The goal of this paper is to establish Green function estimates for a class purely discontinuous symmetric Markov processes with jump kernels degenerate at the boundary and critical killing potentials. kernel potential depend on several parameters. We sharp two-sided functions these all admissible values parameters involved. Depending regions where belong, are different. In fact, have three dif...

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

1-type and biharmonic curves by using laplace operator in lorentzian 3-space arestudied and some theorems and characterizations are given for these curves.

Asymptotic expansions for U-statistics and V-statistics with degenerate kernels are investigated, respectively, the remainder term O(n1−p/2), some p≥4, is shown in both cases. From results, it obtained that asymptotic Crame´r–von Mises statistics of uniform distribution U(0,1) hold On1−p/2 any p≥4. The scheme proof based on three steps. first one almost sure convergence a Fourier series expansi...

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computation time. In this respect, the B-test family combines favorable properties of p...

In this paper, we are interested in finding a numerical solution of linear BVP for Fredholm IDE with degenerate kernel subjected to impulsive actions. By Dzumabaev’s parametrization method the original problem is reduced multipoint system IDEs additional parameters. For fixed parameters, special Cauchy FIDEs on subintervals obtained and by using problem, algebraic equations parameters construct...

Topologically protected helical states at a mass-inverted quantum dot in graphene are studied by analyzing both tight-binding and kernel polynomial method calculations. The is introduced considering heterojunction between two different mass domains, which similar to the domain wall bilayer graphene. numerical results show emergent metallic channels across gap when signs of terms opposite. eigen...