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230101 Pure Mathematics
6Mathematics
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3Abelian topological group
3Banach space
3Exponential function
3Free locally convex space
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3Quotient group
3Separable quotient problem
3Topological group
20199 Other Mathematical Sciences
20802 Computation Theory and Mathematics
2Compact groups
2Coproducts
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2Free topological group

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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

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

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

Editors' cut : Managing scholarly journals in mathematics and IT

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2005**Type:**Text , Journal article**Relation:**Journal of Research and Practice in Information Technology Vol. 37, no. 4 (2005), p. 299-309**Full Text:**false**Reviewed:****Description:**The first version of this essay was jointly delivered by the authors as a colloquium lecture at the University of Ballarat on 24 November, 2004. A second, expanded and illustrated version was published in German in the Mitteilungen der Deutschen Mathematikervereinigung early in 2005. Because of the very positive feedback, the authors decided it would be useful to publish a version in English in a computing journal. The purpose of the essay is to provide advice and information to authors of articles about publishing in scholarly journals from an editor's perspective. Of particular importance are remarks about etiquette.**Description:**C1

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

The Structure of Compact Groups : A primer for students - A handbook for the expert

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2006**Type:**Text , Book**Full Text:**false**Description:**Dealing with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. The first edition of 1998 was well received by reviewers and has been frequently quoted in the areas of instruction and research. For the present new edition, the text has been improved in various sections. New material has been added in order to reflect ongoing research.**Description:**2003002192

An open mapping theorem for pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Journal article**Relation:**Journal of the Australian Mathematical Society Vol. 83, no. 1 (2007), p. 55-77**Full Text:**false**Reviewed:****Description:**A pro-Lie group is a projective limit of finite dimensional Lie groups. It is proved that a surjective continuous group homomorphism between connected pro-Lie groups is open. In fact this remains true for almost connected pro-Lie groups where a topological group is called almost connected if the factor group modulo the identity component is compact. As consequences we get a Closed Graph Theorem and the validity of the Second Isomorphism Theorem for pro-Lie groups in the almost connected context. © 2007 Australian Mathematical Society.**Description:**C1**Description:**2003005492

Effectiveness of using quantified intermarket influence for predicting trading signals of stock markets

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at Data Mining and Analytics 2007: Sixth Australasian Data Mining Conference, AusDM 2007 Vol. 70, p. 171-179**Full Text:****Reviewed:**

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at Data Mining and Analytics 2007: Sixth Australasian Data Mining Conference, AusDM 2007 Vol. 70, p. 171-179**Full Text:****Reviewed:**

Open mapping theorem for topological groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 31, no. 2 (2007), p. 533-551**Full Text:**false**Reviewed:****Description:**We survey sufficient conditions that force a surjective continuous homomorphism between topological groups to be open. We present the shortest proof yet of an open mapping theorem between projective limits of finite dimensional Lie groups.**Description:**C1**Description:**2003005915

Quantification of intermarket influence on the Australian All Ordinary Index based on optimization techniques

- Tilakaratne, Chandima, Morris, Sidney, Mammadov, Musa, Hurst, Cameron

**Authors:**Tilakaratne, Chandima , Morris, Sidney , Mammadov, Musa , Hurst, Cameron**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at CTAC 2006: The 13th Biennial Computational Techniques and Applications Conference p. 42-49**Full Text:****Reviewed:**

**Authors:**Tilakaratne, Chandima , Morris, Sidney , Mammadov, Musa , Hurst, Cameron**Date:**2007**Type:**Text , Conference paper**Relation:**Paper presented at CTAC 2006: The 13th Biennial Computational Techniques and Applications Conference p. 42-49**Full Text:****Reviewed:**

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2007**Type:**Text , Book**Full Text:**false**Reviewed:****Description:**A1**Description:**2003005498

Identifying and distinguishing various varieties of abelian topological groups

- McPhail, Carolyn, Morris, Sidney

**Authors:**McPhail, Carolyn , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Dissertationes Mathematicae Vol. , no. 458 (2008), p.**Full Text:**false**Reviewed:****Description:**A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally compact abelian groups; (ii) the class of all k(w)-groups; (iii) the class of all sigma-compact groups; and (iv) the free abelian topological group on [0, 1]. In all cases, hierarchical containments are determined.

Iwasawa's local splitting theorem for pro-Lie groups

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629**Full Text:****Reviewed:****Description:**If the nilradical () of the Lie algebra of a pro-Lie group G is finite dimensional modulo the center (), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. © Walter de Gruyter 2008.**Description:**C1

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Forum Mathematicum Vol. 20, no. 4 (2008), p. 607-629**Full Text:****Reviewed:****Description:**If the nilradical () of the Lie algebra of a pro-Lie group G is finite dimensional modulo the center (), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. © Walter de Gruyter 2008.**Description:**C1

On the pro-lie group theorem and the closed subgroup theorem

- Hofmann, Karl, Morris, Sidney

**Authors:**Hofmann, Karl , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Journal of Lie Theory Vol. 18, no. 2 (2008), p. 383-390**Full Text:**false**Reviewed:****Description:**Let H and M be closed normal subgroups of a pro-Lie group G and assume that H is connected and that G/M is a Lie group. Then there is a closed normal subgroup N of G such that N ? M, that G/N is a Lie group, and that HN is closed in G. As a consequence, H/(H ? N) ? HN/N is an isomorphism of Lie groups. © 2008 Heldermann Verlag.**Description:**C1

Predicting trading signals of stock market indices using neural networks

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2008**Type:**Text , Conference paper**Relation:**Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Auckland 1 December 2008 through 5 December 2008 Vol. 5360 LNAI, p. 522-531**Full Text:**false**Description:**The aim of this paper is to develop new neural network algorithms to predict trading signals: buy, hold and sell, of stock market indices. Most commonly used classification techniques are not suitable to predict trading signals when the distribution of the actual trading signals, among theses three classes, is imbalanced. In this paper, new algorithms were developed based on the structure of feedforward neural networks and a modified Ordinary Least Squares (OLS) error function. An adjustment relating to the contribution from the historical data used for training the networks, and the penalization of incorrectly classified trading signals were accounted for when modifying the OLS function. A global optimization algorithm was employed to train these networks. The algorithms developed in this study were employed to predict the trading signals of day (t+1) of the Australian All Ordinary Index. The algorithms with the modified error functions introduced by this study produced better predictions. Â© 2008 Springer Berlin Heidelberg.

Varieties of abelian topological groups and scattered spaces

- McPhail, Carolyn, Morris, Sidney

**Authors:**McPhail, Carolyn , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 78, no. 3 (Dec 2008), p. 487-495**Full Text:****Reviewed:****Description:**The variety of topological groups generated by the class of all abelian k(omega)-groups has been shown to equal the variety of topological groups generated by the free abelian topological group on [0, 1]. In this paper it is proved that the free abelian topological group on a compact Hausdorff space X generates the same variety if and only if X is not scattered.

**Authors:**McPhail, Carolyn , Morris, Sidney**Date:**2008**Type:**Text , Journal article**Relation:**Bulletin of the Australian Mathematical Society Vol. 78, no. 3 (Dec 2008), p. 487-495**Full Text:****Reviewed:****Description:**The variety of topological groups generated by the class of all abelian k(omega)-groups has been shown to equal the variety of topological groups generated by the free abelian topological group on [0, 1]. In this paper it is proved that the free abelian topological group on a compact Hausdorff space X generates the same variety if and only if X is not scattered.

Contributions to the structure theory of connected pro-Lie groups

- Morris, Sidney, Hofmann, Karl

**Authors:**Morris, Sidney , Hofmann, Karl**Date:**2009**Type:**Text , Journal article**Relation:**Topology Proceedings Vol. 33, no. (2009), p. 225-237**Full Text:**false**Description:**We present some recent results in the structure theory of pro-Lie groups and locally compact groups, improvements of known results, and open problems.

Journal of Research and Practice in Information Technology : Editorial

**Authors:**Morris, Sidney**Date:**2009**Type:**Text , Journal article**Relation:**Journal of Research and Practice in Information Technology Vol. 41, no. 1 (2009), p. 1-2**Full Text:**false**Reviewed:**

Modified neural network algorithms for predicting trading signals of stock market indices

- Tilakaratne, Chandima, Mammadov, Musa, Morris, Sidney

**Authors:**Tilakaratne, Chandima , Mammadov, Musa , Morris, Sidney**Date:**2009**Type:**Text , Journal article**Relation:**Journal of Applied Mathematics and Decision Sciences Vol. 2009, no. (2009), p.**Full Text:**false**Reviewed:****Description:**The aim of this paper is to present modified neural network algorithms to predict whether it is best to buy, hold, or sell shares (trading signals) of stock market indices. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The modified network algorithms are based on the structure of feed forward neural networks and a modified Ordinary Least Squares (OLSs) error function. An adjustment relating to the contribution from the historical data used for training the networks and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. These algorithms were employed to predict the trading signals of the Australian All Ordinary Index. The algorithms with the modified error functions introduced by this study produced better predictions.

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