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In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

In this paper we give a generalization of a result of Wei.

The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…

Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.

We describe an algorithm for the computation of generalized (or weighted) Ehrhart series based on Stanley decompositions as implemented in the offspring NmzIntegrate of Normaliz. The algorithmic approach includes elementary proofs of the…

We discuss a generalization of Kummer construction which, on the base of an integral representation of a finite group and local resolution of its quotient, produces a higher dimensional variety with trivial canonical class. As an…

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

In this paper we give a generalization of injective and projective complexes.

We present a survey on recent developments of generalizations of Forelli's analyticity theorem and related pluripotential methods.

The aim of this paper is to extend the coisotropic embedding theorem obtained by M. J. Gotay for pre-symplectic manifolds to more general geometric settings: cosymplectic, contact, cocontact, $k$-symplectic, $k$-cosymplectic, $k$-contact,…

In the paper, we generalize some congruences of Lehmer for general composite numbers.

In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).

We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…

In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…

We prove several results on the additivity of Kodaira dimension under smooth morphisms of smooth projective varieties.

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…

I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.

The paper contains an interesting generalization of the classical Taylor expansion formula and four applications