27 results
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2. The Undirected Power Graph of a Finite Group.
- Author
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Pourgholi, G. R., Yousefi-Azari, H., and Ashrafi, A. R.
- Subjects
FINITE groups ,FC-groups ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
The power graph $${\fancyscript{P}}(G)$$ of a group $$G$$ is the graph which has a vertex set of the group elements and two elements are adjacent if one is a power of the other. Chakrabarty, Ghosh, and Sen proved the main properties of the undirected power graph of a finite group. The aim of this paper is to generalize some results of their work and presenting some counterexamples for one of the problems raised by these authors. It is also proved that the power graph of a $$p$$ -group is $$2$$ -connected if and only if the group is a cyclic or generalized quaternion group and if $$G$$ is a nilpotent group which is not of prime power order then the power graph $${\fancyscript{P}}(G)$$ is $$2$$ -connected. We also prove that the number of edges of the power graph of the simple groups is less than or equal to the number of edges in the power graph of the cyclic group of the same order. This partially answers to a question in an earlier paper. Finally, we give a complete classification of groups in which the power graph is a union of complete graphs sharing a common vertex. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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3. Congruence Lattices of Symmetric Extended De Morgan Algebras.
- Author
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Lei-Bo Wang and Jie Fang
- Subjects
CONGRUENCE lattices ,LATTICE theory ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper, we characterize the congruence lattice of a symmetric extended De Morgan algebra $$L$$ . We show that the congruence lattice of the algebra $$L$$ is a pseudocomplemented lattice, and that such a congruence lattice is a Stone lattice if and only if the lattice of the compact congruences on $$L$$ forms a complete Boolean lattice. In particular, we prove that the congruence lattice of $$L$$ is a Boolean lattice if and only if, it is a relative Stone lattice, which is the case, if and only if $$L$$ is finite. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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4. Gauss and Ricci Equations in Contact Manifolds with a Quarter-Symmetric Metric Connection.
- Author
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De, Avik and Uddin, Siraj
- Subjects
MATHEMATICAL equivalence ,MANIFOLDS (Mathematics) ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
In the present paper, we study the extrinsic and intrinsic geometry of submanifolds of an almost contact metric manifold admitting a quarter-symmetric metric connection. We deduce Gauss, Codazzi and Ricci equations corresponding to the quarter-symmetric metric connection and show some applications of these equations. Finally, we give an example verifying the results. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
5. Properties of Chip-Firing Games on Complete Graphs.
- Author
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Wei Zhuang, Weihua Yang, Lianzhu Zhang, and Xiaofeng Guo
- Subjects
GRAPH theory ,GRAPHIC methods ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
Björner, Lovász and Shor introduced a chip-firing game on a finite graph $$G$$ as follows. We put some chips on each vertex of $$G$$ , we say that a vertex is ready if it has at least as many chips as its degree, in which case we can fire it and the result is that it distributes one chip to each of its neighbors, this may cause other vertices to be ready, and so on. This game continues until no vertex can be fired. In this paper, we study chip-firing games on complete graphs. We obtain a sufficient and necessary condition for chip-firing games on complete graphs to be finite. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
6. Graph Convergence for the H(., .)-Co-accretive Mapping with an Application.
- Author
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Ahmad, R., Akram, M., and Dilshad, M.
- Subjects
MATHEMATICAL mappings ,MATHEMATICAL functions ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper, we introduce a concept of graph convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping in Banach spaces and prove an equivalence theorem between graph convergence and resolvent operator convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping. Further, we consider a system of generalized variational inclusions involving $$H(\cdot ,\cdot )$$ -co-accretive mapping in real $$q$$ -uniformly smooth Banach spaces. Using resolvent operator technique, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions under some suitable conditions. Further, we discuss the convergence of iterative algorithm using the concept of graph convergence. Our results can be viewed as a refinement and generalization of some known results in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
7. Degree Powers in C5-Free Graphs.
- Author
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Ran Gu, Xueliang Li, and Yongtang Shi
- Subjects
GRAPHIC methods ,GRAPH theory ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
Let $$G$$ be a graph with degree sequence $$d_1,d_2,\ldots ,d_n$$ . Given a positive integer $$p$$ , denote by $$e_p(G)=\sum _{i=1}^n d_i^p$$ . Caro and Yuster introduced a Turán-type problem for $$e_p(G)$$ : given an integer $$p$$ , how large can $$e_p(G)$$ be if $$G$$ has no subgraph of a particular type. They got some results for the subgraph of particular type to be a clique of order $$r+1$$ and a cycle of even length, respectively. Denote by $$ex_p(n,H)$$ the maximum value of $$e_p(G)$$ taken over all graphs with $$n$$ vertices that do not contain $$H$$ as a subgraph. Clearly, $$ex_1(n,H)=2ex(n,H)$$ , where $$ex(n,H)$$ denotes the classical Turán number. In this paper, we consider $$ex_p(n, C_5)$$ and prove that for any positive integer $$p$$ and sufficiently large $$n$$ , there exists a constant $$c=c(p)$$ such that the following holds: if $$ex_p(n, C_5)=e_p(G)$$ for some $$C_5$$ -free graph $$G$$ of order $$n$$ , then $$G$$ is a complete bipartite graph having one vertex class of size $$cn+o(n)$$ and the other $$(1-c)n+o(n)$$ . [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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8. Covering Problems for Functions n-Fold Symmetric and Convex in the Direction of the Real Axis II.
- Author
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Koczan, Leopold and Zaprawa, Pawel
- Subjects
SET theory ,DIFFERENTIAL equations ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
Let $${\mathcal {F}}$$ denote the class of all functions univalent in the unit disk $$\Delta \equiv \{\zeta \in {\mathbb {C}}\,:\,\left| \zeta \right| <1\}$$ and convex in the direction of the real axis. The paper deals with the subclass $${\mathcal {F}}^{(n)}$$ of these functions $$f$$ which satisfy the property $$f(\varepsilon z)=\varepsilon f(z)$$ for all $$z\in \Delta $$ , where $$\varepsilon =e^{2\pi i/n}$$ . The functions of this subclass are called $$n$$ -fold symmetric. For $${\mathcal {F}}^{(n)}$$ , where $$n$$ is odd positive integer, the following sets, $$\bigcap _{f\in {\mathcal {F}}^{(n)}} f(\Delta )$$ -the Koebe set and $$\bigcup _{f\in {\mathcal {F}}^{(n)}} f(\Delta )$$ -the covering set, are discussed. As corollaries, we derive the Koebe and the covering constants for $${\mathcal {F}}^{(n)}$$ . [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
9. Third-Order Differential Superordination Involving the Generalized Bessel Functions.
- Author
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Huo Tang, Srivastava, H. M., Deniz, Erhan, and Shu-Hai Li
- Subjects
BESSEL functions ,DIFFERENTIAL equations ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
There are many articles in the literature dealing with the first-order and the second-order differential subordination and differential superordination problems for analytic functions in the unit disk, but there are only a few articles dealing with the third-order differential subordination problems. The concept of third-order differential subordination in the unit disk was introduced by Antonino and Miller, and studied recently by Tang and Deniz. Let $$\Omega $$ be a set in the complex plane $$\mathbb {C}$$ , let $$\mathfrak {p}(z)$$ be analytic in the unit disk $$\mathbb {U}=\{z:z\in \mathbb {C}\quad \text {and} \quad |z|<1\}$$ , and let $$\psi : \mathbb {C}^4\times \mathbb {U}\rightarrow \mathbb {C}$$ . In this paper, we investigate the problem of determining properties of functions $$\mathfrak {p}(z)$$ that satisfy the following third-order differential superordination: As applications, we derive some third-order differential superordination results for analytic functions in $$\mathbb {U}$$ , which are associated with a family of generalized Bessel functions. The results are obtained by considering suitable classes of admissible functions. New third-order differential sandwich-type results are also obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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10. On Supercyclicity of Tuples of Operators.
- Author
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Soltani, R., Hedayatian, K., and Robati, B. Khani
- Subjects
INFINITY (Mathematics) ,MATRICES (Mathematics) ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper, we use a result of N. S. Feldman to show that there are no supercyclic subnormal tuples in infinite dimensions. Also, we investigate some spectral properties of hypercyclic tuples of operators. Besides, we prove that if $$T$$ is a supercyclic $$\ell $$ -tuple of commuting $$n\times n$$ complex matrices, then $$\ell \ge n$$ and also there exists a supercyclic $$n$$ -tuple of commuting diagonal $$n\times n$$ matrices. Furthermore, we see that if $$T=(T_{1},\ldots ,T_{n})$$ is a supercyclic $$n$$ -tuple of commuting $$n\times n$$ complex matrices, then $$T_{j}$$ 's are simultaneously diagonalizable. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
11. Limit Theorems for a Galton-Watson Process with Immigration in Varying Environments.
- Author
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Zhenlong Gao and Yanhua Zhang
- Subjects
LIMIT theorems ,LIMITS (Mathematics) ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson branching processes with time-dependent immigration in varying environments. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
12. Concomitants of Order Statistics and Record Values from Morgenstern Type Bivariate-Generalized Exponential Distribution.
- Author
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Tahmasebi, S. and Jafari, A. A.
- Subjects
BIVARIATE analysis ,EXPONENTIAL functions ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper, we introduce the Morgenstern type bivariate-generalized exponential distribution. This distribution is an extension of Morgenstern type bivariate exponential distribution (MTBED), and the marginal distributions are generalized exponential distribution. We study some properties of this bivariate distribution. Also, some distributional properties of concomitants of order statistics as well as record values for the MTBED are studied. Recurrence relations between moments of concomitants are also obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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13. The b-Chromatic Index of a Graph.
- Author
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Jakovac, Marko and Peterin, Iztok
- Subjects
GRAPHIC methods ,CHROMATICITY ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
The b-chromatic index $$\varphi '(G)$$ of a graph $$G$$ is the largest integer $$k$$ such that $$G$$ admits a proper $$k$$ -edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound $$m'(T)$$ or one less, where $$m'(T)$$ is connected with the number of edges of high degree. Some conditions are given for which graphs have the b-chromatic index strictly less than $$m'(G)$$ , and for which conditions it is exactly $$m'(G)$$ . In the last part of the paper, regular graphs are considered. It is proved that with four exceptions, the b-chromatic index of cubic graphs is $$5$$ . The exceptions are $$K_4$$ , $$K_{3,3}$$ , the prism over $$K_3$$ , and the cube $$Q_3$$ . [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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14. Normality Criteria of Meromorphic Functions Sharing a Holomorphic Function.
- Author
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Da-Wei Meng and Pei-Chu Hu
- Subjects
HOLOMORPHIC functions ,MULTIPLICITY (Mathematics) ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
Take three integers $$m\ge 0,\,k\ge 1$$ , and $$n\ge 2$$ . Let $$a\ (\not \equiv 0)$$ be a holomorphic function in a domain $$D$$ of $$\mathbb {C}$$ such that multiplicities of zeros of $$a$$ are at most $$m$$ and divisible by $$n+1$$ . In this paper, we mainly obtain the following normality criterion: Let $${{{\fancyscript{F}}}}$$ be the family of meromorphic functions on $$D$$ such that multiplicities of zeros of each $$f\in {{\fancyscript{F}}}$$ are at least $$k+m$$ and such that multiplicities of poles of $$f$$ are at least $$m+1$$ . If each pair $$(f,g)$$ of $${{\fancyscript{F}}}$$ satisfies that $$f^{n}f^{(k)}$$ and $$g^{n}g^{(k)}$$ share $$a$$ (ignoring multiplicity), then $${{\fancyscript{F}}}$$ is normal. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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15. Ear Decomposition of Factor-Critical Graphs and Number of Maximum Matchings.
- Author
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Yan Liu and Shenlin Zhang
- Subjects
GRAPH theory ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
A connected graph $$G$$ is said to be factor-critical if $$G-v$$ has a perfect matching for every vertex $$v$$ of $$G$$ . Lovász proved that every factor-critical graph has an ear decomposition. In this paper, the ear decomposition of the factor-critical graphs $$G$$ satisfying that $$G-v$$ has a unique perfect matching for any vertex $$v$$ of $$G$$ with degree at least 3 is characterized. From this, the number of maximum matchings of factor-critical graphs with the special ear decomposition is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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16. On the Permanental Polynomials of Matrices.
- Author
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Wei Li and Heping Zhang
- Subjects
POLYNOMIALS ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
An $$m\times n\,\{0,1\}$$ -matrix $$A$$ is said to be totally convertible if there exists a matrix $$B$$ obtained from $$A$$ by changing some 1's in $$A$$ to $$-1$$ 's such that for any submatrix $$A^{\prime }$$ of $$A$$ of order $$m$$ , the corresponding submatrix $$B^{\prime }$$ of $$B$$ satisfies $$\mathrm{per}(xI-A^{\prime })=\det (xI-B^{\prime })$$ . In this paper, motivated by the well-known Pólya's problem, our object is to characterize those totally convertible matrices. Associate a matrix $$A$$ with a bipartite graph $$G^{*}_A$$ . We first prove that a square matrix $$A$$ is totally convertible if and only if $$G^{*}_A$$ is Pfaffian, and then we generalize this result to an $$m\times n$$ $$\{0,1\}$$ -matrix. Moreover, the characterization of a totally convertible matrix provides an equivalent condition to compute the permanental polynomial of a bipartite graph by the characteristic polynomial of the skew adjacency matrix of its orientation graph. As applications, we give some explicit expressions of the permanental polynomials of two totally convertible matrices by the technique of Pfaffian orientation. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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17. Random Coincidence Points of Expansive Type Completely Random Operators.
- Author
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Anh, Pham The
- Subjects
RANDOM operators ,OPERATOR theory ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper, we present some results on the existence of random coincidence points of expansive type completely random operators. Some applications to random fixed point theorems and random equations are given. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
18. Maximal Energy of Subdivisions of Graphs with a Fixed Chromatic Number.
- Author
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Meiling Hu, Weigen Yan, and Wei Qiu
- Subjects
GRAPHIC methods ,GRAPH theory ,EIGENVALUES ,ALGORITHMS ,MATHEMATICS - Abstract
The energy of a simple graph $$G$$ , denoted by $$E(G)$$ , is defined as the sum of the absolute values of eigenvalues of $$G$$ . In this paper, we show that, among all subdivisions of graphs with $$n$$ vertices and chromatic number $$k$$ , the subdivision of the Turán graph $$T(n,k)$$ has the maximal energy. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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19. On Graded Second and Coprimary Modules and Graded Secondary Representations.
- Author
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Seçil Çeken and Alkan, Mustafa
- Subjects
ARBITRARY constants ,NOETHERIAN rings ,ARBITRARY waveform generators ,ALGORITHMS ,MATHEMATICS - Abstract
In this paper we introduce and study the concepts of graded second (gr-second) and graded coprimary (gr-coprimary) modules which are different from second and coprimary modules over arbitrary-graded rings. We list some properties and characterizations of gr-second and gr-coprimary modules and also study graded prime submodules of modules with gr-coprimary decompositions. We also deal with graded secondary representations for graded injective modules over commutative-graded rings. By using the concept of $$\sigma $$ -suspension $$(\sigma )M$$ of a graded module $$M,$$ we prove that a graded injective module over a commutative graded Noetherian ring has a graded secondary representation. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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20. Cohen-Macaulayness of Bipartite Graphs, Revisited.
- Author
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Zaare-Nahandi, Rashid
- Subjects
BIPARTITE graphs ,GRAPH theory ,COHEN-Macaulay rings ,ALGORITHMS ,MATHEMATICS - Abstract
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this paper, we give some different combinatorial conditions for a bipartite graph which are equivalent to Cohen-Macaulayness of the graph. We prove that a bipartite graph is Cohen-Macaulay if and only if it is well covered and has a unique perfect matching. We also provide a fast algorithm to check Cohen-Macaulayness of a given bipartite graph. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
21. The Extremal Function for Two Disjoint Cycles.
- Author
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Yunshu Gao and Ji, Naidan
- Subjects
GRAPH theory ,GRAPHIC methods ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order $$n\ge 9$$ and size at least $$\lfloor \frac{7n-13}{2}\rfloor $$ contains two disjoint theta graphs. We also show that every 2-edge-connected graph of order $$n\ge 6$$ and size at least $$3n-5$$ contains two disjoint cycles, such that any specified vertex with degree at least three belongs to one of them. The lower bound on size in both is sharp in general. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
22. Upper Bounds on the Signed (k, k)-Domatic Number of Digraphs.
- Author
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Volkmann, Lutz
- Subjects
DIRECTED graphs ,GRAPH theory ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
Let $$D$$ be a simple digraph with vertex set $$V(D)$$ , and let $$f:V(D)\rightarrow \{-1,1\}$$ be a two-valued function. If $$k\ge 1$$ is an integer and $$\sum _{x\in N^-[v]}f(x)\ge k$$ for each $$v\in V(D)$$ , where $$N^-[v]$$ consists of $$v$$ and all vertices of $$D$$ from which arcs go into $$v$$ , then $$f$$ is a signed $$k$$ -dominating function on $$D$$ . A set $$\{f_1,f_2,\ldots ,f_d\}$$ of distinct signed $$k$$ -dominating functions on $$D$$ with the property that $$\sum _{i=1}^df_i(x)\le k$$ for each $$x\in V(D)$$ , is called a signed $$(k,k)$$ -dominating family (of functions) on $$D$$ . The maximum number of functions in a signed $$(k,k)$$ -dominating family on $$D$$ is the signed $$(k,k)$$ -domatic number of $$D$$ . In this article, we mainly present upper bounds on the signed $$(k,k)$$ -domatic number, in particular for regular digraphs. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
23. Distortion Theorem for Locally Biholomorphic Bloch Mappings on the Unit Ball Bn*.
- Author
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Jianfei Wang
- Subjects
BIHOLOMORPHIC mappings ,MATHEMATICAL variables ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
In this note, we establish a distortion theorem for locally biholomorphic Bloch mappings $$f$$ satisfying $$||f||_{0}=1$$ and $$\det f'(0)=\alpha \in (0,1],$$ where $$\Vert f\Vert _{0}=\mathrm {sup}\{(1-|z|^{2})^\frac{n+1}{2n}|\det f'(z)| ^\frac{1}{n}:z\in \mathcal {B}^{n}\}.$$ This result extends the result of Bonk, Minda, and Yanagihara of one complex variable to higher dimensions. Moreover, a lower estimate for the radius of the largest univalent ball in the image of $$f$$ centered at $$f(0)$$ is given. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
24. The U-Radius for Classes of Analytic Functions.
- Author
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Ali, Rosihan M. and Alarifi, Najla M.
- Subjects
ANALYTIC functions ,MATHEMATICAL inequalities ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
Let $$\mathcal {U}$$ denote the class of normalized analytic functions $$f$$ in the open unit disk $$\mathbb {D}$$ satisfying The $$\mathcal {U}$$ -radius is obtained for several classes of functions. These include the class of normalized analytic functions $$f$$ satisfying the inequality $${{\mathrm{Re}}}\, f(z)/g(z)>0$$ or $$\left| f(z)/g(z)-1\right| < 1$$ in $$\mathbb {D},$$ where $$g$$ belongs to a certain class of functions, the class of functions $$f$$ satisfying $$|f'(z)-1|<1$$ in $$\mathbb {D},$$ and functions $$f$$ satisfying $${{\mathrm{Re}}}\, f(z)/z>\alpha , 0 \le \alpha < 1,$$ in $$\mathbb {D}.$$ A recent conjecture by Obradović and Ponnusamy concerning the radius of univalence for a product involving univalent functions is also shown to hold true. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
25. Some Notes on CN Rings.
- Author
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Junchao Wei
- Subjects
RING theory ,RINGS of integers ,MATHEMATICS theorems ,ALGORITHMS ,MATHEMATICS - Abstract
A ring $$R$$ is $$CN$$ if and only if for any $$x\in N(R)$$ and $$y\in R$$ , $$((1+x)y)^{n+k}=(1+x)^{n+k}y^{n+k}$$ , where $$n$$ is a fixed positive integer and $$k=0, 1,2$$ ; (2) Let $$R$$ be a $$CN$$ ring and $$n\ge 1$$ . If for any $$x, y\in R\backslash N(R)$$ , $$(xy)^{n+k}=x^{n+k}y^{n+k}$$ , where $$k=0, 1,2$$ , then $$R$$ is commutative; (3) Let $$R$$ be a ring and $$n\ge 1$$ . If for any $$x\in R\backslash N(R)$$ and $$y\in R$$ , $$(xy)^k=x^ky^k$$ , $$k=n, n+1, n+2$$ , then $$R$$ is commutative; (4) $$NLI $$ exchange rings are clean. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
26. Fekete--Szegö Problem for a Certain Subclass of Close-to-convex Functions.
- Author
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Kowalczyk, Bogumiła and Lecko, Adam
- Subjects
STAR-like functions ,REAL variables ,FIXED point theory ,ALGORITHMS ,MATHEMATICS - Abstract
Given a starlike function $$g\in \mathcal S^*,$$ an analytic standardly normalized function $$f$$ in the unit disk $$\mathbb {D}$$ is called close-to-convex with respect to $$g$$ if there exists $$\delta \in (-\pi /2,\pi /2)$$ such that For the class $$\mathcal C(h)$$ of all close-to-convex functions with respect to $$h(z):=z/(1-z),\ z\in \mathbb {D},$$ a Fekete-Szegö problem is examined. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
27. The Diamond Integral on Time Scales.
- Author
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Brito da Cruz, Artur M. C., Martins, Natália, and Torres, Delfim F. M.
- Subjects
INTEGRALS ,MATHEMATICAL inequalities ,MINKOWSKI geometry ,ALGORITHMS ,MATHEMATICS - Abstract
We define a more general type of integral on time scales. The new diamond integral is a refined version of the diamond-alpha integral introduced in 2006 by Sheng et al. A mean value theorem for the diamond integral is proved, as well as versions of Holder's, Cauchy-Schwarz's, and Minkowski's inequalities. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
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