in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

Nonlocal modeling has drawn more and attention becomes steadily powerful in scientific computing. In this paper, we demonstrate the superiority of a first-principle nonlocal model—Wigner function—in treating singular potentials which are often used to model interaction between point charges quantum science. The nature Wigner equation is fully exploited convert potential into kernel with weak or...

We compute the equilibrium measure in dimension $$d=s+4$$ associated to a Riesz s-kernel interaction with an external field given by power of Euclidean norm. Our study reveals that can be mixture continuous part and singular part. Depending on value power, threshold phenomenon occurs consists reduction or condensation In particular, logarithmic case $$s=0$$ ( $$d=4$$ ), there is sphere special ...

To make the kernel-based tracking algorithms more reliable, in this work, we mainly deal with two major singular cases in kernel-based tracking, concerned with kernel observability and tracking stability. Singular kernel observability indicates that the motions of interest cannot be uniquely recovered by the kernel. We present a novel multiple collaborative kernel approach, in which a complex m...

We present an analytical description of the motion in the singular logarithmic potential of the form Φ = ln √ x1/b 2 + x2, a potential which plays an important role in the modeling of triaxial systems (like elliptical galaxies) or bars in the centers of galaxy disks. In order to obtain information about the motion near the singularity, we resort to McGehee -type transformations and regularize t...

We investigate the structure of the nonlocal closure relation in the kinetic equation for a soliton gas. This kinetic equation represents an integro-differential nonlinear system which has been recently shown to possess a number of remarkable properties and seems to be a representative of an entirely new class of integrable systems. In this paper, we identify the nonlocal kinetic closure relati...

Studies of models of current flow behaviour in Electrical Impedance Tomography (EIT) have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the technique. This behaviour imposes severe restrictions on the numerical techniques used in image reconstruction algorithms. In this paper we have considered a simple two dimensional case and we h...