Management of the postal services en India: a study with reference to Kerala circle

School of management studies, Cochin university of Science and Technology

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

Use of circle-segments as a data visualization technique for feature selection in pattern classification

One of the issues associated with pattern classification using data based machine learning systems is the “curse of dimensionality”. In this paper, the circle-segments method is proposed as a feature selection method to identify important input features before the entire data set is provided for learning with machine learning systems. Specifically, four machine learning systems are deployed for classification, viz. Multilayer Perceptron (MLP), Support Vector Machine (SVM), Fuzzy ARTMAP (FAM), and k-Nearest Neighbour (kNN). The integration between the circle-segments method and the machine learning systems has been applied to two case studies comprising one benchmark and one real data sets. Overall, the results after feature selection using the circle segments method demonstrate improvements in performance even with more than 50% of the input features eliminated from the original data sets.

A statistical law for multiplicities of SU(3) irreps (lambda, mu) in the plethysm {eta} circle times(3) {m} -> (lambda, mu)

A statistical law for the multiplicities of the SU(3) irreps (lambda, mu) in the reduction of totally symmetric irreducible representations {m} of U(N), N = (eta + 1) (eta + 2)/2 with eta being the three-dimensional oscillator major shell quantum number, is derived in terms of the quadratic and cubic invariants of SU(3), by determining the first three terms of an asymptotic expansion for the multiplicities. To this end, the bivariate Edgeworth expansion known in statistics is used. Simple formulae, in terms of m and eta, for all the parameters in the expansion are derived. Numerical tests with large m and eta = 4, 5 and 6 show good agreement with the statistical formula for the SU(3) multiplicities.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Coincidences of self-maps on Klein bottle fiber bundles over the circle

The main purpose of this work is to study coincidences of fiber-preserving self-maps over the circle S 1 for spaces which are fiberbundles over S 1 and the fiber is the Klein bottle K. We classify pairs of self-maps over S 1 which can be deformed fiberwise to a coincidence free pair of maps. © 2012 Pushpa Publishing House.

A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

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