Avoiding modules, co-avoiding modules, Goldie dimension and its dual

2015 ◽  
Vol 14 (06) ◽  
pp. 1550081
Author(s):  
Babak Amini ◽  
Afshin Amini ◽  
Ehsan Momtahan
Keyword(s):  
Module Theory ◽  
Goldie Dimension ◽  
Finite Case ◽  
Infinite Case

We introduce and study two concepts in module theory which are dual to each other. It will be revealed that, in the finite case, they are new equivalent concepts for the Goldie dimension of modules and the dual Goldie dimension. However, we shall observe, in the infinite case, they are different concepts.

LINEAR AND NONLINEAR INTERSUBBAND OPTICAL ABSORPTION OF FINITE AND INFINITE SEMI-PARABOLIC QUANTUM WELLS

2011 ◽  
Vol 25 (07) ◽  
pp. 497-507 ◽  
Author(s):  
M. J. KARIMI ◽  
A. KESHAVARZ ◽  
A. POOSTFORUSH
Keyword(s):  
Refractive Index ◽  
Optical Properties ◽  
Optical Absorption ◽  
Quantum Well ◽  
Quantum Wells ◽  
Resonant Peak ◽  
Energy Eigenvalues ◽  
Finite Case ◽  
Infinite Case ◽  
Index Changes

In this work, the optical absorption coefficients and the refractive index changes for the infinite and finite semi-parabolic quantum well are calculated. Numerical calculations are performed for typical GaAs / Al x Ga 1-x As semi-parabolic quantum well. The energy eigenvalues and eigenfunctions of these systems are calculated numerically. Optical properties are obtained using the compact density matrix approach. Results show that the energy eigenvalues and the matrix elements of the infinite and finite cases are different. The calculations reveal that the resonant peaks of the optical properties of the finite case occur at lower values of the incident photon energy with respect to the infinite case. Results indicate that the maximum value of the refractive index changes for the finite case are greater than that of the infinite case. Our calculations also show that in contrast to the infinite case, the resonant peak value of the total absorption coefficient in the case of the finite well is a non-monotonic function of the semi-parabolic confinement frequency.

scholarly journals m-Polar Generalization of Fuzzy T-Ordering Relations: An Approach to Group Decision Making

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 51
Author(s):  
Azadeh Zahedi Khameneh ◽  
Adem Kilicman
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Fuzzy Data ◽  
Fuzzy Relations ◽  
Ranking Problem ◽  
Finite Case ◽  
Aggregation Functions ◽  
Infinite Case ◽  
Fuzzy Setting ◽  
Minimum Operator

Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example.

scholarly journals Groups isomorphic to their non-nilpotent subgroups

1998 ◽  
Vol 40 (2) ◽  
pp. 257-262 ◽  
Author(s):  
Howard Smith ◽  
James Wiegold
Keyword(s):  
Finite Groups ◽  
Proper Subgroup ◽  
Complete Classification ◽  
Finitely Generated ◽  
Infinite Groups ◽  
Finite Case ◽  
Locally Nilpotent ◽  
Infinite Case ◽  
Natural Generalisation ◽  
Abelian Subgroups

We were concerned in [12] with groups G that are isomorphic to all of their non-abelian subgroups. In order to exclude groups with all proper subgroups abelian, which are well understood in the finite case [7] and which include Tarski groups in the infinite case, we restricted attention to the class X of groups G that are isomorphic to their nonabelian subgroups and that contain proper subgroups of this type; such groups are easily seen to be 2-generator, and a complete classification was given in [12, Theorem 2] for the case G soluble. In the insoluble case, G/Z(G) is infinite simple [12; Theorem 1], though not much else was said in [12] about such groups. Here we examine a property which represents a natural generalisation of that discussed above. Let us say that a group G belongs to the class W if G is isomorphic to each of its non-nilpotent subgroups and not every proper subgroup of G is nilpotent. Firstly, note that finite groups in which all proper subgroups are nilpotent are (again) well understood [9]. In addition, much is known about infinite groups with all proper subgroups nilpotent (see, in particular, [8] and [13] for further discussion) although, even in the locally nilpotent case, there are still some gaps in our understanding of such groups. We content ourselvesin the present paper with discussing finitely generated W-groups— note that a W-group is certainly finitely generated or locally nilpotent. We shall have a little more to say about the locally nilpotent case below.

Multi-Scale Homogenization of Transversal Waves in Periodic Composite Beams

2017 ◽  
Vol 09 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Xiangkun Sun ◽  
Changwei Zhou ◽  
Mohamed Ichchou ◽  
Jean-Pierre Lainé ◽  
Abdel-Malek Zine
Keyword(s):  
Homogenization Method ◽  
Homogenization Theory ◽  
Flexural Wave ◽  
Frequency Range ◽  
Mean Values ◽  
Multi Scale ◽  
Finite Case ◽  
Periodic Composite ◽  
Asymptotic Homogenization Method ◽  
Infinite Case

This paper deals with the deduction of new homogenized models for the flexural wave in bi-periodic beams. According to the homogenization theory, the long-wave assumption is used and the valid frequency range of homogenized models is limited to the first Bragg band gap. However, the classical homogenization method, whose idea is taking the component’s mean values as effective material properties, has limitations in mimicking the dispersive behavior and the real valid frequency range is far less than the limit. Thus, enriched homogenized models, derived by the multi-scale asymptotic homogenization method, are proposed to provide more accurate homogenization models with larger real valid frequency range. The new homogenized models are validated by investigating the dispersion relation in the infinite case and the frequency response function in the finite case. Wave finite element method (WFEM) are used to provide associated references. A parametric study is carried out in the infinite case while two different boundary conditions are considered in the finite case.

ELEMENTS WITH SQUARE ROOTS IN COMPACT GROUPS

2010 ◽  
Vol 03 (03) ◽  
pp. 495-500
Author(s):  
Francesco G. Russo
Keyword(s):  
Compact Groups ◽  
Square Root ◽  
Square Roots ◽  
Finite Case ◽  
Infinite Case

The probability that a randomly chosen element has a square root is studied in [1, 2, 8] in the finite case. Here we deal with the infinite case.

scholarly journals INFINITE UTILITARIANISM: MORE IS ALWAYS BETTER

2004 ◽  
Vol 20 (2) ◽  
pp. 307-330 ◽  
Author(s):  
LUC LAUWERS ◽  
PETER VALLENTYNE
Keyword(s):  
Infinite Number ◽  
Natural Order ◽  
Moral Value ◽  
Recent Contribution ◽  
Finite Case ◽  
Catching Up ◽  
Strong Principle ◽  
Weakened Version ◽  
Infinite Case

We address the question of how finitely additive moral value theories (such as utilitarianism) should rank worlds when there are an infinite number of locations of value (people, times, etc.). In the finite case, finitely additive theories satisfy both Weak Pareto and a strong anonymity condition. In the infinite case, however, these two conditions are incompatible, and thus a question arises as to which of these two conditions should be rejected. In a recent contribution, Hamkins and Montero (2000) have argued in favor of an anonymity-like isomorphism principle and against Weak Pareto. After casting doubt on their criticism of Weak Pareto, we show how it, in combination with certain other plausible principles, generates a plausible and fairly strong principle for the infinite case. We further show that where locations are the same in all worlds, but have no natural order, this principle turns out to be equivalent to a strengthening of a principle defended by Vallentyne and Kagan (1997), and also to a weakened version of the catching-up criterion developed by Atsumi (1965) and by von Weizsäcker (1965).

Open Problems in Partition Regularity

2003 ◽  
Vol 12 (5-6) ◽  
pp. 571-583 ◽  
Author(s):  
Neil Hindman ◽  
Imre Leader ◽  
Dona Strauss
Keyword(s):  
Ramsey Theory ◽  
Infinite Matrix ◽  
Natural Numbers ◽  
Open Problems ◽  
Finite Case ◽  
Infinite Case

A finite or infinite matrix A with rational entries is called partition regular if, whenever the natural numbers are finitely coloured, there is a monochromatic vector x with . Many of the classical theorems of Ramsey Theory may naturally be interpreted as assertions that particular matrices are partition regular.While in the finite case partition regularity is well understood, very little is known in the infinite case. Our aim in this paper is to present some of the natural and appealing open problems in the area.

scholarly journals Parallel interpolation, splitting, and relevance in belief change

2007 ◽  
Vol 72 (3) ◽  
pp. 994-1002 ◽  
Author(s):  
George Kourousias ◽  
David Makinson
Keyword(s):  
Propositional Logic ◽  
Belief Change ◽  
Interpolation Theorem ◽  
Splitting Theorem ◽  
Classical Propositional Logic ◽  
Finite Case ◽  
Relevance Criterion ◽  
Infinite Case ◽  
Disjoint Sets

AbstractThe splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGM partial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use it to prove the splitting theorem in the infinite case, and show how AGM belief change operations may be modified, if desired, so as to ensure satisfaction of Parikh's relevance criterion.

Molecular Dynamics Simulations of Polymer-Nanotube Composites

1999 ◽  
Vol 593 ◽  
Author(s):  
S. J. V. Frankland ◽  
D. W. Brenner
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Load Transfer ◽  
Amorphous Polymer ◽  
Large Strains ◽  
Polyethylene Matrix ◽  
Finite Case ◽  
Nanotube Composites ◽  
Infinite Case ◽  
Dynamics Simulations

ABSTRACTThe structure and mechanical properties of nanocomposites composed of (10,10) carbon nanotubes in an amorphous polyethylene matrix have been modeled with molecular dynamics simulations. Two systems were studied, an infinite nanotube (via periodic boundaries) and a finite capped nanotube 6 nm in length. In the infinite case the modulus in the direction of the nanotube is given by the upper bound of the rule of mixtures, as expected under isostrain conditions for a well-aligned fiber-reinforced composite. In the finite case, no load transfer is observed at low strain, consistent with the weak nanotube-polymer adhesion and a subcritical nanotube length. The simulations predict that regions of amorphous polymer close to the bulk density remain around the nanotubes at relatively large strains, and that the density decrease during strain results primarily from chain disentanglement and alignment in regions between nanotubes.

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