357 results
Search Results
2. Corrections and complements to my paper 'On a class of operator monotone functions of several variables'
- Author
-
A. R. Mirotin
- Subjects
Discrete mathematics ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,021107 urban & regional planning ,02 engineering and technology ,Finite-rank operator ,Compact operator ,Strongly monotone ,Shift operator ,01 natural sciences ,Semi-elliptic operator ,Algebra ,Pseudo-monotone operator ,Monotone polygon ,Multiplication operator ,0101 mathematics ,Mathematics - Published
- 2017
3. On the Characterizations of Wave Front Sets in Terms of the Short-Time Fourier Transform
- Author
-
Stevan Pilipović and Bojan Prangoski
- Subjects
Wavefront ,General Mathematics ,010102 general mathematics ,Short paper ,Mathematical analysis ,Short-time Fourier transform ,02 engineering and technology ,01 natural sciences ,Sobolev space ,symbols.namesake ,020303 mechanical engineering & transports ,Fourier transform ,0203 mechanical engineering ,symbols ,0101 mathematics ,Mathematics - Abstract
© 2019, Pleiades Publishing, Ltd. It is well known that the classical and Sobolev wave fronts were extended to nonequivalent global versions by the use of the short-time Fourier transform. In this very short paper, we give complete characterizations of the former wave front sets in terms of the short-time Fourier transform.
- Published
- 2019
4. Multipliers in spaces of Bessel potentials: The case of indices of nonnegative smoothness.
- Author
-
Belyaev, A. and Shkalikov, A.
- Subjects
MULTIPLIERS (Mathematical analysis) ,MATHEMATICS ,ELLIPTIC operators ,TOPOLOGY ,PHYSICAL distribution of goods - Abstract
The aim of the paper is to study spaces of multipliers acting from the Bessel potential space H (ℝ) to the other Bessel potential space H (ℝ). We obtain conditions ensuring the equivalence of uniform and standard multiplier norms on the space of multipliers In the case , the space M[ H (ℝ) → H (ℝ) can be described explicitly. Namely, we prove in this paper that the latter space coincides with the space H (ℝ) of uniformly localized Bessel potentials introduced by Strichartz. It is also proved that if both smoothness indices s and t are nonnegative, then such a description is possible only for the given values of the indices. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
5. Inequalities for Rational Functions with Prescribed Poles.
- Author
-
Rather, N. A., Iqbal, A., and Dar, Ishfaq
- Subjects
- *
POLISH people , *POLYNOMIALS , *GENERALIZATION , *MATHEMATICS - Abstract
For rational functions , where is a polynomial of degree at the most and , with we use simple but elegant techniques to strengthen generalizations of certain results which extend some widely known polynomial inequalities of Erdős-Lax and Turán to rational functions . In return these reinforced results, in the limiting case, lead to the corresponding refinements of the said polynomial inequalities. As an illustration and as an application of our results, we obtain some new improvements of the Erdős-Lax and Turán type inequalities for polynomials. These improved results take into account the size of the constant term and the leading coefficient of the given polynomial. As a further factor of consideration, during the course of this paper we will demonstrate how some recently obtained results could have been proved without invoking the results of Dubinin [Distortion theorems for polynomials on the circle, Sb. Math. 191(12) (2000) 1797–1807]. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
6. On the existence of phase transition for the 1D p-adic countable state Potts model.
- Author
-
Mukhamedov, F.
- Subjects
POTTS model ,LATTICE models (Statistical physics) ,PRIME numbers ,INTEGERS ,MATHEMATICS - Abstract
In the present paper we establish the existence of a phase transition for one-dimensional the countable state p-adic Potts model. To establish such results, we investigate an infinite dimensional nonlinear p-adic operator associated with the model. It turns out that the finding condition does not depend on values of the prime p, and therefore, an analogous fact is not true when the number of spins is finite. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
7. The Groups <italic>G</italic>2<italic>n</italic> with Additional Structures.
- Author
-
Kim, Seongjeong
- Subjects
GROUP theory ,ABSTRACT algebra ,FINITE groups ,INTEGERS ,COMPOSITE numbers ,MATHEMATICS - Abstract
In the paper [1], V. O. Manturov introduced the groups
G k depending on two natural parametersn n >k and naturally related to topology and to the theory of dynamical systems. The groupG 2 , which is the simplest part ofn G k , is isomorphic to the group of pure free braids on n strands. In the present paper, we study the groupsn G 2 supplied with additional structures-parity and points; these groups are denoted byn G 2 andn ,p G 2 . First,we define the groupsn ,d G 2 andn ,p G 2 , then study the relationship between the groupsn ,d G 2 ,n G 2 , andn ,p G 2 . Finally, we give an example of a braid onn ,d n + 1 strands, which is not the trivial braid onn + 1 strands, by using a braid on n strands with parity. After that, the author discusses links inS ×g S 1 that can determine diagrams with points; these points correspond to the factor S1 in the productS ×g S 1 . [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
8. Stability Property of Functional Equations in Modular Spaces: A Fixed-Point Approach.
- Author
-
Saha, P., Mondal, Pratap, and Choudhury, B. S.
- Subjects
FUNCTIONAL equations ,MATHEMATICS - Abstract
We investigate the Hyers–Ulam–Rassias stability property of a quadratic functional equation. The analysis is done in the context of modular spaces. The type of stability considered here is very general in character which has been considered in various domains of mathematics. The speciality of the functional equation considered here is that it has a geometrical background behind its introduction. We approach the problem by applying a fixed point method for which a version of the contraction mapping principle in modular spaces is utilized. Also the results in this paper are established without using some familiar conditions on modular spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
9. Coupled fixed-point results for T-contractions on cone metric spaces with applications.
- Author
-
Rahimi, H., Vetro, P., and Rad, G.
- Subjects
METRIC spaces ,SET theory ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., 'Remarks on 'Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings',' Math. Comput. Modelling 54, 1467-1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
10. Basis property of eigen- and associated functions of an operator with nondense domain of definition in the example of the Orr-Sommerfeld problem.
- Author
-
Shiryaev, E.
- Subjects
DIFFERENTIAL operators ,INTEGRO-differential equations ,HYDRODYNAMICS ,NAVIER-Stokes equations ,MATHEMATICS - Abstract
In the paper, we propose a method for proving the unconditional basis property of eigen- and associated functions of an integro-differential operator defined on a nondense domain of definition. In particular, we obtain a new simpler proof of the unconditional basis property of eigenand associated functions of the spectral Orr-Sommerfeld problem, well-known in hydromechanics, which reduces to the eigenvalue problem for the operator under study. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
11. Submathematics and Tropical Mathematics.
- Author
-
Maslov, V. P.
- Subjects
MATHEMATICS ,NONLINEAR differential equations - Abstract
The notions of "tropical mathematics" and "subtropical mathematics" are studied. The main principles of tropical analysis and examples of their application to various problems are considered. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
12. Converses of Jessen's inequality on time scales.
- Author
-
Barić, J., Bohner, M., Jakšić, R., and Pečarić, J.
- Subjects
GENERALIZATION ,MEAN value theorems ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
In this paper, some converses of Jessen's inequality, in terms of the time scale calculus, are proved. The obtained results are used to derive new converse inequalities for generalized means, power means and Hölder's inequality. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
13. On the maximal operators of Fejér means with respect to the character system of the group of 2-adic integers in hardy spaces.
- Author
-
Gát, G. and Nagy, K.
- Subjects
HARDY spaces ,INTEGERS ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fejér (or ( C, 1)) means of Fourier series of integrable functions with respect the character system of the group of 2-adic integers. This question was answered by Gá t in 1997. The aim of this paper is to investigate the maximal operator of the sup |σ|. Among other things, we prove that this operator is bounded from the Hardy space H to the Lebesgue space L if and only if 1/2 < p < ∞. The two-dimensional maximal operator is also discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
14. Unitary automorphisms of the space of Hankel matrices: II. the case of even order.
- Author
-
Ikramov, Kh.
- Subjects
HANKEL functions ,HANKEL operators ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
Earlier, for odd n, the author described unitary n × n matrices U with the following property: if H is a Hankel matrix, then U* HU is a Hankel matrix as well. In the present paper, it is shown that this description also holds for even n starting from n = 4. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
15. Regularized trace of the Dirac operator.
- Author
-
Shcherbakov, A.
- Subjects
DIRAC operators ,QUANTUM operators ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
Formulas for the regularized trace of the one-dimensional non-self-adjoint Dirac operator with L-potential are obtained. The cases of periodic and antiperiodic boundary conditions as well as of the Dirichlet boundary conditions are considered. The formulas are obtained by using the method of similar operators on the basis of results from the papers [1] and [2]. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
16. Finite groups with large irreducible character.
- Author
-
Kazarin, L. and Poiseeva, S.
- Subjects
FINITE groups ,IRREDUCIBLE polynomials ,ORTHOGONAL functions ,ABELIAN groups ,MATHEMATICS - Abstract
In the general case, the order of a finite nonidentity group G is substantially larger than the squared degree of every irreducible character Θ of G, i.e., Θ(1)< G. In the present paper, we study finite groups with an irreducible character Θ such that . [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
17. On the mean value of the measure of irrationality of real numbers.
- Author
-
Shatskov, D.
- Subjects
MEAN value theorems ,REAL numbers ,INTEGERS ,DELUSIONS ,MATHEMATICS - Abstract
This paper deals with the asymptotic behavior of the integral (here the minimum is taken over integers q and ∥·∥ denotes the distance to the nearest integer). [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
18. Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces.
- Author
-
Avsyankin, O. G.
- Subjects
MATHEMATICAL convolutions ,MATHEMATICAL analysis ,MATHEMATICAL functions ,INTEGRAL operators ,MATHEMATICS - Abstract
Sufficient conditions for the compactness in generalized Morrey spaces of the composition of a convolution operator and the operator of multiplication by an essentially bounded function are obtained. Very weak conditions on the function are also obtained under which the commutator of the operator of multiplication by such a function and a convolution operator is compact. The compactness of convolution operators in domains of cone type is investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
19. On Classes of Subcompact Spaces
- Author
-
Alexander V. Osipov, E. G. Pytkeev, and V. I. Belugin
- Subjects
Condensed Matter::Quantum Gases ,Combinatorics ,Compact space ,High Energy Physics::Lattice ,General Mathematics ,Cardinal number ,Hausdorff space ,Space (mathematics) ,Mathematics - Abstract
This paper continues the study of P. S. Alexandroff’s problem: When can a Hausdorff space $$X$$ be one-to-one continuously mapped onto a compact Hausdorff space? For a cardinal number $$\tau$$ , the classes of $$a_\tau$$ -spaces and strict $$a_\tau$$ -spaces are defined. A compact space $$X$$ is called an $$a_\tau$$ -space if, for any $$C\in[X]^{\le\tau}$$ , there exists a one-to-one continuous mapping of $$X\setminus C$$ onto a compact space. A compact space $$X$$ is called a strict $$a_\tau$$ -space if, for any $$C\in[X]^{\le\tau}$$ , there exits a one-to-one continuous mapping of $$X\setminus C$$ onto a compact space $$Y$$ , and this mapping can be continuously extended to the whole space $$X$$ . In this paper, we study properties of the classes of $$a_\tau$$ - and strict $$a_\tau$$ -spaces by using Raukhvarger’s method of special continuous paritions.
- Published
- 2021
20. Estimates of Derivatives in Sobolev Spaces in Terms of Hypergeometric Functions
- Author
-
T. A. Garmanova
- Subjects
Sobolev space ,Combinatorics ,General Mathematics ,Order (ring theory) ,Interval (graph theory) ,Hypergeometric function ,Legendre polynomials ,Mathematics - Abstract
The paper deals with sharp estimates of derivatives of intermediate order $$k\le n-1$$ in the Sobolev space $$\mathring W^n_2[0;1]$$ , $$n\in\mathbb N$$ . The functions $$A_{n,k}(x)$$ under study are the smallest possible quantities in inequalities of the form $$|y^{(k)}(x)|\le A_{n,k}(x)\|y^{(n)}\|_{L_2[0;1]}.$$ The properties of the primitives of shifted Legendre polynomials on the interval $$[0;1]$$ are used to obtain an explicit description of these functions in terms of hypergeometric functions. In the paper, a new relation connecting the derivatives and primitives of Legendre polynomials is also proved.
- Published
- 2021
21. On Recovering the Sturm–Liouville Differential Operators on Time Scales
- Author
-
Maria Kuznetsova
- Subjects
Mathematics - Spectral Theory ,Pure mathematics ,General Mathematics ,FOS: Mathematics ,Sturm–Liouville theory ,Boundary value problem ,Mathematics::Spectral Theory ,Differential operator ,Spectral Theory (math.SP) ,34A55, 34B24, 34N05 ,Eigenvalues and eigenvectors ,Mathematics - Abstract
We study Sturm–Liouville differential operators on the time scales consisting of finitely many isolated points and closed intervals. In the author’s previous paper, it was established that such operators are uniquely determined by the spectral characteristics of all classical types. In the present paper, an algorithm for their recovery based on the method of spectral mappings is obtained. We also prove that the eigenvalues of two Sturm–Liouville boundary-value problems on time scales with one common boundary condition alternate.
- Published
- 2021
22. Collectives of Automata in Finitely Generated Groups
- Author
-
Il'ya Anatol'evich Ivanov-Pogodaev, D. V. Gusev, and A. Ya. Kanel-Belov
- Subjects
Discrete mathematics ,Computational complexity theory ,Cayley graph ,Group (mathematics) ,General Mathematics ,Automata theory ,Context (language use) ,Finitely generated group ,Algebraic number ,Element (category theory) ,Mathematics - Abstract
The present paper is devoted to traversing a maze by a collective of automata. This part of automata theory gave rise to a fairly wide range of diverse problems ([1], [2]), including those related to problems of the theory of computational complexity and probability theory. It turns out that the consideration of complicated algebraic objects, such as Burnside groups, can be interesting in this context. In the paper, we show that the Cayley graph a finitely generated group cannot be traversed by a collective of automata if and only if the group is infinite and its every element is periodic.
- Published
- 2020
23. Modern thermodynamics as a branch of mathematics (mathematical physics).
- Author
-
Maslov, V.
- Subjects
THERMODYNAMICS ,MATHEMATICAL physics ,MATHEMATICS ,MATHEMATICAL proofs ,ANALYTIC number theory ,NUMBER theory ,METASTABLE states ,EQUILIBRIUM - Abstract
A parallel between physical derivation and mathematical proof in classical thermodynamics is drawn. A relationship between thermodynamics and analytic number theory is demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
24. Lattice of Definability in the Order of Rational Numbers
- Author
-
Alexei Semenov and An. A. Muchnik
- Subjects
Rational number ,Pure mathematics ,Automorphism group ,020303 mechanical engineering & transports ,0203 mechanical engineering ,General Mathematics ,Lattice (order) ,010102 general mathematics ,02 engineering and technology ,0101 mathematics ,01 natural sciences ,Linear subspace ,Mathematics - Abstract
A lattice of definability subspaces in the order of rational numbers is described. It is proved that this lattice consists of five subspaces defined in the paper that are generated by the following relations: “equality,” “less,” “between,” “cycle,” and “linkage.” For each of the subspaces, its width (the minimum number of arguments of a generating relation) is found and a convenient description of the automorphism group is given. Although the structure of this lattice was known previously, the proof in the paper is of syntactic nature and avoids the use of a group-theoretical method.
- Published
- 2020
25. 2-Colorings of Hypergraphs with Large Girth
- Author
-
Yu. A. Demidovich
- Subjects
Hypergraph ,Degree (graph theory) ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Girth (graph theory) ,01 natural sciences ,Upper and lower bounds ,Combinatorics ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Has property ,Homogeneous ,Simple (abstract algebra) ,0101 mathematics ,Mathematics - Abstract
A hypergraph $$H=(V,E)$$ has property $$B_k$$ if there exists a 2-coloring of the set $$V$$ such that each edge contains at least $$k$$ vertices of each color. We let $$m_{k,g}(n)$$ and $$m_{k,b}(n)$$ , respectively, denote the least number of edges of an $$n$$ -homogeneous hypergraph without property $$B_k$$ which contains either no cycles of length at least $$g$$ or no two edges intersecting in more than $$b$$ vertices. In the paper, upper bounds for these quantities are given. As a consequence, we obtain results for $$m^{*}_k(n)$$ , i.e., for the least number of edges of an $$n$$ -homogeneous simple hypergraph without property $$B_k$$ . Let $$\Delta(H)$$ be the maximal degree of vertices of a hypergraph $$H$$ . By $$\Delta_k(n,g)$$ we denote the minimal degree $$\Delta$$ such that there exists an $$n$$ -homogeneous hypergraph $$H$$ with maximal degree $$\Delta$$ and girth at least $$g$$ but without property $$B_k$$ . In the paper, an upper bound for $$\Delta_k(n,g)$$ is obtained.
- Published
- 2020
26. Local Mappings Generated by Multiplication on Rings of Matrices
- Author
-
N. M. Umrzaqov and F. N. Arzikulov
- Subjects
Pure mathematics ,Rational number ,Mathematics::Commutative Algebra ,General Mathematics ,Unital ,Mathematics::Rings and Algebras ,010102 general mathematics ,02 engineering and technology ,01 natural sciences ,Matrix ring ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Division ring ,Symmetric matrix ,Multiplier (economics) ,0101 mathematics ,Associative property ,Mathematics - Abstract
In the present paper, the notion of (additive) local multiplier on the ring of matrices over an arbitrary unital associative ring is introduced and investigated. It is proved that every local left multiplier on the matrix ring over a division ring is a left multiplier. Also, in the present paper, the notion of (additive) local Jordan multiplier on a Jordan ring of symmetric matrices is introduced and investigated. It is proved that every local Jordan multiplier on the Jordan ring of symmetric matrices over the field of rational numbers is a Jordan multiplier. Also corollaries of these results are proved.
- Published
- 2020
27. Residual Nilpotence of Groups with One Defining Relation
- Author
-
D. I. Moldavanskii
- Subjects
Group (mathematics) ,General Mathematics ,010102 general mathematics ,Prime number ,02 engineering and technology ,Residual ,01 natural sciences ,Prime (order theory) ,Combinatorics ,Mathematics::Group Theory ,Nilpotent ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Simple (abstract algebra) ,Order (group theory) ,0101 mathematics ,Mathematics - Abstract
All groups in the family of Baumslag-Solitar groups (i.e., groups of the form G(m,n) = 〈a, b; a−1bma = bn〉, where m and n are nonzero integers) for which the residual nilpotence condition holds if and only if the residual p-finiteness condition holds for some prime number p are described. It has turned out, in particular, that the group G(pr, −pr), where p is an odd prime and r ≥ 1, is residually nilpotent, but it is residually q-finite for no prime q. Thus, an answer to the existence problem for noncyclic one-relator groups possessing such a property (formulated by McCarron in his 1996 paper) is obtained. A simple proof of the statement that an arbitrary residually nilpotent noncyclic one-relator group which has elements of finite order is residual p-finite for some prime p, which was announced in the same paper of McCarron, is also given.
- Published
- 2020
28. Uniqueness of the Continuation of a Certain Function to a Positive Definite Function
- Author
-
A. D. Manov
- Subjects
Class (set theory) ,Continuous function (set theory) ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Function (mathematics) ,Positive-definite matrix ,Extension (predicate logic) ,01 natural sciences ,Combinatorics ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Positive-definite function ,Interval (graph theory) ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In 1940, M. G. Krein obtained necessary and sufficient conditions for the extension of a continuous function f defined in an interval (-a, a), a > 0, to a positive definite function on the whole number axis R. In addition, Krein showed that the function 1 - |x|, |x| < a, can be extended to a positive definite one on R if and only if 0 < a ≤ 2, and this function has a unique extension only in the case a = 2. The present paper deals with the problem of uniqueness of the extension of the function 1 - |x|, |x| ≤ a, a G (0,1), for a class of positive definite functions on R whose support is contained in the closed interval [-1,1] (the class T). It is proved that if a ∈ [1/2,1] and Re ϕ(x) = 1 - |x|, |x| ≤ a, for some ϕ ∈ T, then ϕ(x) = (1 - |x|) +, x G R. In addition, for any a G (0,1/2), there exists a function ϕ ∈ T such that ϕ(x) = 1 - |x|, |x| ≤ a, but ϕ(x) ≠ (1 - |x|)+. Also the paper deals with extremal problems for positive definite functions and nonnegative trigonometric polynomials indirectly related to the extension problem under consideration.
- Published
- 2020
29. New Theta-Function Identities of Level 6 in the Spirit of Ramanujan
- Author
-
K. R. Rajanna, B. R. Srivatsa Kumar, and R. Narendra
- Subjects
Combinatorics ,symbols.namesake ,General Mathematics ,symbols ,Partition (number theory) ,Theta function ,Mathematics ,Ramanujan's sum - Abstract
Michael Somos discovered several theta-function identities of various levels by computer and offered no proof for them. These identities highly resemble some of Ramanujan’s identities. The main focus of this paper is to prove some of these theta-function identities, in particular those of level 6 that have been discovered using computational searches. Some of the the Somos identities that we are discussing in this paper cannot be expressed in the form of P −−Q type. Furthermore, we establish certain colored partition identities for them.
- Published
- 2019
30. On Threshold Probability for the Stability of Independent Sets in Distance Graphs
- Author
-
M. M. Pyaderkin
- Subjects
General Mathematics ,010102 general mathematics ,Discrete geometry ,02 engineering and technology ,Coding theory ,01 natural sciences ,Graph ,Combinatorics ,020303 mechanical engineering & transports ,Threshold probability ,0203 mechanical engineering ,Exponential stability ,Independent set ,Stability theory ,0101 mathematics ,Mathematics ,Independence number - Abstract
This paper considers the so-called distance graph G(n, r, s);its vertices can be identified with the r-element subsets of the set {1, 2,…,n}, and two vertices are joined by an edge if the size of the intersection of the corresponding subsets equals s. Note that, in the case s = 0, such graphs are known as Kneser graphs. These graphs are closely related to the Erdős-Ko-Rado problem; they also play an important role in combinatorial geometry and coding theory. We study properties of random subgraphs of the graph G(n, r, s) in the Erdős-Renyi model, in which each edge is included in the subgraph with a certain fixed probability p independently of the other edges. It is known that if r > 2s + 1, then, for p = 1/2, the size of an independent set is asymptotically stable in the sense that the independence number of a random subgraph is asymptotically equal to that of the initial graph G(n, r, s). This gives rise to the question of how small p must be for asymptotic stability to cease. The main result of this paper is the answer to this question.
- Published
- 2019
31. Conditions for the Lp, λ-Boundedness of the Riesz Potential Generated by the Gegenbauer Differential Operator
- Author
-
V. S. Guliev and É. Dzh. Ibragimov
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Riesz potential ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,02 engineering and technology ,Type (model theory) ,Differential operator ,01 natural sciences ,020303 mechanical engineering & transports ,0203 mechanical engineering ,0101 mathematics ,Mathematics - Abstract
The results obtained in this paper refine and supplement a Hardy-Littlewood-Sobolev type theorem on the boundedness of the Riesz potential generated by the Gegenbauer differential operator on the spaces Lp, λ proved in an earlier paper of the second author.
- Published
- 2019
32. Multipliers of Absolute Convergence
- Author
-
V. Sh. Tsagareishvili and G. Tutberidze
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Function (mathematics) ,Absolute convergence ,01 natural sciences ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Convergence (routing) ,0101 mathematics ,Trigonometric fourier series ,Fourier series ,Convergent series ,Mathematics - Abstract
The paper deals with sequences of positive numbers (dn) such that, multiplying the Fourier coefficients (Cn(f)) of functions from given function classes by these numbers, one obtains a convergent series of the form \(\sum {{\rm{|}}{C_n}(f){{\rm{|}}^p}{d_n}, 1 \le p < 2} \). It is established that the resulting conditions cannot be strengthened in a certain sense. The results of the paper imply, in particular, some well-known results for trigonometric Fourier series.
- Published
- 2019
33. On the Complexity of the Differential-Algebraic Description of Analytic Complexity Classes
- Author
-
Valerii Konstantinovich Beloshapka
- Subjects
Pure mathematics ,Trace (linear algebra) ,Differential equation ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Function (mathematics) ,01 natural sciences ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Simple (abstract algebra) ,Complexity class ,Order (group theory) ,0101 mathematics ,Algebraic number ,Differential (mathematics) ,Mathematics - Abstract
The objective of this paper is to trace the increase in the complexity of the description of classes of analytic complexity (introduced by the author in previous works) under the passage from the class Cl1 to the class Cl2. To this end, two subclasses, Cl 1 + and Cl 1 ++ , of Cl2 that are not contained in Cl1 are described from the point of view of the complexity of the differential equations determining these subclasses. It turns out that Cl 1 + has fairly simple defining relations, namely, two differential polynomials of differential order 5 and algebraic degree 6 (Theorem 1), while a criterion for a function to belong to Cl 1 ++ obtained in the paper consists of one relation of order 6 and five relations of order 7, which have degree 435 (Theorem 2). The “complexity drop” phenomenon is discussed; in particular, those functions in the class Cl 1 + which are contained in Cl1 are explicitly described (Theorem 3).
- Published
- 2019
34. Finite Groups without Elements of Order Six
- Author
-
N. A. Minigulov and A. S. Kondrat'ev
- Subjects
Pure mathematics ,Finite group ,Property (philosophy) ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,Structure (category theory) ,Order (group theory) ,0102 computer and information sciences ,Classification of finite simple groups ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In 1977, in three papers by Podufalov, by Gordon, and by Fletcher, Stellmacher, and Stewart, finite simple groups without elements of order 6 were determined independently. In the present paper, using this result, we obtain a sufficiently complete description of the structure of a general finite group with this property.
- Published
- 2018
35. Simple Asymptotics for a Generalized Wave Equation with Degenerating Velocity and Their Applications in the Linear Long Wave Run-Up Problem
- Author
-
A. Yu. Anikin, Vladimir E. Nazaikinskii, and S. Yu. Dobrokhotov
- Subjects
General Mathematics ,Operator (physics) ,010102 general mathematics ,Mathematical analysis ,Degenerate energy levels ,Boundary (topology) ,02 engineering and technology ,Wave equation ,01 natural sciences ,Domain (mathematical analysis) ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Initial value problem ,Vector field ,0101 mathematics ,Invariant (mathematics) ,Mathematics - Abstract
Asymptotic solutions of the wave equation degenerating on the boundary of the domain (where the wave propagation velocity vanishes as the square root of the distance from the boundary) can be represented with the use of a modified canonical operator on a Lagrangian submanifold, invariant with respect to theHamiltonian vector field, of the nonstandard phase space constructed by the authors in earlier papers. The present paper provides simple expressions in a neighborhood of the boundary for functions represented by such a canonical operator and, in particular, for the solution of the Cauchy problem for the degenerate wave equation with initial data localized in a neighborhood of an interior point of the domain.
- Published
- 2018
36. The green function of the discrete finite-gap one-energy two-dimensional Schrödinger operator on the quad graph.
- Author
-
Vasilevskii, B.
- Subjects
SCHRODINGER equation ,GREEN'S functions ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
The finite-gap approach to constructing the discrete Schrödinger operator on a quad graph expressed as a two-dimensional integer sublattice in d-dimensional space is used. The Green function for this operator is explicitly expressed as an integral over special contours of the differential constructed from spectral data. The resulting function has a well-known asymptotics. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
37. Completely decomposable quotient divisible abelian groups with UA-rings of endomorphisms.
- Author
-
Lyubimtsev, O.
- Subjects
ABELIAN groups ,ENDOMORPHISMS ,ALGEBRA ,POLYNOMIALS ,MATHEMATICS - Abstract
A ring K is called a unique addition ring (a UA-ring) if there exists a unique binary operation + on the multiplicative semigroup ( K, · ) of K such that ( K, ·, +) is a ring. We say that an abelian group is an End-UA-group if its endomorphism ring is a UA-ring. We find End-UA-groups in the class of completely decomposable quotient divisible abelian groups. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
38. On effective σ-boundedness and σ-compactness in Solovay's model.
- Author
-
Kanovei, V. and Lyubetsky, V.
- Subjects
FUNCTIONS of bounded variation ,COMPACT spaces (Topology) ,ZENO'S paradoxes ,INTEGERS ,MATHEMATICS - Abstract
Two dichotomy theorems on the effective σ-boundedness and effective σ-compactness of ordinal definable point sets in Solovay's model are proved. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
39. Conformally Flat Algebraic Ricci Solitons on Lie Groups
- Author
-
P. N. Klepikov
- Subjects
Pure mathematics ,General Mathematics ,Operator (physics) ,010102 general mathematics ,Dimension (graph theory) ,Diagonalizable matrix ,Lie group ,Type (model theory) ,01 natural sciences ,Ricci soliton ,030507 speech-language pathology & audiology ,03 medical and health sciences ,Mathematics::Differential Geometry ,0101 mathematics ,Algebraic number ,0305 other medical science ,Eigenvalues and eigenvectors ,Mathematics - Abstract
The paper is devoted to the study of conformally flat Lie groups with left-invariant (pseudo) Riemannianmetric of an algebraic Ricci soliton. Previously conformally flat algebraic Ricci solitons on Lie groups have been studied in the case of small dimension and under an additional diagonalizability condition on the Ricci operator. The present paper continues these studies without the additional requirement that the Ricci operator be diagonalizable. It is proved that any nontrivial conformally flat algebraic Ricci soliton on a Lie group must be steady and have Ricci operator of Segre type {(1... 1 2)} with a unique eigenvalue (equal to 0).
- Published
- 2018
40. Statistical Transition of Bose Gas to Fermi Gas
- Author
-
Victor Pavlovich Maslov
- Subjects
Condensed Matter::Quantum Gases ,Polylogarithm ,Bose gas ,Distribution (number theory) ,General Mathematics ,010102 general mathematics ,01 natural sciences ,symbols.namesake ,Quantum mechanics ,0103 physical sciences ,symbols ,Jump ,Fermi–Dirac statistics ,010307 mathematical physics ,0101 mathematics ,Fermi gas ,Mathematics ,Sign (mathematics) ,Fermi Gamma-ray Space Telescope - Abstract
It is well known that the formula for the Fermi distribution is obtained from the formula for the Bose distribution if the argument of the polylogarithm, the activity a, the energy, and the number of particles change sign. The paper deals with the behavior of the Bose–Einstein distribution as a → 0; in particular, the neighborhood of the point a = 0 is studied in great detail, and the expansion of both the Bose distribution and the Fermi distribution in powers of the parameter a is used. During the transition from the Bose distribution to the Fermi distribution, the principal term of the distribution for the specific energy undergoes a jump as a → 0. In this paper,we find the value of the parameter a, close to zero, but not equal to zero, for which the Bose distribution (in the statistical sense) becomes zero. This allows us to find the point a, distinct from zero, at which a jump of the specific energy occurs. Using the value of the number of particles on the caustic, we can obtain the jump of the total energy of the Bose system to the Fermi system. Near the value a = 0, the author uses Gentile statistics, whichmakes it possible to study the transition fromthe Bose statistics to the the Fermi statistics in great detail. Here an important role is played by the self-consistent equation obtained by the author earlier.
- Published
- 2018
41. Distance-Regular Shilla Graphs with b2 = c2
- Author
-
M. S. Nirova and A. A. Makhnev
- Subjects
Vertex (graph theory) ,Combinatorics ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,Antipodal point ,0102 computer and information sciences ,0101 mathematics ,01 natural sciences ,Graph ,Mathematics - Abstract
A Shilla graph is defined as a distance-regular graph of diameter 3 with second eigen-value θ1 equal to a3. For a Shilla graph, let us put a = a3 and b = k/a. It is proved in this paper that a Shilla graph with b2 = c2 and noninteger eigenvalues has the following intersection array: $$\left\{ {\frac{{{b^2}\left( {b - 1} \right)}}{2},\frac{{\left( {b - 1} \right)\left( {{b^2} - b + 2} \right)}}{2},\frac{{b\left( {b - 1} \right)}}{4};1,\frac{{b\left( {b - 1} \right)}}{4},\frac{{b{{\left( {b - 1} \right)}^2}}}{2}} \right\}$$ If Γ is a Q-polynomial Shilla graph with b2 = c2 and b = 2r, then the graph Γ has intersection array $$\left\{ {2tr\left( {2r + 1} \right),\left( {2r + 1} \right)\left( {2rt + t + 1} \right),r\left( {r + t} \right);1,r\left( {r + t} \right),t\left( {4{r^2} - 1} \right)} \right\}$$ and, for any vertex u in Γ, the subgraph Γ3(u) is an antipodal distance-regular graph with intersection array $$\left\{ {t\left( {2r + 1} \right),\left( {2r - 1} \right)\left( {t + 1} \right),1;1,t + 1,t\left( {2r + 1} \right)} \right\}$$ The Shilla graphs with b2 = c2 and b = 4 are also classified in the paper.
- Published
- 2018
42. The Groups G2 n with Additional Structures
- Author
-
Seongjeong Kim
- Subjects
Combinatorics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,Braid ,010307 mathematical physics ,0101 mathematics ,Parity (mathematics) ,01 natural sciences ,Mathematics - Abstract
In the paper [1], V. O. Manturov introduced the groups G k n depending on two natural parameters n > k and naturally related to topology and to the theory of dynamical systems. The group G2 n , which is the simplest part of G k n , is isomorphic to the group of pure free braids on n strands. In the present paper, we study the groups G2 n supplied with additional structures–parity and points; these groups are denoted by G2n,p and G2n,d. First,we define the groups G2n,p and G2n,d, then study the relationship between the groups G2 n , G2n,p, and G2n,d. Finally, we give an example of a braid on n + 1 strands, which is not the trivial braid on n + 1 strands, by using a braid on n strands with parity. After that, the author discusses links in S g × S1 that can determine diagrams with points; these points correspond to the factor S1 in the product S g × S1.
- Published
- 2018
43. Multipliers in spaces of Bessel potentials: The case of indices of nonnegative smoothness
- Author
-
A. A. Shkalikov and A. A. Belyaev
- Subjects
General Mathematics ,010102 general mathematics ,Bessel potential ,02 engineering and technology ,01 natural sciences ,Combinatorics ,symbols.namesake ,020303 mechanical engineering & transports ,0203 mechanical engineering ,symbols ,Multiplier (economics) ,0101 mathematics ,Bessel function ,Mathematics - Abstract
The aim of the paper is to study spaces of multipliers acting from the Bessel potential space H (ℝ n ) to the other Bessel potential space H (ℝ n ). We obtain conditions ensuring the equivalence of uniform and standard multiplier norms on the space of multipliers $$M\left[ {H_p^s({\mathbb{R}^n}) \to H_q^t({\mathbb{R}^n})} \right]fors,t \in \mathbb{R},p,q > 1.$$ In the case $$p,q > 1,p \leqslant q,s > \frac{n}{p},t \geqslant 0,s - \frac{n}{p} \geqslant t - \frac{n}{q}$$ , the space M[H (ℝ n ) → H (ℝ n ) can be described explicitly. Namely, we prove in this paper that the latter space coincides with the space H , unif (ℝ n ) of uniformly localized Bessel potentials introduced by Strichartz. It is also proved that if both smoothness indices s and t are nonnegative, then such a description is possible only for the given values of the indices.
- Published
- 2017
44. On optimal harvesting of a resource on a circle
- Author
-
S. V. Skopincev, L. V. Lokutsievskiy, and Mikhail Il'ich Zelikin
- Subjects
0106 biological sciences ,Class (computer programming) ,Mathematical optimization ,Profit (real property) ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Control (management) ,Function (mathematics) ,01 natural sciences ,010601 ecology ,Maximum principle ,Resource (project management) ,Fraction (mathematics) ,Quality (business) ,0101 mathematics ,Mathematics ,media_common - Abstract
This paper studies the optimality in the problem of cyclic harvesting of a resource distributed on a circle with a certain prescribed density. The velocity ofmotion of the collecting device and the fraction of the resource harvested at a given time play the role of control. The problem is to choose a control maximizing a given quality functional. The paper presents the maximum principle for this (infinite-dimensional) problem. The maximum principle can be written as two inequalities which can be conveniently verified. The class of problems with a concave profit function is solved completely. At the end of the paper, several examples are considered to illustrate the developed technique.
- Published
- 2017
45. Uniform asymptotics of the boundary values of the solution in a linear problem on the run-up of waves on a shallow beach
- Author
-
Vladimir E. Nazaikinskii, S. Yu. Dobrokhotov, and A. A. Tolchennikov
- Subjects
General Mathematics ,010102 general mathematics ,Mathematical analysis ,02 engineering and technology ,Mixed boundary condition ,01 natural sciences ,Robin boundary condition ,Elliptic boundary value problem ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Neumann boundary condition ,Free boundary problem ,Cauchy boundary condition ,Boundary value problem ,0101 mathematics ,Trace operator ,Mathematics - Abstract
We consider the Cauchy problem with spatially localized initial data for a two-dimensional wave equation with variable velocity in a domain Ω. The velocity is assumed to degenerate on the boundary ∂Ω of the domain as the square root of the distance to ∂Ω. In particular, this problems describes the run-up of tsunami waves on a shallow beach in the linear approximation. Further, the problem contains a natural small parameter (the typical source-to-basin size ratio) and hence admits analysis by asymptotic methods. It was shown in the paper “Characteristics with singularities and the boundary values of the asymptotic solution of the Cauchy problem for a degenerate wave equation” [1] that the boundary values of the asymptotic solution of this problem given by a modified Maslov canonical operator on the Lagrangian manifold formed by the nonstandard characteristics associatedwith the problemcan be expressed via the canonical operator on a Lagrangian submanifold of the cotangent bundle of the boundary. However, the problem as to how this restriction is related to the boundary values of the exact solution of the problem remained open. In the present paper, we show that if the initial perturbation is specified by a function rapidly decaying at infinity, then the restriction of such an asymptotic solution to the boundary gives the asymptotics of the boundary values of the exact solution in the uniform norm. To this end, we in particular prove a trace theorem for nonstandard Sobolev type spaces with degeneration at the boundary.
- Published
- 2017
46. Mixed generalized modulus of smoothness and approximation by the 'angle' of trigonometric polynomials
- Author
-
N. V. Omel’chenko and Konstantin Vsevolodovich Runovskii
- Subjects
General Mathematics ,010102 general mathematics ,Mathematical analysis ,Inverse ,Modulus ,02 engineering and technology ,01 natural sciences ,Moduli ,Periodic function ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Rate of convergence ,Lattice (order) ,0101 mathematics ,Trigonometry ,Fourier series ,Mathematics - Abstract
The notion of general mixed modulus of smoothness of periodic functions of several variables in the spaces Lp is introduced. The proposed construction is, on the one hand, a natural generalization of the general modulus of smoothness in the one-dimensional case, which was introduced in a paper of the first author and in which the coefficients of the values of a given function at the nodes of a uniform lattice are the Fourier coefficients of a 2π-periodic function called the generator of the modulus; while, on the other hand, this construction is a generalization of classical mixed moduli of smoothness and of mixed moduli of arbitrary positive order. For the modulus introduced in the paper, in the case 1 ≤ p ≤ +∞, the direct and inverse theorems on the approximation by the “angle” of trigonometric polynomials are proved. The previous estimates of such type are obtained as direct consequences of general results, new mixed moduli are constructed, and a universal structural description of classes of functions whose best approximation by “angle” have a certain order of convergence to zero is given.
- Published
- 2016
47. Metrically and topologically projective ideals of Banach algebras
- Author
-
N. T. Nemesh
- Subjects
Discrete mathematics ,Pure mathematics ,General Mathematics ,010102 general mathematics ,01 natural sciences ,Identity (mathematics) ,Banach algebra ,Bounded function ,0103 physical sciences ,Metric (mathematics) ,Ideal (order theory) ,010307 mathematical physics ,0101 mathematics ,Projective test ,Commutative property ,Approximate identity ,Mathematics - Abstract
In the present paper, necessary conditions for the metric and topological projectivity of closed ideals of Banach algebras are given. In the case of commutative Banach algebras, a criterion for the metric and topological projectivity of ideals admitting a bounded approximate identity is obtained. The main result of the paper is as follows: a closed ideal of an arbitrary C*-algebra is metrically or topologically projective if and only if it admits a self-adjoint right identity.
- Published
- 2016
48. Coupled fixed-point results for T-contractions on cone metric spaces with applications
- Author
-
Pasquale Vetro, G. Soleimani Rad, Hamidreza Rahimi, Rahimi, H., Vetro, P., and Rad, G.
- Subjects
coupled fixed point ,Pure mathematics ,cone metric space ,General Mathematics ,Injective metric space ,Mathematical analysis ,Periodic point ,Fixed point ,Nonlinear integral equation ,Convex metric space ,T-contraction ,Metric space ,Cone (topology) ,Settore MAT/05 - Analisi Matematica ,subsequentially convergent ,sequentially convergent ,Mathematics - Abstract
The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., “Remarks on “Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings”,” Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.
- Published
- 2015
49. Essential signatures and canonical bases of irreducible representations of the group G 2
- Author
-
A. A. Gornitskii
- Subjects
Combinatorics ,Group (mathematics) ,Simple (abstract algebra) ,General Mathematics ,Irreducible representation ,Lie algebra ,Structure (category theory) ,Fundamental representation ,Basis (universal algebra) ,(g,K)-module ,Mathematics - Abstract
We consider representations of simple Lie algebras and the problem of constructing a “canonical” weight basis in an arbitrary irreducible finite-dimensional highest-weight module. Vinberg suggested a method for constructing such bases by applying the lowering operators corresponding to all negative roots to the highest-weight vector and put forward a number of conjectures on the parametrization and structure of such bases. It follows from papers by Feigin, Fourier, and Littelmann that these conjectures are true for the cases of A n and C n . In the present paper, we prove these conjectures for the case of G 2 by using a different approach suggested by Vinberg.
- Published
- 2015
50. Erratum to: Sharp Constant in Jackson’s Inequality with Modulus of Smoothness for Uniform Approximations of Periodic Functions
- Author
-
S. A. Pichugov
- Subjects
Periodic function ,Modulus of smoothness ,Approximations of π ,General Mathematics ,Mathematical analysis ,Vinogradov ,Jackson's inequality ,Trigonometric polynomial ,Constant (mathematics) ,Polygonal line ,Mathematics - Abstract
My paper contains an error. Namely, inequality (9) does not hold. For example, for k = 2, I do not know whether the error in the argument can be corrected and whether the main result of the paper is valid. I wish to express gratitude to O. L. Vinogradov for pointing out the error.
- Published
- 2018
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.