*Correspondence: [email protected] 2School of Information & Statistics, Guangxi University of Financial and Economics, Nanning, Guangxi 530003, China Full list of author information is available at the end of the article Abstract In this paper, we establish some generalizations and refinements of the Hölder inequality on time scales via the diamond-α dynamic integral, which is defined as a li...

In this paper, we research some properties of Codazzi pairs on almost para Norden manifolds. Let $(M_{2n},\ \varphi ,\ g,G)$ be an manifold. Firstly, $g$-conjugate connection, $G$-conjugate connection and $\varphi $-conjugate a linear $\mathrm{\nabla }$ $M_{2n}$ denoted by ${\mathrm{\nabla }}^{*\
 },\ {\mathrm{\nabla }}^{\dagger \ }}^{\varphi are defined it is demonstrated that the spaces ...

In this paper, we study Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ introduced by Zhang \cite{Zh} in the complex space forms $N(4c)(c=0\ or \ 1)$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$ is trace-free second fundamental form. We obtain some Simons' type integral inequalities rigidity theorems for such submanifolds. Moreover $\mathbb{C}^n$ $\nabla^*\nabla^*T=0$ introduce a...

In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla u)) = f $. Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.

The experimental electron density rho(r) of the two isomorphic salts KMnO(4) and KClO(4) was determined by a multipole analysis of accurate X-ray diffraction data at 120 K. The quantum theory of atoms in molecules was applied to rho(r) and to its Laplacian nabla(2)rho(r). The bonds were characterized using the topological parameters at the bond critical points of the density rho(r), nabla(2)rho...

Little is known about the influence of substrate-bound gradients on neuronal development, since it has been difficult to fabricate gradients over the distances typically required for biological studies (a few hundred micrometers). This article demonstrates a generally applicable technique for the fabrication of substrate-bound gradients of proteins with complex shapes, using laminar flows in mi...

Abstract We propose a new finite difference scheme for the degenerate parabolic equation $$\begin{aligned} \partial _t u - \text{ div }(|\nabla u|^{p-2}\nabla u) =f, \quad p\ge 2. \end{aligned}$$ ? t u - ...

We aim to find the complements of Bennett-Leindler type inequalities in nabla time scale calculus by changing exponent from $0<\zeta< 1$ $\zeta>1.$ Different literature, directions new inequalities, where $\zeta>1,$ are same as that previous obtained for 1$. By these settings, we not only complement existing but also generalize them involving more exponents. The dual...

<p style='text-indent:20px;'>In this paper, we study the following three species predator-prey model with prey-taxis:</p><p style='text-indent:20px;'><disp-formula> <label>*</label> <tex-math id="E1"> \begin{document}$ \left\{ \begin{array}{lll} u_t = d_1\Delta u+\chi_1\nabla\cdot(u\nabla v)+r_1u(1-u-kv-b_1w), &\quad x\in \Omega, t>0, \\ ...

This paper addresses the problems of stability a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on proposed generalized definition integral, some related definitions calculus are given. Then, several useful inequalities in sense fractional-order difference extended to cases. Meanwhile, basis and Lyapunov direct method, sufficient conditions guaranteeing asymptotic orig...