1,592 results
Search Results
2. Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space
- Author
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Yang Peng and Xian Feng Zhao
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Compact space ,Bergman space ,Applied Mathematics ,General Mathematics ,Spectral structure ,Harmonic (mathematics) ,Orthogonal complement ,Toeplitz matrix ,Dual (category theory) ,Mathematics - Abstract
In this paper, we characterize that the boundedness, compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space. This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng’s paper [Trans. Amer. Math. Soc., 354, 2495–2520 (2002)].
- Published
- 2021
3. Nψ,ϕ-type Quotient Modules over the Bidisk
- Author
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Chang Hui Wu and Tao Yu
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Essential spectrum ,Hardy space ,Characterization (mathematics) ,Type (model theory) ,01 natural sciences ,symbols.namesake ,Compact space ,Compression (functional analysis) ,0103 physical sciences ,Quotient module ,symbols ,010307 mathematical physics ,0101 mathematics ,Quotient ,Mathematics - Abstract
Let H2(ⅅ2) be the Hardy space over the bidisk ⅅ2, and let Mψ,ϕ = [(ψ(z) − ϕ(w))2] be the submodule generated by (ψ(z) − ϕ(w))2, where ψ(z) and ϕ(w) are nonconstant inner functions. The related quotient module is denoted by Nψ,ϕ = H2(ⅅ2) ⊖ Mψ,ϕ. In this paper, we give a complete characterization for the essential normality of Nψ,ϕ. In particular, if ψ(z)= z, we simply write Mψ,ϕ and Nψ,ϕ as Mϕ and Nϕ respectively. This paper also studies compactness of evaluation operators L(0)∣nϕ and R(0)ϕnϕ, essential spectrum of compression operator Sz on Nϕ, essential normality of compression operators Sz and Sw on Nϕ.
- Published
- 2020
4. On Counting Certain Abelian Varieties Over Finite Fields
- Author
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Chia-Fu Yu and Jiangwei Xue
- Subjects
Isogeny ,Pure mathematics ,Class (set theory) ,Current (mathematics) ,Mathematics - Number Theory ,Series (mathematics) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,01 natural sciences ,Connection (mathematics) ,Finite field ,Simple (abstract algebra) ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,010307 mathematical physics ,0101 mathematics ,Abelian group ,Mathematics - Abstract
This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers, the current authors and T.-C. Yang obtain explicit formulas for the numbers of superspecial abelian surfaces over finite fields. In this paper, we give an explicit formula for the size of the isogeny class of simple abelian surfaces with real Weil number $\sqrt{q}$. This establishes a key step that one may extend our previous explicit calculations of superspecial abelian surfaces to those of supersingular abelian surfaces.The second part is to introduce the notion of genera and ideal complexes of abelian varieties with additional structures in a general setting. The purpose is to generalize the results of Yu on abelian varieties with additional structures to similitude classes, which establishes more results on the connection between geometrically defined and arithmetically defined masses for further investigation., Comment: 23 pages. Section 5.4 corrected
- Published
- 2020
5. KAM Tori for the Derivative Quintic Nonlinear Schrödinger Equation
- Author
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Guang Hua Shi and Dong Feng Yan
- Subjects
Kolmogorov–Arnold–Moser theorem ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mean value ,Zero (complex analysis) ,Torus ,Derivative ,01 natural sciences ,Quintic function ,010101 applied mathematics ,symbols.namesake ,symbols ,0101 mathematics ,Nonlinear Schrödinger equation ,Mathematical physics ,Mathematics - Abstract
This paper is concerned with one-dimensional derivative quintic nonlinear Schrodinger equation, $${\rm{i}}u_t-u_{xx}+{\rm{i}}(|u|^4u)_x=0, \;\; x\in\mathbb{T}.$$ The existence of a large amount of quasi-periodic solutions with two frequencies for this equation is established. The proof is based on partial Birkhoff normal form technique and an unbounded KAM theorem. We mention that in the present paper the mean value of u does not need to be zero, but small enough, which is different from the assumption (1.7) in Geng-Wu [J. Math. Phys., 53, 102702 (2012)].
- Published
- 2020
6. Magic Labeling of Disjoint Union Graphs
- Author
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Tao Wang, De Ming Li, and Ming Ju Liu
- Subjects
Vertex (graph theory) ,Degree (graph theory) ,Applied Mathematics ,General Mathematics ,020206 networking & telecommunications ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Graph ,Combinatorics ,Edge coloring ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Mathematics - Abstract
Let G be a graph with vertex set V(G), edge set E(G) and maximum degree Δ respectively. G is called degree-magic if it admits a labelling of the edges by integers {1, 2, …, |E(G)|} such that for any vertex v the sum of the labels of the edges incident with v is equal to $${{1 + \left| {E(G)} \right|} \over 2} \cdot d(v)$$ , where d(v) is the degree of v. Let f be a proper edge coloring of G such that for each vertex v ∈ V(G), |{e : e ∈ Ev, f(e) ≤ Δ/2}| = |{e : e ∈ Ev, f(e) > Δ/2}|, and such an f is called a balanced edge coloring of G. In this paper, we show that if G is a supermagic even graph with a balanced edge coloring and m ≥ 1, then (2m + 1)G is a supermagic graph. If G is a d-magic even graph with a balanced edge coloring and n ≥ 2, then nG is a d-magic graph. Results in this paper generalise some known results.
- Published
- 2019
7. The Answer to a Problem Posed by Zhao and Ho
- Author
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Jing Lu, Kai Yun Wang, and Bin Zhao
- Subjects
Subcategory ,Pure mathematics ,Kolmogorov space ,Closed set ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,Set (abstract data type) ,Negative - answer ,symbols.namesake ,010201 computation theory & mathematics ,Mathematics::Category Theory ,symbols ,0101 mathematics ,Construct (philosophy) ,Reflective subcategory ,Counterexample ,Mathematics - Abstract
Zhao and Ho asked in a recent paper that for each T0 space X, whether KB(X) (the set of all irreducible closed sets of X whose suprema exist) is the canonical k-bounded sobrification of X in the sense of Keimel and Lawson. In this paper, we construct a counterexample to give a negative answer. We also consider the subcategory Topκ of the category Top0 of T0 spaces, and prove that the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category KBSob of k-bounded sober spaces is a full reflective subcategory of the category Topκ.
- Published
- 2018
8. Analytic Fragmentation Semigroups and Classical Solutions to Coagulation–fragmentation Equations — a Survey
- Author
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Jacek Banasiak
- Subjects
010101 applied mathematics ,Mathematical and theoretical biology ,Semigroup ,Applied Mathematics ,General Mathematics ,Ecology (disciplines) ,010102 general mathematics ,Fragmentation (computing) ,Applied mathematics ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In the paper we present a survey of recent results obtained by the author that concern discrete fragmentation–coagulation models with growth. Models like that are particularly important in mathematical biology and ecology where they describe the aggregation of living organisms. The main results discussed in the paper are the existence of classical semigroup solutions to the fragmentation–coagulation equations.
- Published
- 2018
9. A Cartan’s Second Main Theorem Approach in Nevanlinna Theory
- Author
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Min Ru
- Subjects
Pure mathematics ,Subspace theorem ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Holomorphic function ,Algebraic variety ,Diophantine approximation ,01 natural sciences ,Nevanlinna theory ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Projective variety ,Subspace topology ,Mathematics - Abstract
In 2002, in the paper entitled “A subspace theorem approach to integral points on curves”, Corvaja and Zannier started the program of studying integral points on algebraic varieties by using Schmidt’s subspace theorem in Diophantine approximation. Since then, the program has led a great progress in the study of Diophantine approximation. It is known that the counterpart of Schmidt’s subspace in Nevanlinna theory is H. Cartan’s Second Main Theorem. In recent years, the method of Corvaja and Zannier has been adapted by a number of authors and a big progress has been made in extending the Second Main Theorem to holomorphic mappings from C into arbitrary projective variety intersecting general divisors by using H. Cartan’s original theorem. We call such method “a Cartan’s Second Main Theorem approach”. In this survey paper, we give a systematic study of such approach, as well as survey some recent important results in this direction including the recent work of the author with Paul Voja.
- Published
- 2018
10. Minimal Complex Surfaces with Levi–Civita Ricci-flat Metrics
- Author
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Kefeng Liu and Xiaokui Yang
- Subjects
0209 industrial biotechnology ,Pure mathematics ,Class (set theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,02 engineering and technology ,Link (geometry) ,Riemannian geometry ,01 natural sciences ,Connection (mathematics) ,symbols.namesake ,Continuation ,020901 industrial engineering & automation ,Complex geometry ,symbols ,Curvature form ,Mathematics::Differential Geometry ,0101 mathematics ,Mathematics - Abstract
This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli–Chern class on compact complex manifolds, and proved that the (1, 1) curvature form of the Levi–Civita connection represents the first Aeppli–Chern class which is a natural link between Riemannian geometry and complex geometry. In this paper, we study the geometry of compact complex manifolds with Levi–Civita Ricci-flat metrics and classify minimal complex surfaces with Levi–Civita Ricci-flat metrics. More precisely, we show that minimal complex surfaces admitting Levi–Civita Ricci-flat metrics are Kahler Calabi–Yau surfaces and Hopf surfaces.
- Published
- 2018
11. On p-convergent Operators on Banach Lattices
- Author
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Elroy D. Zeekoei and Jan Fourie
- Subjects
Unbounded operator ,Discrete mathematics ,Mathematics::Functional Analysis ,Approximation property ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Spectrum (functional analysis) ,Finite-rank operator ,Compact operator ,01 natural sciences ,Strictly singular operator ,010101 applied mathematics ,Pseudo-monotone operator ,0101 mathematics ,C0-semigroup ,Mathematics - Abstract
The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and Sanchez in the paper entitled “Dunford–Pettis-like properties of continuous vector function spaces”. In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications (together with the notion of a weak p-convergent operator, which we introduce in the present paper) to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.
- Published
- 2017
12. A revised pre-order principle and set-valued Ekeland variational principles with generalized distances
- Author
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Jing Hui Qiu
- Subjects
Pure mathematics ,021103 operations research ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,0211 other engineering and technologies ,Regular polygon ,02 engineering and technology ,01 natural sciences ,Vector optimization ,Variational principle ,0101 mathematics ,Variational analysis ,Mathematics - Abstract
In my former paper “A pre-order principle and set-valued Ekeland variational principle” (see [J. Math. Anal. Appl., 419, 904–937 (2014)]), we established a general pre-order principle. From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles (denoted by EVPs) in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy’s EVP in [On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381–396 (2011)], where the perturbation contains a weak τ-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle, but also can be applied to obtain the above Khanh and Quy’s EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances.
- Published
- 2017
13. Further investigation into split common fixed point problem for demicontractive operators
- Author
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Oluwatosin Temitope Mewomo and Yekini Shehu
- Subjects
Mathematical optimization ,Sequence ,Iterative method ,Applied Mathematics ,General Mathematics ,Computation ,010102 general mathematics ,Hilbert space ,01 natural sciences ,010101 applied mathematics ,symbols.namesake ,Convergence (routing) ,symbols ,Common fixed point ,0101 mathematics ,Operator norm ,Mathematics - Abstract
Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.
- Published
- 2016
14. Hom-Gel’fand–Dorfman super-bialgebras and Hom-Lie conformal superalgebras
- Author
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Sheng Chen, Cai Xia He, and La Mei Yuan
- Subjects
Applied Mathematics ,General Mathematics ,Mathematics::Rings and Algebras ,010102 general mathematics ,Lie superalgebra ,Conformal map ,01 natural sciences ,Algebra ,Quadratic equation ,Mathematics::Quantum Algebra ,Mathematics::Category Theory ,0103 physical sciences ,Physics::Accelerator Physics ,010307 mathematical physics ,0101 mathematics ,Equivalence (formal languages) ,Mathematics::Representation Theory ,Mathematics - Abstract
The aim of this paper is to introduce and study Hom-Gel’fand–Dorfman super-bialgebras and Hom-Lie conformal superalgebras. In this paper, we provide different ways for constructing Hom-Gel’fand–Dorfman super-bialgebras. Also, we obtain some infinite-dimensional Hom-Lie superalgebras from affinization of Hom-Gel’fand–Dorfman super-bialgebras. Finally, we give a general construction of Hom-Lie conformal superalgebras from Hom-Lie superalgebras and establish the equivalence between quadratic Hom-Lie conformal superalgebras and Hom-Gel’fand–Dorfman super-bialgebras.
- Published
- 2016
15. L p estimates of rough maximal functions along surfaces with applications
- Author
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Abdulla M. Jarrah and Ahmad Al-Salman
- Subjects
Discrete mathematics ,Class (set theory) ,Pure mathematics ,General theorem ,Applied Mathematics ,General Mathematics ,Block (permutation group theory) ,Maximal function ,Singular integral ,Space (mathematics) ,Singular integral operators ,Mathematics - Abstract
In this paper, we study the Lp mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the Lp boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(Sn−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.
- Published
- 2016
16. The problem of split convex feasibility and its alternating approximation algorithms
- Author
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Zhen Hua He and Ji Tao Sun
- Subjects
Convex analysis ,Combinatorics ,Applied Mathematics ,General Mathematics ,Regular polygon ,Convex set ,Approximation algorithm ,Applied mathematics ,Convex combination ,Dykstra's projection algorithm ,Mathematics - Abstract
This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is established. According to this algorithm, some strong convergent theorems are obtained and an affirmative answer to the question raised by Moudafi is given. At the same time, this paper also generalizes the problem of split convex feasibility.
- Published
- 2015
17. On the number of limit cycles of a Z 4-equivariant quintic near-Hamiltonian system
- Author
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Mao An Han and Xianbo Sun
- Subjects
Hopf bifurcation ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Heteroclinic bifurcation ,Upper and lower bounds ,Quintic function ,Hamiltonian system ,symbols.namesake ,Limit cycle ,symbols ,Equivariant map ,Limit (mathematics) ,Mathematics - Abstract
In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z4-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.
- Published
- 2015
18. Viscosity iterative algorithm for variational inequality problems and fixed point problems of strict pseudo-contractions in uniformly smooth Banach spaces
- Author
-
Gang Cai
- Subjects
Pure mathematics ,Iterative method ,Applied Mathematics ,General Mathematics ,Viscosity (programming) ,Variational inequality ,Mathematical analysis ,Convergence (routing) ,Banach space ,Countable set ,Uniformly convex space ,Fixed point ,Mathematics - Abstract
The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.
- Published
- 2015
19. Two classes of operators with irreducibility and the small and compact perturbations of them
- Author
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Yun Nan Zhang and Li Qiong Lin
- Subjects
Discrete mathematics ,Nuclear operator ,Applied Mathematics ,General Mathematics ,Finite-rank operator ,Spectral theorem ,Operator theory ,Compact operator ,Operator norm ,Compact operator on Hilbert space ,Mathematics ,Quasinormal operator - Abstract
This paper gives the concepts of finite dimensional irreducible operators ((FDI) operators) and infinite dimensional irreducible operators ((IDI) operators). Discusses the relationships of (FDI) operators, (IDI) operators and strongly irreducible operators ((SI) operators) and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an (FDI) operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in (ΣFDI)(X) with respect to the strong-operator topology and every compact operator K can be approximated by operators in (ΣFDI)(X) with respect to the norm topology on a Banach space X with a Schauder basis, where (ΣFDI)(X):= {T ∈ B(X): T = Σ =1 ⊕T i , T i ∈ (FDI), k ∈ ℕ}.
- Published
- 2015
20. Schatten-p class (0 < p ≤ ∞) Toeplitz operators on generalized Fock spaces
- Author
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Jin Xia, Xiao Feng Wang, and Lian Hua Xiao
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,Kernel (set theory) ,Mathematics::Operator Algebras ,Applied Mathematics ,General Mathematics ,Schatten class operator ,Compact operator ,Toeplitz matrix ,Fock space ,Algebra ,Schatten norm ,Borel measure ,Toeplitz operator ,Mathematics - Abstract
In this paper, we discuss the Schatten-p class (0 < p ≤ ∞) of Toeplitz operators on generalized Fock space with the symbol in positive Borel measure. It makes a great difference from other papers by using the estimates of the kernel and the weight together instead of separately estimating each other. We also get the equivalent conditions when a Toeplitz operator is in the Schatten-p class.
- Published
- 2015
21. Graded Hochschild cohomology of a path algebra with oriented cycles
- Author
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De Zhan Tan and Fang Li
- Subjects
Applied Mathematics ,General Mathematics ,Mathematics::Rings and Algebras ,Quiver ,Graded ring ,Differential operator ,Mathematics::Algebraic Topology ,Cohomology ,Graded Lie algebra ,Filtered algebra ,Algebra ,Mathematics::K-Theory and Homology ,Differential graded algebra ,Standard basis ,Mathematics::Representation Theory ,Mathematics - Abstract
The aim of this paper is to characterize the first graded Hochschild cohomology of a hereditary algebra whose Gabriel quiver is admitted to have oriented cycles. The interesting conclusion we have obtained shows that the standard basis of the first graded Hochschild cohomology depends on the genus of a quiver as a topological object. In this paper, we overcome the limitation of the classical Hochschild cohomology for hereditary algebra where the Gabriel quiver is assumed to be acyclic. As preparation, we first investigate the graded differential operators on a path algebra and the associated graded Lie algebra.
- Published
- 2014
22. Trigonometric series with a generalized monotonicity condition
- Author
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Vilmos Totik, Lei Feng, and Song Ping Zhou
- Subjects
Applied Mathematics ,General Mathematics ,Uniform convergence ,Mathematical analysis ,Monotonic function ,Trigonometric series ,symbols.namesake ,Fourier analysis ,Decomposition (computer science) ,symbols ,Applied mathematics ,Sine series ,Classical theorem ,Mathematics - Abstract
In this paper, we consider numerical and trigonometric series with a very general monotonicity condition. First, a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting. In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.
- Published
- 2014
23. Robustness of F-tests in singular linear models
- Author
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Jiajia Zhang, Ji Luo, and Hong Bing Qiu
- Subjects
Generalized linear model ,General linear model ,F-test ,Covariance matrix ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Design matrix ,Linear model ,Applied mathematics ,Generalized linear array model ,System of linear equations ,Mathematics - Abstract
F-test is the most popular test in the general linear model. However, there is few discussions on the robustness of F-test under the singular linear model. In this paper, the necessary and sufficient conditions of robust F-test statistic are given under the general linear models or their partition models, which allows that the design matrix has deficient rank and the covariance matrix of error is a nonnegative definite matrix with parameters. The main results obtained in this paper include the existing findings of the general linear model under the definite covariance matrix. The usage of the theorems is illustrated by an example.
- Published
- 2014
24. Entire functions sharing an entire function of smaller order with their difference operators
- Author
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Xiao-Min Li and Hong Xun Yi
- Subjects
Discrete mathematics ,Applied Mathematics ,General Mathematics ,Entire function ,Calculus ,Order (group theory) ,Uniqueness ,Creating shared value ,Mathematics - Abstract
We study a uniqueness question of entire functions sharing an entire function of smaller order with their difference operators, and deal with a question posed by Liu and Yang. The results in this paper extend the corresponding results obtained by Liu-Yang and by Liu-Laine respectively. Examples are provided to show that the results in this paper, in a sense, are the best possible.
- Published
- 2014
25. Explicit stationary distribution of the (L, 1)-reflecting random walk on the half line
- Author
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Q. Zhao, Yi Qiang, Wenming Hong, and Ke Zhou
- Subjects
Combinatorics ,Heterogeneous random walk in one dimension ,Stationary distribution ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Structure (category theory) ,Half line ,Expression (computer science) ,Stationary sequence ,Random walk ,Positive recurrence ,Mathematics - Abstract
In this paper, we consider the (L, 1) state-dependent reflecting random walk (RW) on the half line, which is an RW allowing jumps to the left at a maximal size L. For this model, we provide an explicit criterion for (positive) recurrence and an explicit expression for the stationary distribution. As an application, we prove the geometric tail asymptotic behavior of the stationary distribution under certain conditions. The main tool employed in the paper is the intrinsic branching structure within the (L, 1)-random walk.
- Published
- 2014
26. Some results associated with the longest run in a strongly ergodic Markov chain
- Author
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Xian Yuan Wu and Ya Zhe Zhang
- Subjects
Combinatorics ,Discrete mathematics ,Sequence ,Markov chain ,Applied Mathematics ,General Mathematics ,Ergodic theory ,Countable set ,Limit law ,State markov chain ,Type (model theory) ,Space (mathematics) ,Mathematics - Abstract
This paper discusses the asymptotic behaviors of the longest run on a countable state Markov chain. Let \(\left\{ {X_a } \right\}_{a \in Z_ + }\) be a stationary strongly ergodic reversible Markov chain on countablestate space S = {1, 2, ...}. Let T ⊂ S be an arbitrary finite subset of S. Denote by L n the length of the longest run of consecutive i’s for i ∈ T, that occurs in the sequence X 1, ..., X n . In this paper, we obtain a limit law and a week version of an Erdos-Renyi type law for L n . A large deviation result of L n is also discussed.
- Published
- 2013
27. Vector cascade algorithms with infinitely supported masks in weighted L 2-spaces
- Author
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Jian Bin Yang
- Subjects
Limit of a function ,Matrix (mathematics) ,Integer matrix ,Euclidean space ,Applied Mathematics ,General Mathematics ,Functional equation ,Cascade algorithm ,Function (mathematics) ,Space (mathematics) ,Algorithm ,Mathematics - Abstract
In this paper, we shall study the solutions of functional equations of the form $$\Phi \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\Phi (M \cdot - \alpha ),}$$ where Φ = (ϕ 1, ...,ϕ r ) T is an r × 1 column vector of functions on the s-dimensional Euclidean space, $$a: = (a(\alpha ))_{\alpha \in \mathbb{Z}^s }$$ is an exponentially decaying sequence of r×r complex matrices called refinement mask and M is an s × s integer matrix such that limn → ∞ M −n = 0. We are interested in the question, for a mask a with exponential decay, if there exists a solution Φ to the functional equation with each function ϕ j , j = 1, ..., r, belonging to L 2(ℝ s ) and having exponential decay in some sense? Our approach will be to consider the convergence of vector cascade algorithms in weighted L 2 spaces. The vector cascade operator Q a,M associated with mask a and matrix M is defined by $$Q_{a,M} f: = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )f(M \cdot - \alpha ), f = \left( {f_1 , \ldots f_r } \right)^T \in \left( {L_{2,\mu } \left( {\mathbb{R}^s } \right)} \right)^r .}$$ The iterative scheme (Q f)n=1,2,... is called a vector cascade algorithm or a vector subdivision scheme. The purpose of this paper is to provide some conditions for the vector cascade algorithm to converge in (L 2 (ℝ s )) r , the weighted L 2 space. Inspired by some ideas in [Jia, R. Q., Li, S.: Refinable functions with exponential decay: An approach via cascade algorithms. J. Fourier Anal. Appl., 17, 1008–1034 (2011)], we prove that if the vector cascade algorithm associated with a and M converges in (L 2(ℝ s )) r , then its limit function belongs to (L 2, μ (ℝ s )) r for some µ > 0.
- Published
- 2012
28. A large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function
- Author
-
Ming Wang Zhang
- Subjects
Discrete mathematics ,Logarithm ,Applied Mathematics ,General Mathematics ,Proper convex function ,Regular polygon ,Function (mathematics) ,Combinatorics ,Quadratic equation ,Logarithmically convex function ,Convex function ,Algorithm ,Interior point method ,Mathematics - Abstract
In this paper, we present a large-update interior-point algorithm for convex quadratic semi-definite optimization based on a new kernel function. The proposed function is strongly convex. It is not self-regular function and also the usual logarithmic function. The goal of this paper is to investigate such a kernel function and show that the algorithm has favorable complexity bound in terms of the elegant analytic properties of the kernel function. The complexity bound is shown to be \(O\left( {\sqrt n \left( {\log n} \right)^2 \log \frac{n} {\varepsilon }} \right)\). This bound is better than that by the classical primal-dual interior-point methods based on logarithmic barrier function and recent kernel functions introduced by some authors in optimization fields. Some computational results have been provided.
- Published
- 2012
29. Criteria for the single-valued metric generalized inverses of multi-valued linear operators in banach spaces
- Author
-
Jian Zhang, Yu Wen Wang, and Yun An Cui
- Subjects
Unbounded operator ,Pure mathematics ,Generalized inverse ,Approximation property ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Banach space ,Finite-rank operator ,Compact operator ,C0-semigroup ,Strictly singular operator ,Mathematics - Abstract
Let X, Y be Banach spaces and M be a linear subspace in X × Y = {{x, y}|x ∈ X, y ∈ Y}. We may view M as a multi-valued linear operator from X to Y by taking M(x) = {y|{x, y} ∈ M}. In this paper, we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M. The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.
- Published
- 2012
30. Convex mean curvature flow with a forcing term in direction of the position vector
- Author
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Guang Han Li, Jing Mao, and Chuan Xi Wu
- Subjects
Normalization (statistics) ,Mean curvature flow ,Mean curvature ,Hypersurface ,Applied Mathematics ,General Mathematics ,Round sphere ,Mathematical analysis ,Regular polygon ,Convex function ,Convexity ,Mathematics - Abstract
A smooth, compact and strictly convex hypersurface evolving in ℝn+1 along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We show that the convexity is preserving as the case of mean curvature flow, and the evolving convex hypersurfaces may shrink to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if it is large enough. The flow can converge to a round sphere if the forcing term satisfies suitable conditions which will be given in the paper. Long-time existence and convergence of normalization of the flow are also investigated.
- Published
- 2012
31. The asymptotic behavior of Chern-Simons Higgs model on a compact Riemann surface with boundary
- Author
-
Meng Wang
- Subjects
Applied Mathematics ,General Mathematics ,Riemann surface ,Mathematical analysis ,Boundary (topology) ,Riemann Xi function ,symbols.namesake ,Gaussian curvature ,symbols ,Neumann boundary condition ,Almost everywhere ,Mathematics::Differential Geometry ,Compact Riemann surface ,Mathematics ,Geodesic curvature - Abstract
We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition. In the previous paper, we show that the Chern-Simons Higgs equation with parameter λ > 0 has at least two solutions (uλ1, uλ2) for λ sufficiently large, which satisfy that uλ1 → −u0 almost everywhere as λ → ∞, and that uλ2 → −∞ almost everywhere as λ → ∞, where u0 is a (negative) Green function on M. In this paper, we study the asymptotic behavior of the solutions as λ → ∞, and prove that uλ2 − \(\overline {u_\lambda ^2 } \) converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary ∂M is negative, or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero.
- Published
- 2011
32. General decay pathwise stability of neutral stochastic differential equations with unbounded delay
- Author
-
Chengming Huang, Fuke Wu, and Yang Zi Hu
- Subjects
Stochastic partial differential equation ,Lyapunov function ,Stochastic differential equation ,symbols.namesake ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,symbols ,Polynomial coefficients ,Linear growth ,Stability (probability) ,M-matrix ,Mathematics - Abstract
Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a class of neutral stochastic differential equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.
- Published
- 2011
33. Modified block iterative method for solving convex feasibility problem, equilibrium problems and variational inequality problems
- Author
-
H. W. Joseph Lee, Chi Kin Chan, and Shi Sheng Zhang
- Subjects
Mathematical optimization ,Monotone polygon ,Iterative method ,Intersection (set theory) ,Applied Mathematics ,General Mathematics ,Variational inequality ,Convergence (routing) ,Regular polygon ,Banach space ,Fixed point ,Mathematics - Abstract
The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-ϕ-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem (CFP) and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.
- Published
- 2011
34. Oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve
- Author
-
Guo Chun Wen
- Subjects
Nonlinear system ,Complex differential equation ,Applied Mathematics ,General Mathematics ,Degenerate energy levels ,Elliptic complex ,Mathematical analysis ,Hyperbolic function ,Partial derivative ,Special case ,Domain (mathematical analysis) ,Mathematics - Abstract
The present paper deals with oblique derivative problems for second order nonlinear equations of mixed type with degenerate hyperbolic curve, which include the Tricomi problem as a special case. Firstly the formulation of the problems for the equations is given, next the representation and estimates of solutions for the above problems are obtained, finally the existence of solutions for the problems is proved by the successive iteration of solutions of the equations and the fixed-point principle. In this paper, we use the complex analytic method, namely the new partial derivative notations, elliptic complex functions in the elliptic domain and hyperbolic complex functions in the hyperbolic domain are introduced, such that the second order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients, and then the advantage of complex analytic method can be applied.
- Published
- 2011
35. A class of new large-update primal-dual interior-point algorithms for P *(κ) nonlinear complementarity problems
- Author
-
Hua Ping Chen and Ming Wang Zhang
- Subjects
Class (set theory) ,Linear programming ,Complementarity theory ,Applied Mathematics ,General Mathematics ,Polynomial complexity ,Mathematics::Optimization and Control ,Nonlinear complementarity problem ,Special case ,Mixed complementarity problem ,Algorithm ,Interior point method ,Mathematics - Abstract
In this paper we propose a class of new large-update primal-dual interior-point algorithms for P*(κ) nonlinear complementarity problem (NCP), which are based on a class of kernel functions investigated by Bai et al. in their recent work for linear optimization (LO). The arguments for the algorithms are followed as Peng et al.’s for P*(κ) complementarity problem based on the self-regular functions [Peng, J., Roos, C., Terlaky, T.: Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms, Princeton University Press, Princeton, 2002]. It is worth mentioning that since this class of kernel functions includes a class of non-self-regular functions as special case, so our algorithms are different from Peng et al.’s and the corresponding analysis is simpler than theirs. The ultimate goal of the paper is to show that the algorithms based on these functions have favorable polynomial complexity.
- Published
- 2011
36. Projections on weak*-closed subspace of dual Banach algebras
- Author
-
Ali Ghaffari
- Subjects
Discrete mathematics ,Cancellative semigroup ,Pure mathematics ,Semigroup ,Applied Mathematics ,General Mathematics ,Invariant subspace ,Nest algebra ,Locally compact space ,Locally compact group ,Invariant subspace problem ,Subspace topology ,Mathematics - Abstract
Our first purpose in this paper is to provide necessary conditions for a weak*-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak*-closed left translation invariant subspace in Ma(S)* of a compact cancellative foundation semigroup S is the range of a weak*-weak* continuous projection on Ma(S)* commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A* and B(A*) which commutes with translations and convolution.
- Published
- 2011
37. Strong convergence theorems for strictly asymptotically pseudocontractive mappings in Hilbert spaces
- Author
-
Shi Sheng Zhang
- Subjects
Pure mathematics ,Sequence ,Iterative method ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Hilbert space ,Banach space ,Fixed point ,symbols.namesake ,Fixed-point iteration ,Iterated function ,symbols ,Convergence problem ,Mathematics - Abstract
The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67(7), 2258–2271 (2007)], Kim and Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140–1152 (2006)], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400–2411 (2006)], Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl., 279, 372–379 (2003)], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329(1), 336–346 (2007)], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334–1345 (2007)], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26(11), 1835–1842 (1996)], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12 (2), 77–88 (2002)], Gu [The new composite implicit iteration process with errors for common fixed points of a finite family of strictly pseudocontractive mappings. J. Math. Anal. Appl., 329, 766–776 (2007)].
- Published
- 2011
38. L r convergence for B-valued random elements
- Author
-
Ping Yan Chen and Ding Cheng Wang
- Subjects
L(R) ,Mathematics::Functional Analysis ,Pure mathematics ,Law of large numbers ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Convergence (routing) ,Banach space ,Random element ,Type (model theory) ,Mathematics - Abstract
The paper investigates Lp convergence and Marcinkiewicz-Zygmund strong laws of large numbers for random elements in a Banach space under the condition that the Banach space is of Rademacher type p, 1 < p < 2. The paper also discusses Lr convergence and Lr bound for random elements without any geometric restriction condition on the Banach space.
- Published
- 2011
39. Finite groups with some pronormal subgroups
- Author
-
Zhen Cai Shen and Wujie Shi
- Subjects
Combinatorics ,p-group ,Finite group ,Locally finite group ,Applied Mathematics ,General Mathematics ,Order (group theory) ,Index of a subgroup ,Element (category theory) ,Mathematics - Abstract
A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to Hx in 〈H, Hx〉. A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is pronormal in G. In this paper, we find all PRN-groups and classify minimal non-PRN-groups (non-PRN-group all of whose proper subgroups are PRN-groups). At the end of the paper, we also classify the finite group G, all of whose second maximal subgroups are PRN-groups.
- Published
- 2011
40. A new sequential systems of linear equations algorithm of feasible descent for inequality constrained optimization
- Author
-
Jinbao Jian, Qing Juan Xu, and Daolan Han
- Subjects
Mathematical optimization ,Applied Mathematics ,General Mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Linear matrix inequality ,System of linear equations ,Nonlinear programming ,Convex combination ,Quantum algorithm for linear systems of equations ,Criss-cross algorithm ,Descent direction ,Coefficient matrix ,Algorithm ,Mathematics - Abstract
Based on a new efficient identification technique of active constraints introduced in this paper, a new sequential systems of linear equations (SSLE) algorithm generating feasible iterates is proposed for solving nonlinear optimization problems with inequality constraints. In this paper, we introduce a new technique for constructing the system of linear equations, which recurs to a perturbation for the gradients of the constraint functions. At each iteration of the new algorithm, a feasible descent direction is obtained by solving only one system of linear equations without doing convex combination. To ensure the global convergence and avoid the Maratos effect, the algorithm needs to solve two additional reduced systems of linear equations with the same coefficient matrix after finite iterations. The proposed algorithm is proved to be globally and superlinearly convergent under some mild conditions. What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improving direction is obtained easily and the computation cost of generating a new iterate is reduced. Finally, a preliminary implementation has been tested.
- Published
- 2010
41. g-Besselian frames in Hilbert spaces
- Author
-
Ming Ling Ding and Yu Can Zhu
- Subjects
symbols.namesake ,Pure mathematics ,Applied Mathematics ,General Mathematics ,Frame (networking) ,Stability (learning theory) ,Calculus ,Hilbert space ,symbols ,Mathematics - Abstract
In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.
- Published
- 2010
42. On relations of vector optimization results with C 1,1 data
- Author
-
Karel Pastor and Dušan Bednařík
- Subjects
Dini derivative ,Algebra ,symbols.namesake ,Vector optimization ,Applied Mathematics ,General Mathematics ,symbols ,Calculus ,Mathematics - Abstract
In this article we prove that some of the sufficient and necessary optimality conditions obtained by Ginchev, Guerraggio, Luc [Appl. Math., 51, 5–36 (2006)] generalize (strictly) those presented by Guerraggio, Luc [J. Optim. Theory Appl., 109, 615–629 (2001)]. While the former paper shows examples for which the conditions given there are effective but the ones from the latter paper fail, it does not prove that generally the conditions it proposes are stronger. In the present note we complete this comparison with the lacking proof.
- Published
- 2010
43. Uniform convergence of wavelet solution to the sideways heat equation
- Author
-
Jinru Wang
- Subjects
Wavelet ,Applied Mathematics ,General Mathematics ,Uniform convergence ,Mathematical analysis ,Cauchy distribution ,Boundary (topology) ,Heat equation ,Interval (mathematics) ,Space (mathematics) ,Scaling ,Mathematics - Abstract
We consider the problem ut(x, t), 0 ≤ x < 1, t ≥ 0, where the Cauchy data g(t) is given at x = 1. This is an ill-posed problem in the sense that a small disturbance on the boundary g(t) can produce a big alteration on its solution (if it exists). We shall define a wavelet solution to obtain the well-posed approximating problem in the scaling space Vj. In the previous papers, the theoretical results concerning the error estimate are L2-norm and the solutions aren’t stable at x = 0. However, in practice, the solution is usually required to be stable at the boundary. In this paper we shall give uniform convergence on interval x ∈ [0, 1].
- Published
- 2010
44. Continuity in weak topology: First order linear systems of ODE
- Author
-
Gang Meng and Meirong Zhang
- Subjects
Applied Mathematics ,General Mathematics ,Mathematical analysis ,Linear system ,Ode ,Lyapunov exponent ,Dirac operator ,symbols.namesake ,Weak operator topology ,Ordinary differential equation ,symbols ,Lp space ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In this paper we study important quantities defined from solutions of first order linear systems of ordinary differential equations. It will be proved that many quantities, such as solutions, eigenvalues of one-dimensional Dirac operators, Lyapunov exponents and rotation numbers, depend on the coefficients in a very strong way. That is, they are not only continuous in coefficients with respect to the usual Lp topologies, but also with respect to the weak topologies of the Lp spaces. The continuity results of this paper are a basis to study these quantities in a quantitative way.
- Published
- 2010
45. Center, limit cycles and isochronous center of a Z 4-equivariant quintic system
- Author
-
Chao Xiong Du, Hei Long Mi, and Yirong Liu
- Subjects
Pure mathematics ,Simple (abstract algebra) ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Equivariant map ,Center (algebra and category theory) ,Vector field ,Limit (mathematics) ,Algebraic number ,Symbolic computation ,Quintic function ,Mathematics - Abstract
In this paper, we study the limit cycles bifurcations of four fine focuses in Z 4-equivariant vector fields and the problems that its four singular points can be centers and isochronous centers at the same time. By computing the Liapunov constants and periodic constants carefully, we show that for a certain Z 4-equivariant quintic systems, there are four fine focuses of five order and five limit cycles can bifurcate from each, we also find conditions of center and isochronous center for this system. The process of proof is algebraic and symbolic by using common computer algebra soft such as Mathematica, the expressions after being simplified in this paper are simple relatively. Moreover, what is worth mentioning is that the result of 20 small limit cycles bifurcating from several fine focuses is good for Z 4-equivariant quintic system and the results where multiple singular points become isochronous centers at the same time are less in published references.
- Published
- 2010
46. Gradient estimates for the equation Δu + cu −α = 0 on Riemannian manifolds
- Author
-
Yun Yan Yang
- Subjects
Nonlinear system ,Elliptic curve ,Steady state ,Applied Mathematics ,General Mathematics ,Bounded function ,Mathematical analysis ,Domain (ring theory) ,Boundary (topology) ,Thin-film equation ,Riemannian manifold ,Mathematics ,Mathematical physics - Abstract
Let (M, g) be a complete non-compact Riemannian manifold without boundary. In this paper, we give the gradient estimates on positive solutions to the following elliptic equation with singular nonlinearity: $$ \Delta u\left( x \right) + cu^{ - \alpha } \left( x \right) = 0 in M $$ , where α > 0, c are two real constants. When c < 0 and M is a bounded smooth domain in ℝn, the above equation is known as the thin film equation, which describes a steady state of the thin film (see Guo-Wei [Manuscripta Math., 120, 193–209 (2006)]). The results in this paper can be viewed as an supplement of that of J. Li [J. Funct. Anal., 100, 233–256 (1991)], where the nonlinearity is the positive power of u.
- Published
- 2010
47. On the classification of positive quaternionic Kähler manifolds with b 4 = 1
- Author
-
Jin Hong Kim and Hee Kwon Lee
- Subjects
Betti number ,Applied Mathematics ,General Mathematics ,Dimension (graph theory) ,Kähler manifold ,Rank (differential topology) ,Type (model theory) ,Upper and lower bounds ,Combinatorics ,Algebra ,Mathematics::Differential Geometry ,Symmetry (geometry) ,Mathematics::Symplectic Geometry ,Mathematics - Abstract
Let M be a positive quaternionic Kahler manifold of dimension 4m. We already showed that if the symmetry rank is greater than or equal to \( \left[ {\tfrac{m} {2}} \right] + 2 \) and the fourth Betti number b4 is equal to one, then M is isometric to ℍPm. The goal of this paper is to report that we can improve the lower bound of the symmetry rank by one for higher even-dimensional positive quaternionic Kahler manifolds. Namely, it is shown in this paper that if the symmetry rank of M with b4(M) = 1 is greater than or equal to \( \tfrac{m} {2} + 1 \) for m ≥ 10, then M is isometric to ℍPm. One of the main strategies of this paper is to apply a more delicate argument of Frankel type to positive quaternionic Kahler manifolds with certain symmetry rank.
- Published
- 2010
48. On rough Marcinkiewicz integrals along surfaces
- Author
-
Huoxiong Wu and Jian Kai Xu
- Subjects
symbols.namesake ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,symbols ,Maximal operator ,Maximal function ,Singular integral ,Hardy space ,Mathematics - Abstract
In this paper, the authors establish the L p -mapping properties of certain classes of Marcinkiewicz integral operators along surfaces with rough kernels. The results in this paper essentially extend as well as improve previously known results.
- Published
- 2010
49. Bifurcations of limit cycles in a Z 4-equivariant quintic planar vector field
- Author
-
Yuhai Wu, Li Xin Tian, and Xue Di Wang
- Subjects
Hopf bifurcation ,Period-doubling bifurcation ,Applied Mathematics ,General Mathematics ,Mathematical analysis ,Saddle-node bifurcation ,Bifurcation diagram ,symbols.namesake ,Pitchfork bifurcation ,symbols ,Homoclinic bifurcation ,Bogdanov–Takens bifurcation ,Infinite-period bifurcation ,Nonlinear Sciences::Pattern Formation and Solitons ,Mathematics - Abstract
In this paper, a Z 4-equivariant quintic planar vector field is studied. The Hopf bifurcation method and polycycle bifurcation method are combined to study the limit cycles bifurcated from the compounded cycle with 4 hyperbolic saddle points. It is found that this special quintic planar polynomial system has at least four large limit cycles which surround all singular points. By applying the double homoclinic loops bifurcation method and Hopf bifurcation method, we conclude that 28 limit cycles with two different configurations exist in this special planar polynomial system. The results acquired in this paper are useful for studying the weakened 16th Hilbert’s Problem.
- Published
- 2010
50. Convergence theorems for λ-strict pseudo-contractions in q-uniformly smooth Banach spaces
- Author
-
Hai Yun Zhou
- Subjects
Discrete mathematics ,Weak convergence ,Applied Mathematics ,General Mathematics ,Eberlein–Šmulian theorem ,Hilbert space ,Banach space ,Banach manifold ,symbols.namesake ,symbols ,Unconditional convergence ,Lp space ,Modes of convergence ,Mathematics - Abstract
In this paper, we continue to discuss the properties of iterates generated by a strict pseudocontraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336–349 (2007)]. In order to get a strong convergence theorem, we modify the normal Mann’s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.: Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51–60 (2005)] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.
- Published
- 2010
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