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GEOMETRY OF MODULUS SPACES

by R. Khalil, D. Hussein, W. Amin
"... Abstract. Let φ be a modulus function, i.e., continuous strictly increasing function on [0, ∞), such that φ(0) = 0, φ(1) = 1, and φ(x + y) ≤ φ(x) + φ(y) for all x, y in [0, ∞). It is the object of this paper to characterize, for any Banach space X, extreme points, exposed points, and smooth point ..."
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Abstract. Let φ be a modulus function, i.e., continuous strictly increasing function on [0, ∞), such that φ(0) = 0, φ(1) = 1, and φ(x + y) ≤ φ(x) + φ(y) for all x, y in [0, ∞). It is the object of this paper to characterize, for any Banach space X, extreme points, exposed points, and smooth

Some Maximum Modulus Polynomial Rings and Constant Modulus Spaces

by Abtin Daghighi
"... Copyright c © 2014 Abtin Daghighi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let F ∈ C1(Ω,C) be a not necessarily open function ..."
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sufficient condition for subspaces of polyanalytic functions to have constant modulus spaces containing only constants.

modulus

by Malaya J. Mat, Tanweer Jalal A, Reyaz Ahmadb
"... A new generalized vector-valued paranormed sequence space using ..."
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A new generalized vector-valued paranormed sequence space using

Equalization Using the Constant Modulus Criterion: A

by C. Richard Johnson, Philip Schniter, Thomas J. Endres, James D. Behm, Donald R. Brown, Raúl, A. Casas - Review,” Proccedings of the IEEE, Invited , 1997
"... This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help cata ..."
Abstract - Cited by 136 (22 self) - Add to MetaCart
This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help

Modulus and the Poincaré inequality on metric measure spaces

by Stephen Keith, Kai Rajala - Mathematische Zeitschrift
"... Abstract. We show that, in a complete metric measure space equipped with a doubling Borel regular measure, the Poincare ́ inequality with upper gradients in-troduced by Heinonen and Koskela [HK98] is equivalent to the Poincare ́ inequality with “approximate Lipschitz constants ” used by Semmes in [S ..."
Abstract - Cited by 39 (2 self) - Add to MetaCart
Abstract. We show that, in a complete metric measure space equipped with a doubling Borel regular measure, the Poincare ́ inequality with upper gradients in-troduced by Heinonen and Koskela [HK98] is equivalent to the Poincare ́ inequality with “approximate Lipschitz constants ” used by Semmes

A NOTE ON THE MODULUS OF U-CONVEXITY AND MODULUS OF

by W -convexity, Zhanfei Zuo, Yunan Cui
"... ABSTRACT. We present some sufficient conditions for which a Banach space X has normal structure in term of the modulus of U-convexity, modulus of W ∗-convexity and the coefficient of weak orthogonality. Some known results are improved. ..."
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ABSTRACT. We present some sufficient conditions for which a Banach space X has normal structure in term of the modulus of U-convexity, modulus of W ∗-convexity and the coefficient of weak orthogonality. Some known results are improved.

Discrete Modulus of Smoothness of Splines with Equally Spaced Knots

by Yingkang Hu, Xiang Ming Yu , 1995
"... . We study the behavior of moduli of smoothness of splines s of order r with equally spaced knots fx i g, x i+1 \Gamma x i = h. The main results are (1) For each 0 m ! r, all quantities h j !m\Gammaj (s (j) ; h)p , 0 j m, are equivalent and can be measured by a discrete norm of the mth differ ..."
Abstract - Cited by 9 (6 self) - Add to MetaCart
, in the results above, all the quantities can still be measured by the corresponding discrete modulus multiplied by a power of t=h. The results generalize the notion of discrete norm of B-spline series in case of equal spacing. As an application, we use these results to prove that ! 3 is the best rate of convex

An Analysis of Constant Modulus Receivers

by Hanks H. Zeng, Lang Tong, C. Richard Johnson, Jr. - IEEE Trans. on Signal Processing , 1999
"... This paper investigates connections between (nonblind) Wiener receivers and blind receivers designed by minimizing the constant modulus (CM) cost. Applicable to both T-spaced and fractionally spaced FIR equalization, the main results include 1) a test for the existence of CM local minima near Wiener ..."
Abstract - Cited by 9 (3 self) - Add to MetaCart
This paper investigates connections between (nonblind) Wiener receivers and blind receivers designed by minimizing the constant modulus (CM) cost. Applicable to both T-spaced and fractionally spaced FIR equalization, the main results include 1) a test for the existence of CM local minima near

Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients

by Asanga Ratnaweera, Saman K. Halgamuge, Harry C. Watson - IEEE Transactions on Evolutionary Computation , 2004
"... Abstract—This paper introduces a novel parameter automation strategy for the particle swarm algorithm and two further extensions to improve its performance after a predefined number of generations. Initially, to efficiently control the local search and convergence to the global optimum solution, tim ..."
Abstract - Cited by 194 (2 self) - Add to MetaCart
to the particle swarm optimization along with TVAC (MPSO-TVAC), by adding a small perturbation to a randomly selected modulus of the velocity vector of a random particle by predefined probability. Second, we introduce a novel particle swarm concept “self-organizing hierarchical particle swarm optimizer with TVAC

Direct Solution of Modulus Constraints

by F. Schaffalitzky
"... The modulus constraint is a constraint on the position of the plane at infinity (1 ) which applies to the problem of self-calibration in the case of constant internals. For any pair of cameras which are known to have the same internal parameters, the classical modulus constraint is the vanishing of ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
The modulus constraint is a constraint on the position of the plane at infinity (1 ) which applies to the problem of self-calibration in the case of constant internals. For any pair of cameras which are known to have the same internal parameters, the classical modulus constraint is the vanishing
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