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46Miller, Mirka
22Morris, Sidney
17Kruger, Alexander
15Sugeng, Kiki Ariyanti
14Lin, Yuqing
13Baca, Martin
13Rubinov, Alex
13Ryan, Joe
12Pineda-Villavicencio, Guillermo
11Hofmann, Karl
9Kelarev, Andrei
9Outrata, Jiri
7Gabriyelyan, Saak
7Mammadov, Musa
6Balbuena, Camino
6Yearwood, John
6Yost, David
5Abawajy, Jemal
5Baskoro, Edy
5López, Marco

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210102 Applied Mathematics
12Graph theory
110802 Computation Theory and Mathematics
11Mathematics
8Antimagic labeling
6Data mining
6Variational analysis
50103 Numerical and Computational Mathematics
5Metric regularity
5Moore bound
5Normal cone
5Number theory
40906 Electrical and Electronic Engineering
4Connectivity
4Degree/diameter problem
4Lie group
4Numerical methods
4Problem solving
4Slope

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Sigma-porosity in monotonic analysis with applications to optimization

**Authors:**Rubinov, Alex**Date:**2005**Type:**Text , Journal article**Relation:**Abstract and Applied Analysis Vol. 2005, no. 3 (2005), p. 287-305**Full Text:**false**Reviewed:****Description:**We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are $sigma$-porous in corresponding spaces. Some applications to optimization are given.**Description:**C1**Description:**We introduce and study some metric spaces of increasing positively homogeneous (IPH) functions, decreasing functions, and conormal (upward) sets. We prove that the complements of the subset of strictly increasing IPH functions, of the subset of strictly decreasing functions, and of the subset of strictly conormal sets are $\sigma$-porous in corresponding spaces. Some applications to optimization are given.**Description:**2003001421

Sophus Lie's third fundamental theorem and the adjoint functor theorem

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Group Theory Vol. 8, no. 1 (2005), p. 115-133**Full Text:**false**Reviewed:****Description:**The essential attributes of a Lie group G are the associated Lie algebra LðGÞ and the exponential function exp : LðGÞ ! G. The prescription L operates not only on Lie groups but also on morphisms between them: it is a functor. Many features of Lie theory are shared by classes of topological groups which are much larger than that of Lie groups; these classes include the classes of compact groups, locally compact groups, and pro-Lie groups, that is, complete topological groups having arbitrarily small normal subgroups N such that G=N is a (finitedimensional) Lie group. Considering the functor L it is therefore appropriate to contemplate more general classes of topological groups. Certain functorial properties of the assignment of a Lie algebra to a topological group (where possible) will be essential. What is new here is that we will introduce a functorial assignment from Lie algebras to groups and investigate to what extent it is inverse to the Lie algebra functor L. While the Lie algebra functor is well known and is cited regularly, the existence of a Lie group functor available to be cited and applied appears less well known. Sophus Lie’s Third Fundamental Theorem says that for each finite-dimensional real Lie algebra there is a Lie group whose Lie algebra is (isomorphic to) the given one; but even in classical circumstances it is not commonly known that this happens in a functorial fashion and what the precise relationship between the Lie algebra functor and the Lie group functor is.**Description:**C1**Description:**2003001415

Super (a,d)-vertex-antimagic total labelings

- Miller, Mirka, Sugeng, Kiki Ariyanti, Lin, Yuqing, Baca, Martin

**Authors:**Miller, Mirka , Sugeng, Kiki Ariyanti , Lin, Yuqing , Baca, Martin**Date:**2005**Type:**Text , Journal article**Relation:**The Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 55, no. (2005), p. 91-102**Full Text:**false**Reviewed:****Description:**C1**Description:**2003001401

Hermite-Hadamard-type inequalities for increasing convex-along-rays function

- Rubinov, Alex, Dragomir, S. S, Dutta, J.

**Authors:**Rubinov, Alex , Dragomir, S. S , Dutta, J.**Date:**2004**Type:**Text , Journal article**Relation:**Analysis Vol. 24, no. 2 (2004), p. 171-181**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000933

On d-antimagic labelings of prisms

- Lin, Yuqing, Slamin,, Baca, Martin, Miller, Mirka

**Authors:**Lin, Yuqing , Slamin, , Baca, Martin , Miller, Mirka**Date:**2004**Type:**Text , Journal article**Relation:**Ars Combinatoria: A Canadian Journal of Combinatorics Vol. 72, no. (2004), p. 65-76**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000907

On non-polynomiality of XOR over Zn2

- Grosek, Otokar, Miller, Mirka, Ryan, Joe

**Authors:**Grosek, Otokar , Miller, Mirka , Ryan, Joe**Date:**2004**Type:**Text , Journal article**Relation:**Tatra Mountains Mathematical Publications Vol. 29, no. (2004), p. 183-191**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000905

Statistical cluster points of sequences in finite dimensional spaces

- Pehlivan, Serpil, Guncan, A., Mammadov, Musa

**Authors:**Pehlivan, Serpil , Guncan, A. , Mammadov, Musa**Date:**2004**Type:**Text , Journal article**Relation:**Czechoslovak Mathematical Journal Vol. 54, no. 1 (2004), p. 95-102**Full Text:**false**Reviewed:****Description:**In this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of T-statistical convergence. A sequence x is**Description:**C1**Description:**2003000896

The exponential function of locally connected compact Abelian groups

- Hofmann, Karl, Morris, Sidney, Poguntke, D.

**Authors:**Hofmann, Karl , Morris, Sidney , Poguntke, D.**Date:**2004**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 16, no. 1 (2004), p. 1-16**Full Text:**false**Reviewed:****Description:**It is shown that the following four conditions are equivalent for a compact connected abelian group G :(i)the exponential function of G is open onto its image;(ii)G has arbitrarily small connected direct summands N such that G =N is a .nite dimensional torus;(iii)the arc component G[suba] of the identity is locally arcwise connected;(iv)the character group G G is a torsion free group in which every .nite rank pure subgroup is free and is a direct summand.**Description:**C1**Description:**2003000909

The structure of abelian pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2004**Type:**Text , Journal article**Relation:**Mathematische Zeitschrift Vol. 248, no. 4 (Dec 2004), p. 867-891**Full Text:**false**Reviewed:****Description:**A pro-Lie group is a projective limit of a projective system of finite dimensional Lie groups. A prodiscrete group is a complete abelian topological group in which the open normal subgroups form a basis of the filter of identity neighborhoods. It is shown here that an abelian pro-Lie group is a product of (in general infinitely many) copies of the additive topological group of reals and of an abelian pro-Lie group of a special type; this last factor has a compact connected component, and a characteristic closed subgroup which is a union of all compact subgroups; the factor group modulo this subgroup is pro-discrete and free of nonsingleton compact subgroups. Accordingly, a connected abelian pro-Lie group is a product of a family of copies of the reals and a compact connected abelian group. A topological group is called compactly generated if it is algebraically generated by a compact subset, and a group is called almost connected if the factor group modulo its identity component is compact. It is further shown that a compactly generated abelian pro-Lie group has a characteristic almost connected locally compact subgroup which is a product of a finite number of copies of the reals and a compact abelian group such that the factor group modulo this characteristic subgroup is a compactly generated prodiscrete group without nontrivial compact subgroups.**Description:**C1**Description:**2003000910

**Authors:**Mammadov, Musa**Date:**2003**Type:**Text , Journal article**Relation:**Abstract and Applied Analysis Vol. 2003, no. 11 (2003), p. 631-650**Full Text:**false**Reviewed:****Description:**We study the turnpike property for the nonconvex optimal control problems described by the differential inclusion x˙∈a(x). We study the infinite horizon problem of maximizing the functional ∫0Tu(x(t))dt as T grows to infinity. The turnpike theorem is proved for the case when a turnpike set consists of several optimal stationary points.**Description:**C1**Description:**2003000343

Cardinalities of locally compact groups and their Stone-Čech compactifications

- Itzkowitz, Gerald, Morris, Sidney, Tkachuk, Vladimir

**Authors:**Itzkowitz, Gerald , Morris, Sidney , Tkachuk, Vladimir**Date:**2003**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 67, no. 3 (2003), p. 353-364**Full Text:**false**Reviewed:****Description:**If G is any Hausdorff topological group and**Description:**C1**Description:**2003000377

Continuous subdifferential approximations and their applications

**Authors:**Bagirov, Adil**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 115, no. 5 (2003), p. 2567-2609**Full Text:**false**Reviewed:****Description:**In this paper, we study continuous approximations to the Clarke subdifferential and the Demyanov– Rubinov quasidifferential. Different methods have been proposed and discussed for the construction of the continuous approximations. Numerical methods for minimization of the locally Lipschitzian functions which are based on the continuous approximations are described and their convergence is studied. To test the proposed methods, numerical experiments have been carried out and discussed in the paper.**Description:**C1**Description:**2003000423

Lagrange-type functions in constrained optimization

- Rubinov, Alex, Yang, Xiao, Bagirov, Adil, Gasimov, Rafail

**Authors:**Rubinov, Alex , Yang, Xiao , Bagirov, Adil , Gasimov, Rafail**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 115, no. 4 (2003), p. 2437-2505**Full Text:**false**Reviewed:****Description:**We examine various kinds of nonlinear Lagrange-type functions for constrained optimization problems. In particular, we study the weak duality, the zero duality gap property, and the existence of an exact parameter for these functions. The paper contains a detailed survey of results in these directions and comparison of different methods proposed by different authors. Some new results are also given.**Description:**C1**Description:**2003000358

Maximal monotonicity, conjugation and the duality product

- Burachik, Regina, Svaiter, B.F.

**Authors:**Burachik, Regina , Svaiter, B.F.**Date:**2003**Type:**Text , Journal article**Relation:**Proceedings of the American Mathematical Society Vol. 131, no. 8 (2003), p. 2379-2383**Full Text:**false**Reviewed:****Description:**Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.**Description:**C1**Description:**2003002558

On Fréchet subdifferentials

**Authors:**Kruger, Alexander**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 116, no. 3 (2003), p. 3325-3358**Full Text:****Reviewed:****Description:**2003002852

**Authors:**Kruger, Alexander**Date:**2003**Type:**Text , Journal article**Relation:**Journal of Mathematical Sciences Vol. 116, no. 3 (2003), p. 3325-3358**Full Text:****Reviewed:****Description:**2003002852

Projective limits of finite-dimensional Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2003**Type:**Text , Journal article**Relation:**Proceedings of the London Mathematical Society Vol. 87, no. 3 (Nov 2003), p. 647-676**Full Text:**false**Reviewed:****Description:**For a topological group G we define N to be the set of all normal subgroups modulo which G is a finite-dimensional Lie group. Call G a pro-Lie group if, firstly, G is complete, secondly, N is a filter basis, and thirdly, every identity neighborhood of G contains some member of N. It is easy to see that every pro-Lie group G is a projective limit of the projective system of all quotients of G modulo subgroups from N. The converse implication emerges as a difficult proposition, but it is shown here that any projective limit of finite-dimensional Lie groups is a pro-Lie group. It is also shown that a closed subgroup of a pro-Lie group is a pro-Lie group, and that for any closed normal subgroup N of a pro-Lie group G, for any one parameter subgroup Y : R G/N there is a one parameter subgroup X : R G such that X(t) N = Y(t) for any real number t. The category of all pro-Lie groups and continuous group homomorphisms between them is closed under the formation of all limits in the category of topological groups and the Lie algebra functor on the category of pro-Lie groups preserves all limits and quotients.**Description:**C1**Description:**2003000376

Twisted sums with C(K) spaces

- Cabello Sanchez, Felix, Castillo, Jesus, Kalton, Nigel, Yost, David

**Authors:**Cabello Sanchez, Felix , Castillo, Jesus , Kalton, Nigel , Yost, David**Date:**2003**Type:**Text , Journal article**Relation:**Transactions of the American Mathematical Society Vol. 355, no. (2003), p. 4523-4541**Full Text:****Reviewed:****Description:**If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 -->**Description:**C1**Description:**2003002201

**Authors:**Cabello Sanchez, Felix , Castillo, Jesus , Kalton, Nigel , Yost, David**Date:**2003**Type:**Text , Journal article**Relation:**Transactions of the American Mathematical Society Vol. 355, no. (2003), p. 4523-4541**Full Text:****Reviewed:****Description:**If X is a separable Banach space, we consider the existence of non-trivial twisted sums 0 -->**Description:**C1**Description:**2003002201

Undergraduate mathematics curricula - A new approach

- Giri, Jason, Pierce, Robyn, Turville, Christopher

**Authors:**Giri, Jason , Pierce, Robyn , Turville, Christopher**Date:**2003**Type:**Text , Journal article**Relation:**New Zealand Journal of Mathematics Vol. 32 , no. Supplementary Issue (2003), p. 155-162**Full Text:**false**Reviewed:****Description:**C1**Description:**2003000363

Attracting sets for increasing co-radiant and topical operators

- Kloeden, Peter, Rubinov, Alex

**Authors:**Kloeden, Peter , Rubinov, Alex**Date:**2002**Type:**Text , Journal article**Relation:**Mathematische Nachrichten Vol. 243, no. (2002), p. 134-145**Full Text:**false**Reviewed:****Description:**A generalization of the Perron-Frobenius theorem to increasing positively homogeneous of degree one operators is extended to increasing co-radiant and topical operators, which are of interest in mathematical economics. In particular, small attracting sets containing the limit points of all sequences generated by iteration of such operators are determined.**Description:**C1**Description:**2003000150

Hadamard type inequality for quasiconvex functions in higher dimensions

**Authors:**Rubinov, Alex , Dutta, J.**Date:**2002**Type:**Text , Journal article**Relation:**Journal of Mathematical Analysis and Applications Vol. 270, no. 1 (2002), p. 80-91**Full Text:**false**Reviewed:****Description:**In this article we study a Hadamard type inequality for nonnegative evenly quasiconvex functions. The approach of our study is based on the notion of abstract convexity. We also provide an explicit calculation to evaluate the asymptotically sharp constant associated with the inequality over a unit square in the two-dimensional plane. © 2002 Elsevier Science (USA). All rights reserved.**Description:**2003000149

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