118 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. 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
6. 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
7. 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
8. 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
9. 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
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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
- Full Text
- View/download PDF
10. 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
11. 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
12. Some results on generalized finite operators and range kernel orthogonality in Hilbert spaces
- Author
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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
13. Universal inequalities of the poly-drifting Laplacian on smooth metric measure spaces
- Author
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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
14. Fractional Hermite-Hadamard-type inequalities for interval-valued co-ordinated convex functions
- Author
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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
15. Deterministic and random approximation by the combination of algebraic polynomials and trigonometric polynomials
- Author
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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
16. Range-Kernel orthogonality and elementary operators on certain Banach spaces
- Author
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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
17. Semiprimeness of semigroup algebras
- Author
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Junying Guo and Xiaojiang Guo
- Subjects
Pure mathematics ,Semigroup ,Mathematics::Operator Algebras ,semigroup algebra ,General Mathematics ,semiprime algebra ,semiprimitive algebra ,20m25 ,primitive abundant semigroup ,16s36 ,QA1-939 ,complete quiver ,Mathematics ,locally ample semigroup - Abstract
Abundant semigroups originate from p.p. rings and are generalizations of regular semigroups. The main aim of this paper is to study the primeness and the primitivity of abundant semigroup algebras. We introduce and studyD∗{{\mathcal{D}}}^{\ast }-graphs and Fountain matrices of a semigroup. Based onD∗{{\mathcal{D}}}^{\ast }-graphs and Fountain matrices, we determine when a contracted semigroup algebra of a primitive abundant semigroup is prime (respectively, semiprime, semiprimitive, or primitive). It is well known that for any algebraA{\mathcal{A}}with unity,A{\mathcal{A}}is primitive (prime) if and only if so isMn(A){M}_{n}\left({\mathcal{A}}). Our results can be viewed as some kind of generalizations of such a known result. In addition, it is proved that any contracted semigroup algebra of a locally ample semigroup whose set of idempotents is locally finite (respectively, locally pseudofinite and satisfying the regularity condition) is isomorphic to some contracted semigroup algebra of primitive abundant semigroups. Moreover, we obtain sufficient and necessary conditions for these classes of contracted semigroup algebras to be prime (respectively, semiprime, semiprimitive, or primitive). Finally, the structure of simple contracted semigroup algebras of idempotent-connected abundant semigroups is established. Our results enrich and extend the related results on regular semigroup algebras.
- Published
- 2021
18. Blow-up results of the positive solution for a class of degenerate parabolic equations
- Author
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Chenyu Dong and Juntang Ding
- Subjects
blow-up solution ,Class (set theory) ,Pure mathematics ,degenerate parabolic equation ,General Mathematics ,Degenerate energy levels ,QA1-939 ,35k65 ,blow-up time ,Parabolic partial differential equation ,Mathematics ,35k92 - Abstract
This paper is devoted to discussing the blow-up problem of the positive solution of the following degenerate parabolic equations: ( r ( u ) ) t = div ( ∣ ∇ u ∣ p ∇ u ) + f ( x , t , u , ∣ ∇ u ∣ 2 ) , ( x , t ) ∈ D × ( 0 , T ∗ ) , ∂ u ∂ ν + σ u = 0 , ( x , t ) ∈ ∂ D × ( 0 , T ∗ ) , u ( x , 0 ) = u 0 ( x ) , x ∈ D ¯ . \left\{\begin{array}{ll}{(r\left(u))}_{t}={\rm{div}}(| \nabla u{| }^{p}\nabla u)+f\left(x,t,u,| \nabla u\hspace{-0.25em}{| }^{2}),& \left(x,t)\in D\times \left(0,{T}^{\ast }),\\ \frac{\partial u}{\partial \nu }+\sigma u=0,& \left(x,t)\in \partial D\times \left(0,{T}^{\ast }),\\ u\left(x,0)={u}_{0}\left(x),& x\in \overline{D}.\end{array}\right. Here p > 0 p\gt 0 , the spatial region D ⊂ R n ( n ≥ 2 ) D\subset {{\mathbb{R}}}^{n}\hspace{0.33em}\left(n\ge 2) is bounded, and its boundary ∂ D \partial D is smooth. We give the conditions that cause the positive solution of this degenerate parabolic problem to blow up. At the same time, for the positive blow-up solution of this problem, we also obtain an upper bound of the blow-up time and an upper estimate of the blow-up rate. We mainly carry out our research by means of maximum principles and first-order differential inequality technique.
- Published
- 2021
19. Power moments of automorphic L-functions related to Maass forms for SL3(ℤ)
- Author
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Huafeng Liu, Deyu Zhang, and Jing Huang
- Subjects
Pure mathematics ,General Mathematics ,automorphic form ,11f66 ,Automorphic form ,QA1-939 ,11f03 ,L-function ,l-function ,Mathematics ,Power (physics) ,power moments - Abstract
Let f f be a self-dual Hecke-Maass eigenform for the group S L 3 ( Z ) S{L}_{3}\left({\mathbb{Z}}) . For 1 2 < σ < 1 \frac{1}{2}\lt \sigma \lt 1 fixed we define m ( σ ) m\left(\sigma ) ( ≥ 2 \ge 2 ) as the supremum of all numbers m m such that ∫ 1 T ∣ L ( s , f ) ∣ m d t ≪ f , ε T 1 + ε , \underset{1}{\overset{T}{\int }}| L\left(s,f){| }^{m}{\rm{d}}t{\ll }_{f,\varepsilon }{T}^{1+\varepsilon }, where L ( s , f ) L\left(s,f) is the Godement-Jacquet L-function related to f f . In this paper, we first show the lower bound of m ( σ ) m\left(\sigma ) for 2 3 < σ < 1 \frac{2}{3}\lt \sigma \lt 1 . Then we establish asymptotic formulas for the second, fourth and sixth powers of L ( s , f ) L\left(s,f) as applications.
- Published
- 2021
20. Some estimates for commutators of Littlewood-Paley g-functions
- Author
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Guanghui Lu
- Subjects
Pure mathematics ,General Mathematics ,commutator ,Commutator (electric) ,law.invention ,generalized morrey space ,30l99 ,Littlewood paley ,law ,littlewood-paley g-function ,QA1-939 ,non-homogeneous metric measure space ,space rbmo(μ) ,42b25 ,42b35 ,Mathematics - Abstract
The aim of this paper is to establish the boundedness of commutator [ b , g ˙ r ] \left[b,{\dot{g}}_{r}] generated by Littlewood-Paley g g -functions g ˙ r {\dot{g}}_{r} and b ∈ RBMO ( μ ) b\in {\rm{RBMO}}\left(\mu ) on non-homogeneous metric measure space. Under assumption that λ \lambda satisfies ε \varepsilon -weak reverse doubling condition, the author proves that [ b , g ˙ r ] \left[b,{\dot{g}}_{r}] is bounded from Lebesgue spaces L p ( μ ) {L}^{p}\left(\mu ) into Lebesgue spaces L p ( μ ) {L}^{p}\left(\mu ) for p ∈ ( 1 , ∞ ) p\in \left(1,\infty ) and also bounded from spaces L 1 ( μ ) {L}^{1}\left(\mu ) into spaces L 1 , ∞ ( μ ) {L}^{1,\infty }\left(\mu ) . Furthermore, the boundedness of [ b , g ˙ r b,{\dot{g}}_{r} ] on Morrey space M q p ( μ ) {M}_{q}^{p}\left(\mu ) and on generalized Morrey L p , ϕ ( μ ) {L}^{p,\phi }\left(\mu ) is obtained.
- Published
- 2021
21. On the type 2 poly-Bernoulli polynomials associated with umbral calculus
- Author
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Dae San Kim, Dmitry V. Dolgy, Jin-Woo Park, and Taekyun Kim
- Subjects
Pure mathematics ,General Mathematics ,Type (model theory) ,umbral calculus ,11b83 ,modified poly-exponential functions ,Bernoulli polynomials ,symbols.namesake ,type 2 poly-bernoulli polynomials ,symbols ,QA1-939 ,Mathematics ,Umbral calculus - Abstract
Type 2 poly-Bernoulli polynomials were introduced recently with the help of modified polyexponential functions. In this paper, we investigate several properties and identities associated with those polynomials arising from umbral calculus techniques. In particular, we express the type 2 poly-Bernoulli polynomials in terms of several special polynomials, like higher-order Cauchy polynomials, higher-order Euler polynomials, and higher-order Frobenius-Euler polynomials.
- Published
- 2021
22. On intersections of two non-incident subgroups of finite p-groups
- Author
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Jiao Wang
- Subjects
Pure mathematics ,metacyclic p-group ,commutator subgroup ,General Mathematics ,Commutator subgroup ,20d15 ,QA1-939 ,finite p-group ,Mathematics - Abstract
In this paper, we investigate finite p-groups G G such that whenever A , B < G A,B\lt G are non-incident, then A ∩ B ⊴ ⟨ A , B ⟩ A\cap B\hspace{0.33em}⊴\hspace{0.33em}\langle A,B\rangle . This partially solves a problem proposed by Y. Berkovich.
- Published
- 2021
23. Some estimates for the commutators of multilinear maximal function on Morrey-type space
- Author
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Xiao Yu, Pu Zhang, and Hongliang Li
- Subjects
Pure mathematics ,Multilinear map ,Mathematics::Functional Analysis ,General Mathematics ,010102 general mathematics ,Mathematics::Analysis of PDEs ,Mathematics::Classical Analysis and ODEs ,commutator ,Commutator (electric) ,Type (model theory) ,Space (mathematics) ,01 natural sciences ,law.invention ,010101 applied mathematics ,orlicz function ,multilinear maximal function ,law ,QA1-939 ,Maximal function ,morrey-type space ,42b20 ,0101 mathematics ,42b25 ,Mathematics - Abstract
In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.
- Published
- 2021
24. On a new generalization of some Hilbert-type inequalities
- Author
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Wei Song, Xiaoyu Wang, and Minghui You
- Subjects
Pure mathematics ,Inequality ,41a17 ,Generalization ,hilbert-type inequality ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Type (model theory) ,Partial fraction decomposition ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,26d15 ,partial fraction expansion ,symbols ,QA1-939 ,euler number ,0101 mathematics ,Euler number ,Bernoulli number ,Mathematics ,media_common ,bernoulli number - Abstract
In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established. By convention, the equivalent Hardy-type inequality is also considered. Furthermore, by introducing the partial fraction expansions of trigonometric functions, some special and interesting Hilbert-type inequalities with the constant factors represented by the higher derivatives of trigonometric functions, the Euler number and the Bernoulli number are presented at the end of the paper.
- Published
- 2021
25. On some fixed point theorems for multivalued F-contractions in partial metric spaces
- Author
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Santosh Kumar and Sholastica Luambano
- Subjects
Pure mathematics ,General Mathematics ,partial metric spaces ,010102 general mathematics ,Fixed-point theorem ,Mathematics::General Topology ,01 natural sciences ,fixed point theorems ,010101 applied mathematics ,Metric space ,54h25 ,multivalued f-contraction mappings ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,0101 mathematics ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,47h10 ,Mathematics - Abstract
Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.
- Published
- 2021
26. Properties of multiplication operators on the space of functions of bounded φ-variation
- Author
-
René Erlín Castillo, Harold Vacca-González, and Julio C. Ramos-Fernández
- Subjects
Pure mathematics ,bounded variation functions ,General Mathematics ,010102 general mathematics ,Compact operator ,Space (mathematics) ,01 natural sciences ,fredholm operators ,010101 applied mathematics ,Variation (linguistics) ,46e40 ,Multiplication operator ,Bounded function ,multiplication operator ,QA1-939 ,Multiplication ,26b30 ,0101 mathematics ,26a45 ,47b38 ,Mathematics ,compact operators - Abstract
In this paper, the functions u ∈ B V φ [ 0 , 1 ] u\in B{V}_{\varphi }\left[0,1] which define compact and Fredholm multiplication operators M u {M}_{u} acting on the space of functions of bounded φ \varphi -variation are studied. All the functions u ∈ B V φ [ 0 , 1 ] u\hspace{-0.08em}\in \hspace{-0.08em}B{V}_{\varphi }\left[0,\hspace{-0.08em}1] which define multiplication operators M u : B V φ [ 0 , 1 ] → B V φ [ 0 , 1 ] {M}_{u}:B{V}_{\varphi }\left[0,1]\to B{V}_{\varphi }\left[0,1] with closed range are characterized.
- Published
- 2021
27. Multiple solutions and ground state solutions for a class of generalized Kadomtsev-Petviashvili equation
- Author
-
Chunfang Chen, Chenggui Yuan, Yuting Zhu, and Jianhua Chen
- Subjects
Class (set theory) ,Pure mathematics ,General Mathematics ,010102 general mathematics ,35j20 ,Kadomtsev–Petviashvili equation ,01 natural sciences ,multiplicity of solutions ,35j60 ,010101 applied mathematics ,ground state solutions ,generalized kadomtsev-petviashvili equation ,QA1-939 ,0101 mathematics ,Ground state ,Mathematics - Abstract
In this paper, we study the following generalized Kadomtsev-Petviashvili equation u t + u x x x + ( h ( u ) ) x = D x − 1 Δ y u , {u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where ( t , x , y ) ∈ R + × R × R N − 1 \left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1} , N ≥ 2 N\ge 2 , D x − 1 f ( x , y ) = ∫ − ∞ x f ( s , y ) d s {D}_{x}^{-1}f\left(x,y)={\int }_{-\infty }^{x}f\left(s,y){\rm{d}}s , f t = ∂ f ∂ t {f}_{t}=\frac{\partial f}{\partial t} , f x = ∂ f ∂ x {f}_{x}=\frac{\partial f}{\partial x} and Δ y = ∑ i = 1 N − 1 ∂ 2 ∂ y i 2 {\Delta }_{y}={\sum }_{i=1}^{N-1}\frac{{\partial }^{2}}{{\partial }_{{y}_{i}}^{2}} . We get the existence of infinitely many nontrivial solutions under certain assumptions in bounded domain without Ambrosetti-Rabinowitz condition. Moreover, by using the method developed by Jeanjean [13], we establish the existence of ground state solutions in R N {{\mathbb{R}}}^{N} .
- Published
- 2021
28. A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
- Author
-
Esra Kaya
- Subjects
Pure mathematics ,Variable exponent ,Laplace transform ,b-maximal operator ,General Mathematics ,010102 general mathematics ,Mathematics::Classical Analysis and ODEs ,generalized translation operator ,Singular integral ,Differential operator ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,42a50 ,symbols ,QA1-939 ,variable exponent lebesgue spaces ,singular integrals ,0101 mathematics ,Lp space ,42b25 ,Bessel function ,42b35 ,Mathematics - Abstract
In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator ( B B -maximal operator) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the B B -maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the B B -maximal operator is not bounded on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces in the case of p − = 1 {p}_{-}=1 . We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B B -maximal function) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.
- Published
- 2021
29. Weak and strong estimates for linear and multilinear fractional Hausdorff operators on the Heisenberg group
- Author
-
Mingquan Wei, Xingsong Zhang, Yangkendi Deng, and Dunyan Yan
- Subjects
Pure mathematics ,Multilinear map ,hausdorff operator ,General Mathematics ,010102 general mathematics ,Hausdorff space ,heisenberg group ,01 natural sciences ,010101 applied mathematics ,sharp bound ,multilinear ,Heisenberg group ,QA1-939 ,42b20 ,0101 mathematics ,42b35 ,Mathematics - Abstract
This paper is devoted to the weak and strong estimates for the linear and multilinear fractional Hausdorff operators on the Heisenberg group H n {{\mathbb{H}}}^{n} . A sharp strong estimate for T Φ m {T}_{\Phi }^{m} is obtained. As an application, we derive the sharp constant for the product Hardy operator on H n {{\mathbb{H}}}^{n} . Some weak-type ( p , q ) \left(p,q) ( 1 ≤ p ≤ ∞ ) \left(1\le p\le \infty ) estimates for T Φ , β {T}_{\Phi ,\beta } are also obtained. As applications, we calculate some sharp weak constants for the fractional Hausdorff operator on the Heisenberg group. Besides, we give an explicit weak estimate for T Φ , β → m {T}_{\Phi ,\overrightarrow{\beta }}^{m} under some mild assumptions on Φ \Phi . We extend the results of Guo et al. [Hausdorff operators on the Heisenberg group, Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 11, 1703–1714] to the fractional setting.
- Published
- 2021
30. Fully degenerate Bell polynomials associated with degenerate Poisson random variables
- Author
-
Hye Kyung Kim
- Subjects
poisson random variable ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Degenerate energy levels ,Poisson distribution ,11b83 ,01 natural sciences ,degenerate poisson random variable ,11b73 ,bell polynomials and numbers ,Bell polynomials ,010101 applied mathematics ,symbols.namesake ,the poisson degenerate central moments ,symbols ,degenerate bell polynomials and numbers ,05a19 ,QA1-939 ,0101 mathematics ,Random variable ,Mathematics - Abstract
Many mathematicians have studied degenerate versions of quite a few special polynomials and numbers since Carlitz’s work (Utilitas Math. 15 (1979), 51–88). Recently, Kim et al. studied the degenerate gamma random variables, discrete degenerate random variables and two-variable degenerate Bell polynomials associated with Poisson degenerate central moments, etc. This paper is divided into two parts. In the first part, we introduce a new type of degenerate Bell polynomials associated with degenerate Poisson random variables with parameter α > 0 \alpha \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the fully degenerate Bell polynomials. We derive some combinatorial identities for the fully degenerate Bell polynomials related to the n n th moment of the degenerate Poisson random variable, special numbers and polynomials. In the second part, we consider the fully degenerate Bell polynomials associated with degenerate Poisson random variables with two parameters α > 0 \alpha \gt 0 and β > 0 \beta \hspace{-0.15em}\gt \hspace{-0.15em}0 , called the two-variable fully degenerate Bell polynomials. We show their connection with the degenerate Poisson central moments, special numbers and polynomials.
- Published
- 2021
31. Solvability of the abstract evolution equations in Ls-spaces with critical temporal weights
- Author
-
Qinghua Zhang and Zhizhong Tan
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,maximal regularity ,sectorial operator ,34k30 ,critical l s-space ,01 natural sciences ,010101 applied mathematics ,evolution equation ,Evolution equation ,QA1-939 ,0101 mathematics ,47d06 ,solvability ,Mathematics - Abstract
This paper deals with the abstract evolution equations in L s {L}^{s} -spaces with critical temporal weights. First, embedding and interpolation properties of the critical L s {L}^{s} -spaces with different exponents s s are investigated, then solvability of the linear evolution equation, attached to which the inhomogeneous term f f and its average Φ f \Phi f both lie in an L 1 / s s {L}_{1\hspace{-0.08em}\text{/}\hspace{-0.08em}s}^{s} -space, is established. Based on these results, Cauchy problem of the semi-linear evolution equation is treated, where the nonlinear operator F ( t , u ) F\left(t,u) has a growth number ρ ≥ s + 1 \rho \ge s+1 , and its asymptotic behavior acts like α ( t ) / t \alpha \left(t)\hspace{-0.1em}\text{/}\hspace{-0.1em}t as t → 0 t\to 0 for some bounded function α ( t ) \alpha \left(t) like ( − log t ) − p {\left(-\log t)}^{-p} with 2 ≤ p < ∞ 2\le p\lt \infty .
- Published
- 2021
32. On q-analogue of Janowski-type starlike functions with respect to symmetric points
- Author
-
Bakhtiar Ahmad, Muhammad Zubair, Raees Khan, Muhammad Ghaffar Khan, and Zabidin Salleh
- Subjects
Pure mathematics ,starlike functions ,General Mathematics ,010102 general mathematics ,janowski functions ,02 engineering and technology ,30c45 ,Type (model theory) ,30c50 ,01 natural sciences ,0202 electrical engineering, electronic engineering, information engineering ,holomorphic functions ,QA1-939 ,020201 artificial intelligence & image processing ,0101 mathematics ,subordinations ,Mathematics - Abstract
The main objective of the present paper is to define a class of q q -starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.
- Published
- 2021
33. Quasi-ideal Ehresmann transversals: The spined product structure
- Author
-
Pei Wang, Xiangjun Kong, and Jian Tang
- Subjects
Pure mathematics ,Ideal (set theory) ,green’s∼-relations ,20m10 ,General Mathematics ,010102 general mathematics ,Structure (category theory) ,Green's relations ,spined product ,quasi-ideal ,01 natural sciences ,010101 applied mathematics ,ehresmann transversal ,u-abundant semigroup ,Product (mathematics) ,Mathematics::Category Theory ,QA1-939 ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics - Abstract
In any U-abundant semigroup with an Ehresmann transversal, two significant components R and L are introduced in this paper and described by Green’s ∼ \sim -relations. Some interesting properties associated with R and L are explored and some equivalent conditions for the Ehresmann transversal to be a quasi-ideal are acquired. Finally, a spined product structure theorem is established for a U-abundant semigroup with a quasi-ideal Ehresmann transversal by means of R and L.
- Published
- 2021
34. On non-normal cyclic subgroups of prime order or order 4 of finite groups
- Author
-
Zhangjia Han and Pengfei Guo
- Subjects
Normal subgroup ,Pure mathematics ,20f16 ,General Mathematics ,010102 general mathematics ,MathematicsofComputing_GENERAL ,0102 computer and information sciences ,01 natural sciences ,minimal subgroups ,normal subgroups ,010201 computation theory & mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,Order (group theory) ,Non normality ,t-groups ,20e34 ,maximal subgroups ,0101 mathematics ,supersolvable groups ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,Mathematics - Abstract
In this paper, we call a finite group G G an N L M NLM -group ( N C M NCM -group, respectively) if every non-normal cyclic subgroup of prime order or order 4 (prime power order, respectively) in G G is contained in a non-normal maximal subgroup of G G . Using the property of N L M NLM -groups and N C M NCM -groups, we give a new necessary and sufficient condition for G G to be a solvable T T -group (normality is a transitive relation), some sufficient conditions for G G to be supersolvable, and the classification of those groups whose all proper subgroups are N L M NLM -groups.
- Published
- 2021
35. Simply connected topological spaces of weighted composition operators
- Author
-
Cezhong Tong, Zhan Zhang, and Biao Xu
- Subjects
Pure mathematics ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,deformation retraction ,Topological space ,Composition (combinatorics) ,operator norm topology ,lcsh:QA1-939 ,01 natural sciences ,weighted composition operator ,47b33 ,simple connectedness ,0103 physical sciences ,Simply connected space ,46c05 ,010307 mathematical physics ,0101 mathematics ,hilbert-schmidt norm topology ,Geometry and topology ,Mathematics - Abstract
In this paper, we prove that the topological spaces of nonzero weighted composition operators acting on some Hilbert spaces of analytic functions on the unit open ball are simply connected.
- Published
- 2020
36. On an equivalence between regular ordered Γ-semigroups and regular ordered semigroups
- Author
-
Anjeza Krakulli and Fabiana Çullhaj
- Subjects
Pure mathematics ,20m12 ,20m10 ,Mathematics::Operator Algebras ,General Mathematics ,010102 general mathematics ,regular ordered semigroup ,20m17 ,ordered semigroup ,quasi-ideal ,01 natural sciences ,20m05 ,regular ordered γ-semigroup ,010101 applied mathematics ,ordered γ-semigroup ,06f05 ,QA1-939 ,0101 mathematics ,Equivalence (formal languages) ,Mathematics - Abstract
In this paper, we develop a technique which enables us to obtain several results from the theory of Γ-semigroups as logical implications of their semigroup theoretical analogues.
- Published
- 2020
37. Noetherian properties in composite generalized power series rings
- Author
-
Jung Wook Lim and Dong Yeol Oh
- Subjects
Noetherian ,Power series ,13b35 ,Pure mathematics ,13a02 ,generalized power series ring ,13a15 ,General Mathematics ,noetherian ring ,010102 general mathematics ,Composite number ,13e05 ,01 natural sciences ,d+〚eγ⁎,≤〛,d+〚iγ⁎,≤〛 ,0103 physical sciences ,QA1-939 ,010307 mathematical physics ,0101 mathematics ,Geometry and topology ,Mathematics - Abstract
Let(Γ,≤)({\mathrm{\Gamma}},\le )be a strictly ordered monoid, and letΓ⁎=Γ\{0}{{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\}. LetD⊆ED\subseteq Ebe an extension of commutative rings with identity, and letIbe a nonzero proper ideal ofD. SetD+〚EΓ⁎,≤〛≔f∈〚EΓ,≤〛|f(0)∈DandD+〚IΓ⁎,≤〛≔f∈〚DΓ,≤〛|f(α)∈I,forallα∈Γ⁎.\begin{array}{l}D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {E}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(0)\in D\right\}\hspace{.5em}\text{and}\\ \hspace{0.2em}D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {D}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(\alpha )\in I,\hspace{.5em}\text{for}\hspace{.25em}\text{all}\hspace{.5em}\alpha \in {{\mathrm{\Gamma}}}^{\ast }\right\}.\end{array}In this paper, we give necessary conditions for the ringsD+〚EΓ⁎,≤〛D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt]to be Noetherian when(Γ,≤)({\mathrm{\Gamma}},\le )is positively ordered, and sufficient conditions for the ringsD+〚EΓ⁎,≤〛D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt]to be Noetherian when(Γ,≤)({\mathrm{\Gamma}},\le )is positively totally ordered. Moreover, we give a necessary and sufficient condition for the ringD+〚IΓ⁎,≤〛D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt]to be Noetherian when(Γ,≤)({\mathrm{\Gamma}},\le )is positively totally ordered. As corollaries, we give equivalent conditions for the ringsD+(X1,…,Xn)E[X1,…,Xn]D+({X}_{1},\ldots ,{X}_{n})E{[}{X}_{1},\ldots ,{X}_{n}]andD+(X1,…,Xn)I[X1,…,Xn]D+({X}_{1},\ldots ,{X}_{n})I{[}{X}_{1},\ldots ,{X}_{n}]to be Noetherian.
- Published
- 2020
38. On the equivalence of three-dimensional differential systems
- Author
-
Jian Zhou and Shiyin Zhao
- Subjects
0209 industrial biotechnology ,Pure mathematics ,General Mathematics ,010102 general mathematics ,periodic solutions ,02 engineering and technology ,Differential systems ,reflective integral ,01 natural sciences ,34a12 ,020901 industrial engineering & automation ,three-dimensional polynomial system ,equivalent systems ,QA1-939 ,0101 mathematics ,Equivalence (measure theory) ,Mathematics - Abstract
In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.
- Published
- 2020
39. An equivalent quasinorm for the Lipschitz space of noncommutative martingales
- Author
-
Congbian Ma and Yanbo Ren
- Subjects
Pure mathematics ,General Mathematics ,martingale ,lcsh:Mathematics ,Lipschitz continuity ,Space (mathematics) ,lcsh:QA1-939 ,Noncommutative geometry ,Quasinorm ,noncommutative space ,46l53 ,46l52 ,hardy space ,60g42 ,Geometry and topology ,Mathematics - Abstract
In this paper, an equivalent quasinorm for the Lipschitz space of noncommutative martingales is presented. As an application, we obtain the duality theorem between the noncommutative martingale Hardy space h p c ( ℳ ) {h}_{p}^{c}( {\mathcal M} ) (resp. h p r ( ℳ ) {h}_{p}^{r}( {\mathcal M} ) ) and the Lipschitz space λ β c ( ℳ ) {\lambda }_{\beta }^{c}( {\mathcal M} ) (resp. λ β r ( ℳ ) {\lambda }_{\beta }^{r}( {\mathcal M} ) ) for 0 < p < 1 0\lt p\lt 1 , β = 1 p − 1 \beta =\tfrac{1}{p}-1 . We also prove some equivalent quasinorms for h p c ( ℳ ) {h}_{p}^{c}( {\mathcal M} ) and h p r ( ℳ ) {h}_{p}^{r}( {\mathcal M} ) for p = 1 p=1 or 2 < p < ∞ 2\lt p\lt \infty .
- Published
- 2020
40. The prime and maximal spectra and the reticulation of residuated lattices with applications to De Morgan residuated lattices
- Author
-
Liviu-Constantin Holdon
- Subjects
residuated lattice ,prime spectrum ,Pure mathematics ,General Mathematics ,ideal ,02 engineering and technology ,reticulation ,03g05 ,01 natural sciences ,Prime (order theory) ,06a06 ,0202 electrical engineering, electronic engineering, information engineering ,0101 mathematics ,de morgan laws ,Mathematics ,filter ,Mathematics::Commutative Algebra ,lcsh:Mathematics ,010102 general mathematics ,maximal spectrum ,pure ideal ,08a72 ,lcsh:QA1-939 ,03g25 ,bounded distributive lattices ,stable topology ,020201 artificial intelligence & image processing ,03b22 - Abstract
In this paper, by using the ideal theory in residuated lattices, we construct the prime and maximal spectra (Zariski topology), proving that the prime and maximal spectra are compact topological spaces, and in the case of De Morgan residuated lattices they become compact T 0 {T}_{0} topological spaces. At the same time, we define and study the reticulation functor between De Morgan residuated lattices and bounded distributive lattices. Moreover, we study the I-topology (I comes from ideal) and the stable topology and we define the concept of pure ideal. We conclude that the I-topology is in fact the restriction of Zariski topology to the lattice of ideals, but we use it for simplicity. Finally, based on pure ideals, we define the normal De Morgan residuated lattice (L is normal iff every proper ideal of L is a pure ideal) and we offer some characterizations.
- Published
- 2020
41. Meromorphic solutions of certain nonlinear difference equations
- Author
-
Zhiqiang Mao, Dan Zheng, and Huifang Liu
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,difference equations ,39b32 ,exponential polynomials ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,30d35 ,QA1-939 ,0101 mathematics ,meromorphic solutions ,Geometry and topology ,Mathematics ,Meromorphic function - Abstract
This paper focuses on finite-order meromorphic solutions of nonlinear difference equation f n ( z ) + q ( z ) e Q ( z ) Δ c f ( z ) = p ( z ) {f}^{n}(z)+q(z){e}^{Q(z)}{\text{Δ}}_{c}f(z)=p(z) , where p , q , Q p,q,Q are polynomials, n ≥ 2 n\ge 2 is an integer, and Δ c f {\text{Δ}}_{c}f is the forward difference of f. A relationship between the growth and zero distribution of these solutions is obtained. Using this relationship, we obtain the form of these solutions of the aforementioned equation. Some examples are given to illustrate our results.
- Published
- 2020
42. On surrounding quasi-contractions on non-triangular metric spaces
- Author
-
Farshid Khojasteh, Vladimir Rakočević, Zoran D. Mitrović, and Erdal Karapınar
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,non-triangular metric spaces ,b-metric spaces ,01 natural sciences ,010101 applied mathematics ,Metric space ,54h25 ,quasi-contraction ,QA1-939 ,0101 mathematics ,47h10 ,Mathematics - Abstract
The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular metric spaces. As applications of our theorems, we deduce certain well-known results in b-metric spaces as corollaries.
- Published
- 2020
43. A systolic inequality with remainder in the real projective plane
- Author
-
Tahl Nowik and Mikhail G. Katz
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Inequality ,Riemannian submersion ,General Mathematics ,media_common.quotation_subject ,Quantitative Biology::Tissues and Organs ,Physics::Medical Physics ,53a30 ,0211 other engineering and technologies ,02 engineering and technology ,01 natural sciences ,symbols.namesake ,Real projective plane ,FOS: Mathematics ,QA1-939 ,Mathematics::Metric Geometry ,0101 mathematics ,Remainder ,Geometric inequality ,systole ,021101 geological & geomatics engineering ,media_common ,Mathematics ,geometric inequality ,cauchy-schwarz theorem ,53C23, 53A30 ,010102 general mathematics ,Systolic geometry ,probabilistic variance ,53c23 ,Term (time) ,Differential Geometry (math.DG) ,Metric (mathematics) ,symbols ,riemannian submersion - Abstract
The first paper in systolic geometry was published by Loewner's student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric on the real projective plane. We prove a stronger version of Pu's systolic inequality with a remainder term., Comment: 5 pages, to appear in Open Mathematics
- Published
- 2020
44. On split involutive regular BiHom-Lie superalgebras
- Author
-
Shengxiang Wang, Xiaohui Zhang, and Shuangjian Guo
- Subjects
Pure mathematics ,17b05 ,root space ,General Mathematics ,010102 general mathematics ,involutive ,17b65 ,17b20 ,01 natural sciences ,010101 applied mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,QA1-939 ,0101 mathematics ,Mathematics::Representation Theory ,GeneralLiterature_REFERENCE(e.g.,dictionaries,encyclopedias,glossaries) ,structure theory ,Mathematics ,bihom-lie superalgebra - Abstract
The goal of this paper is to examine the structure of split involutive regular BiHom-Lie superalgebras, which can be viewed as the natural generalization of split involutive regular Hom-Lie algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split involutive regular BiHom-Lie superalgebra L {\mathfrak{L}} is of the form L = U + ∑ α I α {\mathfrak{L}}=U+{\sum }_{\alpha }{I}_{\alpha } with U a subspace of a maximal abelian subalgebra H and any I α , a well-described ideal of L {\mathfrak{L}} , satisfying [I α , I β ] = 0 if [α] ≠ [β]. In the case of L {\mathfrak{L}} being of maximal length, the simplicity of L {\mathfrak{L}} is also characterized in terms of connections of roots.
- Published
- 2020
45. Two types of hypergeometric degenerate Cauchy numbers
- Author
-
Takao Komatsu
- Subjects
11c20 ,Pure mathematics ,secondary: 11b37 ,15a15 ,General Mathematics ,010102 general mathematics ,Degenerate energy levels ,Cauchy distribution ,determinants ,33c05 ,degenerate cauchy numbers ,01 natural sciences ,Hypergeometric distribution ,010101 applied mathematics ,zeta functions ,QA1-939 ,11m41 ,0101 mathematics ,primary: 11b75 ,hypergeometric cauchy numbers ,Geometry and topology ,Mathematics ,hypergeometric functions - Abstract
In 1985, Howard introduced degenerate Cauchy polynomials together with degenerate Bernoulli polynomials. His degenerate Bernoulli polynomials have been studied by many authors, but his degenerate Cauchy polynomials have been forgotten. In this paper, we introduce some kinds of hypergeometric degenerate Cauchy numbers and polynomials from the different viewpoints. By studying the properties of the first one, we give their expressions and determine the coefficients. Concerning the second one, called H-degenerate Cauchy polynomials, we show several identities and study zeta functions interpolating these polynomials.
- Published
- 2020
46. Rough sets based on fuzzy ideals in distributive lattices
- Author
-
Kuanyun Zhu, Yongwei Yang, and Xiaolong Xin
- Subjects
0209 industrial biotechnology ,Pure mathematics ,generalized rough set ,General Mathematics ,High Energy Physics::Lattice ,set-valued mapping ,08a72 ,rough set ,02 engineering and technology ,distributive lattice ,Fuzzy logic ,03g10 ,020901 industrial engineering & automation ,fuzzy ideals ,Distributive property ,0202 electrical engineering, electronic engineering, information engineering ,QA1-939 ,020201 artificial intelligence & image processing ,Rough set ,Geometry and topology ,06b10 ,Mathematics - Abstract
In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in a distributive lattice. A novel congruence relation induced by a fuzzy ideal of a distributive lattice is introduced. Moreover, we study the special properties of rough sets which can be constructed by means of the congruence relations determined by fuzzy ideals in distributive lattices. Finally, the properties of the generalized rough sets with respect to fuzzy ideals in distributive lattices are also investigated.
- Published
- 2020
47. Orthogonal polynomials for exponential weights x2α(1 – x2)2ρe–2Q(x) on [0, 1)
- Author
-
Rong Liu
- Subjects
Pure mathematics ,42c05 ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Orthonormal polynomial ,010103 numerical & computational mathematics ,exponential weights ,lcsh:QA1-939 ,01 natural sciences ,markov inequalities ,33c45 ,Exponential function ,orthonormal polynomials ,Orthogonal polynomials ,christoffel functions ,0101 mathematics ,Geometry and topology ,Mathematics - Abstract
Let Wα,ρ = xα(1 – x2)ρe–Q(x), where α > – $\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1. This paper deals with orthogonal polynomials for the weights $\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$ and gives bounds on orthogonal polynomials, zeros, Christoffel functions and Markov inequalities. In addition, estimates of fundamental polynomials of Lagrange interpolation at the zeros of the orthogonal polynomial and restricted range inequalities are obtained.
- Published
- 2020
48. Hyers-Ulam stability of quadratic forms in 2-normed spaces
- Author
-
Jae-Hyeong Bae and Won-Gil Park
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,Mathematics::Operator Algebras ,General Mathematics ,linear 2-normed space ,hyers-ulam stability ,010102 general mathematics ,Stability (learning theory) ,Mathematics::Classical Analysis and ODEs ,39b52 ,01 natural sciences ,quadratic form ,010101 applied mathematics ,Nonlinear Sciences::Chaotic Dynamics ,Quadratic form ,39b72 ,QA1-939 ,0101 mathematics ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics - Abstract
In this paper, we obtain Hyers-Ulam stability of the functional equations f (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w), f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w) and f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w) in 2-Banach spaces. The quadratic forms ax 2 + bxy + cy 2, ax 2 + by 2 and axy are solutions of the above functional equations, respectively.
- Published
- 2019
49. Regular Banach space net and abstract-valued Orlicz space of range-varying type
- Author
-
Zhang Qinghua and Zhu Yue-ping
- Subjects
Pure mathematics ,Mathematics::Functional Analysis ,General Mathematics ,lcsh:Mathematics ,010102 general mathematics ,Banach space ,Type (model theory) ,Net (mathematics) ,Space (mathematics) ,lcsh:QA1-939 ,01 natural sciences ,real interpolation space ,010101 applied mathematics ,Range (mathematics) ,46b10 ,46e40 ,46e30 ,partially continuous modular net ,banach space net ,0101 mathematics ,range-varying orlicz space ,Mathematics - Abstract
This paper investigates the abstract-valued Orlicz space of range-varying type. We firstly give the notions and examples of partially continuous modular net and regular Banach space net of type (II), then deal with the definitions, constructions, and geometrical properties of the range-varying Orlicz spaces, including representation of the dual $\begin{array}{} L_{+}^{\varphi} \end{array}$(I, Xθ(⋅))*, and reflexivity of Lφ(I, Xθ(⋅)), under some reasonable conditions. As an application, we finally make another approach to the real interpolation spaces constructed by a generalized Φ-function.
- Published
- 2019
50. F-biharmonic maps into general Riemannian manifolds
- Author
-
Rong Mi
- Subjects
Pure mathematics ,lp-norm ,58e20 ,General Mathematics ,010102 general mathematics ,0211 other engineering and technologies ,Harmonic (mathematics) ,02 engineering and technology ,53c43 ,01 natural sciences ,Sobolev inequality ,harmonic ,Biharmonic equation ,QA1-939 ,Mathematics::Differential Geometry ,sobolev inequality ,0101 mathematics ,Lp space ,Geometry and topology ,Mathematics ,021101 geological & geomatics engineering - Abstract
Let ψ:(M, g) → (N, h) be a map between Riemannian manifolds (M, g) and (N, h). We introduce the notion of the F-bienergy functional $$\begin{array}{} \displaystyle E_{F,2}(\psi)=\int\limits_{M}F\left(\frac{|\tau(\psi)|^{2}}{2}\right)\text{d}V_{g}, \end{array}$$ where F : [0, ∞) → [0, ∞) be C3 function such that F′ > 0 on (0, ∞), τ(ψ) is the tension field of ψ. Critical points of τF,2 are called F-biharmonic maps. In this paper, we prove a nonexistence result for F-biharmonic maps from a complete non-compact Riemannian manifold of dimension m = dimM ≥ 3 with infinite volume that admit an Euclidean type Sobolev inequality into general Riemannian manifold whose sectional curvature is bounded from above. Under these geometric assumptions we show that if the Lp-norm (p > 1) of the tension field is bounded and the m-energy of the maps is sufficiently small, then every F-biharmonic map must be harmonic. We also get a Liouville-type result under proper integral conditions which generalize the result of [Branding V., Luo Y., A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds, 2018, arXiv: 1806.11441v2].
- Published
- 2019
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