Related papers: Partition of unity systems and B-splines
Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming…
Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral.…
In this paper, we investigate fractional B splines and their connections with Fourier analysis, and establish connections with generalized Stirling-type numbers and distribution theory. Employing a generating function approach inspired by…
We introduce B-splines on the line of quaternionic order $B_q$ ($q$ in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions $B_q$ are defined first by their Fourier transforms, then as the…
The description of the complex separability structure of quantum states in terms of partially ordered sets has been recently put forward. In this work, we address the question of how to efficiently determine these structures for unknown…
We present a method to detect entanglement partitions of multipartite quantum systems, by exploiting their inherent symmetries. Structures like genuinely multipartite entanglement, $m$-separability and entanglement depth are detected as…
Group theoretic methods to construct all N-particle singlet states by iterative recursion are presented. These techniques are applied to the quantum correlations of four spin one-half particles in their singlet states. Multipartite…
This paper is about partitioning in parallel and distributed simulation. That means decomposing the simulation model into a numberof components and to properly allocate them on the execution units. An adaptive solution based on…
For spaces of constant, linear, and quadratic splines of maximal smoothness on the Powell-Sabin 12-split of a triangle, the so-called S-bases were recently introduced. These are simplex spline bases with B-spline-like properties on the…
A double partition problem asks for a number of nonnegative integer solutions to a system of two linear Diophantine equations with integer coefficients. Artur Cayley suggested a reduction of a double partition to a sum of scalar partitions…
In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
Motivated by Pittel's study of minimally intersecting set partitions, we investigate minimally intersecting set partitions of type B. We find a formula for the number of minimally intersecting r-tuples of $B_n$-partitions, as well as a…
We introduce here a direct method to construct multivariate explicit B-spline bases. B-splines are piecewise polynomials, which are defined on adjacent tetrahedra and which are $C^{r}$ continuous throughout. The $C^{r}$ continuity is…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
We describe a family of twisted partition functions for the relativistic spinning particle models. For suitable choices of fugacities this computes a refined Euler characteristics that counts the dimension of the physical states for…
We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…
Discrimination of unitary operations is a fundamental quantum information processing task. Assisted with linear optical elements, we experimentally demonstrate perfect discrimination between single-bit unitary operations using two…