Related papers: Approximate solution of the integral equations inv…
This note is devoted to discussing multivariate approximation of continuous functions on $[0,1]^d$ with analytic Korobov kernels in the worst and average case settings. We only consider algorithms that use finitely many evaluations of…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…
Parallel fixed-parameter tractability studies how parameterized problems can be solved in parallel. A surprisingly large number of parameterized problems admit a high level of parallelization, but this does not mean that we can also…
We consider finite element approximations for a one dimensional second order stochastic differential equation of boundary value type driven by a fractional Brownian motion with Hurst index $H\le 1/2$. We make use of a sequence of…
We give an explicit integral formula for the Dunkl kernel associated to root system of type $A_2$ and parameter $k>0$, by exploiting recent result in [1].
The numerical method for solution of the weakly regular scalar Volterra integral equation of the 1st kind is proposed. The kernels of such equations have jump discontinuities on the continuous curves which starts at the origin. The…
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point technique when the elliptic equations contain second order…
In this thesis, we present results related to complementarity problems. We study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed…
Existence of mass-conserving weak solutions to the coagulation-fragmentation equation is established when the fragmentation mechanism produces an infinite number of fragments after splitting. The coagulation kernel is assumed to increase at…
For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction…
In the first part of the article we establish the existence in the sense of sequences of solutions in $H^{2}(R)$ for some nonhomogeneous linear differential equation in which one of the terms has the argument translated by a constant. It is…
We take into account a coagulation model that simulates a distinct kind of dynamics. In this model, two particles collide to produce a single particle, but the resulting particle decreases in size, allowing each particle to be fully…
The optimal control problem of connecting any two trajectories in a behavior B with maximal persistence of that behavior is put forth and a compact solution is obtained for a general class of behaviors. The behavior B is understood in the…
Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original…
A multidimensional extremal problem in the idempotent algebra setting is considered which consists in minimizing a nonlinear functional defined on a finite-dimensional semimodule over an idempotent semifield. The problem integrates two…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
We derive quantitative estimates for large stochastic systems of interacting particles perturbed by both idiosyncratic and environmental noises, as well as singular kernels. We prove that the (mollified) empirical process converges to the…
We study the nonlocal-to-local convergence for a nonlocal Cahn-Hilliard equation with anisotropic and singular kernels. In particular, we show convergence of weak solutions of the nonlocal Cahn-Hilliard equation to weak solutions of a…
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators are used to model anomalous diffusion and, for a special…