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We prove the Noether-Lefschetz conjecture on the moduli space of quasi-polarized K3 surfaces. This is deduced as a particular case of a general theorem that states that low degree cohomology classes o...
Abstract. In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P + aH = b in a locally symmetric Lorentz space Ln+11 . Furthermore, we study complete or compact lin...
We use the famous Benci-Rabinowitz’s Saddle Point Theorem ([3])with Cerami-Palais-Smale condition to study the existence of new periodic solutions with a fixed period for second order Hamiltonian syst...
Abstract: A {\it krausz $(k,m)$-partition} of a graph $G$ is the partition of $G$ into cliques, such that any vertex belongs to at most $k$ cliques and any two cliques have at most $m$ vertices in com...
Abstract: In this paper we formulate some generalizations of Agoh's conjecture. We provide a proof of one of them. We also formulate conjectures involving congruence modulo primes about hyperbolic sec...
It is a folklore fact that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion m...
It is well-known that point-set topology (without additional structure) lacks the capacity to generalize the analytic concepts of completeness, boundedness, and other typically-metric properties. The...
Nekrasov-Okounkov identity gives a product representation of the sum over partitions of a certain function of partition hook length. In this paper we give several generalizations of the Nekrasov-Okoun...
We consider the following generalization of the seminal Erdős-Ko-Rado theorem, due to Frankl [6]. For some k ≥ 2, let F be a k-wise intersecting family of r-subsets of an n element set X, i.e. fo...
We use geometric methods to study two natural two-component generalizations of the periodic Camassa–Holm and Degasperis–Procesi equations.
The Lax pair formulation of the two-component Camassa-Holm equation (CH2) is generalized to produce an integrable multi-component family, CH(n,k), of equations with n components and 1  jkj  n veloci...
Classification of finite groups is a central problem in theory of groups.Even though finite abelian groups have been completely classified, a lot still remains to be done as far as non-abelian groups ...
We consider two-component integrable generalizations of the dispersionless 2DTL hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hi...
We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical $C$- and $S$-integrable Partial Differential E...

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