We study Yang-Baxter equations with orthosymplectic supersymmetry. extend a new approach of the construction spinor and metaplectic $\hat{\cal R}$-operators orthogonal symplectic symmetries to supersymmetric case symmetry. In this R}$-operator is given by ratio two operator valued Euler Gamma-functions. illustrate calculating such R}$ operators in explicit form for special cases $osp(n|2m)$ alg...

In this paper, we prove existence and regularity results for solutions of some nonlinear Dirichlet problems an elliptic equation defined by a degenerate coercive operator singular right hand side. \begin{equation}\label{01} \left\{ \begin{array}{lll} -\displaystyle\mbox{div}( a(x,u,\nabla u))&=\displaystyle\frac{f}{u^{\gamma}} & \mbox{ in } \Omega \\ u&>0 &\mbox{ }\Omega u&=0 on \delta\Omega \e...

We study the obstacle problem for fully nonlinear elliptic operators with an anisotropic degeneracy on gradient: $$ \left{\begin{array}{rll} \min\left{f-|Du|^\gamma F(D^2u),u-\phi\right} &= 0 & \textrm{ in } \Omega,\ u = g \partial \Omega, \end{array}\right. some parameter $\gamma\geq 0$, uniformly operator $F$, bounded source term $f$, and suitably smooth $\phi$ boundary datum $g$. obtain exis...

Abstract: Consider a sequence of polynomials of bounded degree evaluated in independent Gaussian, Gamma or Beta random variables. We show that, if this sequence converges in law to a nonconstant distribution, then (i) the limit distribution is necessarily absolutely continuous with respect to the Lebesgue measure and (ii) the convergence automatically takes place in the total variation topology...

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral, one can list out almost all of the extended densities for the pathway parameter q < 1 and q → 1. Here, we bring out the idea of thickeror thinner-tailed models as...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

If \(m \geq 3\) and \(r 1\), we prove that any natural linear operator \(A\) lifting 2-vector fields \(\Lambda \in \Gamma (\bigwedge^2 TM)\) (i.e., skew-symmetric tensor of type (2,0)) on \(m\)-dimensional manifolds \(M\) into \(A(\Lambda)\) \(r\)-jet prolongation \(J^rTM\) the tangent bundle \(TM\) is zero one.

We derive exact statistical properties of a recursive fragmentation process. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution, P(x) approximately x(-2p), in one dimension. In d dimensions, the volume distribution diverges algebraically in the small fragment limit, P(V) approximately V-gamma, with gamma=2p(1/d). Hence, the entire range of e...