447 results
Search Results
2. SOME NORMALITY CRITERIA AND A COUNTEREXAMPLE TO THE CONVERSE OF BLOCH’S PRINCIPLE
- Author
-
Kuldeep Singh Charak and S.D. Sharma
- Subjects
Pure mathematics ,Distribution (number theory) ,Mathematics::Complex Variables ,General Mathematics ,media_common.quotation_subject ,010102 general mathematics ,Holomorphic function ,01 natural sciences ,010101 applied mathematics ,Converse ,0101 mathematics ,Differential (infinitesimal) ,Value (mathematics) ,Normality ,Mathematics ,Meromorphic function ,Counterexample ,media_common - Abstract
In this paper we continue our earlier investigations on normal families of meromorphic functions\cite{CS2}. Here, we prove some value distribution results which lead to some normality criteria for a family of meromorphic functions involving the sharing of a holomorphic function by more general differential polynomials generated by members of the family and get some recently known results extended and improved. In particular, the main result of this paper leads to a counterexample to the converse of Bloch's principle.
- Published
- 2016
3. SEMIPERMUTABILITY IN GENERALISED SOLUBLE GROUPS
- Author
-
James C. Beidleman, Adolfo Ballester-Bolinches, and R. Ialenti
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,Finitely-generated abelian group ,0101 mathematics ,01 natural sciences ,Quotient ,Mathematics - Abstract
Some classes of finitely generated hyperabelian groups defined in terms of semipermutability and S-semipermutability are studied in the paper. The classification of finitely generated hyperabelian groups all of whose finite quotients are PST-groups recently obtained by Robinson is behind our results. An alternative proof of such a classification is also included in the paper.
- Published
- 2016
4. FRAGMENTABILITY BY THE DISCRETE METRIC
- Author
-
Warren B. Moors
- Subjects
Uniform continuity ,Pure mathematics ,Isolated point ,Topological game ,General Mathematics ,Topological tensor product ,Discrete space ,Metric (mathematics) ,Topological space ,Topology ,Separable space ,Mathematics - Abstract
In a recent paper, topological spaces $(X,{\it\tau})$ that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are ${\it\sigma}$-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.
- Published
- 2015
5. DISCRETENESS CRITERIA FOR MÖBIUS GROUPS ACTING ON II
- Author
-
Xian-Tao Wang and Liu-Lan Li
- Subjects
Pure mathematics ,Inequality ,Group (mathematics) ,General Mathematics ,media_common.quotation_subject ,Ambiguity ,Fixed point ,Relation (history of concept) ,Mathematics ,media_common - Abstract
Jørgensen’s famous inequality gives a necessary condition for a subgroup of PSL(2,ℂ) to be discrete. It is also true that if Jørgensen’s inequality holds for every nonelementary two-generator subgroup, the group is discrete. The sufficient condition has been generalized to many settings. In this paper, we continue the work of Wang, Li and Cao (‘Discreteness criteria for Möbius groups acting on $\overline {\mathbb {R}}^n$’, Israel J. Math.150 (2005), 357–368) and find three more (infinite) discreteness criteria for groups acting on $\overline {\mathbb {R}}^n$; we also correct a linguistic ambiguity of their Theorem 3.3 where one of the necessary conditions might be vacuously fulfilled. The results of this paper are obtained by using known results regarding two-generator subgroups and a careful analysis of the relation among the fixed point sets of various elements of the group.
- Published
- 2009
6. THE SET OF SOLUTIONS OF INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES
- Author
-
Aneta Sikorska-Nowak, Donal O'Regan, and Ravi P. Agarwal
- Subjects
Discrete mathematics ,Set (abstract data type) ,Pure mathematics ,General Mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Banach space ,Existence theorem ,Integral equation ,Mathematics - Abstract
In this paper, we first prove an existence theorem for the integrodifferential equation(*)wheref,k,xare functions with values in a Banach spaceEand the integral is taken in the sense of Henstock–Kurzweil–Pettis. In the second part of the paper we show that the setSof all solutions of the problem (*) is compact and connected in (C(Id,E),ω), where$I_{d} \subset I_{a} $.
- Published
- 2008
7. A new system of variational inclusions with (H, η)-monotone operators
- Author
-
Jianrong Huang and Jian-Wen Peng
- Subjects
symbols.namesake ,Pure mathematics ,Monotone polygon ,General Mathematics ,Resolvent operator ,Convergence (routing) ,Hilbert space ,symbols ,Uniqueness ,Operator theory ,Mathematics - Abstract
In this paper, We introduce and study a new system of variational inclusions involving(H, η)-monotone operators in Hilbert spaces. By using the resolvent operator method associated with (H, η)-monotone operators, we prove the existence and uniqueness of solutions and the convergence of some new three-step iterative algorithms for this system of variational inclusions and its special cases. The results in this paper extends and improves some results in the literature.
- Published
- 2006
8. Parallel metrics and reducibility of the holonomy group
- Author
-
Richard Atkins
- Subjects
Combinatorics ,Pure mathematics ,Group (mathematics) ,Computer Science::Information Retrieval ,General Mathematics ,Holonomy ,Mathematics::Differential Geometry ,Mathematics - Abstract
In this paper we investigate the relationship between the existence of parallel semi-Riemannian metrics of a connection and the reducibility of the associated holonomy group. The question as to whether the holonomy group necessarily reduces in the presence of a specified number of independent parallel semi-Riemannian metrics is completely determined by the the signature of the metrics and the dimension d of the manifold, when d ≠ 4. In particular, the existence of two independent, parallel semi-Riemannian metrics, one of which having signature (p,q) with p ≠ q, implies the holonomy group is reducible. The (p,p) cases, however, may allow for more than one parallel metric and yet an irreducible holonomy group: for n = 2m, m ≥ 3, there exist connections on Rn with irreducible infinitesimal holonomy and which have two independent, parallel metrics of signature (m,m). The case of four-dimensional manifolds, however, depends on the topology of the manifold in question: the presence of three parallel metrics always implies reducibility but reducibility in the case of two metrics of signature (2,2) is guaranteed only for simply connected manifolds. The main theorem in the paper is the construction of a topologically non-trivial four-dimensional manifold with a connection that admits two independent metrics of signature (2,2) and yet has irreducible holonomy. We provide a complete solution to the general problem.
- Published
- 2006
9. Finite presentability of some metabelian Hopf algebras
- Author
-
Dessislava H. Kochloukova
- Subjects
Pure mathematics ,Group action ,Quantum group ,General Mathematics ,Lie algebra ,Representation theory of Hopf algebras ,Lie theory ,Abelian group ,Quasitriangular Hopf algebra ,Hopf algebra ,Mathematics - Abstract
The purpose of this paper is to try to unite some existing methods used in the classification results of metabelian Lie algebras and metabelian discrete groups of homological type FP2 via the language of Hopf algebras. This sheds more light on the similarities between the Lie and group cases and explains partially the differences. Still some of the results in the group case have homotopical flavour, using methods from covering spaces to establish that having homological type FP2 imposes strong condition on the first Σinvariant of the group ([4]). These methods do not have a purely algebraic counterpart. The Lie case was treated in [5, 6] with algebraic methods, and a Lie invariant (with a valuation flavour) for metabelian Lie algebras was proposed. This plays the same role in the Lie theory as the Bieri-Strebel Σ-invariant for metabelian groups. In this paper we do not suggest a new invariant but establish that the main result of [5] holds for some metabelian Hopf algebras. It is interesting to note that in both the Lie and group cases calculations with the second homology group of Abelian objects (Lie algebras or Abelian groups) viewed as modules over a commutative ring via the corresponding diagonal action was always quite helpful. The definition of the diagonal Lie and group actions can be united via the comultiplication map of Hopf algebras, and this was the starting point of our considerations. We study Hopf algebras H = U(L)#kG over a field k, that is, smash products of universal enveloping algebras U(L) of Lie algebras L over k by group rings kG, where G acts via conjugation on L and write X for the category of such Hopf algebras. This category is quite important. If char(k) = 0 it coincides with the category of cocommutative
- Published
- 2005
10. A characterisation of Hilbert spaces via orthogonality and proximinality
- Author
-
Fathi B. Saidi
- Subjects
Pure mathematics ,Hilbert manifold ,Computer Science::Information Retrieval ,General Mathematics ,Mathematical analysis ,Hilbert space ,Banach space ,Rigged Hilbert space ,symbols.namesake ,Orthogonality ,symbols ,Projective Hilbert space ,Subspace topology ,Mathematics ,Reproducing kernel Hilbert space - Abstract
In this paper we adopt the notion of orthogonality in Banach spaces introduced by the author in [6]. There, the author showed that in any two-dimensional subspace F of E, every nonzero element admits at most one orthogonal direction. The problem of existence of such orthogonal direction was not addressed before. Our main purpose in this paper is the investigation of this problem in the case where E is a real Banach space. As a result we obtain a characterisation of Hilbert spaces stating that, if in every two-dimensional subspace F of E every nonzero element admits an orthogonal direction, then E is isometric to a Hilbert space. We conclude by presenting some open problems.
- Published
- 2005
11. Hardy-type inequalities for means
- Author
-
Lars-Erik Persson and Zsolt Páles
- Subjects
Algebra ,Pure mathematics ,General Mathematics ,Of the form ,Type (model theory) ,Mathematics - Abstract
In this paper we consider inequalities of the form, WhereMis a mean. The main results of the paper offer sufficient conditions onMso that the above inequality holds with a finite constantC. The results obtained extend Hardy's and Carleman's classical inequalities together with their various generalisations in a new dirction.
- Published
- 2004
12. From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space
- Author
-
Luc Vrancken, John Bolton, and Christine Scharlach
- Subjects
Pure mathematics ,symbols.namesake ,Minimal surface ,General Mathematics ,Complex projective space ,symbols ,Projective test ,Curvature ,Ellipse ,Submanifold ,Lagrangian ,Pencil (mathematics) ,Mathematics - Abstract
In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.
- Published
- 2002
13. On totally paranormal operators
- Author
-
Christoph Schmoeger
- Subjects
Pure mathematics ,General Mathematics ,Paranormal ,Mathematics education ,Mathematics - Abstract
A continuous linear operator on a complex Banach space is said to be paranormal if ‖Tx‖2 ≤ ‖T2x‖ ‖x‖ for all x ∈ X. T is called totally paranormal if T–λ is paranormal for every λ ∈ C. In this paper we investigate the class of totally paranormal operators. We shall see that Weyl's theorem holds for operators in this class. We also show that for totally paranormal operators the Weyl spectrum satisfies the spectral mapping theorem. In Section 5 of this paper we investigate the operator equations eT = eS and eTeS = eSeT for totally paranormal operators T and S.
- Published
- 2002
14. Covariance factorisation and abstract representation of generalised random fields
- Author
-
José M. Angulo, Vo Anh, and María D. Ruiz-Medina
- Subjects
Algebra ,Pure mathematics ,Random field ,Covariance function ,Multivariate random variable ,Covariance matrix ,General Mathematics ,Duality (mathematics) ,Random element ,White noise ,Covariance ,Mathematics - Abstract
This paper introduces a new concept of duality of generalised random fields using the geometric properties of Sobolev spaces of integer order. Under this duality condition, the covariance operators of a generalised random field and its dual can be factorised. The paper also defines a concept of generalised white noise relative to the geometries of the Sobolev spaces, and via the covariance factorisation, obtains a representation of the generalised random field as a stochastic equation driven by a generalised white noise. This representation is unique except for isometric isomorphisms on the parameter space.
- Published
- 2000
15. ON CERTAIN PRODUCTS OF PERMUTABLE SUBGROUPS
- Author
-
T. M. Mudziiri Shumba, Sesuai Yash Madanha, A. Ballester-Bolinches, and M. C. Pedraza-Aguilera
- Subjects
Pure mathematics ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,General Mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Permutable prime ,Mathematics - Abstract
In this paper, we study the structure of finite groups $G=AB$ which are a weakly mutually $sn$ -permutable product of the subgroups A and B, that is, A permutes with every subnormal subgroup of B containing $A \cap B$ and B permutes with every subnormal subgroup of A containing $A \cap B$ . We obtain generalisations of known results on mutually $sn$ -permutable products.
- Published
- 2021
16. Generic Gateaux differentiability via smooth perturbations
- Author
-
Pando Georgiev and Nadia Zlateva
- Subjects
Bump function ,Mathematics::Functional Analysis ,Pure mathematics ,Continuous function ,Variational principle ,General Mathematics ,Banach space ,Christian ministry ,Differentiable function ,Space (mathematics) ,Mathematics - Abstract
We prove that in a Banach space with an uniformly Gateaux smooth bump function, every continuous function which is directionally differentiable on a dense Gδ subset of the space, is Gateaux differentiable on a dense Gδ subset of the space. Applications of this result are given. The usual applications of the variational principles in Banach spaces refer to differentiability of real valued functions. For example the papers of [B-P] and [D-G-Z] contain results about Gateaux differentiability on dense sets. An application of Ekeland’s variational principle to generic Frechet differentiability is given in the proff of famous Ekeland-Lebourg’s theorem (see [E-L]). In [Ge] an application of the smooth variational principle to generic Gateaux differentiability is presented. In this paper we prove some results about generic Gateaux differentiability of directionally differentiable functions. The tool for proving the main ∗The research was partially supported by the Bulgarian Ministry of Education and Science under contract number MM 506/1995.
- Published
- 1997
17. Metrisation of Moore spaces and abstract topological manifolds
- Author
-
David L. Fearnley
- Subjects
Topological manifold ,Pure mathematics ,Topological algebra ,Computer Science::Information Retrieval ,General Mathematics ,Topological tensor product ,Hausdorff space ,Moore space (algebraic topology) ,Banach manifold ,Topological space ,Manifold ,Mathematics - Abstract
The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.
- Published
- 1997
18. Two characterisations of additive *-automorphisms of B(H)
- Author
-
Lajos Molnár
- Subjects
symbols.namesake ,Pure mathematics ,General Mathematics ,Bounded function ,Linear operators ,Hilbert space ,symbols ,Bijection ,Algebra over a field ,Automorphism ,Mathematics - Abstract
Let H be a complex Hilbert space and let B(H) denote the algebra of all bounded linear operators on H. In this paper we give two necessary and sufficient conditions for an additive bijection of B(H) to be a *-automorphism. Both of the results in the paper are related to the so-called preserver problems.
- Published
- 1996
19. ON THE CONNECTEDNESS OF THE CHABAUTY SPACE OF A LOCALLY COMPACT PRONILPOTENT GROUP
- Author
-
Bilel Kadri
- Subjects
Pure mathematics ,Group (mathematics) ,Social connectedness ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,010307 mathematical physics ,Locally compact space ,0101 mathematics ,Space (mathematics) ,01 natural sciences ,Mathematics - Abstract
Let G be a locally compact group and let ${\mathcal {SUB}(G)}$ be the hyperspace of closed subgroups of G endowed with the Chabauty topology. The main purpose of this paper is to characterise the connectedness of the Chabauty space ${\mathcal {SUB}(G)}$ . More precisely, we show that if G is a connected pronilpotent group, then ${\mathcal {SUB}(G)}$ is connected if and only if G contains a closed subgroup topologically isomorphic to ${{\mathbb R}}$ .
- Published
- 2021
20. Trace functions on inverse semigroup algebras
- Author
-
W. D. Munn and David Easdown
- Subjects
Discrete mathematics ,Pure mathematics ,Inverse semigroup ,Trace (linear algebra) ,Semigroup ,Principal ideal ,General Mathematics ,Bicyclic semigroup ,Semilattice ,Group algebra ,Subring ,Mathematics - Abstract
Let S be an inverse semigroup and let F be a subring of the complex field containing 1 and closed under complex conjugation. This paper concerns the existence of trace functions on F[S], the semigroup algebra of S over F. Necessary and sufficient conditions on S are found for the existence of a trace function on F[S] that takes positive integral values on the idempotents of S. Although F[S] does not always admit a trace function, a weaker form of linear functional is shown to exist for all choices of S. This is used to show that the natural involution on F[S] is special. It also leads to the construction of a trace function on F[S] for the case in which F is the real or complex field and 5 is completely semisimple of a type that includes countable free inverse semigroups. The concept of a trace function on a real or complex algebra had its origin in matrix theory and is of central importance in many algebraic and analytical contexts. In the case of a group algebra, the trace of an element is defined simply to be the coefficient of the identity and is easily seen to possess all the standard properties. With the growth of interest in inverse semigroups (a class of involution semigroups with many group-like features), it is natural to ask whether the corresponding semigroup algebras also admit trace functions. In this paper we consider the semigroup algebra F[S] of an inverse semigroup 5 over a subring F of C that contains 1 and is closed under complex conjugation. In Section 1, where the basic definitions appear, two simple necessary conditions are obtained for the existence of a trace function on F[S] and attention is drawn to those trace functions (called 'strong') with the property that their values on the idempotents of S are positive integers. The main result of Section 2 provides a necessary and sufficient condition for F[S] to admit a strong trace function - namely that each principal ideal of the semilattice of S be finite. Section 3 comprises two examples. The notion of a pseudotrace function relative to a submodule is introduced in Section 4 and it is shown that, for any nonempty finite subset T of 5, F[S] admits a
- Published
- 1995
21. Haar measure and compact right topological groups
- Author
-
Paul Milnes
- Subjects
Pure mathematics ,Compact group ,General Mathematics ,Calculus ,Euclidean group ,Lie group ,Peter–Weyl theorem ,Topological group ,Locally compact space ,Locally compact group ,Haar measure ,Mathematics - Abstract
The consideration of compact right topological groups goes back at least to a paper of Ellis in 1958, where it is shown that a flow is distal if and only if the enveloping semigroup of the flow is such a group (now called the Ellis group of the distal flow). Later Ellis, and also Namioka, proved that a compact right topological group admits a left invariant probability measure. As well, Namioka proved that there is a strong structure theorem for compact right topological groups. More recently, John Pym and the author strengthened this structure theorem enough to be able to establish the existence of Haar measure on a compact right topological group, a probability measure that is invariant under all continuous left and right translations, and is unique as such. Examples of compact right topological groups have been considered earlier. In the present paper, we give concrete representations of several Ellis groups coming from low dimensional nilpotent Lie groups. We study these compact right topological groups, and two others, in some detail, paying attention in particular to the structure theorem and Haar measure, and to the question: is Haar measure uniquely determined by left invariance alone? (It is uniquely determined by right invariance alone.) To assist in answering this question, we develop some sufficient conditions for a positive answer. We suspect that one of the examples, a compact right topological group coming from the Euclidean group of the plane, does not satisfy these conditions; we don't know if the question has a positive answer for this group.
- Published
- 1992
22. ON GRAEV’S THEOREM FOR FREE PRODUCTS OF HAUSDORFF TOPOLOGICAL GROUPS
- Author
-
Guram Samsonadze and Dali Zangurashvili
- Subjects
Pure mathematics ,Free product ,010201 computation theory & mathematics ,General Mathematics ,010102 general mathematics ,Hausdorff space ,0102 computer and information sciences ,Topological group ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
The paper gives a simple proof of Graev’s theorem (asserting that the free product of Hausdorff topological groups is Hausdorff) for a particular case which includes the countable case of $k_\omega $ -groups and the countable case of Lindelöf P-groups. For this it is shown that in these particular cases the topology of the free product of Hausdorff topological groups coincides with the $X_0$ -topology in the Mal’cev sense, where X is the disjoint union of the topological groups identifying their units.
- Published
- 2021
23. A BIJECTION OF INVARIANT MEANS ON AN AMENABLE GROUP WITH THOSE ON A LATTICE SUBGROUP
- Author
-
John Hopfensperger
- Subjects
Surjective function ,Pure mathematics ,General Mathematics ,Lattice (order) ,Amenable group ,Bijection ,Lie group ,Affine transformation ,Locally compact group ,Invariant (mathematics) ,Mathematics - Abstract
Suppose G is an amenable locally compact group with lattice subgroup $\Gamma $ . Grosvenor [‘A relation between invariant means on Lie groups and invariant means on their discrete subgroups’, Trans. Amer. Math. Soc.288(2) (1985), 813–825] showed that there is a natural affine injection $\iota : {\text {LIM}}(\Gamma )\to {\text {TLIM}}(G)$ and that $\iota $ is a surjection essentially in the case $G={\mathbb R}^d$ , $\Gamma ={\mathbb Z}^d$ . In the present paper it is shown that $\iota $ is a surjection if and only if $G/\Gamma $ is compact.
- Published
- 2021
24. A factor theorem for locally convex differentiability spaces
- Author
-
Roger Eyland and Bernice Sharp
- Subjects
Factor theorem ,Pure mathematics ,Computer Science::Information Retrieval ,General Mathematics ,Mathematical analysis ,Regular polygon ,Differentiable function ,Mathematics - Abstract
The main result of this paper is that a continuous convex function with domain in a locally convex space factors through a normed space. In a recent paper by Sharp, topological linear spaces are categorised according to the differentiability properties of their continuous convex functions; we show that under suitable conditions the classification is preserved by linear maps. A technique for deducing results for locally convex spaces from Banach space theory is an immediate consequence. Examples are given and Asplund C(S) spaces are characterised.
- Published
- 1991
25. UNIQUENESS OF EXTENDABLE TEMPERATURES
- Author
-
Neil A. Watson
- Subjects
Dirichlet problem ,Work (thermodynamics) ,Pure mathematics ,Corollary ,Uniqueness theorem for Poisson's equation ,General Mathematics ,ComputingMethodologies_DOCUMENTANDTEXTPROCESSING ,Uniqueness ,Fine topology ,Mathematics - Abstract
Let E and D be open subsets of $\mathbb {R}^{n+1}$ such that $\overline {D}$ is a compact subset of E, and let v be a supertemperature on E. A temperature u on D is called extendable by v if there is a supertemperature w on E such that $w=u$ on D and $w=v$ on $E\backslash \overline D$ . From earlier work of N. A. Watson, [‘Extendable temperatures’, Bull. Aust. Math. Soc.100 (2019), 297–303], either there is a unique temperature extendable by v, or there are infinitely many; a necessary condition for uniqueness is that the generalised solution of the Dirichlet problem on D corresponding to the restriction of v to $\partial _eD$ is equal to the greatest thermic minorant of v on D. In this paper we first give a condition for nonuniqueness and an example to show that this necessary condition is not sufficient. We then give a uniqueness theorem involving the thermal and cothermal fine topologies and deduce a corollary involving only parabolic and coparabolic tusks.
- Published
- 2020
26. RATIONAL NEARLY SIMPLE GROUPS
- Author
-
Farideh Shafiei, Mohammad Reza Darafsheh, and Farrokh Shirjian
- Subjects
010101 applied mathematics ,Finite group ,Pure mathematics ,Simple (abstract algebra) ,General Mathematics ,Simple group ,010102 general mathematics ,Rational group ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
A finite group whose irreducible complex characters are rational-valued is called a rational group. The aim of this paper is to determine the rational almost simple and rational quasi-simple groups.
- Published
- 2020
27. INVARIANT MEANS AND ACTIONS OF SEMITOPOLOGICAL SEMIGROUPS ON COMPLETELY REGULAR SPACES AND APPLICATIONS
- Author
-
Khadime Salame
- Subjects
Pure mathematics ,General Mathematics ,Tychonoff space ,010102 general mathematics ,Fixed-point theorem ,010103 numerical & computational mathematics ,Fixed point ,Topological space ,01 natural sciences ,Locally convex topological vector space ,Locally compact space ,0101 mathematics ,Invariant (mathematics) ,Mathematics ,Haar measure - Abstract
In this paper, we extend the study of fixed point properties of semitopological semigroups of continuous mappings in locally convex spaces to the setting of completely regular topological spaces. As applications, we establish a general fixed point theorem, a convergence theorem and an application to amenable locally compact groups.
- Published
- 2020
28. ON THE HYPERSTABILITY OF THE DRYGAS FUNCTIONAL EQUATION ON A RESTRICTED DOMAIN
- Author
-
Satit Saejung and Jedsada Senasukh
- Subjects
Statement (computer science) ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Fixed-point theorem ,01 natural sciences ,Domain (mathematical analysis) ,010101 applied mathematics ,Functional equation ,Point (geometry) ,Hyperstability ,0101 mathematics ,Normed vector space ,Mathematics - Abstract
We prove hyperstability results for the Drygas functional equation on a restricted domain (a certain subset of a normed space). Our results are more general than the ones proposed by Aiemsomboon and Sintunavarat [‘Two new generalised hyperstability results for the Drygas functional equation’, Bull. Aust. Math. Soc.95 (2017), 269–280] and our proof does not rely on the fixed point theorem of Brzdęk as was the case there. A characterisation of the Drygas functional equation in terms of its asymptotic behaviour is given. Several examples are given to illustrate our generalisations. Finally, we point out a misleading statement in the proof of the second result in the paper by Aiemsomboon and Sintunavarat and propose its correction.
- Published
- 2019
29. ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS
- Author
-
Megan Chang-Lee and Louisa Catalano
- Subjects
Pure mathematics ,010201 computation theory & mathematics ,General Mathematics ,Polynomial ring ,010102 general mathematics ,Locally nilpotent ,0102 computer and information sciences ,0101 mathematics ,01 natural sciences ,Differential polynomial ,Connection (mathematics) ,Mathematics - Abstract
In this paper, we study some connections between the polynomial ring $R[y]$ and the differential polynomial ring $R[x;D]$. In particular, we answer a question posed by Smoktunowicz, which asks whether $R[y]$ is nil when $R[x;D]$ is nil, provided that $R$ is an algebra over a field of positive characteristic and $D$ is a locally nilpotent derivation.
- Published
- 2019
30. LIPSCHITZ-TYPE INEQUALITIES FOR ANALYTIC FUNCTIONS IN BANACH ALGEBRAS
- Author
-
Silvestru Sever Dragomir
- Subjects
010101 applied mathematics ,Pure mathematics ,General Mathematics ,010102 general mathematics ,0101 mathematics ,Perturbation theory ,Type (model theory) ,Lipschitz continuity ,01 natural sciences ,Banach *-algebra ,Analytic function ,Mathematics - Abstract
In this paper we provide some bounds for the quantity$\Vert f(y)-f(x)\Vert$, where$f:D\rightarrow \mathbb{C}$is an analytic function on the domain$D\subset \mathbb{C}$and$x$,$y\in {\mathcal{B}}$, a Banach algebra, with the spectra$\unicode[STIX]{x1D70E}(x)$,$\unicode[STIX]{x1D70E}(y)\subset D$. Applications for the exponential and logarithmic functions on the Banach algebra${\mathcal{B}}$are also given.
- Published
- 2019
31. NOTE ON THE CONVOLUTION OF HARMONIC MAPPINGS
- Author
-
Saminathan Ponnusamy and Liulan Li
- Subjects
Pure mathematics ,Mathematics - Complex Variables ,General Mathematics ,010102 general mathematics ,Regular polygon ,Harmonic (mathematics) ,01 natural sciences ,Convolution ,010101 applied mathematics ,FOS: Mathematics ,Primary: 31A05, Secondary: 30C45, 30C20 ,Complex Variables (math.CV) ,0101 mathematics ,Convex mapping ,Mathematics - Abstract
Dorff et al. \cite{DN} formulated a question concerning the convolution of two right half-plane mappings, where the normalization of the functions was considered incorrectly. In this paper, we have reformulated the open problem in correct form and provided a solution to it in a more general form. In addition, we also obtain two new theorems which correct and improve some other results., 11 pages; An extended version of this article was in a couple of conferences, and also in later workshops in Chennai during 2017 in India. This version will appear in Bulletin of the Australian Mathematical Society
- Published
- 2019
32. A COMPACT QUALITATIVE UNCERTAINTY PRINCIPLE FOR SOME NONUNIMODULAR GROUPS
- Author
-
Wassim Nasserddine
- Subjects
Pure mathematics ,Uncertainty principle ,Fourier algebra ,General Mathematics ,010102 general mathematics ,0102 computer and information sciences ,01 natural sciences ,Connection (mathematics) ,Harmonic analysis ,symbols.namesake ,Identity (mathematics) ,Fourier transform ,010201 computation theory & mathematics ,symbols ,Locally compact space ,0101 mathematics ,Abelian group ,Mathematics - Abstract
Let $G$ be a separable locally compact group with type $I$ left regular representation, $\widehat{G}$ its dual, $A(G)$ its Fourier algebra and $f\in A(G)$ with compact support. If $G=\mathbb{R}$ and the Fourier transform of $f$ is compactly supported, then, by a classical Paley–Wiener theorem, $f=0$. There are extensions of this theorem for abelian and some unimodular groups. In this paper, we prove that if $G$ has no (nonempty) open compact subsets, $\hat{f}$, the regularised Fourier cotransform of $f$, is compactly supported and $\text{Im}\,\hat{f}$ is finite dimensional, then $f=0$. In connection with this result, we characterise locally compact abelian groups whose identity components are noncompact.
- Published
- 2018
33. LEFT SYMMETRIC POINTS FOR BIRKHOFF ORTHOGONALITY IN THE PREDUALS OF VON NEUMANN ALGEBRAS
- Author
-
Naoto Komuro, Kichi-Suke Saito, and Ryotaro Tanaka
- Subjects
symbols.namesake ,Pure mathematics ,Von Neumann algebra ,General Mathematics ,010102 general mathematics ,symbols ,Predual ,Birkhoff orthogonality ,010103 numerical & computational mathematics ,0101 mathematics ,01 natural sciences ,Von Neumann architecture ,Mathematics - Abstract
In this paper, we give a complete description of left symmetric points for Birkhoff orthogonality in the preduals of von Neumann algebras. As a consequence, except for $\mathbb{C}$, $\ell _{\infty }^{2}$ and $M_{2}(\mathbb{C})$, there are no von Neumann algebras whose preduals have nonzero left symmetric points for Birkhoff orthogonality.
- Published
- 2018
34. ON VANISHING CRITERIA THAT CONTROL FINITE GROUP STRUCTURE II
- Author
-
Qingjun Kong and Julian Brough
- Subjects
Pure mathematics ,Finite group ,General Mathematics ,010102 general mathematics ,0103 physical sciences ,Structure (category theory) ,010307 mathematical physics ,0101 mathematics ,Control (linguistics) ,01 natural sciences ,Mathematics - Abstract
The first author [J. Brough, ‘On vanishing criteria that control finite group structure’, J. Algebra458 (2016), 207–215] has shown that for certain arithmetical results on conjugacy class sizes it is enough to consider only the vanishing conjugacy class sizes. In this paper we further weaken the conditions to consider only vanishing elements of prime power order.
- Published
- 2018
35. ON BASE RADICAL OPERATORS FOR CLASSES OF FINITE ASSOCIATIVE RINGS
- Author
-
Lauren K Thornton and Robert McDougall
- Subjects
Pure mathematics ,Class (set theory) ,Semigroup ,General Mathematics ,Mathematics::Rings and Algebras ,010102 general mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Base (topology) ,01 natural sciences ,Mathematics::Quantum Algebra ,Order (group theory) ,0101 mathematics ,Mathematics::Representation Theory ,Associative property ,021101 geological & geomatics engineering ,Mathematics - Abstract
In this paper, class operators are used to give a complete listing of distinct base radical and semisimple classes for universal classes of finite associative rings. General relations between operators reveal that the maximum order of the semigroup formed is 46. In this setting, the homomorphically closed semisimple classes are precisely the hereditary radical classes and hence radical–semisimple classes, and the largest homomorphically closed subclass of a semisimple class is a radical–semisimple class.
- Published
- 2018
36. RELATIVE PERTURBATION BOUNDS FOR THE JOINT SPECTRUM OF COMMUTING TUPLES OF MATRICES
- Author
-
Arnab Patra and Preeti Srivastava
- Subjects
Pure mathematics ,General Mathematics ,Clifford algebra ,Perturbation (astronomy) ,Tuple ,Normal matrix ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In this paper, we study the relative perturbation bounds for joint eigenvalues of commuting tuples of normal $n\times n$ matrices. Some Hoffman–Wielandt-type relative perturbation bounds are proved using the Clifford algebra technique. We also extend a result for diagonalisable matrices which improves a relative perturbation bound for single matrices.
- Published
- 2018
37. ON THE DERIVATION LIE ALGEBRAS OF FEWNOMIAL SINGULARITIES
- Author
-
Naveed Hussain, Huaiqing Zuo, and Stephen S.-T. Yau
- Subjects
Pure mathematics ,Conjecture ,Binomial (polynomial) ,General Mathematics ,010102 general mathematics ,Holomorphic function ,Isolated singularity ,01 natural sciences ,Hypersurface ,Singularity ,0103 physical sciences ,Lie algebra ,Gravitational singularity ,010307 mathematical physics ,0101 mathematics ,Mathematics - Abstract
Let $V$ be a hypersurface with an isolated singularity at the origin defined by the holomorphic function $f:(\mathbb{C}^{n},0)\rightarrow (\mathbb{C},0)$. The Yau algebra, $L(V)$, is the Lie algebra of derivations of the moduli algebra of $V$. It is a finite-dimensional solvable algebra and its dimension $\unicode[STIX]{x1D706}(V)$ is the Yau number. Fewnomial singularities are those which can be defined by an $n$-nomial in $n$ indeterminates. Yau and Zuo [‘A sharp upper estimate conjecture for the Yau number of weighted homogeneous isolated hypersurface singularity’, Pure Appl. Math. Q.12(1) (2016), 165–181] conjectured a bound for the Yau number and proved that this conjecture holds for binomial isolated hypersurface singularities. In this paper, we verify this conjecture for weighted homogeneous fewnomial surface singularities.
- Published
- 2018
38. APPROXIMATION OF HOLOMORPHIC FUNCTIONS ON A CLASS OF CONVEX DOMAINS
- Author
-
Ly Kim Ha
- Subjects
Class (set theory) ,Pure mathematics ,General Mathematics ,Norm (mathematics) ,010102 general mathematics ,Regular polygon ,Holomorphic function ,Boundary (topology) ,0101 mathematics ,Type (model theory) ,01 natural sciences ,Ellipsoid ,Mathematics - Abstract
Let $\unicode[STIX]{x1D6FA}$ be a member of a certain class of convex ellipsoids of finite/infinite type in $\mathbb{C}^{2}$. In this paper, we prove that every holomorphic function in $L^{p}(\unicode[STIX]{x1D6FA})$ can be approximated by holomorphic functions on $\bar{\unicode[STIX]{x1D6FA}}$ in $L^{p}(\unicode[STIX]{x1D6FA})$-norm, for $1\leq p. For the case $p=\infty$, the continuity up to the boundary is additionally required. The proof is based on $L^{p}$ bounds in the additive Cousin problem.
- Published
- 2018
39. A NOTE ON THE FUNDAMENTAL THEOREM OF ALGEBRA
- Author
-
Mohsen Aliabadi
- Subjects
Pure mathematics ,Polynomial ,General Mathematics ,Fundamental theorem of Galois theory ,010102 general mathematics ,Field (mathematics) ,0102 computer and information sciences ,01 natural sciences ,Fundamental theorem of algebra ,symbols.namesake ,010201 computation theory & mathematics ,symbols ,Perfect field ,0101 mathematics ,Algebraically closed field ,Algebraic number ,Mathematics ,Real number - Abstract
The algebraic proof of the fundamental theorem of algebra uses two facts about real numbers. First, every polynomial with odd degree and real coefficients has a real root. Second, every nonnegative real number has a square root. Shipman [‘Improving the fundamental theorem of algebra’, Math. Intelligencer29(4) (2007), 9–14] showed that the assumption about odd degree polynomials is stronger than necessary; any field in which polynomials of prime degree have roots is algebraically closed. In this paper, we give a simpler proof of this result of Shipman.
- Published
- 2018
40. TWO-DIMENSIONAL SHRINKING TARGET PROBLEM IN BETA-DYNAMICAL SYSTEMS
- Author
-
Mumtaz Hussain and Weiliang Wang
- Subjects
Pure mathematics ,Dynamical systems theory ,Lebesgue measure ,General Mathematics ,010102 general mathematics ,01 natural sciences ,010101 applied mathematics ,Set (abstract data type) ,Transformation (function) ,Hausdorff dimension ,Beta (velocity) ,0101 mathematics ,Real number ,Mathematics - Abstract
In this paper, we investigate the two-dimensional shrinking target problem in beta-dynamical systems. Let $\unicode[STIX]{x1D6FD}>1$ be a real number and define the $\unicode[STIX]{x1D6FD}$-transformation on $[0,1]$ by $T_{\unicode[STIX]{x1D6FD}}:x\rightarrow \unicode[STIX]{x1D6FD}x\;\text{mod}\;1$. Let $\unicode[STIX]{x1D6F9}_{i}$ ($i=1,2$) be two positive functions on $\mathbb{N}$ such that $\unicode[STIX]{x1D6F9}_{i}\rightarrow 0$ when $n\rightarrow \infty$. We determine the Lebesgue measure and Hausdorff dimension for the $\limsup$ set $$\begin{eqnarray}W(T_{\unicode[STIX]{x1D6FD}},\unicode[STIX]{x1D6F9}_{1},\unicode[STIX]{x1D6F9}_{2})=\{(x,y)\in [0,1]^{2}:|T_{\unicode[STIX]{x1D6FD}}^{n}x-x_{0}| for any fixed $x_{0},y_{0}\in [0,1]$.
- Published
- 2017
41. MAPPING PROPERTIES OF A SCALE INVARIANT CASSINIAN METRIC AND A GROMOV HYPERBOLIC METRIC
- Author
-
Manas Ranjan Mohapatra and Swadesh Kumar Sahoo
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,51M10, 26A15, 30C20, 30C65, 30F45 ,A domain ,Metric Geometry (math.MG) ,Scale invariance ,Mathematics::Geometric Topology ,01 natural sciences ,Modulus of continuity ,010101 applied mathematics ,Euclidean distance ,Uniform continuity ,Mathematics - Metric Geometry ,FOS: Mathematics ,Identity function ,Ball (mathematics) ,0101 mathematics ,Mathematics - Abstract
In this paper, we consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under M\"obius maps of a punctured ball onto another punctured ball. We obtain a modulus of continuity of the identity map from a domain equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic metric) onto the same domain equipped with the Euclidean metric. The quasi-invariance properties of both the metrics under quasiconformal maps are also established., Comment: 13 pages (to appear in Bull. Aust. Math. Soc.)
- Published
- 2017
42. HOLOMORPHIC AUTOMORPHISMS AND PROPER HOLOMORPHIC SELF-MAPPINGS OF A TYPE OF GENERALISED MINIMAL BALL
- Author
-
Feng Rong and Ben Zhang
- Subjects
Automorphism group ,Pure mathematics ,Mathematics::Complex Variables ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,Holomorphic function ,Automorphism ,01 natural sciences ,010101 applied mathematics ,Ball (mathematics) ,0101 mathematics ,Convex domain ,Mathematics - Abstract
In this paper, we first give a description of the holomorphic automorphism group of a convex domain which is a simple case of the so-called generalised minimal ball. As an application, we show that any proper holomorphic self-mapping on this type of domain is biholomorphic.
- Published
- 2017
43. ON CONVEX COMBINATIONS OF CONVEX HARMONIC MAPPINGS
- Author
-
Álvaro Ferrada-Salas, Rodrigo Hernández, and María J. Martín
- Subjects
Convex hull ,Convex analysis ,Pure mathematics ,General Mathematics ,010102 general mathematics ,Convex set ,Proper convex function ,06 humanities and the arts ,Subderivative ,0603 philosophy, ethics and religion ,01 natural sciences ,060302 philosophy ,Convex optimization ,Convex polytope ,Convex combination ,0101 mathematics ,Mathematics - Abstract
The family ${\mathcal{F}}_{\unicode[STIX]{x1D706}}$ of orientation-preserving harmonic functions $f=h+\overline{g}$ in the unit disc $\mathbb{D}$ (normalised in the standard way) satisfying $$\begin{eqnarray}h^{\prime }(z)+g^{\prime }(z)=\frac{1}{(1+\unicode[STIX]{x1D706}z)(1+\overline{\unicode[STIX]{x1D706}}z)},\quad z\in \mathbb{D},\end{eqnarray}$$ for some $\unicode[STIX]{x1D706}\in \unicode[STIX]{x2202}\mathbb{D}$, along with their rotations, play an important role among those functions that are harmonic and orientation-preserving and map the unit disc onto a convex domain. The main theorem in this paper generalises results in recent literature by showing that convex combinations of functions in ${\mathcal{F}}_{\unicode[STIX]{x1D706}}$ are convex.
- Published
- 2017
44. CONGRUENCES FOR TRUNCATED HYPERGEOMETRIC SERIES
- Author
-
Ji Cai Liu
- Subjects
Elliptic curve ,Pure mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,0101 mathematics ,Hypergeometric function ,Congruence relation ,01 natural sciences ,Mathematics - Abstract
Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross–Koblitz formula. In this paper we prove four supercongruences between two truncated hypergeometric series $_{2}F_{1}$. The results generalise the four Rodriguez-Villegas supercongruences.
- Published
- 2017
45. SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION
- Author
-
José Madrid
- Subjects
010101 applied mathematics ,Sobolev space ,Pure mathematics ,Variation (linguistics) ,General Mathematics ,010102 general mathematics ,Bounded variation ,Maximal function ,Derivative ,0101 mathematics ,01 natural sciences ,Mathematics - Abstract
In this paper we establish new optimal bounds for the derivative of some discrete maximal functions, in both the centred and uncentred versions. In particular, we solve a question originally posed by Bober et al. [‘On a discrete version of Tanaka’s theorem for maximal functions’, Proc. Amer. Math. Soc.140 (2012), 1669–1680].
- Published
- 2016
46. ON PAIRS OF GOLDBACH–LINNIK EQUATIONS
- Author
-
Zhixin Liu and Yafang Kong
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,01 natural sciences ,Algebra ,Riemann hypothesis ,symbols.namesake ,Waring–Goldbach problem ,Goldbach's conjecture ,symbols ,0101 mathematics ,Linear equation ,Mathematics - Abstract
In this paper, we show that every pair of large positive even integers can be represented in the form of a pair of Goldbach–Linnik equations, that is, linear equations in two primes and $k$ powers of two. In particular, $k=34$ powers of two suffice, in general, and $k=18$ under the generalised Riemann hypothesis. Our result sharpens the number of powers of two in previous results, which gave $k=62$, in general, and $k=31$ under the generalised Riemann hypothesis.
- Published
- 2016
47. ON VARIETIES OF ABELIAN TOPOLOGICAL GROUPS WITH COPRODUCTS
- Author
-
Saak Gabriyelyan and Sidney A. Morris
- Subjects
Pure mathematics ,General Mathematics ,010102 general mathematics ,Hilbert space ,Coproduct ,0102 computer and information sciences ,01 natural sciences ,symbols.namesake ,010201 computation theory & mathematics ,Product (mathematics) ,symbols ,Homomorphism ,Topological group ,0101 mathematics ,Abelian group ,Variety (universal algebra) ,Quotient ,Mathematics - Abstract
A class of abelian topological groups was previously defined to be a variety of topological groups with coproducts if it is closed under forming subgroups, quotients, products and coproducts in the category of all abelian topological groups and continuous homomorphisms. This extended research on varieties of topological groups initiated by the second author. The key to describing varieties of topological groups generated by various classes was proving that all topological groups in the variety are a quotient of a subgroup of a product of groups in the generating class. This paper analyses generating varieties of topological groups with coproducts. It focuses on the interplay between forming products and coproducts. It is proved that the variety of topological groups with coproducts generated by all discrete groups contains topological groups which cannot be expressed as a quotient of a subgroup of a product of a coproduct of discrete groups. It is proved that the variety of topological groups with coproducts generated by any infinite-dimensional Hilbert space contains all infinite-dimensional Hilbert spaces, answering an open question. This contrasts with the result that a variety of topological groups generated by a topological group does not contain any infinite-dimensional Hilbert space of greater cardinality.
- Published
- 2016
48. BEST PROXIMITY POINT THEOREMS FOR CYCLIC QUASI-CONTRACTION MAPS IN UNIFORMLY CONVEX BANACH SPACES
- Author
-
Vo Thi Le Hang and Nguyen Van Dung
- Subjects
Pure mathematics ,021103 operations research ,General Mathematics ,010102 general mathematics ,Mathematical analysis ,0211 other engineering and technologies ,Regular polygon ,Banach space ,Uniformly convex space ,02 engineering and technology ,01 natural sciences ,Negative - answer ,0101 mathematics ,Contraction (operator theory) ,Mathematics - Abstract
In this paper we first give a negative answer to a question of Amini-Harandi [‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim.56 (2013), 1667–1674] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi for cyclic strongly quasi-contractions are true under weaker assumptions.
- Published
- 2016
49. THE DIMENSION OF CENTRALISERS OF MATRICES OF ORDER
- Author
-
Hancong Zhao and Dong Zhang
- Subjects
Pure mathematics ,General Mathematics ,Dimension (graph theory) ,Commutator (electric) ,Order (ring theory) ,Integer sequence ,Fast algorithm ,Centralizer and normalizer ,law.invention ,Combinatorics ,law ,Partition (number theory) ,Asymptotic formula ,Mathematics - Abstract
In this paper, we study the integer sequence$(E_{n})_{n\geq 1}$, where$E_{n}$counts the number of possible dimensions for centralisers of$n\times n$matrices. We give an example to show another combinatorial interpretation of$E_{n}$and present an implicit recurrence formula for$E_{n}$, which may provide a fast algorithm for computing$E_{n}$. Based on the recurrence, we obtain the asymptotic formula$E_{n}=\frac{1}{2}n^{2}-\frac{2}{3}\sqrt{2}n^{3/2}+O(n^{5/4})$.
- Published
- 2016
50. A MODIFIED FR CONJUGATE GRADIENT METHOD FOR COMPUTING -EIGENPAIRS OF SYMMETRIC TENSORS
- Author
-
Guanghui Zhou and Meilan Zeng
- Subjects
Pure mathematics ,021103 operations research ,General Mathematics ,0211 other engineering and technologies ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,symbols.namesake ,Power iteration ,Conjugate gradient method ,Jacobian matrix and determinant ,Convergence (routing) ,symbols ,Symmetric tensor ,Applied mathematics ,0101 mathematics ,Mathematics - Abstract
This paper proposes improvements to the modified Fletcher–Reeves conjugate gradient method (FR-CGM) for computing $Z$-eigenpairs of symmetric tensors. The FR-CGM does not need to compute the exact gradient and Jacobian. The global convergence of this method is established. We also test other conjugate gradient methods such as the modified Polak–Ribière–Polyak conjugate gradient method (PRP-CGM) and shifted power method (SS-HOPM). Numerical experiments of FR-CGM, PRP-CGM and SS-HOPM show the efficiency of the proposed method for finding $Z$-eigenpairs of symmetric tensors.
- Published
- 2016
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.