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In this work we study the general system of geodesic equations for the case of a massive particle moving on an arbitrary curved manifold. The investigation is carried out from the symmetry perspective. By exploiting the parametrization…
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…
This paper investigates a generalized hyperbolic circle packing (including circles, horocycles or hypercycles) with respect to the total geodesic curvatures on the surface with boundary. We mainly focus on the existence and rigidity of…
In this paper, we present a novel way to summarize the structure of large graphs, based on non-parametric estimation of edge density in directed multigraphs. Following coclustering approach, we use a clustering of the vertices, with a…
Personalized PageRank (PPR) is a popular node proximity metric in graph mining and network research. Given a graph G=(V,E) and a source node $s \in V$, a single-source PPR (SSPPR) query asks for the PPR value $\vpi(u)$ with respect to s,…
In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
We consider a class of isoperimetric problems on $\mathbb{R}^{N}_{+} $ where the volume and the area element carry two different weights of the type $|x|^lx_N^\alpha$. We solve them in a special case while a more detailed study is contained…
A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off…
In the first part of this paper, we prove that, under some natural non-degeneracy assumptions, the Greedy Parabolic Target-Following Method, based on {\em universal tangent direction} has a favorable local behavior. In view of its global…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
The edge geodesic cover problem of a graph $G$ is to find a smallest number of geodesics that cover the edge set of $G$. The edge $k$-general position problem is introduced as the problem to find a largest set $S$ of edges of $G$ such that…
A framework (a straight-line embedding of a graph into a normed space allowing edges to cross) is globally rigid if any other framework with the same edge lengths with respect to the chosen norm is an isometric copy. We investigate global…
We consider two natural problems arising in geometry which are equivalent to the local solvability of specific equations of Monge-Ampere type. These are: the problem of locally prescribed Gaussian curvature for surfaces in R^3, and the…
This paper seeks to advance the theory of nonexpansive mappings by introducing and exploring a novel class of nonexpansive type mappings, which we aptly designate as perimetric nonexpansive mappings. We establish that the collection of…
We consider the numerical solution of nonlinear elliptic boundary value problems with Kansa's method. We derive analytic formulas for the Jacobian and Hessian of the resulting nonlinear collocation system and exploit them within the…
A local approach to the time integration of PDEs by exponential methods is proposed, motivated by theoretical estimates by A.Iserles on the decay of off-diagonal terms in the exponentials of sparse matrices. An overlapping domain…
We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a result has previously been studied only for certain…
We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…