Phi_T(X,Y) \in \mathbb{F}_q(T)[X,Y]$ for arbitrary $q$ and prove a conjecture of Schweizer. A new identity involving the Catalan numbers plays a central…

We give elementary proofs of the univariate elliptic beta integral with bases $|q|, |p|<1$ and its multiparameter generalizations to integrals on the $A_n$ and $C_n$ root systems. We prove also some new unit circle multiple elliptic beta…

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and…

Extensions (entropies) play a central role in the theory of hyperbolic conservation laws by providing intrinsic selection criteria for weak solutions. For a given hyperbolic system u_t+f(u)_x=0, a standard approach is to analyze directly…

Let $\partial \mathcal{Q}$ be the boundary of a convex polygon in $\mathbb{R}^2$, $e_\alpha = (\cos\alpha, \sin \alpha)$ and $e_{\alpha}^{\bot} = (-\sin\alpha , \cos \alpha)$ be a basis of $\mathbb{R}^2$ for some $\alpha\in[0,2\pi)$ and…

Conforti et al. give a compact extended formulation for a class of bimodular-constrained integer programs, namely those that model the stable set polytope of a graph with no disjoint odd cycles. We extend their techniques to design compact…

For $-\pi\leq\beta_1<\beta_2\leq\pi$ denote by $\Phi_{\beta_1,\beta_2}(Q)$ the number of algebraic numbers on the unit circle with arguments in $[\beta_1,\beta_2]$ of degree $2m$ and with elliptic height at most $Q$. We show that \[…