350 results
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2. On the growth rate of divergent series.
- Author
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Mortici, Cristinel and Rassias, Michael Th.
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DIVERGENT series , *HARMONIC series (Mathematics) , *STOCHASTIC convergence , *DIVERGENCE theorem , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Text The aim of this paper is to present a method to calculate the rate of growth of divergent series. In the case of the harmonic series, we study an alternate of other classical methods presented by L. Comtet, S.M. Zeyman, W. DeTemple and S.-H. Wang. Moreover, the method presented in this paper is suitable for obtaining similar results on other divergent series, as we will show in the final part of our investigation. Video For a video summary of this paper, please visit http://youtu.be/SFR7zY4pvG4 . [ABSTRACT FROM AUTHOR]
- Published
- 2015
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3. The origins of Euler's early work on continued fractions.
- Author
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Cretney, Rosanna
- Subjects
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EULER theorem , *CONTINUED fractions , *NUMERICAL solutions to Riccati equation , *NUMERICAL solutions to differential equations , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, I examine Euler's early work on the elementary properties of continued fractions in the 1730s, and investigate its possible links to previous writings on continued fractions by authors such as William Brouncker. By analysing the content of Euler's first paper on continued fractions, ‘De fractionibus continuis dissertatio’ (1737, published 1744) I conclude that, contrary to what one might expect, Euler's work on continued fractions initially arose not from earlier writings on continued fractions, but from a wish to solve the Riccati differential equation. [Copyright &y& Elsevier]
- Published
- 2014
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4. On representations of Fuss–Catalan algebras.
- Author
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Hussein, Ahmed B.
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ALGEBRA , *MATHEMATICS , *COMPLEX numbers , *NUMBER theory , *MATHEMATICAL analysis - Abstract
Abstract In this paper, we study the representation theory of the Fuss–Catalan algebras, FC n (a , b). We prove that this algebra is cellular with a cellular basis and forms a tower of recollement, as defined by Cox, Martin, Parker, and Xi [7] , and hence, it is quasi-hereditary algebra if a , b are non-zero complex numbers. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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5. Invariant elliptic estimates
- Author
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Cho, Yonggeun, Ozawa, Tohru, and Shim, Yong-Sun
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ELLIPTIC functions , *INVARIANTS (Mathematics) , *LAME'S functions , *ESTIMATION theory , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321–339] via gradient estimate and discuss an application to the Lamé system. [Copyright &y& Elsevier]
- Published
- 2011
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6. 2-signalizers in almost simple groups
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(Korchagina) Capdeboscq, Inna
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GROUP theory , *FINITE groups , *FINITE simple groups , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: This paper offers an exhaustive study of certain 2-signalizers in known non-sporadic finite simple groups. The main result of this paper is relevant to the Generation-2 proof of the Classification of Finite Simple Groups. [Copyright &y& Elsevier]
- Published
- 2010
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7. Uniqueness of meromorphic functions whose derivatives share four small functions
- Author
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Li, Xiao-Min and Yi, Hong-Xun
- Subjects
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MEROMORPHIC functions , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we will prove some uniqueness theorems of meromorphic functions whose derivatives share four distinct small functions. The results in this paper improve those given by R. Nevanlinna, L. Yang, G.D. Qiu, and other authors. An example is provided to show that the results in this paper are best possible. [Copyright &y& Elsevier]
- Published
- 2009
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8. Optimal and perfect difference systems of sets
- Author
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Ding, Cunsheng
- Subjects
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NONLINEAR functional analysis , *SET theory , *SYNCHRONIZATION , *NONLINEAR theories , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: Difference systems of sets (DSS) were introduced in 1971 by Levenstein for the construction of codes for synchronization, and are closely related to cyclic difference families. In this paper, algebraic constructions of difference systems of sets using functions with optimum nonlinearity are presented. All the difference systems of sets constructed in this paper are perfect and optimal. One conjecture on difference systems of sets is also presented. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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9. Ordered spanning sets for quasimodules for Möbius vertex algebras
- Author
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Buhl, Geoffrey
- Subjects
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ALGEBRA , *MATHEMATICAL analysis , *MATHEMATICS , *ALGORITHMS - Abstract
Abstract: Quasimodules for vertex algebras are generalizations of modules for vertex algebras. These new objects arise from a generalization of locality for fields. Quasimodules tie together module theory and twisted module theory, and both twisted and untwisted modules feature Poincaré–Birkhoff–Witt-like spanning sets. This paper generalizes these spanning set results to quasimodules for certain Möbius vertex algebras. In particular this paper presents two spanning sets, one featuring a difference-zero ordering restriction on modes and another featuring a difference-one ordering restriction. [Copyright &y& Elsevier]
- Published
- 2008
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10. Claw-free graphs. IV. Decomposition theorem
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Chudnovsky, Maria and Seymour, Paul
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GRAPHIC methods , *MATHEMATICAL decomposition , *COMBINATORICS , *MATHEMATICS , *PROBABILITY theory , *MATHEMATICAL analysis - Abstract
Abstract: A graph is claw-free if no vertex has three pairwise nonadjacent neighbours. In this series of papers we give a structural description of all claw-free graphs. In this paper, we achieve a major part of that goal; we prove that every claw-free graph either belongs to one of a few basic classes, or admits a decomposition in a useful way. [Copyright &y& Elsevier]
- Published
- 2008
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11. A class of -algebras generalizing both graph algebras and homeomorphism -algebras IV, pure infiniteness
- Author
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Katsura, Takeshi
- Subjects
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MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA , *INFINITY (Mathematics) - Abstract
Abstract: This is the final one in the series of papers where we introduce and study the -algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated -algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as -algebras associated with topological graphs. [Copyright &y& Elsevier]
- Published
- 2008
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12. On tracial approximation
- Author
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Elliott, George A. and Niu, Zhuang
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *LINEAR algebra - Abstract
Abstract: Let be a class of unital C*-algebras. The class of C*-algebras which can be tracially approximated (in the Egorov-like sense first considered by Lin) by the C*-algebras in is studied (Lin considered the case that consists of finite-dimensional C*-algebras or the tensor products of such with ). In particular, the question is considered whether, for any simple separable , there is a C*-algebra B which is a simple inductive limit of certain basic homogeneous C*-algebras together with C*-algebras in , such that the Elliott invariant of A is isomorphic to the Elliott invariant of B. An interesting case of this question is answered. In the final part of the paper, the question is also considered which properties of C*-algebras are inherited by tracial approximation. (Results of this kind are obtained which are used in the proof of the main theorem of the paper, and also in the proof of the classification theorem of the second author given in [Z. Niu, A classification of tracially approximately splitting tree algebra, in preparation] and [Z. Niu, A classification of certain tracially approximately subhomogeneous C*-algebras, PhD thesis, University of Toronto, 2005]—which also uses the main result of the present paper.) [Copyright &y& Elsevier]
- Published
- 2008
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13. A -analogue of Kazhdan's property (T)
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Pavlov, A.A. and Troitsky, E.V.
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MATHEMATICAL analysis , *MODULES (Algebra) , *MATHEMATICS , *ALGEBRA - Abstract
Abstract: This paper deals with a “naive” way of generalizing Kazhdan''s property (T) to -algebras. Our approach differs from the approach of Connes and Jones, which has already demonstrated its utility. Nevertheless, it turns out that our approach is applicable to a rather subtle question in the theory of -Hilbert modules. Namely, we prove that a separable unital -algebra A has property MI (module infinite—i.e. any countably generated self-dual Hilbert module over A is finitely generated and projective) if and only if A does not satisfy our definition of property (T). The commutative case was studied in an earlier paper. [Copyright &y& Elsevier]
- Published
- 2007
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14. On the uniqueness theorems of meromorphic functions with weighted sharing of three values
- Author
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Li, Xiao-Min and Xu, Hui-Cai
- Subjects
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MEROMORPHIC functions , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we deal with the problem of uniqueness and weighted sharing of two meromorphic functions with their first derivatives having the same fixed points with the same multiplicities. The results in this paper improve those given by K. Tohge, Xiao-Min Li and Hong-Xun Yi. [Copyright &y& Elsevier]
- Published
- 2007
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15. Dlab's theorem and tilting modules for stratified algebras
- Author
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Frisk, Anders
- Subjects
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ALGEBRA , *MATHEMATICAL analysis , *MATHEMATICS , *BIOLOGICAL variation - Abstract
Abstract: In the first part of the paper we give a characterization for an associative algebra to be standardly stratified in the sense of Cline, Parshall and Scott, generalizing a theorem of V. Dlab. In the second part of the paper we construct characteristic tilting modules for standardly stratified algebras and use them to estimate the finitistic dimension of such algebras. These tilting modules give rise to the Ringel duality concept for stratified algebras. We also define and investigate a generalization of the notion of properly stratified algebras to the above setup. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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16. Cyclic algebras over p-adic curves
- Author
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Saltman, David J.
- Subjects
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *ADELES (Mathematics) - Abstract
Abstract: In this paper we study division algebras over the function fields of curves over . The first and main tool is to view these fields as function fields over nonsingular S which are projective of relative dimension 1 over the p adic ring . A previous paper showed such division algebras had index bounded by assuming the exponent was n and n was prime to p. In this paper we consider algebras of prime degree (and hence exponent) and show these algebras are cyclic. We also find a geometric criterion for a Brauer class to have index q. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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17. Equivalences of derived categories for selfinjective algebras
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Al-Nofayee, Salah
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *FINITE groups - Abstract
Abstract: Rickard proved in his paper [J. Rickard, Equivalences of derived categories for symmetric algebras, J. Algebra 257 (2002) 460–481] that if Λ is a finite-dimensional symmetric k-algebra and if there is a set of objects in satisfying some conditions, then there is a derived equivalence taking these objects to the simple modules of another algebra Γ. In this paper we generalize Rickard''s results to finite-dimensional selfinjective k-algebras by adding an extra condition. We use the techniques of Rickard''s paper in this paper. [Copyright &y& Elsevier]
- Published
- 2007
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18. On strongly α-preinvex functions
- Author
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Fan, Liya and Guo, Yunlian
- Subjects
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MATHEMATICAL functions , *DIFFERENTIAL equations , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, by means of a series of counterexamples, we study in a systematic way the relationships among (pseudo, quasi) α-preinvexity, (strict, strong, pseudo, quasi) α-invexity and (strict, strong, pseudo, quasi) αη-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of Noor and Noor [M.A. Noor, K.I. Noor, Some characterizations of strongly preinvex functions, J. Math. Anal. Appl. 316 (2006) 697–706]. [Copyright &y& Elsevier]
- Published
- 2007
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19. The sub-elliptic obstacle problem: regularity of the free boundary in Carnot groups of step two
- Author
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Danielli, Donatella, Garofalo, Nicola, and Petrosyan, Arshak
- Subjects
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MATHEMATICAL analysis , *NUMERICAL analysis , *ASYMPTOTIC expansions , *MATHEMATICS - Abstract
Abstract: The sub-elliptic obstacle problem arises in various branches of the applied sciences, e.g., in mechanical engineering and robotics, mathematical finance, image reconstruction and neurophysiology. In the recent paper [Donatella Danielli, Nicola Garofalo, Sandro Salsa, Variational inequalities with lack of ellipticity. I. Optimal interior regularity and non-degeneracy of the free boundary, Indiana Univ. Math. J. 52 (2) (2003) 361–398; MR1976081 (2004c:35424)] it was proved that weak solutions to the sub-elliptic obstacle problem in a Carnot group belong to the Folland–Stein (optimal) Lipschitz class (the analogue of the well-known interior local regularity for the classical obstacle problem). However, the regularity of the free boundary remained a challenging open problem. In this paper we prove that, in Carnot groups of step , the free boundary is (Euclidean) near points satisfying a certain thickness condition. This constitutes the sub-elliptic counterpart of a celebrated result due to Caffarelli [Luis A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139 (3–4) (1977) 155–184; MR0454350 (56 #12601)]. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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20. 5-Arc transitive cubic Cayley graphs on finite simple groups
- Author
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Xu, Shang Jin, Fang, Xin Gui, Wang, Jie, and Xu, Ming Yao
- Subjects
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GRAPH theory , *SET theory , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: In this paper, we determine all connected 5-arc transitive cubic Cayley graphs on the alternating group ; there are only two such graphs (up to isomorphism). By earlier work of the authors, these are the only two non-normal connected cubic arc-transitive Cayley graphs for finite nonabelian simple groups, and so this paper completes the classification of such non-normal Cayley graphs. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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21. Cartan subalgebras of root-reductive Lie algebras
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Dan-Cohen, Elizabeth, Penkov, Ivan, and Snyder, Noah
- Subjects
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MATHEMATICS , *LINEAR algebra , *MATHEMATICAL analysis , *INJECTIONS - Abstract
Abstract: Root-reductive Lie algebras are direct limits of finite-dimensional reductive Lie algebras under injections which preserve the root spaces. It is known that a root-reductive Lie algebra is a split extension of an abelian Lie algebra by a direct sum of copies of finite-dimensional simple Lie algebras as well as copies of the three simple infinite-dimensional root-reductive Lie algebras , , and . As part of a structure theory program for root-reductive Lie algebras, Cartan subalgebras of the Lie algebra were introduced and studied in [K.-H. Neeb, I. Penkov, Cartan subalgebras of , Canad. Math. Bull. 46 (2003) 597–616]. In the present paper we refine and extend the results of [K.-H. Neeb, I. Penkov, Cartan subalgebras of , Canad. Math. Bull. 46 (2003) 597–616] to the case of a general root-reductive Lie algebra . We prove that the Cartan subalgebras of are the centralizers of maximal toral subalgebras and that they are nilpotent and self-normalizing. We also give an explicit description of all Cartan subalgebras of the simple Lie algebras , , and . We conclude the paper with a characterization of the set of conjugacy classes of Cartan subalgebras of the Lie algebras , , , and with respect to the group of automorphisms of the natural representation which preserve the Lie algebra. [Copyright &y& Elsevier]
- Published
- 2007
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22. Chiral equivariant cohomology I
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Lian, Bong H. and Linshaw, Andrew R.
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *HOMOLOGY theory - Abstract
Abstract: We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham complex of Malikov–Schechtman–Vaintrob of a manifold with a group action. The main idea in this paper is to synthesize the algebraic approach to classical equivariant cohomology due to H. Cartan, 2 with [2] Cartan''s theory was further developed by Duflo–Kumar–Vergne [M. Duflo, S. Kumar, M. Vergne, Sur la cohomologie équivariante des variétés différentiables, Astérisque 215 (1993)] and Guillemin–Sternberg [V. Guillemin, S. Sternberg, Supersymmetry and Equivariant de Rham Theory, Springer, 1999]. This paper follows closely the latter approach. the theory of differential vertex algebras, by using an appropriate notion of invariant theory. We also construct the vertex algebra analogues of the Mathai–Quillen isomorphism, the Weil and the Cartan models for equivariant cohomology, and the Chern–Weil map. We give interesting cohomology classes in the new theory that have no classical analogues. [Copyright &y& Elsevier]
- Published
- 2007
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23. Fine Hochschild invariants of derived categories for symmetric algebras
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Zimmermann, Alexander
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *HOMOLOGY (Biology) - Abstract
Abstract: Let A be a symmetric k-algebra over a perfect field k. Külshammer defined for any integer n a mapping on the degree 0 Hochschild cohomology and a mapping on the degree 0 Hochschild homology of A as adjoint mappings of the respective p-power mappings with respect to the symmetrising bilinear form. In an earlier paper it is shown that is invariant under derived equivalences. In the present paper we generalise the definition of to higher Hochschild homology and show the invariance of κ and its generalisation under derived equivalences. This provides fine invariants of derived categories. [Copyright &y& Elsevier]
- Published
- 2007
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24. Hybrid power flow analysis using coupling loss factor of SEA for low-damping system—Part II: Formulation of 3-D case and hybrid PFFEM
- Author
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Park, Young-Ho and Hong, Suk-Yoon
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FINITE element method , *NUMERICAL analysis , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
Abstract: The hybrid power flow analysis (PFA) is an analytic method proposed for the effective prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the PFA algorithm and statistical energy analysis (SEA) coupling concepts. This paper presents the hybrid boundary condition on 3-D case for hybrid PFA in addition to 1-D and 2-D cases which are derived in the other companion paper, and formulates the hybrid power flow finite-element method (PFFEM) including coupling loss factor (CLF) of SEA to extend the application area of hybrid PFA to built-up structures. To verify the derived boundary condition and hybrid PFFEM, numerical analyses were successfully performed for various analytic models and reverberance factors. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
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25. Distributional convolutors for Fourier transform
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Betancor, Jorge J., Jerez, Claudio, Molina, Sandra M., and Rodríguez-Mesa, Lourdes
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MATHEMATICAL analysis , *MATHEMATICS , *ALGEBRA , *LINEAR algebra - Abstract
Abstract: In this paper we complete a distributional Fourier analysis developed by Howell in a serie of papers. We investigate convolution operators in the corresponding distribution spaces. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
26. Inexact proximal point method for general variational inequalities
- Author
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Bnouhachem, Abdellah and Noor, Muhammad Aslam
- Subjects
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MATHEMATICAL optimization , *MATHEMATICS , *MATHEMATICAL analysis , *MAXIMA & minima - Abstract
Abstract: In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor–corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. [Copyright &y& Elsevier]
- Published
- 2006
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27. Polynomial identities of algebras in positive characteristic
- Author
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Mota Alves, Sérgio and Koshlukov, Plamen
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ALGEBRA , *MATHEMATICS , *SCIENCE , *MATHEMATICAL analysis - Abstract
Abstract: The verbally prime algebras are well understood in characteristic 0 while over a field of positive characteristic little is known about them. In previous papers we discussed some sharp differences between these two cases for the characteristic, and we showed that the so-called Tensor Product Theorem is in part no longer valid in the second case. In this paper we study the Gelfand–Kirillov dimension of the relatively free algebras of verbally prime and related algebras. We compute the GK dimensions of several algebras and thus obtain a new proof of the fact that the algebras and are not PI equivalent in characteristic . Furthermore we show that the following algebras are not PI equivalent in positive characteristic: and ; and when , , and ; and finally, and . Here E stands for the infinite-dimensional Grassmann algebra with 1, and is the subalgebra of of the block matrices with blocks and on the main diagonal with entries from , and off-diagonal entries from ; is the natural grading on E. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
28. Frobenius test exponents for parameter ideals in generalized Cohen–Macaulay local rings
- Author
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Huneke, Craig, Katzman, Mordechai, Sharp, Rodney Y., and Yao, Yongwei
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ALGEBRA , *MATHEMATICS , *SCIENCE , *MATHEMATICAL analysis - Abstract
Abstract: This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring R of prime characteristic p. For a given ideal of R, there is a power Q of p, depending on , such that the Qth Frobenius power of the Frobenius closure of is equal to the Qth Frobenius power of . The paper addresses the question as to whether there exists a uniform which ‘works’ in this context for all parameter ideals of R simultaneously. In a recent paper, Katzman and Sharp proved that there does exists such a uniform when R is Cohen–Macaulay. The purpose of this paper is to show that such a uniform exists when R is a generalized Cohen–Macaulay local ring. A variety of concepts and techniques from commutative algebra are used, including unconditioned strong d-sequences, cohomological annihilators, modules of generalized fractions, and the Hartshorne–Speiser–Lyubeznik Theorem employed by Katzman and Sharp in the Cohen–Macaulay case. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
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29. On a class of Koszul algebras associated to directed graphs
- Author
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Retakh, Vladimir, Serconek, Shirlei, and Wilson, Robert Lee
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ALGEBRA , *MATHEMATICS , *SCIENCE , *MATHEMATICAL analysis - Abstract
Abstract: In [I. Gelfand, V. Retakh, S. Serconek, R.L. Wilson, On a class of algebras associated to directed graphs, Selecta Math. (N.S.) 11 (2005), math.QA/0506507] I. Gelfand and the authors of this paper introduced a new class of algebras associated to directed graphs. In this paper we show that these algebras are Koszul for a large class of layered graphs. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
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30. Sheets and hearts of prime ideals in enveloping algebras of semisimple Lie algebras
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Borho, Walter and Rentschler, Rudolf
- Subjects
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ALGEBRA , *MATHEMATICS , *SCIENCE , *MATHEMATICAL analysis - Abstract
Abstract: Consider the enveloping algebra of a complex semisimple Lie algebra . The heart of a prime ideal I of is the center of the total ring of fractions of . This is an extension field of the field of fractions of the center of . Let d be the degree of this field extension. An old problem of J. Dixmier asked whether . A recent paper of the second author [R. Rentschler, A negative answer to the problem of Dixmier on hearts of prime quotients of enveloping algebras, preprint, 2004] gave a negative answer by an example in . The present paper provides many more examples, involving the so-called sheets of primitive ideals introduced and studied by A. Joseph and the first author in [W. Borho, A. Joseph, Sheets and topology of primitive spectra for semisimple Lie algebras, J. Algebra 244 (2001) 76–167]. A sheet corresponds to a prime ideal I which has a heart of degree d. The main result of this paper is that d equals the covering degree of the sheet as introduced in [W. Borho, A. Joseph, Sheets and topology of primitive spectra for semisimple Lie algebras, J. Algebra 244 (2001) 76–167, 8.7]. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
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31. Semigroup gradings on associative rings
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Bahturin, Y.A. and Zaicev, M.V.
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *ALGEBRAIC fields - Abstract
Abstract: The main aim of this paper is the adaptation of the results of the papers [Y.A. Bahturin, S.K. Sehgal, M.V. Zaicev, Group gradings on associative algebras, J. Algebra 241 (2) (2001) 677–698; Y.A. Bahturin, S.K. Sehgal, M.V. Zaicev, Finite-dimensional graded simple algebras, preprint, and M.V. Zaĭtsev, S.K. Segal, Finite gradings of simple Artinian rings, Vestnik Moskov. Univ. Ser. I Mat. Mekh., vol. 3, 2001, pp. 21–24, 77 (in Russian); translation in Moscow Univ. Math. Bull. 56 (3) (2001) 21–24] about the structure of graded simple rings from the gradings by groups to the gradings by cancellative semigroups. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
32. Comments on: Novel full-search schemes for speeding up image coding using vector quantization
- Author
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Pan, Zhibin, Kotani, Koji, and Ohmi, Tadahiro
- Subjects
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VECTOR analysis , *MATHEMATICAL analysis , *SIGNAL detection , *MATHEMATICS , *UNIVERSAL algebra , *SIGNAL processing - Abstract
Vector quantization (VQ) is a well-known signal compression method. In the framework of VQ, fast search method is one of the key issues because it is the time bottleneck for practical VQ applications. Based on the law-of-cosines and the triangle inequality, the previous work [C.C. Chang, I.C. Lin, Novel full-search schemes for speeding up image coding using vector quantization, Real-Time Imaging 10 (2004) 95–102] has proposed a very efficient fast search method for VQ encoding. However, there still exist a large computational redundancy in its Scheme 1 and some incorrect expressions in its Scheme 2. This paper aims at improving these two issues further by (1) proposing a more efficient implementation method for the Scheme 1 and (2) rewiring the Scheme 2 for correctness. Meanwhile, a mathematical analysis on computational complexity and the experimental results are given to show the effectiveness of the proposed implementation method of the Scheme 1 in this paper. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
33. The Larson–Sweedler theorem for multiplier Hopf algebras
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Van Daele, Alfons and Wang, Shuanhong
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MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *ALGEBRAIC topology - Abstract
Abstract: Any finite-dimensional Hopf algebra has a left and a right integral. Conversely, Larsen and Sweedler showed that, if a finite-dimensional algebra with identity and a comultiplication with counit has a faithful left integral, it has to be a Hopf algebra. In this paper, we generalize this result to possibly infinite-dimensional algebras, with or without identity. We have to leave the setting of Hopf algebras and work with multiplier Hopf algebras. Moreover, whereas in the finite-dimensional case, there is a complete symmetry between the bialgebra and its dual, this is no longer the case in infinite dimensions. Therefore we consider a direct version (with integrals) and a dual version (with cointegrals) of the Larson–Sweedler theorem. We also add some results about the antipode. Furthermore, in the process of this paper, we obtain a new approach to multiplier Hopf algebras with integrals. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
34. Design of an optimal shock-damping isolator with application to casters
- Author
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Pan, Runling, Jiang, Jin, and Buchal, Ralph O.
- Subjects
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MATHEMATICAL optimization , *MATHEMATICAL analysis , *MATHEMATICS , *MAXIMA & minima - Abstract
Abstract: Design of an optimal shock-damping isolator is presented in this paper with specific application to casters. The design is first formulated as an optimization problem to minimize the peak acceleration of a load while keeping the maximal deflection of the isolator within a specified physical limit. The resulting solution is a constant force isolator. However, it is difficult to realize a constant force isolator with conventional mechanisms using linear springs and dampers. To implement such an isolator physically, a novel mechanism employing multiple linear springs has been developed. The structure and the parameters of the springs have been chosen by optimization techniques, and the resulting mechanism has been embodied in a prototype caster design. This paper presents the concept, design procedure, simulation and experimental evaluation results of a prototype optimal shock-damping caster in detail. The peak acceleration of this new design is only 65% of the existing caster. From a manufacturing point of view, this newly designed caster is not much more complex than existing ones. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
35. A theory of Stochastic systems. Part II: Process algebra
- Author
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D’Argenio, Pedro R. and Katoen, Joost-Pieter
- Subjects
- *
MATHEMATICS , *STOCHASTIC processes , *MATHEMATICAL analysis , *DISTRIBUTION (Probability theory) , *SYSTEM analysis - Abstract
Abstract: This paper introduces (pronounce spades), a stochastic process algebra for discrete event systems, that extends traditional process algebra with timed actions whose delay is governed by general (a.o. continuous) probability distributions. The operational semantics is defined in terms of stochastic automata, a model that uses clocks—like in timed automata—to symbolically represent randomly timed systems, cf. the accompanying paper [P.R. D’Argenio, J.-P. Kateon, A theory of stochastic systems. Part I: Stochastic automata. Inf. Comput. (2005), to appear]. We show that stochastic automata and are equally expressive, and prove that the operational semantics of a term up to α-conversion of clocks, is unique (modulo symbolic bisimulation). (Open) probabilistic and structural bisimulation are proven to be congruences for, and are equipped with an equational theory. The equational theory is shown to be complete for structural bisimulation and allows to derive an expansion law. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
36. Central ideals and Cartan invariants of symmetric algebras
- Author
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Héthelyi, László, Horváth, Erzsébet, Külshammer, Burkhard, and Murray, John
- Subjects
- *
ALGEBRA , *MATHEMATICAL analysis , *ALGEBRAIC fields , *MATHEMATICS - Abstract
Abstract: In this paper, we investigate certain ideals in the center of a symmetric algebra A over an algebraically closed field of characteristic . These ideals include the Higman ideal and the Reynolds ideal. They are closely related to the p-power map on A. We generalize some results concerning these ideals from group algebras to symmetric algebras, and we obtain some new results as well. In case , these ideals detect odd diagonal entries in the Cartan matrix of A. In a sequel to this paper, we will apply our results to group algebras. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
37. On QM-abelian surfaces with model of -type over
- Author
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Murabayashi, Naoki
- Subjects
- *
MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis , *CYBERNETICS - Abstract
Abstract: The purpose of this paper is to characterize QM-abelian surfaces which has a model of -type over . The “special” involutions on a corresponding indefinite quaternion algebra (which is defined in Section 2) play an essential role in this paper. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
38. Separable free quadratic algebras over quadratic integers
- Author
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Browkin, J. and Brzeziński, J.
- Subjects
- *
ALGEBRA , *MATHEMATICAL analysis , *ALGEBRAIC fields , *MATHEMATICS - Abstract
Abstract: The aim of the paper is to determine all free separable quadratic algebras over the rings of integers of quadratic fields in terms of the properties of the fundamental unit in the real case. The paper corrects some earlier published results on the subject. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
39. On relations between counting communication complexity classes
- Author
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Damm, Carsten, Krause, Matthias, Meinel, Christoph, and Waack, Stephan
- Subjects
- *
MATHEMATICAL analysis , *MATHEMATICS , *SET theory , *ALGEBRA - Abstract
We develop upper and lower bound arguments for counting acceptance modes of communication protocols. A number of separation results for counting communication complexity classes is established. This extends the investigation of the complexity of communication between two processors in terms of complexity classes initiated by Babai et al. (Proceedings of the 27th IEEE FOCS, 1986, pp. 337–347) and continued in several papers (e.g., J. Comput. System Sci. 41 (1990) 402; 49 (1994) 247; Proceedings of the 36th IEEE FOCS, 1995, pp. 6–15).In particular, it will be shown that for all pairs of distinct primes
p andq the communication complexity classesMODpPcc andMODqPcc are incomparable with regard to inclusion. The same is true forPPcc andMODmPcc , for any numberm⩾2 . Moreover, non-determinism and modularity are incomparable to a large extend. On the other hand, ifm=p1ℓ1·…·prℓr is the prime decomposition ofm⩾2 , then the complexity classesMODmPcc andMODρ(m)Pcc coincide, whereρ(m)=p1·…·pr .The results are obtained by characterizing the modular and probabilistic communication complexity in terms of the minimum rank of matrices ranging over certain equivalence classes. Methods from algebra and analytic geometry are used.This paper is the completely revised and strongly extended version of the conference paper Damm et al. (Proc. 9th Ann. STACS, pp. 281–291) where a subset of the results was presented. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
40. Collective fixed points and maximal elements with applications to abstract economies
- Author
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Lin, Lai-Jiu and Ansari, Qamrul Hasan
- Subjects
- *
MAPS , *MATHEMATICS , *MATHEMATICAL analysis , *EQUILIBRIUM - Abstract
In this paper, we first establish collective fixed points theorems for a family of multivalued maps with or without assuming that the product of these multivalued maps is
Φ -condensing. As an application of our collective fixed points theorem, we derive the coincidence theorem for two families of multivalued maps defined on product spaces. Then we give some existence results for maximal elements for a family ofLS -majorized multivalued maps whose product isΦ -condensing. We also prove some existence results for maximal elements for a family of multivalued maps which are notLS -majorized but their product isΦ -condensing. As applications of our results, some existence results for equilibria of abstract economies are also derived. The results of this paper are more general than those given in the literature. [Copyright &y& Elsevier]- Published
- 2004
- Full Text
- View/download PDF
41. Nested semantics over finite trees are equationally hard
- Author
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Aceto, Luca, Fokkink, Wan, van Glabbeek, Rob, and Ingólfsdóttir, Anna
- Subjects
- *
INFORMATION theory , *MATHEMATICS , *ALGEBRA , *MATHEMATICAL analysis - Abstract
This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
42. Bisimulation on speed: worst-case efficiency
- Author
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Lüttgen, Gerald and Vogler, Walter
- Subjects
- *
MATHEMATICS , *SIMULATION methods & models , *MATHEMATICAL analysis , *ALGEBRA - Abstract
This paper introduces a novel (bi)simulation-based faster-than preorder which relates asynchronous processes, where the relative speeds of system components are indeterminate, with respect to their worst-case timing behavior. The study is conducted for a conservative extension of the process algebra CCS, called TACS, which permits the specification of upper time bounds on action occurrences. TACS complements work in plain process algebras which compares asynchronous processes with respect to their functional reactive behavior only, and in timed process algebras which focus on analyzing synchronous processes. The most unusual contribution is in showing that the proposed faster-than preorder coincides with several other preorders, two of which consider the absolute times at which actions occur in system runs. The paper also develops the semantic theory of TACS by studying congruence properties, equational laws, and abstractions from internal actions. Two examples, one dealing with mail delivery and one relating two implementations of a simple storage system, testify to the practical utility of the new theory. [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
43. Rigidity of inversive distance circle packings revisited.
- Author
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Xu, Xu
- Subjects
- *
COMBINATORICS , *MATHEMATICAL analysis , *INFINITESIMAL geometry , *NONNEGATIVE matrices , *MATHEMATICS - Abstract
Inversive distance circle packing metric was introduced by P Bowers and K Stephenson [7] as a generalization of Thurston's circle packing metric [34] . They conjectured that the inversive distance circle packings are rigid. For nonnegative inversive distance, Guo [22] proved the infinitesimal rigidity and then Luo [27] proved the global rigidity. In this paper, based on an observation of Zhou [37] , we prove this conjecture for inversive distance in ( − 1 , + ∞ ) by variational principles. We also study the global rigidity of a combinatorial curvature introduced in [14,16,19] with respect to the inversive distance circle packing metrics where the inversive distance is in ( − 1 , + ∞ ) . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
44. Ranks of Maharam algebras.
- Author
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Perović, Žikica and Veličković, Boban
- Subjects
- *
SEMIGROUP algebras , *ALGEBRA , *MATHEMATICS , *ABSTRACT algebra , *MATHEMATICAL analysis - Abstract
Solving a well-known problem of Maharam, Talagrand [18] constructed an exhaustive non uniformly exhaustive submeasure, thus also providing the first example of a Maharam algebra that is not a measure algebra. To each exhaustive submeasure one can canonically assign a certain countable ordinal, its exhaustivity rank. In this paper, we use carefully constructed Schreier families and norms derived from them to provide examples of exhaustive submeasures of arbitrary high exhaustivity rank. This gives rise to uncountably many non isomorphic separable atomless Maharam algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
45. Kronecker–Halton sequences in [formula omitted].
- Author
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Hofer, Roswitha
- Subjects
- *
KRONECKER delta , *MATHEMATICAL sequences , *MATHEMATICAL analysis , *POLYNOMIALS , *MATHEMATICS - Abstract
In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
46. On randomly chosen arrangements of q + 1 lines with different slopes in [formula omitted].
- Author
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Blondeau Da Silva, Stéphane
- Subjects
- *
PROBABILITY theory , *MATHEMATICS , *ARITHMETIC , *ALGEBRA , *MATHEMATICAL analysis - Abstract
In this paper, we prove that the expected number of points in F q 2 of multiplicity m , for 0 ≤ m ≤ q + 1 , with respect to a randomly chosen arrangement of q + 1 lines with different slopes, is ( 1 / ( m ! e ) ) q 2 + O ( q ) , as q → ∞ . We further state that the distance between the number of such points in a randomly chosen arrangement and ( 1 / ( m ! e ) ) q 2 is lower than q ln q with probability close to 1 for large q . [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
47. A realization theorem for sets of distances.
- Author
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Geroldinger, Alfred and Schmid, Wolfgang A.
- Subjects
- *
MONOIDS , *SET theory , *KRULL rings , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Let H be an atomic monoid. The set of distances Δ ( H ) of H is the set of all d ∈ N with the following property: there are irreducible elements u 1 , … , u k , v 1 … , v k + d such that u 1 ⋅ … ⋅ u k = v 1 ⋅ … ⋅ v k + d but u 1 ⋅ … ⋅ u k cannot be written as a product of ℓ irreducible elements for any ℓ ∈ N with k < ℓ < k + d . It is well-known (and easy to show) that, if Δ ( H ) is nonempty, then min Δ ( H ) = gcd Δ ( H ) . In this paper we show conversely that for every finite nonempty set Δ ⊂ N with min Δ = gcd Δ there is a finitely generated Krull monoid H such that Δ ( H ) = Δ . [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
48. Liouville theorems for supersolutions of semilinear elliptic equations with drift terms in exterior domains.
- Author
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Hara, Takanobu
- Subjects
- *
LIOUVILLE'S theorem , *SEMILINEAR elliptic equations , *MATHEMATICAL domains , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
In this paper, we prove nonexistence of positive supersolutions of a semilinear equation − div ( A ( x ) ∇ u ) + b ( x ) ⋅ ∇ u = f ( u ) in exterior domains in R n ( n ≥ 3 ), where A ( x ) is bounded and uniformly elliptic, b ( x ) = O ( | x | − 1 ) , div b = 0 and f is a continuous and positive function in ( 0 , ∞ ) satisfying f ( u ) ∼ u q as u → 0 with q ≤ n / ( n − 2 ) . Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
49. Semi-continuous and discrete wavelet frames on n-dimensional spheres.
- Author
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Iglewska-Nowak, I.
- Subjects
- *
WAVELETS (Mathematics) , *COMPUTATIONAL mathematics , *LOCALIZATION problems (Robotics) , *MATHEMATICAL analysis , *MATHEMATICS - Abstract
The paper shows that under some mild conditions n -dimensional spherical wavelets derived from approximate identities build semi-continuous frames. Moreover, for sufficiently dense grids Poisson wavelets on n -dimensional spheres constitute a discrete frame. In the proof we only use the localization properties of the reproducing kernel and its gradient. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
50. Spectral analysis and synthesis on varieties.
- Author
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Székelyhidi, László and Wilkens, Bettina
- Subjects
- *
SPECTRAL synthesis (Mathematics) , *ABELIAN groups , *NOETHERIAN rings , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
In this paper we prove that spectral synthesis holds for a variety on an Abelian group if spectral analysis holds on it and the residue ring of the annihilator of the variety is a Noether ring. This extends the fundamental result of M. Lefranc about spectral synthesis on finitely generated Abelian groups. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
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