Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann studied. For under consideration, existence uniqueness theorems proved. Necessary sufficient conditions solvability all obtained an integral representations solutions given terms corresponding Green’s functions.

AbstractWe have classified symmetric solutions around the origin to four dimensional degenerate Painleve type equation NYA4 with generic values of parameters. We obtained sixteen meromorphic solutions, which are transformed each other by Backlund transformation. calculated linear monodromy for one them, explicitly.

We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of 11-dimensional supergravity. The metric, four-form, and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four-form field equation to ensur...

We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good representations of equations by using the representations of their surrounding words. We used equation embeddings to analyze four collections of scientific ...

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...