456 results
Search Results
2. Generalized split null point of sum of monotone operators in Hilbert spaces
- Author
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H. A. Abass, Olalwale K. Oyewole, Ojen Kumar Narain, Akindele Adebayo Mebawondu, and Kazeem Olalekan Aremu
- Subjects
47h09 ,Pure mathematics ,fixed point problem ,47j25 ,General Mathematics ,47j05 ,Hilbert space ,47h06 ,inertial iterative scheme ,symbols.namesake ,Monotone polygon ,firmly nonexpansive ,symbols ,generalized split monotone variational inclusion ,QA1-939 ,Null point ,Mathematics - Abstract
In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.
- Published
- 2021
3. so-metrizable spaces and images of metric spaces
- Author
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Songlin Yang and Xun Ge
- Subjects
Pure mathematics ,General Mathematics ,MathematicsofComputing_GENERAL ,Mathematics::General Topology ,54e50 ,so-metrizable space ,54e40 ,54e45 ,54e35 ,Metric space ,Metrization theorem ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,σ-mapping ,so-open mapping ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,so-network ,compact-covering mapping ,Mathematics - Abstract
so-metrizable spaces are a class of important generalized metric spaces between metric spaces and s n sn -metrizable spaces where a space is called an so-metrizable space if it has a σ \sigma -locally finite so-network. As the further work that attaches to the celebrated Alexandrov conjecture, it is interesting to characterize so-metrizable spaces by images of metric spaces. This paper gives such characterizations for so-metrizable spaces. More precisely, this paper introduces so-open mappings and uses the “Pomomarev’s method” to prove that a space X X is an so-metrizable space if and only if it is an so-open, compact-covering, σ \sigma -image of a metric space, if and only if it is an so-open, σ \sigma -image of a metric space. In addition, it is shown that so-open mapping is a simplified form of s n sn -open mapping (resp. 2-sequence-covering mapping if the domain is metrizable). Results of this paper give some new characterizations of so-metrizable spaces and establish some equivalent relations among so-open mapping, s n sn -open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.
- Published
- 2021
4. On some new quantum midpoint-type inequalities for twice quantum differentiable convex functions
- Author
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Zhiyue Zhang, Hüseyin Budak, Yu-Ming Chu, Necmettin Alp, Muhammad Ali, and [Belirlenecek]
- Subjects
Pure mathematics ,Inequality ,General Mathematics ,media_common.quotation_subject ,Type (model theory) ,Quantum calculus ,quantum calculus ,01 natural sciences ,Midpoint ,26d15 ,Hermite–Hadamard inequality ,QA1-939 ,26a51 ,Differentiable function ,0101 mathematics ,Quantum ,26d10 ,Mathematics ,media_common ,convex function ,hermite-hadamard inequality ,010102 general mathematics ,010101 applied mathematics ,Computer Science::Graphics ,q-integral ,Convex function - Abstract
The present paper aims to find some new midpoint-type inequalities for twice quantum differentiable convex functions. The consequences derived in this paper are unification and generalization of the comparable consequences in the literature on midpoint inequalities. © 2021 Muhammad Aamir Ali et al., published by De Gruyter. National Natural Science Foundation of China, NSFC: 11301127, 11601485, 11626101, 11701176, 11971241, 61673169 Funding information : The work was supported by the Natural Science Foundation of China (Grant Nos. 61673169, 11301127, 11701176, 11626101, 11601485, 11971241). 2-s2.0-85105011594
- Published
- 2021
5. (p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group
- Author
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Patrizia Pucci and Letizia Temperini
- Subjects
General Mathematics ,variational methods ,35b08 ,nonlinear system ,01 natural sciences ,(p ,Heisenberg group ,0101 mathematics ,Q system ,Geometry and topology ,Mathematics ,Mathematical physics ,Q) Laplacian ,35b33 ,lcsh:Mathematics ,010102 general mathematics ,heisenberg group ,(p,q) laplacian ,35j50 ,lcsh:QA1-939 ,Exponential function ,010101 applied mathematics ,Nonlinear system ,35j47 ,(p,Q) Laplacian, Nonlinear system, Critical exponential nonlinearities, Variational methods, Heisenberg group ,35b09 ,critical exponential nonlinearities ,35r03 - Abstract
The paper deals with the existence of solutions for(p,Q)(p,Q)coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper are the presence of a general coupled critical exponential term of the Trudinger-Moser type and the fact that the system is set inℍn{{\mathbb{H}}}^{n}.
- Published
- 2020
6. Fixed point results for multivalued mappings of Ćirić type via F-contractions on quasi metric spaces
- Author
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Wasfi Shatanawi, Hacer Dağ, Ishak Altun, and KKÜ
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,primary 47h10 ,Fixed point ,Type (model theory) ,multivalued mappings ,01 natural sciences ,010101 applied mathematics ,Metric space ,fixed point ,QA1-939 ,secondary 54h25 ,0101 mathematics ,quasi metric space ,Mathematics - Abstract
Altun, Ishak/0000-0002-7967-0554 WOS:000537813000001 In this paper, we present some fixed point results for multivalued mappings with both closed values and proximinal values on left K-complete quasi metric spaces. We also provide a nontrivial example to illustrate our results. Prince Sultan University [RG-DES-2017-01-17] The authors are thankful to the referees for making valuable suggestions leading to the better presentations of the paper. This work was supported by the Prince Sultan University through the Research Group NAMAM under Grant RG-DES-2017-01-17.
- Published
- 2020
7. Explicit order 3/2 Runge-Kutta method for numerical solutions of stochastic differential equations by using Itô-Taylor expansion
- Author
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Yazid Alhojilan
- Subjects
itô-taylor expansion ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,lcsh:QA1-939 ,01 natural sciences ,stochastic differential equations ,secondary 65c30 ,010104 statistics & probability ,Stochastic differential equation ,Runge–Kutta methods ,symbols.namesake ,pathwise approximation ,Taylor series ,symbols ,runge-kutta method ,Applied mathematics ,Order (group theory) ,primary 60h35 ,0101 mathematics ,Mathematics - Abstract
This paper aims to present a new pathwise approximation method, which gives approximate solutions of order $\begin{array}{} \displaystyle \frac{3}{2} \end{array}$ for stochastic differential equations (SDEs) driven by multidimensional Brownian motions. The new method, which assumes the diffusion matrix non-degeneracy, employs the Runge-Kutta method and uses the Itô-Taylor expansion, but the generating of the approximation of the expansion is carried out as a whole rather than individual terms. The new idea we applied in this paper is to replace the iterated stochastic integrals Iα by random variables, so implementing this scheme does not require the computation of the iterated stochastic integrals Iα. Then, using a coupling which can be found by a technique from optimal transport theory would give a good approximation in a mean square. The results of implementing this new scheme by MATLAB confirms the validity of the method.
- Published
- 2019
8. A new way to represent functions as series
- Author
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Manuel Norman
- Subjects
values of infinite series ,Series (mathematics) ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Function series ,function series ,primary 26a06 ,secondary 41a58 ,lcsh:QA1-939 ,01 natural sciences ,010101 applied mathematics ,Algebra ,lagrange’s mean value theorem ,0101 mathematics ,40a30 ,Geometry and topology ,Mathematics - Abstract
In this paper we will show a new way to represent functions as infinite series, finding some conditions under which a function is expandable with this method, and showing how it allows us to find the values of many interesting series. At the end, we will prove one of the main results of the paper, a Representation Theorem.
- Published
- 2019
9. Research on cooperation strategy between government and green supply chain based on differential game
- Author
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Baizhou Li and Jingwei Zeng
- Subjects
cooperation strategy ,Government ,General Mathematics ,Supply chain ,lcsh:Mathematics ,050901 criminology ,05 social sciences ,green supply chain ,government role ,03-xx ,lcsh:QA1-939 ,Differential game ,0501 psychology and cognitive sciences ,differential game ,0509 other social sciences ,03cxx ,Industrial organization ,050104 developmental & child psychology ,Mathematics - Abstract
Based on the “three bottom line” and stakeholder theory, the paper considers the relationship and cooperation strategy between the government and the supplier and manufacturer of the green supply chain. By constructing the dynamic differential game model, the paper discusses the differences in the optimal effort level, green degree of product, reputation and the optimal benefit under the three situations of noncooperation, government promotion and collaborative cooperation. The results show that the optimal effort level, green degree of product, reputation and the optimal benefit in collaborative cooperation are obviously higher than the situations of non-cooperation and government promotion, and the cooperation of the three parties can promote the development of green supply chain. Government promotion is better than noncooperation. The government plays an active role in improving the optimal benefit and reputation of green supply chain. Finally, the reliability of the proposed proposition is verified by an example analysis, which provides an important reference for improving the efficiency of green supply chain.
- Published
- 2019
10. Rayleigh-Ritz Majorization Error Bounds for the Linear Response Eigenvalue Problem
- Author
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Hong-Xiu Zhong and Zhongming Teng
- Subjects
Rayleigh–Ritz method ,rayleigh-ritz approximation ,65f15 ,linear response eigenvalue problem ,General Mathematics ,Mathematical analysis ,0211 other engineering and technologies ,65l15 ,021107 urban & regional planning ,010103 numerical & computational mathematics ,02 engineering and technology ,error bounds ,01 natural sciences ,Mathematics::Numerical Analysis ,Principal angles ,canonical angles ,majorization ,QA1-939 ,0101 mathematics ,Majorization ,Eigenvalues and eigenvectors ,Geometry and topology ,Mathematics - Abstract
In the linear response eigenvalue problem arising from computational quantum chemistry and physics, one needs to compute a few of smallest positive eigenvalues together with the corresponding eigenvectors. For such a task, most of efficient algorithms are based on an important notion that is the so-called pair of deflating subspaces. If a pair of deflating subspaces is at hand, the computed approximated eigenvalues are partial eigenvalues of the linear response eigenvalue problem. In the case the pair of deflating subspaces is not available, only approximate one, in a recent paper [SIAM J. Matrix Anal. Appl., 35(2), pp.765-782, 2014], Zhang, Xue and Li obtained the relationships between the accuracy in eigenvalue approximations and the distances from the exact deflating subspaces to their approximate ones. In this paper, we establish majorization type results for these relationships. From our majorization results, various bounds are readily available to estimate how accurate the approximate eigenvalues based on information on the approximate accuracy of a pair of approximate deflating subspaces. These results will provide theoretical foundations for assessing the relative performance of certain iterative methods in the linear response eigenvalue problem.
- Published
- 2019
11. Permutations of zero-sumsets in a finite vector space
- Author
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Giovanni Falcone, Marco Pavone, Giovanni Falcone, and Marco Pavone
- Subjects
permutations of zero-sums ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,MathematicsofComputing_GENERAL ,Zero (complex analysis) ,Subset sum ,01 natural sciences ,010101 applied mathematics ,Combinatorics ,subset sum problem ,Settore MAT/05 - Analisi Matematica ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Subset sum problem ,Settore MAT/03 - Geometria ,0101 mathematics ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Vector space ,Mathematics - Abstract
In this paper, we consider a finite-dimensional vector space 𝒫 {{\mathcal{P}}} over the Galois field GF ( p ) {\operatorname{GF}(p)} , with p being an odd prime, and the family ℬ k x {{\mathcal{B}}_{k}^{x}} of all k-sets of elements of 𝒫 {\mathcal{P}} summing up to a given element x. The main result of the paper is the characterization, for x = 0 {x=0} , of the permutations of 𝒫 {\mathcal{P}} inducing permutations of ℬ k 0 {{\mathcal{B}}_{k}^{0}} as the invertible linear mappings of the vector space 𝒫 {\mathcal{P}} if p does not divide k, and as the invertible affinities of the affine space 𝒫 {\mathcal{P}} if p divides k. The same question is answered also in the case where the elements of the k-sets are required to be all nonzero, and, in fact, the two cases prove to be intrinsically inseparable.
- Published
- 2021
12. Transitivity of the εm-relation on (m-idempotent) hyperrings
- Author
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Morteza Norouzi and Irina Cristea
- Subjects
Transitive relation ,Pure mathematics ,20n20 ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,01 natural sciences ,hyperring ,m-idempotent hyperring ,16y99 ,m-complete part ,Idempotence ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,Relation (history of concept) ,Mathematics - Abstract
On a general hyperring, there is a fundamental relation, denoted γ *, such that the quotient set is a classical ring. In a previous paper, the authors defined the relation εm on general hyperrings, proving that its transitive closure ε m ∗ $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a strongly regular equivalence relation smaller than the γ *-relation on some classes of hyperrings, such that the associated quotient structure modulo ε m ∗ $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is an ordinary ring. Thus, on such hyperrings, ε m ∗ $\begin{array}{} \displaystyle \varepsilon^{*}_{m} \end{array}$ is a fundamental relation. In this paper, we discuss the transitivity conditions of the εm -relation on hyperrings and m-idempotent hyperrings.
- Published
- 2018
13. On the boundedness of square function generated by the Bessel differential operator in weighted Lebesque Lp,α spaces
- Author
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Simten Bayrakci
- Subjects
Pure mathematics ,bessel plancherel formula ,General Mathematics ,010102 general mathematics ,bessel transform ,MathematicsofComputing_NUMERICALANALYSIS ,bessel differential operator ,Differential operator ,bessel translation operator ,01 natural sciences ,generalized convolution ,010101 applied mathematics ,symbols.namesake ,generalized translation ,42a85 ,square function ,symbols ,QA1-939 ,0101 mathematics ,Bessel function ,42b35 ,Mathematics - Abstract
In this paper, we consider the square function(Sf)(x)=(∫0∞|(f⊗Φt)(x)|2dtt)1/2$$\begin{array}{} \displaystyle (\mathcal{S}f)(x)=\left( \int\limits_{0}^{\infty }|(f\otimes {\it\Phi}_{t})\left( x\right) |^{2}\frac{dt}{t}\right) ^{1/2} \end{array} $$associated with the Bessel differential operatorBt=d2dt2+(2α+1)tddt,$\begin{array}{} B_{t}=\frac{d^{2}}{dt^{2}}+\frac{(2\alpha+1)}{t}\frac{d}{dt}, \end{array} $α> −1/2,t> 0 on the half-line ℝ+= [0, ∞). The aim of this paper is to obtain the boundedness of this function inLp,α,p> 1. Firstly, we provedL2,α-boundedness by means of the Bessel-Plancherel theorem. Then, its weak-type (1, 1) andLp,α,p> 1 boundedness are proved by taking into account vector-valued functions.
- Published
- 2018
14. Dynamics for a discrete competition and cooperation model of two enterprises with multiple delays and feedback controls
- Author
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Yi Lian, Chaoling Li, and Lin Lu
- Subjects
Cooperation model ,delay ,General Mathematics ,Feedback control ,010102 general mathematics ,competition and cooperation model ,enterprise ,34k20 ,34c25 ,010103 numerical & computational mathematics ,92d25 ,01 natural sciences ,Competition (economics) ,Microeconomics ,feedback control ,Dynamics (music) ,Control theory ,QA1-939 ,0101 mathematics ,permanence ,Mathematics - Abstract
This paper is concerned with a competition and cooperation model of two enterprises with multiple delays and feedback controls. With the aid of the difference inequality theory, we have obtained some sufficient conditions which guarantee the permanence of the model. Under a suitable condition, we prove that the system has global stable periodic solution. The paper ends with brief conclusions.
- Published
- 2017
15. The history of a general criterium on spaceability
- Author
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Víctor M. Sánchez
- Subjects
Pure mathematics ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Banach space ,010103 numerical & computational mathematics ,spaceability ,lcsh:QA1-939 ,01 natural sciences ,operator ideal ,Set (abstract data type) ,Operator (computer programming) ,Calculus ,0101 mathematics ,47l20 ,Mathematics ,Análisis funcional y teoría de operadores - Abstract
There are just a few general criteria on spaceability. This survey paper is the history of one of the first ones. Let I1 and I2 be arbitrary operator ideals and E and F be Banach spaces. The spaceability of the set of operators I1(E, F)\ I2(E, F) is studied. Before stating the criterium, the paper summarizes the main results about lineability and spaceability of differences between particular operator ideals obtained in recent years. They are the seed of the ideas contained in the general criterium.
- Published
- 2017
16. Algebraic and qualitative remarks about the family yy′ = (αxm+k–1 + βxm–k–1)y + γx2m–2k–1
- Author
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Primitivo B. Acosta-Humánez, Alberto Reyes-Linero, and Jorge Rodríguez-Contreras
- Subjects
Pure mathematics ,Liénard equation ,critical points ,General Mathematics ,010102 general mathematics ,Critical points ,legendre equation ,Integrability ,integrability ,01 natural sciences ,primary 12h05 ,Legendre equation ,010101 applied mathematics ,Gegenbauer equation ,QA1-939 ,0101 mathematics ,Algebraic number ,liénard equation ,secondary 34c99 ,Legendre polynomials ,Geometry and topology ,Mathematics ,gegenbauer equation - Abstract
The aim of this paper is the analysis, from algebraic point of view and singularities studies, of the 5-parametric family of differential equations $$\begin{array}{} \displaystyle yy'=(\alpha x^{m+k-1}+\beta x^{m-k-1})y+\gamma x^{2m-2k-1}, \quad y'=\frac{dy}{dx} \end{array}$$ where a, b, c ∈ ℂ, m, k ∈ ℤ and $$\begin{array}{} \displaystyle \alpha=a(2m+k) \quad \beta=b(2m-k), \quad \gamma=-(a^2mx^{4k}+cx^{2k}+b^2m). \end{array}$$ This family is very important because include Van Der Pol equation. Moreover, this family seems to appear as exercise in the celebrated book of Polyanin and Zaitsev. Unfortunately, the exercise presented a typo which does not allow to solve correctly it. We present the corrected exercise, which corresponds to the title of this paper. We solve the exercise and afterwards we make algebraic and of singularities studies to this family of differential equations.
- Published
- 2019
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17. Persistence and Global Attractivity for a Discretized Version of a General Model of Glucose-Insulin Interaction
- Author
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Dinh Cong Huong
- Subjects
Persistence (psychology) ,delay difference equations ,Discretization ,General Mathematics ,Insulin ,medicine.medical_treatment ,full time solution ,lcsh:Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,lcsh:QA1-939 ,01 natural sciences ,non-standard difference ,medicine ,numerical discretized model ,Applied mathematics ,!-limit set of a persistent solution ,0101 mathematics ,Mathematics - Abstract
In this paper, we construct a non-standard finite difference scheme for a general model of glucose-insulin interaction. We establish some new sufficient conditions to ensure that the discretized model preserves the persistence and global attractivity of the continuous model. One of the main findings in this paper is that we derive two important propositions (Proposition 3.1 and Proposition 3.2) which are used to prove the global attractivity of the discretized model. Furthermore, when investigating the persistence and, in some cases, the global attractivity of the discretized model, the nonlinear functions f and h are not required to be differentiable. Hence, our results are more realistic because the statistical data of glucose and insulin are collected and reported in discrete time. We also present some numerical examples and their simulations to illustrate our results.
- Published
- 2016
18. General numerical radius inequalities for matrices of operators
- Author
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Mohammed Al-Dolat, Feras Ali Bani-Ahmad, Mohammed Ali, and Khaldoun Al-Zoubi
- Subjects
cartesian decomposition ,Theoretical computer science ,Spectral radius ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Matrix norm ,010103 numerical & computational mathematics ,Radius ,Operator theory ,01 natural sciences ,operator norm ,47a10 ,47a12 ,QA1-939 ,0101 mathematics ,Operator norm ,numerical radius ,Mathematics ,47a05 - Abstract
Let Ai ∈ B(H), (i = 1, 2, ..., n), and T = [ 0 ⋯ 0 A 1 ⋮ ⋰ A 2 0 0 ⋰ ⋰ ⋮ A n 0 ⋯ 0 ] $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.
- Published
- 2016
19. Very true operators on MTL-algebras
- Author
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Jun Tao Wang, Arsham Borumand Saeid, and Xiao Long Xin
- Subjects
0209 industrial biotechnology ,representation ,General Mathematics ,Representation (systemics) ,02 engineering and technology ,very true mtl-logic ,Algebra ,Mathematics::Logic ,very true mtl-algebra ,020901 industrial engineering & automation ,Subdirectly irreducible algebra ,Computer Science::Logic in Computer Science ,subdirectly irreducible ,0202 electrical engineering, electronic engineering, information engineering ,stabilizer topology ,QA1-939 ,020201 artificial intelligence & image processing ,06f99 ,Computer Science::Formal Languages and Automata Theory ,03f50 ,Mathematics - Abstract
The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.
- Published
- 2016
20. On the weakly(α, ψ, ξ)-contractive condition for multi-valued operators in metric spaces and related fixed point results
- Author
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Marwan Amin Kutbi and Wutiphol Sintunavarat
- Subjects
Discrete mathematics ,021103 operations research ,weakly (α,ψ,ξ)-contractive multivalued mappings ,General Mathematics ,0211 other engineering and technologies ,α-admissible multi-valued mappings ,02 engineering and technology ,Fixed point ,01 natural sciences ,Multi valued ,010101 applied mathematics ,Metric space ,54h25 ,α*-admissible multi-valued mappings ,QA1-939 ,0101 mathematics ,47h10 ,Mathematics - Abstract
The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.
- Published
- 2016
21. Results on the deficiencies of some differential-difference polynomials of meromorphic functions
- Author
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Xiu-Min Zheng and Hong-Yan Xu
- Subjects
General Mathematics ,Discrete orthogonal polynomials ,010102 general mathematics ,39a10 ,deficiency ,01 natural sciences ,010101 applied mathematics ,Algebra ,Classical orthogonal polynomials ,Difference polynomials ,30d35 ,QA1-939 ,meromorphic function ,differential-difference polynomial ,0101 mathematics ,Differential (mathematics) ,Mathematics ,Meromorphic function - Abstract
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z) m f(z+c)f′(z), f(z+c) n f′(z), f(z) m f(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying lim sup r → + ∞ T ( r , f ) T ( r , f ′ ) < + ∞ , $$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ < }} + \infty ,$$ and c be a non-zero complex constant, then δ(∞, f(z) m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c) n f′(z))≥ δ(∞, f′). We also investigate the value distribution of some differential-difference polynomials taking small function a(z) with respect to f(z).
- Published
- 2016
22. Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
- Author
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Akram M. Zeki, Sherzod Turaev, Rawad Abdulghafor, and Farruh Shahidi
- Subjects
doubly stochastic quadratic operators ,General Mathematics ,02 engineering and technology ,Center (group theory) ,extreme point ,15a51 ,Fixed point ,46t99 ,01 natural sciences ,Permutation ,Quadratic equation ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,Mathematics::Metric Geometry ,0101 mathematics ,Extreme point ,Invariant (mathematics) ,Trajectory (fluid mechanics) ,Mathematics ,Simplex ,010102 general mathematics ,Mathematical analysis ,15a63 ,46a55 ,fixed point ,trajectory ,020201 artificial intelligence & image processing ,simplex - Abstract
The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.
- Published
- 2016
23. Structures of W(2.2) Lie conformal algebra
- Author
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Henan Wu and Lamei Yuan
- Subjects
Pure mathematics ,conformal derivation ,conformal module ,General Mathematics ,Conformal map ,Lambda ,01 natural sciences ,0103 physical sciences ,FOS: Mathematics ,QA1-939 ,05c76 ,0101 mathematics ,05c50 ,Geometry and topology ,05c30 ,Mathematics ,Quantitative Biology::Biomolecules ,010102 general mathematics ,central extension ,Mathematics - Rings and Algebras ,Cohomology ,Lie conformal algebra ,Rings and Algebras (math.RA) ,05c05 ,cohomology ,010307 mathematical physics - Abstract
The purpose of this paper is to study $W(2,2)$ Lie conformal algebra, which has a free $\mathbb{C}[\partial]$-basis $\{L, M\}$ such that $[L_\lambda L]=(\partial+2\lambda)L$, $[L_\lambda M]=(\partial+2\lambda)M$, $[M_\lambda M]=0$. In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes., Comment: 13 pages. arXiv admin note: text overlap with arXiv:1601.06917
- Published
- 2016
24. Retracts of Ultrahomogeneous Structures in the Context of Katetov Functors
- Author
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Dragan Mašulović
- Subjects
Algebra ,Functor ,Katetov functors ,Fraïsse limits ,General Mathematics ,Retract ,lcsh:Mathematics ,Context (language use) ,retracts ,lcsh:QA1-939 ,Mathematics - Abstract
In this paper, we characterize retracts of a wide class of Fraïssé limits using the tools developed in a recent paper by W. Kubis and the present author, which we refer to as Katetov functors. This approach enables us to conclude that in many cases, a structure is a retract of a Fraïssé limit if and only if it is algebraically closed in the surrounding category.
- Published
- 2015
25. Automorphism groups of rational elliptic surfaces with section and constant J-map
- Author
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Tolga Karayayla
- Subjects
Discrete mathematics ,Surface (mathematics) ,14j50 ,Pure mathematics ,Group (mathematics) ,mordell-weil group ,General Mathematics ,Outer automorphism group ,automorphism group ,j map ,Automorphism ,Section (fiber bundle) ,Mathematics::Group Theory ,Inner automorphism ,rational elliptic surface ,Elliptic surface ,singular fiber ,QA1-939 ,elliptic surface ,14j27 ,Complex manifold ,14j26 ,Mathematics - Abstract
In this paper, the automorphism groups of relatively minimal rational elliptic surfaces with section which have constant J-maps are classified. The ground field is ℂ. The automorphism group of such a surface β: B → ℙ1, denoted by Au t(B), consists of all biholomorphic maps on the complex manifold B. The group Au t(B) is isomorphic to the semi-direct product MW(B) ⋊ Aut σ (B) of the Mordell-Weil groupMW(B) (the group of sections of B), and the subgroup Aut σ (B) of the automorphisms preserving a fixed section σ of B which is called the zero section on B. The Mordell-Weil group MW(B) is determined by the configuration of singular fibers on the elliptic surface B due to Oguiso and Shioda [9]. In this work, the subgroup Aut σ (B) is determined with respect to the configuration of singular fibers of B. Together with a previous paper [4] where the case with non-constant J-maps was considered, this completes the classification of automorphism groups of relatively minimal rational elliptic surfaces with section.
- Published
- 2014
26. Note on group distance magic complete bipartite graphs
- Author
-
Sylwia Cichacz
- Subjects
Vertex (graph theory) ,Astrophysics::High Energy Astrophysical Phenomena ,General Mathematics ,Magic (programming) ,graph labeling ,abelian group ,Magic graph ,Graph ,Combinatorics ,Magic constant ,05c25 ,Bipartite graph ,Bijection ,Physics::Atomic and Molecular Clusters ,FOS: Mathematics ,QA1-939 ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,05c78 ,Abelian group ,Mathematics - Abstract
A $\Gamma$-distance magic labeling of a graph $G=(V,E)$ with $|V | = n$ is a bijection $\ell$ from $V$ to an Abelian group $\Gamma$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}\ell(y)$ of every vertex $x \in V$ is equal to the same element $\mu \in \Gamma$, called the \emph{magic constant}. A graph $G$ is called a \emph{group distance magic graph} if there exists a $\Gamma $-distance magic labeling for every Abelian group $\Gamma$ of order $|V(G)|$. In this paper we prove that some complete $k$-partite graphs are $\mathbb{Z}_p$-distance magic. Moreover we prove that $K_{m,n}$ is a group distance magic if and only if $n+m \not \equiv 2 \pmod 4$. We also show that if $n+m \equiv 2 \pmod 4$, then there does not exist a group $\Gamma$ of order $n+m$ such that there exists a $\Gamma$-distance labeling for $K_{m,n}$., Comment: Since the politc of the Journal I submitted the paper I need to withdraw the paper from arxiv
- Published
- 2014
27. Existence and uniqueness of solutions to weakly singular integral-algebraic and integro-differential equations
- Author
-
M. V. Bulatov, Ewa Weinmüller, and Pedro M. Lima
- Subjects
Pure mathematics ,Integro-differential equations ,Independent equation ,45F15 ,General Mathematics ,lcsh:Mathematics ,Mathematical analysis ,65R20 ,Delay differential equation ,Singular integral ,lcsh:QA1-939 ,Volterra integral equation ,symbols.namesake ,Singular solution ,Simultaneous equations ,symbols ,Differential algebraic equation ,Weakly singular ,Two-dimensional Volterra integral-algebraic equations ,Mathematics ,Numerical partial differential equations - Abstract
We consider systems of integral-algebraic and integro-differential equations with weakly singular kernels. Although these problem classes are not in the focus of the main stream literature, they are interesting, not only in their own right, but also because they may arise from the analysis of certain classes of differential-algebraic systems of partial differential equations. In the first part of the paper, we deal with two-dimensional integral-algebraic equations. Next, we analyze Volterra integral equations of the first kind in which the determinant of the kernel matrix k(t, x) vanishes when t = x. Finally, the third part of the work is devoted to the analysis of degenerate integro-differential systems. The aim of the paper is to specify conditions which are sufficient for the existence of a unique continuous solution to the above problems. Theoretical findings are illustrated by a number of examples.
- Published
- 2014
28. The visibility parameter for words and permutations
- Author
-
Ligia-Loreta Cristea and Helmut Prodinger
- Subjects
Discrete mathematics ,General Mathematics ,permutations ,Visibility (geometry) ,Characterization (mathematics) ,q-enumeration ,words ,Combinatorics ,Combinatorics on words ,Number theory ,05a05 ,QA1-939 ,Alphabet ,Algebra over a field ,05a30 ,Graphs and Combinatorics ,Finite set ,Computer Science::Formal Languages and Automata Theory ,Mathematics - Abstract
We investigate the visibility parameter, i.e., the number of visible pairs, first for words over a finite alphabet, then for permutations of the finite set {1, 2, …, n}, and finally for words over an infinite alphabet whose letters occur with geometric probabilities. The results obtained for permutations correct the formula for the expectation obtained in a recent paper by Gutin et al. [Gutin G., Mansour T., Severini S., A characterization of horizontal visibility graphs and combinatorics on words, Phys. A, 2011, 390 (12), 2421–2428], and for words over a finite alphabet the formula obtained in the present paper for the expectation is more precise than that obtained in the cited paper. More importantly, we also compute the variance for each case.
- Published
- 2013
29. On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method
- Author
-
Haci Mehmet Baskonus and Hasan Bulut
- Subjects
fractional adams-bashforth-moulton method ,fractional nonlinear ordinary differential equation ,General Mathematics ,Ordinary differential equation ,Mathematical analysis ,QA1-939 ,fractional calculus ,Mathematics ,Fractional calculus ,Linear multistep method - Abstract
In this paper, we apply the Fractional Adams-Bashforth-Moulton Method for obtaining the numerical solutions of some linear and nonlinear fractional ordinary differential equations. Then, we construct a table including numerical results for both fractional differential equations. Then, we draw two dimensional surfaces of numerical solutions and analytical solutions by considering the suitable values of parameters. Finally, we use the L2 nodal norm and L∞ maximum nodal norm to evaluate the accuracy of method used in this paper.
- Published
- 2015
30. Compact perturbations of operators with property (t)
- Author
-
Xinling Yu, Weijuan Shi, and Guoxing Ji
- Subjects
47b20 ,47a10 ,function of operator ,weyl-type theorem ,General Mathematics ,QA1-939 ,property (t) ,compact perturbation ,Mathematics - Abstract
Let ℋ {\mathcal{ {\mathcal H} }} be an infinite dimensional complex Hilbert space and ℬ ( ℋ ) {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) the algebra of all bounded linear operators on ℋ {\mathcal{ {\mathcal H} }} . For an operator T ∈ ℬ ( ℋ ) T\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) , we say property ( t ) \left(t) holds for T T if σ ( T ) ⧹ σ u w ( T ) = Π 00 ( T ) \sigma \left(T)\hspace{-0.08em}\setminus \hspace{-0.08em}{\sigma }_{uw}\left(T)={\Pi }_{00}\left(T) , where σ ( T ) \sigma \left(T) and σ u w ( T ) {\sigma }_{uw}\left(T) denote the spectrum and the Weyl essential approximate point spectrum of T T , respectively, and Π 00 ( T ) = { λ ∈ iso σ ( T ) : 0 < n ( T − λ ) < ∞ } {\Pi }_{00}\left(T)=\left\{\lambda \in {\rm{iso}}\sigma \left(T):0\lt n\left(T-\lambda )\lt \infty \right\} . In this paper, we consider the stability of property ( t ) \left(t) under (small) compact perturbations. Also, we explore the relations between the stability of property ( t ) \left(t) and the stability of Weyl-type theorems. Moreover, we characterize those operators T T satisfying that property ( t ) \left(t) holds for f ( T ) f\left(T) for each function f f analytic on some neighborhood of σ ( T ) \sigma \left(T) .
- Published
- 2021
31. The role of w-tilting modules in relative Gorenstein (co)homology
- Author
-
Driss Bennis, Enrique Duarte, Juan R. García Rozas, and Luis Oyonarte
- Subjects
18g25 ,General Mathematics ,gorenstein modules ,QA1-939 ,(weakly) wakamatsu tilting module ,auslander class ,bass class ,16e30 ,Mathematics - Abstract
LetRRbe a ring,CCbe a leftRR-module andS=EndR(C)S={{\rm{End}}}_{R}\left(C). WhenCCis semidualizing, the Auslander classAC(S){{\mathcal{A}}}_{C}\left(S)and the Bass classℬC(R){{\mathcal{ {\mathcal B} }}}_{C}\left(R)associated withCChave been the subject of extensive investigations. It has been proved that these classes, also known as Foxby classes, are one of the central concepts of (relative) Gorenstein homological algebra. In this paper, we answer several natural questions which arise when we weaken the condition ofCCbeing semidualizing: if we letCCbe w-tilting (see Definition 2.1), we establish the conditions for the pair(AC(S),AC(S)⊥1)\left({{\mathcal{A}}}_{C}\left(S),{{\mathcal{A}}}_{C}{\left(S)}^{{\perp }_{1}})to be a perfect cotorsion theory and for the pair(BC⊥1(R),BC(R))\left({}^{{\perp }_{1}}B_{C}\left(R),{B}_{C}\left(R))to be a complete hereditary cotorsion theory. This tells us when the classes of Auslander and Bass are preenveloping and precovering, which generalizes a number of results disseminated in the literature. We investigate Gorenstein flat modules relative to a not necessarily semidualizing moduleCCand we find conditions for the class ofGC{G}_{C}-projective modules to be special precovering, the class ofGC{G}_{C}-flat modules to be covering, the one of GorensteinCC-projective modules to be precovering and that of GorensteinCC-injective modules to be preenveloping. We also find how to recover Foxby classes fromAddR(C){{\rm{Add}}}_{R}\left(C)-resolutions ofRR.
- Published
- 2021
32. Global optimization and applications to a variational inequality problem
- Author
-
Azhar Hussain, Muhammad Adeel, Hassen Aydi, and Dumitru Baleanu
- Subjects
65k10 ,General Mathematics ,cyclic contraction ,QA1-939 ,best proximity point ,variational inequality ,47h10 ,Mathematics - Abstract
In the present paper, we study the existence and convergence of the best proximity point for cyclic Θ \Theta -contractions. As consequences, we extract several fixed point results for such cyclic mappings. As an application, we present some solvability theorems in the topic of variational inequalities.
- Published
- 2021
33. On multi-step methods for singular fractional q-integro-differential equations
- Author
-
Sayyedeh Narges Hajiseyedazizi, Mohammad Esmael Samei, Jehad Alzabut, and Yu-ming Chu
- Subjects
General Mathematics ,QA1-939 ,34b16 ,multi-step methods ,34a08 ,39a13 ,singularity ,Mathematics ,q-integro-differential equation - Abstract
The objective of this paper is to investigate, by applying the standard Caputo fractional q-derivative of order α \alpha , the existence of solutions for the singular fractional q-integro-differential equation D q α [ k ] ( t ) = Ω ( t , k 1 , k 2 , k 3 , k 4 ) {{\mathcal{D}}}_{q}^{\alpha }\left[k]\left(t)=\Omega \left(t,{k}_{1},{k}_{2},{k}_{3},{k}_{4}) , under some boundary conditions where Ω \Omega is singular at some point 0 ≤ t ≤ 1 0\le t\le 1 , on a time scale T t 0 = { t : t = t 0 q n } ∪ { 0 } {{\mathbb{T}}}_{{t}_{0}}=\left\{t:t={t}_{0}{q}^{n}\right\}\cup \left\{0\right\} , for n ∈ N n\in {\mathbb{N}} where t 0 ∈ R {t}_{0}\in {\mathbb{R}} and q ∈ ( 0 , 1 ) q\in \left(0,1) . We consider the compact map and avail the Lebesgue dominated theorem for finding solutions of the addressed problem. Besides, we prove the main results in context of completely continuous functions. Our attention is concentrated on fractional multi-step methods of both implicit and explicit type, for which sufficient existence conditions are investigated. Finally, we present some examples involving graphs, tables and algorithms to illustrate the validity of our theoretical findings.
- Published
- 2021
34. L∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition
- Author
-
Madjda Miloudi, Samira Saadi, and Mohamed Haiour
- Subjects
47h09 ,algorithm ,General Mathematics ,fixed point hamilton-jacobi-bellman equation ,65m12 ,contraction ,finite element ,60h15 ,QA1-939 ,l∞-error estimate ,65f30 ,65l60 ,47h10 ,Mathematics - Abstract
In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.
- Published
- 2021
35. The discrete maximum principle for Galerkin solutions of elliptic problems
- Author
-
Tomáš Vejchodský
- Subjects
65n30 ,35b50 ,General Mathematics ,Mathematical analysis ,discrete maximum principle ,Field (mathematics) ,Function (mathematics) ,Projection (linear algebra) ,Finite element method ,finite element metho ,monotone methods ,galerkin solution ,Maximum principle ,Number theory ,Discontinuous Galerkin method ,QA1-939 ,Galerkin method ,Mathematics - Abstract
This paper provides an equivalent characterization of the discrete maximum principle for Galerkin solutions of general linear elliptic problems. The characterization is formulated in terms of the discrete Green's function and the elliptic projection of the boundary data. This general concept is applied to the analysis of the discrete maximum principle for the higher-order finite elements in one-dimension and to the lowest-order finite elements on simplices of arbitrary dimension. The paper surveys the state of the art in the field of the discrete maximum principle and provides new generalizations of several results. © 2012 Versita Warsaw and Springer-Verlag Wien.
- Published
- 2012
36. Large dimensional sets not containing a given angle
- Author
-
Viktor Harangi
- Subjects
28a80 ,Euclidean space ,General Mathematics ,Dimension (graph theory) ,Minkowski–Bouligand dimension ,sets without given angles ,Effective dimension ,Combinatorics ,self-similar sets ,Compact space ,Number theory ,Hausdorff dimension ,QA1-939 ,28a78 ,Inductive dimension ,hausdorff dimension ,Mathematics - Abstract
We say that a set in a Euclidean space does not contain an angle α if the angle determined by any three points of the set is not equal to α. The goal of this paper is to construct compact sets of large Hausdorff dimension that do not contain a given angle α ∈ (0,π). We will construct such sets in ℝ n of Hausdorff dimension c(α)n with a positive c(α) depending only on α provided that α is different from π/3, π/2 and 2π/3. This improves on an earlier construction (due to several authors) that has dimension c(α) log n. The main result of the paper concerns the case of the angles π/3 and 2π/3. We present self-similar sets in ℝ n of Hausdorff dimension $c{{\sqrt[3]{n}} \mathord{\left/ {\vphantom {{\sqrt[3]{n}} {\log n}}} \right. \kern-\nulldelimiterspace} {\log n}}$ with the property that they do not contain the angles π/3 and 2π/3. The constructed sets avoid not only the given angle α but also a small neighbourhood of α.
- Published
- 2011
37. Dominating and total dominating partitions in cubic graphs
- Author
-
Michael A. Henning and Justin Southey
- Subjects
Domatic number ,Discrete mathematics ,vertex partition ,hypergraph transversal ,General Mathematics ,cubic graphs ,Disjoint sets ,Connected dominating set ,Bidimensionality ,Combinatorics ,Dominating set ,05c69 ,QA1-939 ,Cubic graph ,total domination ,Maximal independent set ,Mathematics ,Complement (set theory) - Abstract
In this paper, we continue the study of domination and total domination in cubic graphs. It is known [Henning M.A., Southey J., A note on graphs with disjoint dominating and total dominating sets, Ars Combin., 2008, 89, 159–162] that every cubic graph has a dominating set and a total dominating set which are disjoint. In this paper we show that every connected cubic graph on nvertices has a total dominating set whose complement contains a dominating set such that the cardinality of the total dominating set is at most (n+2)/2, and this bound is essentially best possible.
- Published
- 2011
38. Affine compact almost-homogeneous manifolds of cohomogeneity one
- Author
-
Daniel Guan
- Subjects
Pure mathematics ,General Mathematics ,Fano plane ,53c10 ,53c55 ,Connected sum ,futaki invariants ,32q20 ,Global analysis ,Ricci-flat manifold ,QA1-939 ,32l05 ,fourth order differential equations ,Mathematics::Symplectic Geometry ,14m17 ,kähler-einstein metrics ,Mathematics ,Mathematical analysis ,fibre bundles ,existence ,53c21 ,fano manifolds ,extremal metrics ,Mathematics::Geometric Topology ,Manifold ,almost-homogeneous manifolds ,Hypersurface ,cohomogeneity one ,32m12 ,Differential topology ,Mathematics::Differential Geometry ,Affine transformation ,geodesic stability - Abstract
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.
- Published
- 2009
39. Solution of integral equations via coupled fixed point theorems in 𝔉-complete metric spaces
- Author
-
Gunaseelan Mani, Arul Joseph Gnanaprakasam, Jung Rye Lee, and Choonkil Park
- Subjects
orthogonal set ,orthogonal metric space ,coupled fixed point ,54h25 ,orthogonal continuous ,General Mathematics ,QA1-939 ,orthogonal preserving ,orthogonal 𝔉-contraction ,47h10 ,Mathematics - Abstract
The concept of coupled 𝔉-orthogonal contraction mapping is introduced in this paper, and some coupled fixed point theorems in orthogonal metric spaces are proved. The obtained results generalize and extend some of the well-known results in the literature. An example is presented to support our results. Furthermore, we apply our result to obtain the existence theorem for a common solution of the integral equations: ζ ( v ) = ð ( v ) + ∫ 0 M Ξ ( v , β ) Ω ( β , ζ ( β ) , ξ ( β ) ) d β , v ∈ [ 0 , H ] , ξ ( v ) = ð ( v ) + ∫ 0 M Ξ ( v , β ) Ω ( β , ξ ( β ) , ζ ( β ) ) d β , v ∈ [ 0 , H ] , \left\{\begin{array}{ll}\zeta \left({\mathfrak{v}})=ð\left({\mathfrak{v}})+\underset{0}{\overset{{\mathfrak{M}}}{\displaystyle \int }}\Xi \left({\mathfrak{v}},\beta )\Omega \left(\beta ,\zeta \left(\beta ),\xi \left(\beta )){\rm{d}}\beta ,& {\mathfrak{v}}\in \left[0,{\mathscr{H}}],\\ \xi \left({\mathfrak{v}})=ð\left({\mathfrak{v}})+\underset{0}{\overset{{\mathfrak{M}}}{\displaystyle \int }}\Xi \left({\mathfrak{v}},\beta )\Omega \left(\beta ,\xi \left(\beta ),\zeta \left(\beta )){\rm{d}}\beta ,& {\mathfrak{v}}\in \left[0,{\mathscr{H}}],\end{array}\right. where (a) ð : M → R ð:{\mathfrak{M}}\to {\mathbb{R}} and Ω : M × R × R → R \Omega :{\mathfrak{M}}\times {\mathbb{R}}\times {\mathbb{R}}\to {\mathbb{R}} are continuous; (b) Ξ : M × M \Xi :{\mathfrak{M}}\times {\mathfrak{M}} is continuous and measurable at β ∈ M , ∀ \beta \in {\mathfrak{M}},\hspace{0.33em}\forall v ∈ M {\mathfrak{v}}\in {\mathfrak{M}} ; (c) Ξ ( v , β ) ≥ 0 , ∀ v , β ∈ M \Xi \left({\mathfrak{v}},\beta )\ge 0,\hspace{0.33em}\forall {\mathfrak{v}},\beta \in {\mathfrak{M}} and ∫ 0 H Ξ ( v , β ) d β ≤ 1 , ∀ v ∈ M {\int }_{0}^{{\mathscr{H}}}\Xi \left({\mathfrak{v}},\beta ){\rm{d}}\beta \le 1,\hspace{0.33em}\forall {\mathfrak{v}}\in {\mathfrak{M}} .
- Published
- 2021
40. Comparison of modified ADM and classical finite difference method for some third-order and fifth-order KdV equations
- Author
-
Abey Sherif Kelil and Appanah Rao Appadu
- Subjects
35a22 ,General Mathematics ,modified adomian decomposition method ,Finite difference method ,classical finite difference method ,34a45 ,35a25 ,Third order ,Nonlinear Sciences::Exactly Solvable and Integrable Systems ,blow up ,QA1-939 ,Order (group theory) ,Applied mathematics ,Korteweg–de Vries equation ,nonlinear kdv equations ,Mathematics - Abstract
The KdV equation, which appears as an asymptotic model in physical systems ranging from water waves to plasma physics, has been studied. In this paper, we are concerned with dispersive nonlinear KdV equations by using two reliable methods: Shehu Adomian decomposition method (STADM) and the classical finite difference method for solving three numerical experiments. STADM is constructed by combining Shehu’s transform and Adomian decomposition method, and the nonlinear terms can be easily handled using Adomian’s polynomials. The Shehu transform is used to accelerate the convergence of the solution series in most cases and to overcome the deficiency that is mainly caused by unsatisfied conditions in other analytical techniques. We compare the approximate and numerical results with the exact solution for the two numerical experiments. The third numerical experiment does not have an exact solution and we compare profiles from the two methods vs the space domain at some values of time. This study provides us with information about which of the two methods are effective based on the numerical experiment chosen. Knowledge acquired will enable us to construct methods for other related partial differential equations such as stochastic Korteweg-de Vries (KdV), KdV-Burgers, and fractional KdV equations.
- Published
- 2021
41. Symmetric pairs and pseudosymmetry of Θ-Yetter-Drinfeld categories for Hom-Hopf algebras
- Author
-
Wei Liu and Xiaoli Fang
- Subjects
hom-hopf algebra ,symmetric pair ,16t15 ,16t05 ,General Mathematics ,Mathematics::Category Theory ,Mathematics::Quantum Algebra ,Mathematics::Rings and Algebras ,QA1-939 ,θ-yetter-drinfeld module ,Mathematics - Abstract
In this paper, we investigate a more general category of Θ \Theta -Yetter-Drinfeld modules ( Θ ∈ Aut H ( H ) \Theta \in {\rm{Aut}}\hspace{0.33em}H\left(H) ) over a Hom-Hopf algebra, which unifies two different definitions of Hom-Yetter-Drinfeld category introduced by Makhlouf and Panaite, Li and Ma, respectively. We show that the category of Θ \Theta -Yetter-Drinfeld modules with a bijective antipode S S is a braided tensor category and some solutions of the Hom-Yang-Baxter equation and the Yang-Baxter equation can be constructed by this category. Also by the method of symmetric pairs, we prove that if a Θ \Theta -Yetter-Drinfeld category over a Hom-Hopf algebra H H is symmetric, then H H is trivial. Finally, we find a sufficient and necessary condition for a Θ \Theta -Yetter-Drinfeld category to be pseudosymmetric.
- Published
- 2021
42. Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
- Author
-
Hadia Messaoudene, Asma Alharbi, and Nadia Mesbah
- Subjects
Pure mathematics ,General Mathematics ,Hilbert space ,numerical range ,class ℛ¯1 ,symbols.namesake ,Range (mathematics) ,Orthogonality ,47a12 ,orthogonality ,Kernel (statistics) ,symbols ,47a30 ,QA1-939 ,finite operator ,47b47 ,Mathematics - Abstract
Let ℋ {\mathcal{ {\mathcal H} }} be a complex Hilbert space and ℬ ( ℋ ) {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) denotes the algebra of all bounded linear operators acting on ℋ {\mathcal{ {\mathcal H} }} . In this paper, we present some new pairs of generalized finite operators. More precisely, new pairs of operators ( A , B ) ∈ ℬ ( ℋ ) × ℬ ( ℋ ) \left(A,B)\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }})\times {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}) satisfying: ∥ A X − X B − I ∥ ≥ 1 , for all X ∈ ℬ ( ℋ ) . \parallel AX-XB-I\parallel \ge 1,\hspace{1.0em}\hspace{0.1em}\text{for all}\hspace{0.1em}\hspace{0.33em}X\in {\mathcal{ {\mathcal B} }}\left({\mathcal{ {\mathcal H} }}). An example under which the class of such operators is not invariant under similarity orbit is given. Range kernel orthogonality of generalized derivation is also studied.
- Published
- 2021
43. Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces
- Author
-
Chuanxi Wu, Jing Mao, Feng Du, and Lanbao Hou
- Subjects
Pure mathematics ,General Mathematics ,eigenvalues ,53c20 ,53c42 ,Measure (mathematics) ,smooth metric measure space ,weighted ricci curvature ,Metric (mathematics) ,QA1-939 ,Mathematics::Differential Geometry ,poly-drifting laplacian ,Laplace operator ,universal inequalities ,Eigenvalues and eigenvectors ,Mathematics ,35p15 - Abstract
In this paper, we study the eigenvalue problem of poly-drifting Laplacian on complete smooth metric measure space ( M , ⟨ , ⟩ , e − ϕ d v ) \left(M,\langle ,\rangle ,{e}^{-\phi }{\rm{d}}v) , with nonnegative weighted Ricci curvature Ric ϕ ≥ 0 {{\rm{Ric}}}^{\phi }\ge 0 for some ϕ ∈ C 2 ( M ) \phi \in {C}^{2}\left(M) , which is uniformly bounded from above, and successfully obtain several universal inequalities of this eigenvalue problem.
- Published
- 2021
44. Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions
- Author
-
Sundas Khan, Hüseyin Budak, Muhammad Ali, Hasan Kara, Yu-Ming Chu, and [Belirlenecek]
- Subjects
Pure mathematics ,Hermite polynomials ,Inequality ,hermite-hadamard inequality ,General Mathematics ,media_common.quotation_subject ,fractional integrals ,Type (model theory) ,Interval valued ,26d15 ,Hadamard transform ,Hermite–Hadamard inequality ,QA1-939 ,26a51 ,Convex function ,interval-valued functions ,26d10 ,Mathematics ,media_common - Abstract
In this work, we introduce the notions about the Riemann-Liouville fractional integrals for interval-valued functions on co-ordinates. We also establish Hermite-Hadamard and some related inequalities for co-ordinated convex interval-valued functions by applying the newly defined fractional integrals. The results of the present paper are the extension of several previously published results. © 2021 Huseyin Budak et al., published by De Gruyter. 2-s2.0-85117069629
- Published
- 2021
45. Deterministic and random approximation by the combination of algebraic polynomials and trigonometric polynomials
- Author
-
Zhihua Zhang
- Subjects
Pure mathematics ,Fourier approximation ,Differential equation ,42-xx ,General Mathematics ,41-xx ,differential equations ,trigonometric polynomial ,fourier approximation ,Trigonometric polynomial ,QA1-939 ,65-xx ,Trigonometry ,Mathematics ,Algebraic polynomial - Abstract
Fourier approximation plays a key role in qualitative theory of deterministic and random differential equations. In this paper, we will develop a new approximation tool. For an m m -order differentiable function f f on [ 0 , 1 0,1 ], we will construct an m m -degree algebraic polynomial P m {P}_{m} depending on values of f f and its derivatives at ends of [ 0 , 1 0,1 ] such that the Fourier coefficients of R m = f − P m {R}_{m}=f-{P}_{m} decay fast. Since the partial sum of Fourier series R m {R}_{m} is a trigonometric polynomial, we can reconstruct the function f f well by the combination of a polynomial and a trigonometric polynomial. Moreover, we will extend these results to the case of random processes.
- Published
- 2021
46. On kernels by monochromatic paths in the corona of digraphs
- Author
-
Iwona Włoch
- Subjects
Discrete mathematics ,General Mathematics ,Corona ,Number theory ,Product (mathematics) ,QA1-939 ,counting ,Monochromatic color ,Algebra over a field ,kernel by monochromatic paths ,corona ,Mathematics ,05c20 - Abstract
In this paper we derive necessary and sufficient conditions for the existence of kernels by monochromatic paths in the corona of digraphs. Using these results, we are able to prove the main result of this paper which provides necessary and sufficient conditions for the corona of digraphs to be monochromatic kernel-perfect. Moreover we calculate the total numbers of kernels by monochromatic paths, independent by monochromatic paths sets and dominating by monochromatic paths sets in this digraphs product.
- Published
- 2008
47. On stable least squares solution to the system of linear inequalities
- Author
-
Evald Ubi
- Subjects
Recursive least squares filter ,90c05 ,system of linear inequalities ,General Mathematics ,Mathematical analysis ,MathematicsofComputing_NUMERICALANALYSIS ,65k05 ,Generalized least squares ,successive projection ,Least squares ,Iteratively reweighted least squares ,Revised simplex method ,Non-linear least squares ,method of least squares ,QA1-939 ,Applied mathematics ,Total least squares ,Linear least squares ,householder transformation ,Mathematics - Abstract
The system of inequalities is transformed to the least squares problem on the positive ortant. This problem is solved using orthogonal transformations which are memorized as products. Author’s previous paper presented a method where at each step all the coefficients of the system were transformed. This paper describes a method applicable also to large matrices. Like in revised simplex method, in this method an auxiliary matrix is used for the computations. The algorithm is suitable for unstable and degenerate problems primarily.
- Published
- 2007
48. Range-Kernel orthogonality and elementary operators on certain Banach spaces
- Author
-
Ahmed Bachir, Khalid Ouarghi, Abdelkader Segres, and Nawal Ali Sayyaf
- Subjects
trace class operators ,Pure mathematics ,schatten p-classes ,Nuclear operator ,General Mathematics ,Banach space ,47b10 ,Kernel (algebra) ,Range (mathematics) ,46b20 ,47b20 ,Orthogonality ,range-kernel orthogonality ,47a30 ,QA1-939 ,elementary operator ,47b47 ,Mathematics - Abstract
The characterization of the points in C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , the Von Neuman-Schatten p-classes, that are orthogonal to the range of elementary operators has been done for certain kinds of elementary operators. In this paper, we shall study this problem of characterization on an abstract reflexive, smooth and strictly convex Banach space for arbitrary operator. As an application, we consider other kinds of elementary operators defined on the spaces C p : 1 ≤ p < ∞ ( ℋ ) {C}_{p{:}_{1\le p\lt \infty }}\left({\mathcal{ {\mathcal H} }}) , and finally, we give a counterexample to Mecheri’s result given in this context.
- Published
- 2021
49. Global existence and boundedness in a two-species chemotaxis system with nonlinear diffusion
- Author
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Yongjie Han, Ting Huang, and Zhibo Hou
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General Mathematics ,Mathematical analysis ,Chemotaxis ,35q92 ,boundedness ,92c17 ,chemotaxis system ,logistic source ,35k55 ,QA1-939 ,Nonlinear diffusion ,nonlinear diffusion ,Mathematics - Abstract
This paper is concerned with a chemotaxis system u t = Δ u m − ∇ ⋅ ( χ 1 ( w ) u ∇ w ) + μ 1 u ( 1 − u − a 1 v ) , x ∈ Ω , t > 0 , v t = Δ v n − ∇ ⋅ ( χ 2 ( w ) v ∇ w ) + μ 2 v ( 1 − a 2 u − v ) , x ∈ Ω , t > 0 , w t = Δ w − ( α u + β v ) w , x ∈ Ω , t > 0 , \left\{\begin{array}{ll}{u}_{t}=\Delta {u}^{m}-\nabla \cdot \left({\chi }_{1}\left(w)u\nabla w)+{\mu }_{1}u\left(1-u-{a}_{1}v),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {v}_{t}=\Delta {v}^{n}-\nabla \cdot \left({\chi }_{2}\left(w)v\nabla w)+{\mu }_{2}v\left(1-{a}_{2}u-v),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {w}_{t}=\Delta w-\left(\alpha u+\beta v)w,& x\in \Omega ,\hspace{0.33em}t\gt 0,\end{array}\right. under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ R 3 \Omega \subset {{\mathbb{R}}}^{3} with smooth boundary, where μ 1 , μ 2 > 0 {\mu }_{1},{\mu }_{2}\gt 0 , a 1 , a 2 > 0 {a}_{1},{a}_{2}\gt 0 , α , β > 0 \alpha ,\beta \gt 0 , and the chemotactic sensitivity function χ i ∈ C 1 ( [ 0 , ∞ ) ) {\chi }_{i}\in {C}^{1}({[}0,\infty )) , χ i ′ ≥ 0 {\chi }_{i}^{^{\prime} }\ge 0 . It is proved that for any large initial data, for any m , n > 1 m,n\gt 1 , the system admits a global weak solution, which is uniformly bounded.
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- 2021
50. Long time decay for 3D Navier-Stokes equations in Fourier-Lei-Lin spaces
- Author
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Lotfi Jlali
- Subjects
long time decay ,navier-stokes equations ,General Mathematics ,Mathematical analysis ,Time decay ,critical spaces ,35d35 ,symbols.namesake ,Fourier transform ,35q30 ,symbols ,QA1-939 ,Navier–Stokes equations ,Mathematics - Abstract
In this paper, we study the long time decay of global solution to the 3D incompressible Navier-Stokes equations. We prove that if u ∈ C ( R + , X − 1 , σ ( R 3 ) ) u\in {\mathcal{C}}\left({{\mathbb{R}}}^{+},{{\mathcal{X}}}^{-1,\sigma }\left({{\mathbb{R}}}^{3})) is a global solution to the considered equation, where X i , σ ( R 3 ) {{\mathcal{X}}}^{i,\sigma }\left({{\mathbb{R}}}^{3}) is the Fourier-Lei-Lin space with parameters i = − 1 i=-1 and σ ≥ − 1 \sigma \ge -1 , then ‖ u ( t ) ‖ X − 1 , σ \Vert u\left(t){\Vert }_{{{\mathcal{X}}}^{-1,\sigma }} decays to zero as time goes to infinity. The used techniques are based on Fourier analysis.
- Published
- 2021
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