On invariant Finsler metrics under (almost) β-changes

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

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Complete Moment Balancing of Contra Planar 5R Linkages

Volume 4: 36th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2012-70034 ◽

2012 ◽

Author(s):

Brian Moore ◽

Clément Gosselin

Keyword(s):

Special Class ◽

Sufficient Conditions ◽

Complete Classification ◽

Necessary And Sufficient Conditions ◽

Design Parameters ◽

Balancing Conditions ◽

Necessary And Sufficient

In this paper, the complete shaking force and moment balancing conditions for a special class of planar 5R linkages, the contra 5R linkage, is considered. Contra 5R linkages are planar 5R linkages in which the two input links are mechanically coupled and rotate at the same speed in opposite directions. A method to derive necessary and sufficient conditions on the design parameters to achieve moment balancing without introducing additional components is presented. Using this method, a complete classification of all shaking force and moment balanced contra 5R linkages is given.

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Functions and equations in classes of distributive lattices with pseudocomplementation

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500010312 ◽

1974 ◽

Vol 19 (2) ◽

pp. 191-203

Author(s):

R. Beazer

Keyword(s):

Special Class ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Distributive Lattices ◽

Necessary And Sufficient

In (8), R. L. Goodstein gave necessary and sufficient conditions for the solvability of equations over distributive lattices with 0 and 1 together with an algorithm for computing a solution whenever one exists. In addition, the same problem was considered for a special class of equations over distributive lattices with pseudocomplementation. The validity of several of Goodstein's results for distributive lattices without 0 and 1 was pointed out by Rudeanu in (15) and (16).

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On projective invariants of spherically symmetric Finsler spaces in Rn

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887815500747 ◽

2015 ◽

Vol 12 (07) ◽

pp. 1550074 ◽

Cited By ~ 4

Author(s):

Nasrin Sadeghzadeh ◽

Maedeh Hesamfar

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Flag Curvature ◽

Finsler Metrics ◽

Spherically Symmetric ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Finsler Spaces ◽

Projective Invariants ◽

Necessary And Sufficient

In this paper, we study projective invariants of spherically symmetric Finsler metrics in Rn. We find the necessary and sufficient conditions for the metrics to be Weyl, Douglas and generalized Douglas–Weyl (GDW) types. In particular, we find the necessary and sufficient condition for the metrics to be of scalar flag curvature. Also we show that two classes of GDW and Douglas spherically symmetric Finsler metrics coincide.

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Rings whose modules have maximal or minimal subprojectivity domain

Journal of Algebra and Its Applications ◽

10.1142/s0219498815500838 ◽

2015 ◽

Vol 14 (06) ◽

pp. 1550083 ◽

Cited By ~ 3

Author(s):

Yılmaz Durğun

Keyword(s):

Special Class ◽

Simple Module ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Projective Modules ◽

Alternative Perspective ◽

Necessary And Sufficient

Given modules M and N, M is said to be N-subprojective if for every epimorphism g : B → N and homomorphism f : M → N, there exists a homomorphism h : M → B such that gh = f. For a module M, the subprojectivity domain of M is defined to be the collection of all modules N such that M is N-subprojective. As an alternative perspective on the projectivity of a module, a module M is said to be p-indigent if its subprojectivity domain is smallest possible, namely, consisting of exactly the projective modules. Properties of subprojectivity domains and of p-indigent modules are studied. For various classes of modules (such as simple and singular), necessary and sufficient conditions for the existence of p-indigent modules of those types are studied. We characterize the rings over which every (simple) module is projective or p-indigent. In addition, we use our results to provide a characterization of a special class of QF-rings in which the subinjectivity and subprojectivity domains of all modules coincide. As the projective analog of indigent modules, p-indigent modules were introduced by Holston, López-Permouth, Mastromatteo and Simental-Rodriguez. The paper is inspired by similar ideas and problems in papers by Aydoğdu and López-Permouth and by Alizade, Büyükaşık and Er, where an injective version of p-indigent modules is introduced and studied.

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Square element graph of square-subtract rings

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830921501421 ◽

2021 ◽

pp. 2150142

Author(s):

Bijon Biswas ◽

S. Kar ◽

M. K. Sen

Keyword(s):

Special Class ◽

Undirected Graph ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Vertex Set ◽

Necessary And Sufficient

If [Formula: see text] is a ring then the square element graph [Formula: see text] is the simple undirected graph whose vertex set consists of all non-zero elements of [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text] for some [Formula: see text]. In this paper, we provide some necessary and sufficient conditions for the connectedness of [Formula: see text], where [Formula: see text] is a ring with identity. We mainly characterize some special class of ring [Formula: see text] which we call square-subtract ring for which the graph [Formula: see text] is connected.

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On conformally related spherically symmetric Finsler metrics

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816501188 ◽

2016 ◽

Vol 13 (10) ◽

pp. 1650118 ◽

Cited By ~ 3

Author(s):

Maryam Maleki ◽

Nasrin Sadeghzadeh ◽

Tahereh Rajabi

Keyword(s):

Einstein Metrics ◽

Finsler Geometry ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Finsler Metrics ◽

Spherically Symmetric ◽

Conformal Transformations ◽

Conformal Change ◽

Projective Invariant ◽

Necessary And Sufficient

In this paper, we study the projective invariant quantities in Finsler geometry which remain invariant under the conformal change of metrics. In particular, we obtain the necessary and sufficient conditions of a given Douglas and Weyl and generalized Douglas–Weyl (GDW) metric to be invariant under the conformal transformations. Finally, we introduce some explicit examples of these metrics. Also, some of these [Formula: see text]-conformal transformations of Einstein metrics are considered.

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Hendricks libraries and Tsetlin piles

Advances in Applied Probability ◽

10.2307/1426732 ◽

1982 ◽

Vol 14 (1) ◽

pp. 37-55 ◽

Cited By ~ 2

Author(s):

Jacques-Edouard Dies

Keyword(s):

Markov Chains ◽

Large Class ◽

Special Class ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Stationary Measure ◽

Sufficient Condition ◽

Positive Recurrence ◽

Necessary And Sufficient

In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.

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On the Class of (q,α,β)-Metrics

ISRN Geometry ◽

10.1155/2014/596090 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8

Author(s):

Ahmad Alimohammadi

Keyword(s):

Sufficient Conditions ◽

Riemannian Metric ◽

Necessary And Sufficient Conditions ◽

Finsler Metrics ◽

Projectively Flat ◽

Necessary And Sufficient

We study a class of Finsler metrics in the form F=α+βq/αq-1, where α is a Riemannian metric, β is a 1-form, and 1<q<2. F is called (q,α,β)-metrics. We find the necessary and sufficient conditions under which the class of (q,α,β)-metrics is locally projectively flat and Douglas metrics, respectively.

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The extinction time of a general birth and death process with catastrophes

Journal of Applied Probability ◽

10.1017/s0021900200116031 ◽

1986 ◽

Vol 23 (04) ◽

pp. 851-858 ◽

Cited By ~ 1

Author(s):

P. J. Brockwell

Keyword(s):

Laplace Transform ◽

Size Distribution ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Death Process ◽

Extinction Time ◽

Birth And Death Process ◽

Different Types ◽

The Laplace Transform ◽

Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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