274 results
Search Results
2. Bounds on F-index of tricyclic graphs with fixed pendant vertices
- Author
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Sana Akram, Muhammad Javaid, and Muhammad Jamal
- Subjects
chemistry.chemical_classification ,Index (economics) ,010304 chemical physics ,extremal graphs ,tricyclic graphs ,General Mathematics ,01 natural sciences ,f-index ,Combinatorics ,03 medical and health sciences ,0302 clinical medicine ,chemistry ,030220 oncology & carcinogenesis ,0103 physical sciences ,QA1-939 ,05c12 ,05c35 ,05c50 ,Mathematics ,Geometry and topology ,Tricyclic - Abstract
The F-index F(G) of a graph G is obtained by the sum of cubes of the degrees of all the vertices in G. It is defined in the same paper of 1972 where the first and second Zagreb indices are introduced to study the structure-dependency of total π-electron energy. Recently, Furtula and Gutman [J. Math. Chem. 53 (2015), no. 4, 1184–1190] reinvestigated F-index and proved its various properties. A connected graph with order n and size m, such that m = n + 2, is called a tricyclic graph. In this paper, we characterize the extremal graphs and prove the ordering among the different subfamilies of graphs with respect to F-index in $\begin{array}{} \displaystyle {\it\Omega}^{\alpha}_n \end{array}$, where $\begin{array}{} \displaystyle {\it\Omega}^{\alpha}_n \end{array}$ is a complete class of tricyclic graphs with three, four, six and seven cycles, such that each graph has α ≥ 1 pendant vertices and n ≥ 16 + α order. Mainly, we prove the bounds (lower and upper) of F(G), i.e $$\begin{array}{} \displaystyle 8n+12\alpha +76\leq F(G)\leq 8(n-1)-7\alpha + (\alpha+6)^3 ~\mbox{for each}~ G\in {\it\Omega}^{\alpha}_n. \end{array}$$
- Published
- 2020
3. A new characterization of a proper type B semigroup
- Author
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Zhi Pei, Chunhua Li, and Baogen Xu
- Subjects
type b semigroup ,Pure mathematics ,20m10 ,Mathematics::Operator Algebras ,Semigroup ,Computer Science::Information Retrieval ,General Mathematics ,010102 general mathematics ,e-unitary ,proper ,0102 computer and information sciences ,Characterization (mathematics) ,Type (model theory) ,01 natural sciences ,06f05 ,010201 computation theory & mathematics ,q-semigroup ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
In this paper, we develop the elementary theory of inverse semigroups to the cases of type B semigroups. The main aim of this paper is to study proper type B semigroups. We introduce first the concept of a left admissible triple. After obtaining some basic properties of left admissible triple, we give the definition of a Q-semigroup and get a structure theorem of Q-semigroup. In particular, we introduce the notion of an admissible triple and give some characterization of proper type B semigroups. It is proved that an arbitrary Q-semigroup with an admissible triple is an E-unitary type B semigroup.
- Published
- 2020
4. Determinants of two kinds of matrices whose elements involve sine functions
- Author
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Michał Różański
- Subjects
11c20 ,15a06 ,Pure mathematics ,40a05 ,lcsh:Mathematics ,General Mathematics ,fourier series ,010102 general mathematics ,determinant ,lcsh:QA1-939 ,01 natural sciences ,sine matrix ,010101 applied mathematics ,Alternating series ,alternating series ,Sine ,0101 mathematics ,42a05 ,Fourier series ,Mathematics - Abstract
The presented paper is strictly connected, among others, with the paper On the sum of some alternating series, Comp. Math. Appl. (2011), written by Wituła and Słota. A problem concerning the form of determinants formulated in the cited paper is solved here. Next, the obtained result is adapted to solve some system of linear equations and the description of the sum of alternating series.
- Published
- 2019
5. Stabilizers in EQ-algebras
- Author
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Wei Wang, Xiao Yun Cheng, Mei Wang, and Jun Tao Wang
- Subjects
0209 industrial biotechnology ,Pure mathematics ,(fuzzy) prefilter ,lcsh:Mathematics ,General Mathematics ,08a72 ,02 engineering and technology ,lcsh:QA1-939 ,eq-algebra ,020901 industrial engineering & automation ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,(fuzzy) stabilizer ,fuzzy congruence relation ,03e72 ,Mathematics - Abstract
The main goal of this paper is to introduce the notion of stabilizers in EQ-algebras and develop stabilizer theory in EQ-algebras. In the paper, we introduce (fuzzy) left and right stabilizers and investigate some related properties of them. Then, we discuss the relations among (fuzzy) stabilizers, (fuzzy) prefilters (filters) and (fuzzy) co-annihilators. Also, we obtain that the set of all prefilters in a good EQ-algebra forms a relative pseudo-complemented lattice, where Str(F, G) is the relative pseudo-complemented of F with respect to G. These results will provide a solid algebraic foundation for the consequence connectives in higher fuzzy logic.
- Published
- 2019
6. Dynamics of two-species delayed competitive stage-structured model described by differential-difference equations
- Author
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Guoxin Liu, Sufang Han, Yaqin Li, Lianglin Xiong, and Tianwei Zhang
- Subjects
lcsh:Mathematics ,General Mathematics ,010102 general mathematics ,Dynamics (mechanics) ,almost periodic solution ,Differential difference equations ,34k20 ,stability ,92b05 ,92d25 ,lcsh:QA1-939 ,stage structure ,01 natural sciences ,coincidence degree ,010101 applied mathematics ,34k13 ,competitive model ,Applied mathematics ,Stage (hydrology) ,0101 mathematics ,Structured model ,Mathematics - Abstract
Overf the last few years, by utilizing Mawhin’s continuation theorem of coincidence degree theory and Lyapunov functional, many scholars have been concerned with the global asymptotical stability of positive periodic solutions for the non-linear ecosystems. In the real world, almost periodicity is usually more realistic and more general than periodicity, but there are scarcely any papers concerning the issue of the global asymptotical stability of positive almost periodic solutions of non-linear ecosystems. In this paper we consider a kind of delayed two-species competitive model with stage structure. By means of Mawhin’s continuation theorem of coincidence degree theory, some sufficient conditions are obtained for the existence of at least one positive almost periodic solutions for the above model with nonnegative coefficients. Furthermore, the global asymptotical stability of positive almost periodic solution of the model is also studied. The work of this paper extends and improves some results in recent years. An example and simulations are employed to illustrate the main results of this paper.
- Published
- 2019
7. Augmented, free and tensor generalized digroups
- Author
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Raúl Velásquez, José Gregorio Rodríguez-Nieto, and Olga Salazar-Diaz
- Subjects
20n99 ,Pure mathematics ,Semidirect product ,20e06 ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,digroups ,group actions ,Group action ,free and tensor groups ,Tensor (intrinsic definition) ,QA1-939 ,20a05 ,20e34 ,semidirect product ,0101 mathematics ,20b10 ,Mathematics ,20a10 - Abstract
The concept of generalized digroup was proposed by Salazar-Díaz, Velásquez and Wills-Toro in their paper “Generalized digroups” as a non trivial extension of groups. In this way, many concepts and results given in the category of groups can be extended in a natural form to the category of generalized digroups. The aim of this paper is to present the construction of the free generalized digroup and study its properties. Although this construction is vastly different from the one given for the case of groups, we will use this concept, the classical construction for groups and the semidirect product to construct the tensor generalized digroup as well as the semidirect product of generalized digroups. Additionally, we give a new structural result for generalized digroups using compatible actions of groups and an equivariant map from a group set to the group corresponding to notions of associative dialgebras and augmented racks.
- Published
- 2019
8. Computational uncertainty quantification for random non-autonomous second order linear differential equations via adapted gPC: a comparative case study with random Fröbenius method and Monte Carlo simulation
- Author
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Juan Carlos Cortés, Marc Jornet, and Julia Calatayud
- Subjects
Non-autonomous and random dynamical systems ,Adaptive generalized Polynomial Chaos ,General Mathematics ,Comparative case ,Monte Carlo method ,random Fröbenius method ,Random Frobenius method ,010103 numerical & computational mathematics ,01 natural sciences ,93e03 ,non-autonomous and random dynamical systems ,computational uncertainty quantification ,Stochastic Galerkin projection technique ,Linear differential equation ,34f05 ,QA1-939 ,Applied mathematics ,Order (group theory) ,60h35 ,0101 mathematics ,Uncertainty quantification ,Mathematics ,Final version ,Computational uncertainty quantification ,random fröbenius method ,93E03 ,adaptive generalized Polynomial Chaos ,stochastic Galerkin projection technique ,010101 applied mathematics ,Frobenius method ,34F05 ,60H35 ,MATEMATICA APLICADA - Abstract
[EN] This paper presents a methodology to quantify computationally the uncertainty in a class of differential equations often met in Mathematical Physics, namely random non-autonomous second-order linear differential equations, via adaptive generalized Polynomial Chaos (gPC) and the stochastic Galerkin projection technique. Unlike the random Frobenius method, which can only deal with particular random linear differential equations and needs the random inputs (coefficients and forcing term) to be analytic, adaptive gPC allows approximating the expectation and covariance of the solution stochastic process to general random second-order linear differential equations. The random inputs are allowed to functionally depend on random variables that may be independent or dependent, both absolutely continuous or discrete with infinitely many point masses. These hypotheses include a wide variety of particular differential equations, which might not be solvable via the random Frobenius method, in which the random input coefficients may be expressed via a Karhunen-Loeve expansion., This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. The authors are grateful for the valuable comments raised by the reviewer, which have improved the final version of the paper.
- Published
- 2018
9. A stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises under uncertain environment
- Author
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Baizhou Li and Shi Yin
- Subjects
low carbon technology sharing ,021103 operations research ,General Mathematics ,05 social sciences ,0211 other engineering and technologies ,91a23 ,chemistry.chemical_element ,02 engineering and technology ,Innovation system ,92d25 ,chemistry ,90b50 ,superior and inferior enterprises ,uncertain environment ,0502 economics and business ,Differential game ,QA1-939 ,stochastic differential game ,collaborative innovation ,Carbon ,Mathematics ,050203 business & management ,Industrial organization - Abstract
Considering the fact that the development of low carbon economy calls for the low carbon technology sharing between interested enterprises, this paper study a stochastic differential game of low carbon technology sharing in collaborative innovation system of superior enterprises and inferior enterprises. In the paper, we consider the random interference factors that include the uncertain external environment and the internal understanding limitations of decision maker. In the model, superior enterprises and inferior enterprises are separated entities, and they play Stacklberg master-slave game, Nash non-cooperative game, and cooperative game, respectively. We discuss the feedback equilibrium strategies of superior enterprises and inferior enterprises, and it is found that some random interference factors in sharing system can make the variance of improvement degree of low carbon technology level in the cooperation game higher than the variance in the Stackelberg game, and the result of Stackelberg game is similar to the result of Nash game. Additionally, a government subsidy incentive and a special subsidy that inferior enterprises give to superior enterprises are proposed.
- Published
- 2018
10. Binomials transformation formulae for scaled Fibonacci numbers
- Author
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Edyta Hetmaniok, Roman Wituła, and Bożena Piątek
- Subjects
δ-lucas numbers ,Fibonacci number ,General Mathematics ,llb83 ,010102 general mathematics ,binomial transformation ,0102 computer and information sciences ,Pisano period ,llb39 ,01 natural sciences ,Combinatorics ,Transformation (function) ,010201 computation theory & mathematics ,Fibonacci polynomials ,QA1-939 ,0101 mathematics ,δ-fibonacci numbers ,Mathematics - Abstract
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
- Published
- 2017
11. A convergence analysis of SOR iterative methods for linear systems with weak H-matrices
- Author
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Zichen Xue, Shuanghua Luo, and Cheng-yi Zhang
- Subjects
diagonally equipotent matrices ,15a18 ,Iterative method ,General Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,010103 numerical & computational mathematics ,01 natural sciences ,weak h-matrices ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Convergence (routing) ,diagonally dominant matrices ,QA1-939 ,Applied mathematics ,0101 mathematics ,Geometry and topology ,Mathematics ,15a06 ,convergence ,Computer Science::Information Retrieval ,010102 general mathematics ,Linear system ,15a42 ,Relaxation (iterative method) ,nonstricly diagonally dominant matrices ,sor iterative methods - Abstract
It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative methods are convergent for linear systems with weak H-matrices. Furthermore, some numerical examples are given to demonstrate the convergence results obtained in this paper.
- Published
- 2016
12. Inequalities of harmonic univalent functions with connections of hypergeometric functions
- Author
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Hiba F. Al-Janaby, Rabha W. Ibrahim, Muhammad Zaini Ahmad, and Janusz Sokół
- Subjects
Pure mathematics ,Subharmonic function ,General Mathematics ,Mathematical analysis ,Harmonic (mathematics) ,univalent function ,Generalized hypergeometric function ,analytic function ,Convolution ,harmonic function ,Harmonic function ,QA1-939 ,Hypergeometric function ,unit disk ,Mathematics ,Analytic function ,Univalent function - Abstract
Let SH be the class of functions f = h+g that are harmonic univalent and sense-preserving in the open unit disk U = { z : |z| < 1} for which f (0) = f'(0)-1=0. In this paper, we introduce and study a subclass H( α, β) of the class SH and the subclass NH( α, β) with negative coefficients. We obtain basic results involving sufficient coefficient conditions for a function in the subclass H( α, β) and we show that these conditions are also necessary for negative coefficients, distortion bounds, extreme points, convolution and convex combinations. In this paper an attempt has also been made to discuss some results that uncover some of the connections of hypergeometric functions with a subclass of harmonic univalent functions.
- Published
- 2015
13. Hom-structures on semi-simple Lie algebras
- Author
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Wenjuan Xie, Wende Liu, and Quanqin Jin
- Subjects
Pure mathematics ,lcsh:Mathematics ,General Mathematics ,Simple Lie group ,Hom-structure ,Jordan algebra ,Non-associative algebra ,Killing form ,lcsh:QA1-939 ,Kac–Moody algebra ,Affine Lie algebra ,Lie conformal algebra ,Algebra ,Adjoint representation of a Lie algebra ,Simple Lie algebra ,Generalized Kac–Moody algebra ,Mathematics - Abstract
A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A Hom-structure is referred to as multiplicative if it is also a Lie algebra homomorphism. This paper aims to determine explicitly all the Homstructures on the finite-dimensional semi-simple Lie algebras over an algebraically closed field of characteristic zero. As a Hom-structure on a Lie algebra is not necessarily a Lie algebra homomorphism, the method developed for multiplicative Hom-structures by Jin and Li in [J. Algebra 319 (2008): 1398–1408] does not work again in our case. The critical technique used in this paper, which is completely different from that in [J. Algebra 319 (2008): 1398– 1408], is that we characterize the Hom-structures on a semi-simple Lie algebra g by introducing certain reduction methods and using the software GAP. The results not only improve the earlier ones in [J. Algebra 319 (2008): 1398– 1408], but also correct an error in the conclusion for the 3-dimensional simple Lie algebra sl2. In particular, we find an interesting fact that all the Hom-structures on sl2 constitute a 6-dimensional Jordan algebra in the usual way.
- Published
- 2015
14. Solutions of minus partial ordering equations over von Neumann regular rings
- Author
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Yu Guan and Zhaojia Tong
- Subjects
von neumann regular ring ,General Mathematics ,minus partial ordering ,linear equation ,Algebra ,symbols.namesake ,QA1-939 ,symbols ,Von Neumann regular ring ,Partially ordered set ,Computer Science::Databases ,Mathematics ,Linear equation ,Geometry and topology ,Von Neumann architecture - Abstract
In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.
- Published
- 2015
15. Pointwise density topology
- Author
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Magdalena Górajska
- Subjects
Pointwise ,Pointwise convergence ,Point density ,Density point ,lcsh:Mathematics ,General Mathematics ,Density topology ,lcsh:QA1-939 ,Topology ,Strong topology (polar topology) ,Weak topology (polar topology) ,General topology ,Topology (chemistry) ,Mathematics ,Strong operator topology - Abstract
The paper presents a new type of density topology on the real line generated by the pointwise convergence, similarly to the classical density topology which is generated by the convergence in measure. Among other things, this paper demonstrates that the set of pointwise density points of a Lebesgue measurable set does not need to be measurable and the set of pointwise density points of a set having the Baire property does not need to have the Baire property. However, the set of pointwise density points of any Borel set is Lebesgue measurable.
- Published
- 2014
16. A note on polyexponential and unipoly Bernoulli polynomials of the second kind
- Author
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Minyoung Ma and Dongkyu Lim
- Subjects
Pure mathematics ,General Mathematics ,polyexponential function ,11b83 ,unipoly function ,34a34 ,Bernoulli polynomials ,poly-bernoulli numbers of the second kind ,symbols.namesake ,05a19 ,QA1-939 ,symbols ,Mathematics - Abstract
In this paper, the authors study the poly-Bernoulli numbers of the second kind, which are defined by using polyexponential functions introduced by Kims. Also by using unipoly function, we study the unipoly Bernoulli numbers of the second kind, which are attached to an arithmetic function. We derive their explicit expressions and some identities involving poly-Bernoulli numbers of the second kind and unipoly Bernoulli numbers of the second kind.
- Published
- 2021
17. A posteriori error estimates based on superconvergence of FEM for fractional evolution equations
- Author
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Tang Yuelong and Hua Yuchun
- Subjects
a posteriori error estimates ,35r11 ,65m30 ,General Mathematics ,finite element method ,QA1-939 ,fractional evolution equations ,convergence and superconvergence ,Mathematics - Abstract
In this paper, we consider an approximation scheme for fractional evolution equation with variable coefficient. The space derivative is approximated by triangular finite element and the time fractional derivative is evaluated by the L1 approximation. The main aim of this work is to provide convergence and superconvergence analysis and derive a posteriori error estimates. Some numerical examples are presented to demonstrate our theoretical results.
- Published
- 2021
18. Uniqueness of positive solutions for boundary value problems associated with indefiniteϕ-Laplacian-type equations
- Author
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Guglielmo Feltrin, Fabio Zanolin, and Alberto Boscaggin
- Subjects
Pure mathematics ,General Mathematics ,Boundary value problems ,Indefinite weight ,P-Laplacian ,Positive solutions ,Singular equations ,Superlinear functions ,Uniqueness ,34b16 ,34b15 ,34b18 ,Type (model theory) ,01 natural sciences ,QA1-939 ,Boundary value problem ,0101 mathematics ,uniqueness, indefinite weight, positive solutions, p-Laplacian, boundary value problems, superlinear functions, singular equations ,Mathematics ,010102 general mathematics ,34c25 ,010101 applied mathematics ,p-Laplacian ,Laplace operator - Abstract
This paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with theϕ-Laplacian equation(ϕ(u′))′+a(t)g(u)=0,(\phi \left(u^{\prime} ))^{\prime} +a\left(t)g\left(u)=0,whereϕis a homeomorphism withϕ(0) = 0,a(t) is a stepwise indefinite weight andg(u) is a continuous function. When dealing with thep-Laplacian differential operatorϕ(s) = ∣s∣p−2swithp > 1, and the nonlinear termg(u) = uγwithγ∈R\gamma \in {\mathbb{R}}, we prove the existence of a unique positive solution whenγ ∈ ]−∞\infty, (1 − 2p)/(p − 1)] ∪ ]p − 1, +∞\infty[.
- Published
- 2021
19. Classification of f-biharmonic submanifolds in Lorentz space forms
- Author
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Du Li
- Subjects
f-biharmonic submanifolds ,parallel normal mean curvature vector field ,General Mathematics ,the shape operator ,pseudo-umbilical ,MathematicsofComputing_GENERAL ,lorentz space forms ,53c40 ,QA1-939 ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Mathematics::Differential Geometry ,Mathematics::Symplectic Geometry ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Mathematics - Abstract
In this paper, f-biharmonic submanifolds with parallel normalized mean curvature vector field in Lorentz space forms are discussed. When f f is a constant, we prove that such submanifolds have parallel mean curvature vector field with the minimal polynomial of the shape operator of degree ≤ 2 \le 2 . When f f is a function, we completely classify such pseudo-umbilical submanifolds.
- Published
- 2021
20. The equivalent parameter conditions for constructing multiple integral half-discrete Hilbert-type inequalities with a class of nonhomogeneous kernels and their applications
- Author
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Qiang Chen, Yong Hong, and Bing He
- Subjects
Pure mathematics ,Class (set theory) ,nonhomogeneous kernel ,multiple integral half-discrete hilbert-type inequality ,General Mathematics ,Multiple integral ,010102 general mathematics ,Type (model theory) ,01 natural sciences ,010101 applied mathematics ,operator norm ,bounded operator ,26d15 ,QA1-939 ,equivalent parameter condition ,47a07 ,0101 mathematics ,best constant factor ,Mathematics - Abstract
In this paper, we establish equivalent parameter conditions for the validity of multiple integral half-discrete Hilbert-type inequalities with the nonhomogeneous kernel G ( n λ 1 ∥ x ∥ m , ρ λ 2 ) G\left({n}^{{\lambda }_{1}}\parallel x{\parallel }_{m,\rho }^{{\lambda }_{2}}\hspace{-0.16em}) ( λ 1 λ 2 > 0 {\lambda }_{1}{\lambda }_{2}\gt 0 ) and obtain best constant factors of the inequalities in specific cases. In addition, we also discuss their applications in operator theory.
- Published
- 2021
21. Construction of a family of non-stationary combined ternary subdivision schemes reproducing exponential polynomials
- Author
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Zeze Zhang, Lulu Pan, and Hongchan Zheng
- Subjects
Pure mathematics ,65d17 ,Smoothness (probability theory) ,approximation order ,business.industry ,non-stationary combined ternary scheme ,General Mathematics ,Exponential polynomial ,QA1-939 ,exponential polynomial generation/reproduction ,smoothness ,Ternary operation ,business ,Mathematics ,Subdivision - Abstract
In this paper, we propose a family of non-stationary combined ternary ( 2 m + 3 ) \left(2m+3) -point subdivision schemes, which possesses the property of generating/reproducing high-order exponential polynomials. This scheme is obtained by adding variable parameters on the generalized ternary subdivision scheme of order 4. For such a scheme, we investigate its support and exponential polynomial generation/reproduction and get that it can generate/reproduce certain exponential polynomials with suitable choices of the parameters and reach 2 m + 3 2m+3 approximation order. Moreover, we discuss its smoothness and show that it can produce C 2 m + 2 {C}^{2m+2} limit curves. Several numerical examples are given to show the performance of the schemes.
- Published
- 2021
22. Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus
- Author
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Yu-Ming Chu, Hüseyin Budak, Abdullah Akkurt, Muhammad Ali, and [Belirlenecek]
- Subjects
convex function ,Pure mathematics ,General Mathematics ,010102 general mathematics ,26-xx ,Convex ,Quantum calculus ,Type (model theory) ,Mappings ,quantum calculus ,01 natural sciences ,010101 applied mathematics ,Integral-Inequalities ,ostrowski inequality ,QA1-939 ,q-integral ,Differentiable function ,Hermite-Hadamard Inequalities ,0101 mathematics ,Convex function ,Quantum ,Mathematics - Abstract
In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣ D q 2 b f ∣ | {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣ D q 2 a f ∣ | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving q a {q}_{a} and q b {q}^{b} -quantum integrals. The results presented here are the generalization of already published ones.
- Published
- 2021
23. Asymptotic solution of the Cauchy problem for the singularly perturbed partial integro-differential equation with rapidly oscillating coefficients and with rapidly oscillating heterogeneity
- Author
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Olim D. Tuychiev and Burkhan T. Kalimbetov
- Subjects
General Mathematics ,35r09 ,010102 general mathematics ,Mathematical analysis ,integro-partial differential equation ,solvability of iterative problems ,35f10 ,01 natural sciences ,singularly perturbed ,010101 applied mathematics ,Integro-differential equation ,QA1-939 ,regularization of an integral ,space of non-resonant solutions ,Initial value problem ,0101 mathematics ,iterative problems ,Mathematics - Abstract
In this paper, the regularization method of S. A. Lomov is generalized to integro-differential equations with rapidly oscillating coefficients and with a rapidly oscillating right-hand side. The main goal of the work is to reveal the influence of the oscillating components on the structure of the asymptotics of the solution of this problem. The case of coincidence of the frequencies of a rapidly oscillating coefficient and a rapidly oscillating inhomogeneity is considered. In this case, only the identical resonance is observed in the problem. Other cases of the relationship between frequencies can lead to so-called non-identical resonances, the study of which is nontrivial and requires the development of a new approach. It is supposed to study these cases in our further work.
- Published
- 2021
24. The mixed metric dimension of flower snarks and wheels
- Author
-
Milica Milivojević Danas
- Subjects
graph theory ,General Mathematics ,mixed metric dimension ,flower snarks ,G.2.1 ,G.2.2 ,0102 computer and information sciences ,01 natural sciences ,Combinatorics ,wheel graphs ,discrete mathematics ,FOS: Mathematics ,QA1-939 ,Mathematics - Combinatorics ,05c12 ,0101 mathematics ,Graph property ,05C12 ,Mathematics ,010102 general mathematics ,Graph theory ,Metric dimension ,Exact results ,010201 computation theory & mathematics ,Combinatorics (math.CO) ,Constant (mathematics) - Abstract
New graph invariant, which is called a mixed metric dimension, has been recently introduced. In this paper, exact results of the mixed metric dimension on two special classes of graphs are found: flower snarks J n {J}_{n} and wheels W n {W}_{n} . It is proved that the mixed metric dimension for J 5 {J}_{5} is equal to 5, while for higher dimensions it is constant and equal to 4. For W n {W}_{n} , the mixed metric dimension is not constant, but it is equal to n n when n ≥ 4 n\ge 4 , while it is equal to 4, for n = 3 n=3 .
- Published
- 2021
25. Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers
- Author
-
Feng Qi, Dongkyu Lim, and Muhammet Cihat Dağlı
- Subjects
Pure mathematics ,cauchy number ,Cauchy number ,explicit formula ,General Mathematics ,Degenerate energy levels ,Generating function ,Cauchy distribution ,narumi number ,11b83 ,33b10 ,faà di bruno formula ,generating function ,QA1-939 ,11c08 ,bell polynomial of the second kind ,narumi polynomial ,Mathematics ,degenerate cauchy number - Abstract
In this paper, with the aid of the Faà di Bruno formula and by virtue of properties of the Bell polynomials of the second kind, the authors define a kind of notion of degenerate Narumi numbers and polynomials, establish explicit formulas for degenerate Narumi numbers and polynomials, and derive explicit formulas for the Narumi numbers and polynomials and for (degenerate) Cauchy numbers.
- Published
- 2021
26. A partial order on transformation semigroups with restricted range that preserve double direction equivalence
- Author
-
Kritsada Sangkhanan
- Subjects
maximal and minimal ,20m20 ,General Mathematics ,equivalence ,partial order ,QA1-939 ,compatibility ,transformation semigroup ,Mathematics - Abstract
Let T ( X ) T\left(X) be the full transformation semigroup on a set X X . For an equivalence E E on X X , let T E ∗ ( X ) = { α ∈ T ( X ) : ∀ x , y ∈ X , ( x , y ) ∈ E ⇔ ( x α , y α ) ∈ E } . {T}_{{E}^{\ast }}\left(X)=\left\{\alpha \in T\left(X):\forall x,y\in X,\left(x,y)\in E\iff \left(x\alpha ,y\alpha )\in E\right\}. For each nonempty subset Y Y of X X , we denote the restriction of E E to Y Y by E Y {E}_{Y} . Let T E ∗ ( X , Y ) {T}_{{E}^{\ast }}\left(X,Y) be the intersection of the semigroup T E ∗ ( X ) {T}_{{E}^{\ast }}\left(X) with the semigroup of all transformations with restricted range Y Y under the condition that ∣ X / E ∣ = ∣ Y / E Y ∣ | X\hspace{-0.1em}\text{/}E| =| Y\hspace{-0.16em}\text{/}\hspace{-0.1em}{E}_{Y}| . Equivalently, T E ∗ ( X , Y ) = { α ∈ T E ∗ ( X ) : X α ⊆ Y } {T}_{{E}^{\ast }}\left(X,Y)=\left\{\alpha \in {T}_{{E}^{\ast }}\left(X):X\alpha \subseteq Y\right\} , where ∣ X / E ∣ = ∣ Y / E Y ∣ | X\hspace{-0.1em}\text{/}\hspace{-0.1em}E| =| Y\hspace{-0.16em}\text{/}\hspace{-0.1em}{E}_{Y}| . Then T E ∗ ( X , Y ) {T}_{{E}^{\ast }}\left(X,Y) is a subsemigroup of T E ∗ ( X ) {T}_{{E}^{\ast }}\left(X) . In this paper, we characterize the natural partial order on T E ∗ ( X , Y ) {T}_{{E}^{\ast }}\left(X,Y) . Then we find the elements which are compatible and describe the maximal and minimal elements. We also prove that every element of T E ∗ ( X , Y ) {T}_{{E}^{\ast }}\left(X,Y) lies between maximal and minimal elements. Finally, the existence of an upper cover and a lower cover is investigated.
- Published
- 2021
27. Entire solutions for several general quadratic trinomial differential difference equations
- Author
-
Fen Hu, Hong-Yan Xu, and Jun Luo
- Subjects
General Mathematics ,30d20 ,Differential difference equations ,39a10 ,entire solution ,Trinomial ,Nevanlinna theory ,Quadratic equation ,30d35 ,30d05 ,QA1-939 ,nevanlinna theory ,Applied mathematics ,differential difference equation ,Mathematics - Abstract
This paper is devoted to exploring the existence and the forms of entire solutions of several quadratic trinomial differential difference equations with more general forms. Some results about the forms of entire solutions for these equations are some extensions and generalizations of the previous theorems given by Liu, Yang and Cao. We also give a series of examples to explain the existence of the finite order transcendental entire solutions of such equations.
- Published
- 2021
28. Global attractors for a class of semilinear degenerate parabolic equations
- Author
-
Kaixuan Zhu and Yongqin Xie
- Subjects
Class (set theory) ,Pure mathematics ,asymptotic higher-order integrability ,35b41 ,35b40 ,General Mathematics ,010102 general mathematics ,Degenerate energy levels ,35k65 ,01 natural sciences ,Parabolic partial differential equation ,010101 applied mathematics ,Attractor ,degenerate parabolic equations ,QA1-939 ,polynomial growth of arbitrary order ,0101 mathematics ,global attractors ,Mathematics - Abstract
In this paper, we consider the long-time behavior for a class of semi-linear degenerate parabolic equations with the nonlinearity f f satisfying the polynomial growth of arbitrary p − 1 p-1 order. We establish some new estimates, i.e., asymptotic higher-order integrability for the difference of the solutions near the initial time. As an application, we obtain the ( L 2 ( Ω ) , L p ( Ω ) ) \left({L}^{2}\left(\Omega ),{L}^{p}\left(\Omega )) -global attractors immediately; moreover, such an attractor can attract every bounded subset of L 2 ( Ω ) {L}^{2}\left(\Omega ) with the L p + δ {L}^{p+\delta } -norm for any δ ∈ [ 0 , + ∞ ) \delta \in \left[0,+\infty ) .
- Published
- 2021
29. Third-order differential equations with three-point boundary conditions
- Author
-
Alberto Cabada and Nikolay D. Dimitrov
- Subjects
34b10 ,Differential equation ,General Mathematics ,Fixed-point theorem ,34b15 ,34l30 ,34b18 ,symbols.namesake ,34b08 ,QA1-939 ,Boundary value problem ,Mathematics ,three-point boundary conditions ,degree theory ,Mathematical analysis ,34b05 ,34b27 ,Function (mathematics) ,green’s function ,Nonlinear system ,third-order equations ,Green's function ,Ordinary differential equation ,symbols ,Sign (mathematics) - Abstract
In this paper, a third-order ordinary differential equation coupled to three-point boundary conditions is considered. The related Green’s function changes its sign on the square of definition. Despite this, we are able to deduce the existence of positive and increasing functions on the whole interval of definition, which are convex in a given subinterval. The nonlinear considered problem consists on the product of a positive real parameter, a nonnegative function that depends on the spatial variable and a time dependent function, with negative sign on the first part of the interval and positive on the second one. The results hold by means of fixed point theorems on suitable cones.
- Published
- 2021
30. Asymptotic measure-expansiveness for generic diffeomorphisms
- Author
-
Manseob Lee
- Subjects
Pure mathematics ,Mathematics::Dynamical Systems ,expansive ,37d20 ,37c20 ,generic ,General Mathematics ,homoclinic class ,010102 general mathematics ,axiom a ,Measure (physics) ,01 natural sciences ,measure expansive ,010101 applied mathematics ,hyperbolic ,QA1-939 ,asymptotic measure expansive ,0101 mathematics ,Mathematics - Abstract
In this paper, we will assume M M to be a compact smooth manifold and f : M → M f:M\to M to be a diffeomorphism. We herein demonstrate that a C 1 {C}^{1} generic diffeomorphism f f is Axiom A and has no cycles if f f is asymptotic measure expansive. Additionally, for a C 1 {C}^{1} generic diffeomorphism f f , if a homoclinic class H ( p , f ) H\left(\hspace{0.08em}p,f) that contains a hyperbolic periodic point p p of f f is asymptotic measure-expansive, then H ( p , f ) H\left(\hspace{0.08em}p,f) is hyperbolic of f f .
- Published
- 2021
31. Entire functions that share two pairs of small functions
- Author
-
Bingmao Deng, Xiaohuang Huang, and Mingliang Fang
- Subjects
Discrete mathematics ,unicity ,General Mathematics ,Entire function ,010102 general mathematics ,39a32 ,01 natural sciences ,010101 applied mathematics ,30d35 ,small functions ,derivatives ,QA1-939 ,0101 mathematics ,Mathematics ,entire functions - Abstract
In this paper, we study the unicity of entire functions and their derivatives and obtain the following result: letffbe a non-constant entire function, leta1{a}_{1},a2{a}_{2},b1{b}_{1}, andb2{b}_{2}be four small functions offfsuch thata1≢b1{a}_{1}\not\equiv {b}_{1},a2≢b2{a}_{2}\not\equiv {b}_{2}, and none of them is identically equal to∞\infty. Ifffandf(k){f}^{\left(k)}share(a1,a2)\left({a}_{1},{a}_{2})CM and share(b1,b2)\left({b}_{1},{b}_{2})IM, then(a2−b2)f−(a1−b1)f(k)≡a2b1−a1b2\left({a}_{2}-{b}_{2})f-\left({a}_{1}-{b}_{1}){f}^{\left(k)}\equiv {a}_{2}{b}_{1}-{a}_{1}{b}_{2}. This extends the result due to Li and Yang [Value sharing of an entire function and its derivatives, J. Math. Soc. Japan.51(1999), no. 7, 781–799].
- Published
- 2021
32. Disproving a conjecture of Thornton on Bohemian matrices
- Author
-
Zhibin Du, Jiahao Ye, Yingqiu Xu, and Carlos M. da Fonseca
- Subjects
15a15 ,Conjecture ,General Mathematics ,Mathematics::Rings and Algebras ,integral matrix ,010102 general mathematics ,Integral matrix ,010103 numerical & computational mathematics ,bohemian matrix ,normalized upper hessenberg matrix ,determinant ,01 natural sciences ,Combinatorics ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
In this paper, we disprove a remaining conjecture about Bohemian matrices, in which the numbers of distinct determinants of a normalized Bohemian upper-Hessenberg matrix were conjectured.
- Published
- 2021
33. Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
- Author
-
Gangadharan Murugusundaramoorthy, Huo Tang, K. Vijaya, and S. Sivasubramanian
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Inclusion relation ,30c45 ,30c50 ,Differential operator ,01 natural sciences ,010101 applied mathematics ,(p, q)-differential operator ,partial sum ,analytic ,QA1-939 ,0101 mathematics ,Inclusion (education) ,univalent ,inclusion relation ,Mathematics ,Analytic function - Abstract
Let f k ( z ) = z + ∑ n = 2 k a n z n {f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f ( z ) = z + ∑ n = 2 ∞ a n z n f\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n} . In this paper, we determine sharp lower bounds for Re { f ( z ) / f k ( z ) } {\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\} , Re { f k ( z ) / f ( z ) } {\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\} , Re { f ′ ( z ) / f k ′ ( z ) } {\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re { f k ′ ( z ) / f ′ ( z ) } {\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\} , where f ( z ) f\left(z) belongs to the subclass J p , q m ( μ , α , β ) {{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean ( p , q ) \left(p,q) -differential operator. In addition, the inclusion relations involving N δ ( e ) {N}_{\delta }\left(e) of this generalized function class are considered.
- Published
- 2021
34. Some results on semigroups of transformations with restricted range
- Author
-
Shoufeng Wang and Qingfu Yan
- Subjects
Pure mathematics ,20m20 ,20m10 ,Restricted range ,completely regular ,General Mathematics ,orthodox ,QA1-939 ,green’s ∼-relation ,left (resp. right) ehresmann (resp. restriction) semigroup ,Mathematics - Abstract
Let X X be a non-empty set and Y Y a non-empty subset of X X . Denote the full transformation semigroup on X X by T ( X ) T\left(X) and write f ( X ) = { f ( x ) ∣ x ∈ X } f\left(X)=\{f\left(x)| x\in X\} for each f ∈ T ( X ) f\in T\left(X) . It is well known that T ( X , Y ) = { f ∈ T ( X ) ∣ f ( X ) ⊆ Y } T\left(X,Y)=\{f\in T\left(X)| f\left(X)\subseteq Y\} is a subsemigroup of T ( X ) T\left(X) and R T ( X , Y ) RT\left(X,Y) , the set of all regular elements of T ( X , Y ) T\left(X,Y) , also forms a subsemigroup of T ( X , Y ) T\left(X,Y) . Green’s ∗ \ast -relations and Green’s ∼ \sim \hspace{0.08em} -relations (with respect to a non-empty subset U U of the set of idempotents) were introduced by Fountain in 1979 and Lawson in 1991, respectively. In this paper, we intend to present certain characterizations of these two sets of Green’s relations of the semigroup T ( X , Y ) T\left(X,Y) . This investigation proves that the semigroup T ( X , Y ) T\left(X,Y) is always a left Ehresmann semigroup, and R T ( X , Y ) RT\left(X,Y) is orthodox (resp. completely regular) if and only if Y Y contains at most two elements.
- Published
- 2021
35. Complete consistency for the estimator of nonparametric regression model based on m-END errors
- Author
-
Zhang Shui-Li, Hou Tiantian, and Qu Cong
- Subjects
Statistics::Theory ,convergence rate ,regression model ,62g08 ,General Mathematics ,QA1-939 ,Statistics::Methodology ,62g05 ,60e15 ,complete consistency ,m-end sequence ,Mathematics - Abstract
In this paper, we study the complete consistency for the estimator of nonparametric regression model based on m-END errors and obtain the convergence rates of the complete consistency under more general conditions. Finally, some simulations are illustrated to verify the validity of our results.
- Published
- 2021
36. On sub-class sizes of mutually permutable products
- Author
-
Jinbao Li and Yong Yang
- Subjects
Class (set theory) ,Mathematics::Combinatorics ,sub-class sizes ,General Mathematics ,010102 general mathematics ,MathematicsofComputing_GENERAL ,01 natural sciences ,finite groups ,010101 applied mathematics ,Combinatorics ,Mathematics::Group Theory ,mutually permutable products ,QA1-939 ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,20e45 ,20d10 ,Permutable prime ,0101 mathematics ,20d20 ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Mathematics ,20d40 - Abstract
In this paper, we investigate the influence of sub-class sizes on a mutually permutable factorized group in which the sub-class sizes of some elements of its factors have certain quantitative properties. Some criteria for a group to be p p -nilpotent or p p -supersolvable are given.
- Published
- 2021
37. On reducible non-Weierstrass semigroups
- Author
-
D. Marín-Aragón, Juan Ignacio García-García, Fernando Torres, Alberto Vigneron-Tenorio, and Matemáticas
- Subjects
Pure mathematics ,weierstrass points ,pseudo-frobenius number ,General Mathematics ,Mathematics - Algebraic Geometry ,Intersection ,Genus (mathematics) ,FOS: Mathematics ,QA1-939 ,Number Theory (math.NT) ,Algebraic Geometry (math.AG) ,numerical semigroup ,Mathematics ,Mathematics - Number Theory ,Mathematics::Operator Algebras ,14h55 ,Mathematics::History and Overview ,pseudo-Frobenius number ,14H55, 11P70, 20M14 ,weierstrass semigroup ,Buchweitz semigroup ,Weierstrass semigroup ,Weierstrass points ,20m14 ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,additive combinatorics ,buchweitz semigroup ,11p70 ,Mathematics::Differential Geometry - Abstract
Weierstrass semigroups are well known along the literature. We present a new family of non- Weierstrass semigroups which can be written as an intersection of Weierstrass semigroups. In addition, we provide methods for computing non-Weierstrass semigroups with genus as large as desired., Funding information: Part of this paper was written during a visit of Fernando Torres to the Universidad de Cadiz (Spain) ; his visit was partially supported by Ayudas para Estancias Cortas de Investigadores (EST2018-R0, Programa de Fomento e Impulso de la Investigacion y la Transferencia en la Universidad de Cadiz) . Fernando Torres was partially supported by CNPq/Brazil (Grant 310623/2017-0) . Juan Ignacio Garcia-Garcia, Daniel Marin-Aragon, and Alberto Vigneron-Tenorio were partially supported by Junta de Andalucia research groups FQM-343 and FQM-366, and by the project MTM2017-84890-P (MINECO/FEDER, UE) .
- Published
- 2021
38. Refinements of quantum Hermite-Hadamard-type inequalities
- Author
-
Sundas Khan, Muhammad Ali, Hüseyin Budak, Yu-Ming Chu, and [Belirlenecek]
- Subjects
Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,Mathematics::Classical Analysis and ODEs ,Quantum calculus ,Type (model theory) ,quantum calculus ,01 natural sciences ,26d15 ,Hadamard transform ,Hermite–Hadamard inequality ,QA1-939 ,26a51 ,0101 mathematics ,Quantum ,26d10 ,Mathematics ,media_common ,convex function ,Hermite polynomials ,010102 general mathematics ,Convex ,010101 applied mathematics ,Integral-Inequalities ,Hermite-Hadamard inequality ,q-integral ,Convex function - Abstract
In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities. Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11971241] This work was supported by the Natural Science Foundation of China (Grant No. 11971241) . WOS:000684960600001 2-s2.0-85112658736
- Published
- 2021
39. Determinantal inequalities of Hua-Marcus-Zhang type for quaternion matrices
- Author
-
Feng Qi and Yan Hong
- Subjects
positive definite matrix ,Pure mathematics ,matrix of quaternions ,16h05 ,General Mathematics ,Zhàng ,010103 numerical & computational mathematics ,Positive-definite matrix ,Type (model theory) ,01 natural sciences ,15b33 ,QA1-939 ,eigenvalue ,Physics::Chemical Physics ,0101 mathematics ,Quaternion ,Eigenvalues and eigenvectors ,Mathematics ,Mathematics::Complex Variables ,hua-marcus-zhang type ,010102 general mathematics ,singular value ,15a42 ,15a45 ,Singular value ,determinantal inequality ,20g20 ,11r52 - Abstract
In this paper, the authors extend determinantal inequalities of the Hua-Marcus-Zhang type for positive definite matrices to the corresponding ones for quaternion matrices.
- Published
- 2021
40. Numerical methods for time-fractional convection-diffusion problems with high-order accuracy
- Author
-
Wenjuan Yao, Zhichang Guo, and Gang Dong
- Subjects
2d time-fractional convection-diffusion equation ,convergence ,General Mathematics ,Numerical analysis ,adi scheme ,Convergence (routing) ,37mxx ,QA1-939 ,Applied mathematics ,unconditional stability ,65-xx ,High order ,Convection–diffusion equation ,Mathematics - Abstract
In this paper, we consider the numerical method for solving the two-dimensional time-fractional convection-diffusion equation with a fractional derivative of order α \alpha ( 1 < α < 2 1\lt \alpha \lt 2 ). By combining the compact difference approach for spatial discretization and the alternating direction implicit (ADI) method in the time stepping, a compact ADI scheme is proposed. The unconditional stability and H 1 {H}^{1} norm convergence of the scheme are proved rigorously. The convergence order is O ( τ 3 − α + h 1 4 + h 2 4 ) O\left({\tau }^{3-\alpha }+{h}_{1}^{4}+{h}_{2}^{4}) , where τ \tau is the temporal grid size and h 1 {h}_{1} , h 2 {h}_{2} are spatial grid sizes in the x x and y y directions, respectively. It is proved that the method can even attain ( 1 + α ) \left(1+\alpha ) order accuracy in temporal for some special cases. Numerical results are presented to demonstrate the effectiveness of theoretical analysis.
- Published
- 2021
41. Strong consistency of regression function estimator with martingale difference errors
- Author
-
Yingxia Chen
- Subjects
consistency ,General Mathematics ,Regression function ,Strong consistency ,Estimator ,martingale difference ,Consistency (statistics) ,regression function ,Statistics ,QA1-939 ,62g05 ,60f15 ,Martingale difference sequence ,Mathematics - Abstract
In this paper, we consider the regression model with fixed design: Y i = g ( x i ) + ε i {Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i} , 1 ≤ i ≤ n 1\le i\le n , where { x i } \left\{{x}_{i}\right\} are the nonrandom design points, and { ε i } \left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and g g is an unknown function. Nonparametric estimator g n ( x ) {g}_{n}\left(x) of g ( x ) g\left(x) will be introduced and its strong convergence properties are established.
- Published
- 2021
42. New criteria-based ℋ-tensors for identifying the positive definiteness of multivariate homogeneous forms
- Author
-
Dongjian Bai and Deshu Sun
- Subjects
15a18 ,Multivariate statistics ,Pure mathematics ,65f15 ,positive definiteness ,General Mathematics ,homogeneous multivariate form ,65h17 ,010102 general mathematics ,010103 numerical & computational mathematics ,iterative scheme ,15a69 ,01 natural sciences ,generalized diagonal dominance ,Positive definiteness ,Homogeneous ,ℋ-tensors ,QA1-939 ,0101 mathematics ,Mathematics - Abstract
Positive definite polynomials are important in the field of optimization. ℋ-tensors play an important role in identifing the positive definiteness of an even-order homogeneous multivariate form. In this paper, we propose an iterative scheme for identifying ℋ-tensor and prove that the algorithm can terminate within finite iterative steps. Some numerical examples are provided to illustrate the efficiency and validity of methods.
- Published
- 2021
43. On split regular BiHom-Poisson color algebras
- Author
-
Yaling Tao and Yan Cao
- Subjects
Pure mathematics ,root space ,General Mathematics ,010102 general mathematics ,Root space ,bihom-poisson algebra ,17b22 ,17b65 ,17b75 ,010103 numerical & computational mathematics ,Root system ,Poisson distribution ,01 natural sciences ,symbols.namesake ,bihom-lie color algebra ,17a60 ,QA1-939 ,symbols ,root system ,0101 mathematics ,Mathematics - Abstract
The purpose of this paper is to introduce the class of split regular BiHom-Poisson color algebras, which can be considered as the natural extension of split regular BiHom-Poisson algebras and of split regular Poisson color algebras. Using the property of connections of roots for this kind of algebras, we prove that such a split regular BiHom-Poisson color algebra L L is of the form L = ⊕ [ α ] ∈ Λ / ∼ I [ α ] L={\oplus }_{\left[\alpha ]\in \Lambda \text{/} \sim }{I}_{\left[\alpha ]} with I [ α ] {I}_{\left[\alpha ]} a well described (graded) ideal of L L , satisfying [ I [ α ] , I [ β ] ] + I [ α ] I [ β ] = 0 \left[{I}_{\left[\alpha ]},{I}_{\left[\beta ]}]+{I}_{\left[\alpha ]}{I}_{\left[\beta ]}=0 if [ α ] ≠ [ β ] \left[\alpha ]\ne \left[\beta ] . In particular, a necessary and sufficient condition for the simplicity of this algebra is determined, and it is shown that L L is the direct sum of the family of its simple (graded) ideals.
- Published
- 2021
44. Discussions on the almost 𝒵-contraction
- Author
-
V. M. L. Hima Bindu and Erdal Karapınar
- Subjects
simulation function ,almost contraction ,e contraction ,α admissible ,General Mathematics ,010102 general mathematics ,Geometry ,01 natural sciences ,010101 applied mathematics ,QA1-939 ,55m20, 54h25, 47h10 ,0101 mathematics ,Contraction (operator theory) ,Mathematics ,Geometry and topology ,almost k contraction - Abstract
In this paper, we introduce a new contraction, namely, almost {\mathcal{Z}} contraction with respect to \zeta \in {\mathcal{Z}} , in the setting of complete metric spaces. We proved that such contraction possesses a fixed point and the given theorem covers several existing results in the literature. We consider an example to illustrate our result.
- Published
- 2020
45. A new blow-up criterion for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion
- Author
-
Chunhua Fang, Fan He, Wen Zhu, Chuangxia Huang, Limei Li, and Zaiyun Zhang
- Subjects
General Mathematics ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,dissipation ,35a07 ,Dissipation ,01 natural sciences ,010101 applied mathematics ,Type equation ,35q53 ,n-abc family of camassa-holm type equation ,Dispersion (optics) ,QA1-939 ,dispersion ,0101 mathematics ,blow-up ,Mathematics ,Geometry and topology - Abstract
In this paper, we investigate the Cauchy problem for the N – abc family of Camassa-Holm type equation with both dissipation and dispersion. Furthermore, we establish the blow-up result of the positive solutions in finite time under certain conditions on the initial datum. This result complements the early one in the literature, such as [E. Novruzov, Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation, J. Math. Phys. 54 (2013), no. 9, 092703, DOI 10.1063/1.4820786] and [Z.Y. Zhang, J.H. Huang, and M.B. Sun, Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation revisited, J. Math. Phys. 56 (2015), no. 9, 092701, DOI 10.1063/1.4930198].
- Published
- 2020
46. Inequalities for the generalized trigonometric and hyperbolic functions
- Author
-
Xiangbin Si, Jian-Hui He, Genhong Zhong, and Xiaoyan Ma
- Subjects
Pure mathematics ,huygens inequality ,Inequality ,lcsh:Mathematics ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Hyperbolic function ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,26d05 ,26d07 ,wilker inequality ,cusa-huygens inequality ,generalized trigonometric and hyperbolic functions ,lazarević inequality ,0101 mathematics ,Trigonometry ,Mathematics ,media_common - Abstract
In this paper, the authors present some inequalities of the generalized trigonometric and hyperbolic functions which occur in the solutions of some linear differential equations and physics. By these results, some well-known classical inequalities for them are improved, such as Wilker inequality, Huygens inequality, Lazarević inequality and Cusa-Huygens inequality.
- Published
- 2020
47. On applications of bipartite graph associated with algebraic structures
- Author
-
Xiujun Zhang, Muhammad Kamran Siddiqui, Sarfraz Ahmad, and Muhammed Nadeem
- Subjects
Discrete mathematics ,Wilson loop ,Algebraic structure ,General Mathematics ,nucleus ,010102 general mathematics ,wilson loop ,01 natural sciences ,edge labeling ,010101 applied mathematics ,05e45 ,bipartite graph ,05e15 ,QA1-939 ,Bipartite graph ,05exx ,0101 mathematics ,Mathematics ,Geometry and topology ,05e40 - Abstract
The latest developments in algebra and graph theory allow us to ask a natural question, what is the application in real world of this graph associated with some mathematical system? Groups can be used to construct new non-associative algebraic structures, loops. Graph theory plays an important role in various fields through edge labeling. In this paper, we shall discuss some applications of bipartite graphs, related with Latin squares of Wilson loops, such as metabolic pathways, chemical reaction networks, routing and wavelength assignment problem, missile guidance, astronomy and x-ray crystallography.
- Published
- 2020
48. The domination number of round digraphs
- Author
-
Ruijuan Li, Xinhong Zhang, and Caijuan Xue
- Subjects
Discrete mathematics ,Domination analysis ,domination number ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,purely local tournament ,local tournament ,Computer Science::Discrete Mathematics ,05c69 ,010201 computation theory & mathematics ,QA1-939 ,0101 mathematics ,round digraph ,Mathematics ,Geometry and topology - Abstract
The concept of the domination number plays an important role in both theory and applications of digraphs. Let D = ( V , A ) D=(V,A) be a digraph. A vertex subset T ⊆ V ( D ) T\subseteq V(D) is called a dominating set of D, if there is a vertex t ∈ T t\in T such that t v ∈ A ( D ) tv\in A(D) for every vertex v ∈ V ( D ) \ T v\in V(D)\backslash T . The dominating number of D is the cardinality of a smallest dominating set of D, denoted by γ ( D ) \gamma (D) . In this paper, the domination number of round digraphs is characterized completely.
- Published
- 2020
49. Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields
- Author
-
Xiaolin Chen
- Subjects
Pseudorandom number generator ,Pure mathematics ,General Mathematics ,binary lattice ,010102 general mathematics ,Binary number ,pseudorandom ,0102 computer and information sciences ,11b50 ,01 natural sciences ,Finite field ,010201 computation theory & mathematics ,94a55 ,QA1-939 ,cyclotomic class ,11k45 ,0101 mathematics ,finite field ,character sum ,94a60 ,Mathematics ,Geometry and topology - Abstract
In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices. In 2011, Gyarmati, Mauduit and Sárközy extended the notions of family complexity, collision and avalanche effect from binary sequences to binary lattices. In this paper, we construct pseudorandom binary lattices by using cyclotomic classes in finite fields and study the pseudorandom measure of order k, family complexity, collision and avalanche effect. Results indicate that such binary lattices are “good,” and their families possess a nice structure in terms of family complexity, collision and avalanche effect.
- Published
- 2020
50. Gradient estimates for a weighted nonlinear parabolic equation and applications
- Author
-
N. K. Oladejo, Abimbola Abolarinwa, and S.O. Salawu
- Subjects
35b53 ,parabolic equation ,010308 nuclear & particles physics ,General Mathematics ,harnack inequality ,010102 general mathematics ,Mathematical analysis ,Mathematics::Analysis of PDEs ,gradient estimates ,53c21 ,01 natural sciences ,Nonlinear system ,bakry-émery tensor ,heat kernel ,35k55 ,0103 physical sciences ,58j38 ,QA1-939 ,Mathematics::Differential Geometry ,liouville theorem ,0101 mathematics ,Mathematics - Abstract
This paper derives elliptic gradient estimates for positive solutions to a nonlinear parabolic equation defined on a complete weighted Riemannian manifold. Applications of these estimates yield Liouville-type theorem, parabolic Harnack inequalities and bounds on weighted heat kernel on the lower boundedness assumption for Bakry-Émery curvature tensor.
- Published
- 2020
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