Let \(G=(V(G),E(G))\) be a simple graph. A set \(S \subseteq V(G)\) is strong edge geodetic if there exists an assignment of exactly one shortest path between each pair vertices from S, such that these paths cover all the edges E(G). The cardinality smallest number \(\mathrm{sg_e}(G)\) G. In this paper, problem studied on Cartesian product two paths. exact value computed for \(P_n \,\square \,P...

In this work, byemploying the Leggett-Williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-Laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

Continued fractions have been widely studied in the field of p p -adic numbers alttext="double-struck upper Q Subscript p"> <mml:mr...

The paper studies the interpolation properties of anisotropic net spaces $N_{\bar{p},\bar{q}}(M)$, where $\bar{p}=(p_1, p_2)$, $\bar{q}=(q_1, q_2)$. It is shown that following equality holds with respect to multidimensional method $$ (N_{\bar{p}_0,\bar{q}_0}(M), N_{\bar{p}_1,\bar{q}_1}(M))_{\bar{\theta},\bar{q}}=N_{\bar{p},\bar{q}}(M),\;\;\; \frac{1}{\bar{p}}=\frac{1-\bar{\theta}}{\bar{p}_0}+\f...

In recent paper Fakkousy et al. show that the 3D Hénon-Heiles system with Hamiltonian $$ H = \frac{1}{2} (p_1 ^2 + p_2 p_3 ^2) +\frac{1}{2} (A q_1 C q_2 B q_3 (\alpha \gamma ^2)q_3 \frac{\beta }{3}q_3 ^3 is integrable in sense of Liouville when $$\alpha , \frac{\alpha }{\beta } 1, A C$$ ; or \frac{1}{6}, B-arbitrary; \frac{1}{16}, C, \frac{A}{B} \frac{1}{16}$$ (and course, =\gamma =0$$ which ca...

The space of all probability measures having positive density function on a connected compact smooth manifold $M$, denoted by $\mathcal{P}(M)$, carries the Fisher information metric $G$. We define geometric mean aid which we investigate geometry equipped with show that geodesic segment joining arbitrary $\mu_1$ and $\mu_2$ is expressed using normalized its endpoints. As an application, any two ...

We develop a new approach to construct finite element methods solve the Poisson equation. The idea is use pointwise Laplacian as degree of freedom followed by interpolating solution at given right-hand side function in partial differential then Galerkin projection smaller vector space. This similar that boundary condition standard method. Our results system equations and better number. number u...

The remarkable recent progress in the precision of Lattice QCD computations for a number physical quantities relevant flavour physics has motivated introduction isospin-breaking effects, including particular electromagnetic corrections, to computations. isospin breaking corrections are necessary fully exploit this improved determination fundamental parameters Standard Model, CKM matrix elements...

The paper studies the exact solution of two kinds generalized Fokker-Planck equations in which integral kernels are given either by distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or Prabhakar $k_{2}(\alpha, \gamma; \lambda; t) e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; d\mu$, where is denoted as $e^{-\gamma}_{\alpha, t)$. Both these can be called fading memory fun...