# Djavvat KhadjievNational University of Uzbekistan · Institute of Mathematics

Djavvat Khadjiev

Doctor of Philosophy

## About

37

Publications

1,495

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

216

Citations

Citations since 2017

Introduction

**Skills and Expertise**

## Publications

Publications (37)

Let E_{3} be the 3-dimensional Euclidean space and S be a set such that it has at least two elements. A definition of an S-parametric figure in E_{3} and a definition of a motion of an S-parametric figure in E_{3} are given. Complete systems of G-invariants of a parametric figure in E_{3} for fundamental groups of transformations of E_{3} have obta...

\(E^{2}_{1}\) be the 2-dimensional pseudo-Euclidean space of index 1, \(G=Sim_{L}(E^{2}_{1})\) be the group of all linear pseudo-similarities of \(E^{2}_{1}\) and \(G=Sim_{L}^{+}(E^{2}_{1})\) be the group of all orientation-preserving linear pseudo-similarities of \(E^{2}_{1}\). In this paper, groups \(Sim_{GL}^{+}(E^{2}_{1})\) and \(Sim_{GL}(E^{2}...

An approach to the equivalence problem of vector valued maps is offered which, in particular, covers the equivalence problem of paths and patches of differential geometry with respect to different motion groups. In the last case, in contrary to differential geometry case, it does not need and does not use smoothness of paths and patches to get the...

In this paper, global differential G-invariants of paths in the two-dimensional Euclidean space E2 for the similarity group G=Sim(E2) and the orientation-preserving similarity group G=Sim+(E2) are investigated. A general form of a path in terms of its global G-invariants is obtained. For given two paths ξ(t) and η(t) with the common differential G-...

In this paper, for the orthogonal group G = O (2) and special orthogonal group G = O⁺ (2) global G -invariants of plane paths and plane curves in two-dimensional Euclidean space E2 are studied. Using complex numbers, a method to detect G -equivalences of plane paths in terms of the global G -invariants of a plane path is presented. General evident...

Let (Formula presented.) be the (Formula presented.)-dimensional Euclidean space, (Formula presented.) be the group of all linear similarities of (Formula presented.) and (Formula presented.) be the group of all orientation-preserving linear similarities of (Formula presented.). The present paper is devoted to solutions of problems of global (Formu...

Let E12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E^{2}_{1}}$$\end{document} be the real 2-dimensional pseudo-Euclidean space of index 1, O(1; 1) be the group of...

In the present paper, definitions of an n-ary semicopula on a bounded lattice L, a boolean OR-distributive n-ary semicopula on L and an infinite boolean OR-distributive n-ary semicopula on L are introduced. A relation between the set of all bounded lattices L with a boolean OR-distributive n-ary semicopula on L and the set of all bounded lattices L...

Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complex Banach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator and denoted by Rλ is defined for points of the spectrum, some equivalent conditions for compactness of the quasi-resolven...

We present some relations between an external direct product and an internal direct product of a family of integral -distributive binary aggregation functions. Relations between a direct decomposition of the unit and a family of pairwise comaximal elements in a lattice with an integral -distributive binary aggregation function are investigated. Usi...

Let D be the infinitesimal generator of a strongly continuous periodic one-parameter group of linear operators in a Banach space. Main results: An analog of the resolvent operator (= quasi-resolvent operator of D) is defined for points of the spectrum of D and its evident form is given. The theorem on integral for the operator D, theorems on the ex...

Main results: For every equicontinuous almost periodic linear representation of a group in a complete locally convex space L with the countability property, there exists the unique invariant averaging; it is continuous and is expressed by using the L-valued invariant mean of Bochner and von-Neumann. An analog of Wiener's approximation theorem for a...

Let M(n, p) be the group of all motions of an n-dimensional pseudo-Euclidean space of index p. It is proved that the complete system of M(n,p)-invariant differential rational functions of a path (curve) is a generating system of the differential field of all M(n, p) -invariant differential rational functions of a path (curve), respectively. A funda...

For a lattice with a ∨-distributive t-norm, one useful inequality is obtained. Theorems on relations between a family of pairwise comaximal elements and a direct decomposition of the unit in a lattice with a ∨-distributive t-norm have given. Using these results, the description of all ∨-distributive triangular norms of length 3 and all lattices of...

Let M(n,p) be the group of all transformations of an n-dimensional pseudo-Euclidean space E p n of index p generated by all pseudo-orthogonal transformations and parallel translations of E p n . Definitions of a pseudo-Euclidean type of a curve, an invariant parametrization of a curve and an M(n,p)-equivalence of curves are introduced. All possible...

Let M(n,p) be the group of all transformations of an n-dimensional pseudo-Euclidean space Epn of index p generated by all pseudo-orthogonal transformations and parallel translations of Epn. Definitions of a pseudo-Euclidean type of a null curve, an invariant parametrization of a null curve and an M(n,p)-equivalence of curves are introduced. All pos...

Let be the n-dimensional pseudo-Euclidean space of index p and M(n, p) the group of all transformations of generated by pseudo-orthogonal transformations and parallel translations. We describe the system of generators of the differential field of all M(n, p)-invariant differential rational functions of a map of an open subset . Using this result, w...

The system of generators of the differential field of all G-invariant differential rational functions of a vector field in the n-dimensional Euclidean space ℝ n is described for groups G=M(n) and G=SM(n), where M(n) is the group of all isometries of ℝ n and SM(n) is the group of all Euclidean motions of ℝ n . Using these results, vector field analo...

An approach to a definition of an integral, which differs from definitions of Lebesgue and Henstock–Kurzweil integrals, is considered. We use trigonometrical polynomials instead of simple functions. Let V be the space of all complex trigonometrical polynomials without the free term. The definition of a continuous integral on the space V is introduc...

A definition of an invariant averaging for a linear representation of a group in a locally convex space is given. Main results: A group $H$ is finite if and only if every linear representation of $H$ in a locally convex space has an invariant averaging. A group $H$ is amenable if and only if every almost periodic representation of $H$ in a quasi-co...

A relation between the direct decomposability of an infinitely ∨-distributive t-norm on a complete lattice L and direct decompositions of the neutral element 1 of L is obtained. Some useful applications of this relation are given. In particularly, the description of all T1-lattices without infinitely ∨-distributive t-norms on complete lattices and...

Let $GL(n,R)$ be the general linear group of $n \times n$ real matrices. Definitions of $GL(n,R)$-equivalence and the centro-affine type of curves are introduced. All possible centro-affine types are founded. For every centro affine type all invariant parametrizations of a curve are described. The problem of $GL(n,R)$-equivalence of curves is reduc...

For the equi-affine group ε(n) of transformations of Rn, definitions of an ε(n)-equivalence of curves and an equi-affine type of a curve are introduced. The ε(n)-equivalence of curves is reduced to the problem of the ε(n)-equivalence of paths. A generating system of the differential ring of ε(n)-invariant differential polynomial functions of curves...

Our main results:
1.
The description of all ∨-distributive triangular norms of lengths 2 and 3
2.
Theorem 3.7 which establishes a connection between direct decompositions of infinite ∨- distributive triangular norms on a lattice L and direct decompositions of the biggest element of L.
3.
Theorem 4.3 which establishes a connection between direct dec...

In this paper we have obtained the following results for a differential ring (associative or nonassociative): (1) For a differential ring (D-ring) we introduce definitions of a D-prime D-ideal, D-semiprime D-ideal and a strongly D-nilpotent element. We define the D-prime radical as the intersection of all D-prime D-ideals. For any D-ring the D-prim...

Our main results are the following:
1. Let L be a complete ordered groupoid ([1], ch. XIV). We introduce definitions of r -radical and R -radical elements in L and describe some their properties.
2. Let L be a complete ordered groupoid in which every element is ideal. Denote by L
r
the lattice of all r-radical elements in L. Then L
r
satisfies the...

Let T be the group {e it ∣0≤t<2π}. We consider T with its euclidean topology. Our main results are as follows: 1) Theorem 1 which establishes a connection between spectrums of a continuous linear representation of T in a reflexive Banach space and its conjugate linear representation; 2) Theorem 11 which gives a description of all left (right) simpl...