Given a smooth projective curve X, we give effective very ampleness bounds for generalized theta divisors on the moduli spaces SUX(r, d) and UX(r, d) of semistable vector bundles of rank r and degree d on X with fixed, respectively arbitrary, determinant.

In this paper, we prove that it is always possible to define a realization of the Laplacian $$\Delta _{\kappa ,\theta }$$ on $$L^2(\Omega )$$ subject nonlocal Robin boundary conditions with general jump measures arbitrary open subsets $${\mathbb {R}}^N$$ . This made by using capacity approach an admissible pair $$(\kappa allows associated form $${\mathcal {E}}_{\kappa be closable. The generates...

An $(n,r,h,a,q)$ -Local Reconstruction Code (LRC) is a linear code over notation="LaTeX">$\mathbb {F}_{q}$ of length notation="LaTeX">$n$ , whose codeword symbols are partitioned into notation="LaTeX">$n/r$ local groups each size nota...

We consider an expression for the probability R=P(Y<X) where random variables X and Y denote strength stress, respectively. Our aim is to study effect of dependency between on R. assume that follow exponential distributions their modeled by a copula with parameter theta. obtain closed-form R Farlie-Gumbel-Morgenstern (FGM), Ali-Mikhail-Haq (AMH), Gumbel's bivariate copulas compute Gumbel-Hou...

This paper is devoted to the multivariable $$H^\infty $$ functional calculus associated with a finite commuting family of sectorial operators on Banach space. First we prove that if $$(A_1,\ldots , A_d)$$ such family, $$A_k$$ R-sectorial R-type $$\omega _k\in (0,\pi )$$ $$k=1,\ldots ,d$$ and admits bounded (\Sigma _{\theta _1}\times \cdots \times \Sigma _d})$$ joint for some $$\theta (\omega _k...

This paper is concerned with the following fractional $ p $-Kirchhoff equation \begin{document}$ \begin{eqnarray*} \left\{ \begin{array}{ll} \varepsilon ^{sp}M\left( {\varepsilon ^{sp - N}}\iint_{\mathbb{R}^{2N}}\frac{{{{\left| {u(x) u(y)} \right|}^p}}}{{{{\left| {x y} \right|}^{N + sp}}}}dxdy\right)(-\Delta)_p^su V(x){u^{p 1}} = {u^{p_s^* 1}}+f(u), \\ u>0, \ \mbox{in}\ {\mathbb{R}^N}, \end{...

In this work we consider the fractional Kirchhoff equations with singular nonlinearity, $$\displaylines{ M\Big( \int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}dx dy\Big) (-\Delta)^s_p u = \lambda a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad \text{in }\Omega,\cr \int_{\mathbb{R}^{2N}}\frac{|v(x)-v(y)|^p}{|x-y|^{N+sp}}dx v \mu b(x)|v|^{q-2}v +\fra...