Related papers: All elementary functions from a single binary oper…

One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…

The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…

A generating function is given for the number, $E(l,k)$, of irreducible $k$-fold Euler sums, with all possible alternations of sign, and exponents summing to $l$. Its form is remarkably simple: $\sum_n E(k+2n,k) x^n = \sum_{d|k}\mu(d)…

Ordering identities in the Weyl-Heisenberg algebra generated by single-mode boson operators are investigated. A boson string composed of creation and annihilation operators can be expanded as a linear combination of other such strings, the…

Real continuous submodular functions, as a generalization of the corresponding discrete notion to the continuous domain, gained considerable attention recently. The analog notion for entropy functions requires additional properties: a real…

A longstanding open problem is whether there exists a non-syntactical model of untyped lambda-calculus whose theory is exactly the least equational lambda-theory (=Lb). In this paper we make use of the Visser topology for investigating the…

Let $X$ be a centered Gaussian random variable in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma.$ We study a problem of estimation of a smooth functional of $\Sigma$ based on a sample $X_1,\dots ,X_n$ of $n$…

Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…

Let $a \geq 2$ be an integer. We prove that for every periodic sequence $(s_n)_{n \geq 1}$ in $\{-1, +1\}$ there exists an effectively computable rational number $C_\mathbf{s} > 0$ such that \begin{equation*} \log\operatorname{lcm}(a + s_1,…

We present the universal one-loop effective action for all operators of dimension up to six obtained by integrating out massive, non-degenerate multiplets. Our general expression may be applied to loops of heavy fermions or bosons, and has…

Whilst most engineered systems use signals that are continuous in time, there is a domain of systems in which signals consist of events. Events, like Dirac delta functions, have no meaningful time duration. Many important real-world systems…

When reverse engineering a binary, the analyst must first understand the semantics of the binary's functions through either manual or automatic analysis. Manual semantic analysis is time-consuming, because abstractions provided by high…

We present an algorithm which, for given $n$, generates an unambiguous regular tree grammar defining the set of combinatory logic terms, over the set $\{S,K\}$ of primitive combinators, requiring exactly $n$ normal-order reduction steps to…

A long standing goal of the data management community is to develop general, automated systems that ingest semi-structured documents and output queryable tables without human effort or domain specific customization. Given the sheer variety…

Let $(a_n), (b_n)$ be linear recursive sequences of integers with characteristic polynomials $A(X),B(X)\in \mathbb{Z}[X]$ respectively. Assume that $A(X)$ has a dominating and simple real root $\alpha$, while $B(X)$ has a pair of conjugate…

We show that quantum search can be used to compute the hardness to round an elementary function, that is, to determine the minimum working precision required to compute the values of an elementary function correctly rounded to a target…

We establish a general construction of single-valued elliptic polylogarithms as functions on the once-punctured elliptic curve. Our formalism is an extension of Brown's construction of genus-zero single-valued polylogarithms to the elliptic…

The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…

We consider the minimal differential operator A generated in $L^2(0,\infty)$ by the differential expression $l(y) = (-1)^n y^{(2n)}$. Using the technique of boundary triplets and the corresponding Weyl functions, we find explicit form of…

We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of first-order and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower…