Solvability of some non-local problems for the loaded pseudoparabolic equation

On the Local Solvability of Darboux’s Equation

We reduce the question of local nonsolvability of the Darboux equation, and hence of the isometric embedding problem for surfaces, to the local nonsolvability of a simple linear equation whose type is explicitly determined by the Gaussian curvature. Let (M, g) be a two-dimensional Riemannian manifold. A well-known problem is to ask, when can one realize this locally as a small piece of a surfac...

On solvability of some boundary value problems for a fractional analogue of the Helmholtz equation

In this paper we study some boundary value problems for fractional analogue of Helmholtz equation in a rectangular and in a half-band. Theorems about existence and uniqueness of a solution of the considered problems are proved by spectral method.

Continuous Dependence for the Pseudoparabolic Equation

The extended equivalence and equation solvability problems for groups

The algorithmic aspects of the equivalence problem and the equation solvability problem have received increasing attention in the past two decades. The equivalence problem for a finite algebra A asks whether or not two (term or polynomial) expressions s and t are equivalent over A (denoted by A |= s ≈ t), i.e. if s and t determine the same function over A. The equation solvability is one of the...

ساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings

فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...