A conjectural formula for genus one Gromov-Witten invariants of some local Calabi-Yau n-folds

We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one Bogomol'nyi-Prasad-Sommerfield(BPS) numbers of local Calabi-Yau 5-folds defined by Klemm and Pandharipande.     

Nilpotency of <Emphasis Type=Italic>n</Emphasis>-tuple Lie algebras and associative <Emphasis Type=Italic>n</Emphasis>-tuple algebras

We obtain conditions for the nilpotency of finite-dimensional n-tuple Lie algebras and finite-dimensional associative n-tuple algebras. The established conditions are analogous to theorems of Engel and Wedderburn for Lie algebras and associative algebras.     

About the computation of the signature of surface singularities <Emphasis Type=Italic>z</Emphasis><Superscript><Emphasis Type=Italic>N</Emphasis></Superscript> + <Emphasis Type=Italic>g</Emphasis>(<Emphasis Type=Italic>x,y</Emphasis>) = 0

In this article we describe our experiences with a parallel Singular implementation of the signature of a surface singularity defined by z ^N + g(x; y) = 0.     

On Nilpotent Orbits of SL<Subscript><Emphasis Type=Italic>n</Emphasis></Subscript> and Sp<Subscript>2<Emphasis Type=Italic>n</Emphasis></Subscript> over a Local Non-Archimedean Field

We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the classical groups SL _n and Sp_2n over local non-Archimedean fields with a parametrization, introduced by DeBacker in 2002, which uses the associated Bruhat-Tits building to relate the question to one over the residue field.     

Three-webs <Emphasis Type=Italic>W</Emphasis>(1, <Emphasis Type=Italic>n</Emphasis>, 1) and associated systems of ordinary differential equations

We consider a three-web on a smooth manifold formed by two n-parameter families of curves and a one-parameter family of hypersurfaces. For such webs, we define a family of adapted frames, find the systemof structure equations, and study the differential-geometric objects that arise in differential neighborhoods up to the third order. We prove that each system of ordinary differential equations (SODE) uniquely defines a three-web. This allows us to describe properties of a SODE in terms of the corresponding three-web. In particular, we characterize autonomous SODE.     

Boundary value problem for an <Emphasis Type=Italic>n</Emphasis>th-order operator equation

We consider a boundary value problem and prove that it has a solution.     

Characterizations of some rings with <Emphasis Type=Italic>C</Emphasis>-projective, <Emphasis Type=Italic>C</Emphasis>-(FP)-injective and <Emphasis Type=Italic>C</Emphasis>-flat modules

Let R be a commutative ring and C a semidualizing R-module. We investigate the relations between C-flat modules and C-FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.     

About <Emphasis Type=Italic>I</Emphasis>(<Emphasis Type=Italic>J</Emphasis>)-approximately continuous functions

A generalization of density point with respect to category and I(J)-density topology has been presented in [5]. This papers deals with some basic properties of the corresponding I(J)-approximately continuous functions and gives answer when these functions are of the first Baire class and when they are Darboux functions.     

Radicals of <Emphasis Type=Italic>l</Emphasis>-rings and one-sided <Emphasis Type=Italic>l</Emphasis>-ideals

We consider the plane deformation of an infinite body with a cylindrical inclusion whose mechanical and thermophysical characteristics differ from those of the material of the body for a heat flow and tensile forces given far from the inclusion. Stress intensity factors in the vicinity of a crack located on the continuation of the diameter of the inclusion are determined by the solution of a singular integral equation using the method of mechanical quadratures. We investigate the ratio of the length of the crack to the distance between it and the inclusion at which the regular kernel of the integral equation can be neglected in calculations. In this case, analytic formulas for the determination of the stress intensity factors are obtained.     

<Emphasis Type=Italic>N</Emphasis>-homogeneous <Emphasis Type=Italic>C</Emphasis>*-algebras generated by idempotents

In this paper we consider n-homogeneous C*-algebras generated by idempotents. We prove that a finitely generated unital n-homogeneous (when n is greater than or equals 2) C*-algebra A can be generated by a finite set of idempotents if and only if the algebra A contains at least one nontrivial idempotent.     

Integral representation and embedding theorems for <Emphasis Type=Italic>n</Emphasis>-dimensional multianisotropic spaces with one anisotropic vertex

We prove embedding theorems for the multianisotropic Sobolev spaces generated by the completely regular Newton polyhedron. Under study is the case of the polyhedron with one anisotropic vertex. We obtain a special integral representation of functions in terms of the tuple of multi-indices of the Newton polyhedron.     

Estimates for <Emphasis Type=Italic>n</Emphasis>-widths of two-weighted summation operators on trees

In this paper, we obtain order estimates for the Kolmogorov, Gelfand and linear widths of some discrete function classes on trees, which are generated by a two-weighted summation operator.     

Integrability of invariant geodesic flows on <Emphasis Type=Italic>n</Emphasis>-symmetric spaces

In this article, by modifying the argument shift method, we prove Liouville integrability of geodesic flows of normal metrics (invariant Einstein metrics) on the Ledger–Obata n-symmetric spaces K ⁿ /diag(K), where K is a semisimple (respectively, simple) compact Lie group.