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The problem of distributed function computation is studied, where functions to be computed is not necessarily symbol-wise. A new method to derive a converse bound for distributed computing is proposed; from the structure of functions to be…
Let $h \geq 2$, $k \geq 5$ be integers and $A$ be a nonempty finite set of $k$ integers. Very recently, Tang and Xing studied extended inverse theorems for $hk-h+1 < \left|hA\right| \leq hk+2h-3$. In this paper, we extend the work of Tang…
We propose a notion of iterating functions $f:X^{k}\rightarrow X$ in a way that represents recurrence relations of the form $a_{n+k}=f(a_{n},a_{n+1},...,a_{n+k-1})$. We define a function as $n$-involutory when its $n$th iterate is the…
We present a general setting where wavelet filters and multiresolution decompositions can be defined, beyond the classical $\mathbf L^2(\mathbb R,dx)$ setting. This is done in a framework of {\em iterated function system} (IFS) measures;…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
The inverse source problem for the radiative transfer equation is considered, with partial data. Here it is shown that under certain smoothness conditions on the scattering and absorption coefficients, one can recover sources supported in a…
We study arithmetic distribution relations and the inverse function theorem in algebraic and arithmetic geometry, with an emphasis on versions that can be applied uniformly across families of varieties and maps. In particular, we prove two…
En esta serie de tres articulos, damos una exposicion de varios resultados y problemas abiertos en tres areas de la combinatoria algebraica y geometrica: las matrices totalmente no negativas, las representaciones del grupo simetrico, y los…
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…
Consider the representations of an algebraic group G. In general, polynomial invariant functions may fail to separate orbits. The invariant subring may not be finitely generated, or the number and complexity of the generators may grow…
We derive product and series representations of the gamma function using Newton interpolation series. Using these identities, a new formula for the coefficients in the Taylor series of the reciprocal gamma function is found. We also find…
Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…
In this paper we shall study the inverse problem relative to dynamics of the w function which is a special arithmetic function and shall get some results.
We investigate the internal space of Bessel functions which is associated to the group Z of positive and negative integers defining their orders. As a result we propose and prove a new unifying formula (to be added to the huge literature on…
It is shown that there exist infinitely many non-integers $r>2$ such that the Dehn function of some finitely presented group is $\simeq n^r$. For each positive rational number $s$ we construct pairs of finitely presented groups $H\subset G$…
Prolog's ability to return multiple answers on backtracking provides an elegant mechanism to derive reversible encodings of combinatorial objects as Natural Numbers i.e. {\em ranking} and {\em unranking} functions. Starting from a…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
A real number is called left-computable if there exists a computable increasing sequence of rational numbers converging to it. In this article we are investigating a proper subset of the left-computable numbers. We say that a real number…
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…