Related papers: Inverse-syst.lib, Singular library for computing M…
We present libsharp, a code library for spherical harmonic transforms (SHTs), which evolved from the libpsht library, addressing several of its shortcomings, such as adding MPI support for distributed memory systems and SHTs of fields with…
We present the software library libCreme which we have previously used to successfully calculate convex-roof entanglement measures of mixed quantum states appearing in realistic physical systems. Evaluating the amount of entanglement in…
One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven…
An inverse spectral problem is studied for the matrix Sturm-Liouville operator on a finite interval with the general self-adjoint boundary condition. We obtain a constructive solution based on the method of spectral mappings for the…
Integer Linear Programming (ILP) has a broad range of applications in various areas of artificial intelligence. Yet in spite of recent advances, we still lack a thorough understanding of which structural restrictions make ILP tractable.…
This paper proposes a modal typing system that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the…
We consider canonical systems (with $2p\times 2p$ Hamiltonians $H(x)\geq 0$), which correspond to matrix string equations. Direct and inverse problems are solved in terms of Titchmarsh--Weyl and spectral matrix functions and related…
Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering problem with internal sources. We employ the theory of…
This paper presents a detailed symbolic approach to the study of self-similar tilings. It uses properties of addresses associated with graph-directed iterated function systems to establish conjugacy properties of tiling spaces. Tiles may be…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
We present some contributions to the theory of infinitary rewriting for weakly orthogonal term rewrite systems, in which critical pairs may occur provided they are trivial. We show that the infinitary unique normal form property fails by an…
Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.
Reversible systems feature both forward computations and backward computations, where the latter undo the effects of the former in a causally consistent manner. The compositionality properties and equational characterizations of strong and…
The field of molecular programming allows for the programming of the structure and behavior of matter at the molecular level, even to the point of encoding arbitrary computation. However, current approaches tend to be wasteful in terms of…
In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…
For a topologically complete space $X$ and a family of closed covers $\mathcal A$ of $X$ satisfying a "local refinement condition" and a "completeness condition," we give a construction of an inverse system $\mathbf{ N}_{\mathcal A}$ of…
A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.
We use the inverse scattering method (ISM) to derive concentric non-supersymmetric black rings. The approach used here is fully five-dimensional, and has the modest advantage that it generalizes readily to the construction of more general…