scholarly journals Some remarks on certain classes of semilattices

1982 ◽  
Vol 5 (1) ◽  
pp. 21-30 ◽  
Author(s):  
P. V. Ramana Murty ◽  
M. Krishna Murty
Keyword(s):  
Necessary And Sufficient Condition ◽  
Dense Element ◽  
Pseudocomplemented Semilattice ◽  
Distributive Semilattice ◽  
Interesting Corollary ◽  
Definition Of ◽  
Almost All ◽  
Necessary And Sufficient ◽  
Distributive Semilattices ◽  
Natural Way

In this paper the concept of a∗-semilattice is introduced as a generalization to distributive∗-lattice first introduced by Speed [1]. It is shown that almost all the results of Speed can be extended to a more eneral class of distributive∗-semilattices. In pseudocomplemented semilattices and distributive semilattices the set of annihilators of an element is an ideal in the sense of Grätzer [2]. But it is not so in general and thus we are led to the definition of a weakly distributive semilattice. In§2we actually obtain the interesting corollary that a modular∗-semilattice is weakly distributive if and only if its dense filter is neutral. In§3the concept of a sectionally pseudocomplemented semilattice is introduced in a natural way. It is proved that given a sectionally pseudocomplemented semilattice there is a smallest quotient of it which is a sectionally Boolean algebra. Further as a corollary to one of the theorems it is obtained that a sectionally pseudocomplemented semilattice with a dense element becomes a∗-semilattice. Finally a necessary and sufficient condition for a∗-semilattice to be a pseudocomplemented semilattice is obtained.

scholarly journals A generalized inversion formula for the continuous Jacobi transform

1987 ◽  
Vol 10 (4) ◽  
pp. 671-692 ◽  
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Analytic Function ◽  
Inversion Formula ◽  
Generalized Functions ◽  
Generalized Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Inversion ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

scholarly journals On a Class of Semi-Markov Risk Models Obtained as Classical Risk Models in a Markovian Environment

1984 ◽  
Vol 14 (1) ◽  
pp. 23-43 ◽  
Author(s):  
Jean-Marie Reinhard
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Risk Models ◽  
Markovian Environment ◽  
Necessary And Sufficient ◽  
Natural Way ◽  
Quantities Of Interest

AbstractWe consider a risk model in which the claim inter-arrivals and amounts depend on a markovian environment process. Semi-Markov risk models are so introduced in a quite natural way. We derive some quantities of interest for the risk process and obtain a necessary and sufficient condition for the fairness of the risk (positive asymptotic non-ruin probabilities). These probabilities are explicitly calculated in a particular case (two possible states for the environment, exponential claim amounts distributions).

On the Indispensability of Intentionality

1972 ◽  
Vol 2 (1) ◽  
pp. 127-133
Author(s):  
Harold Morick
Keyword(s):  
Recent Literature ◽  
Essential Property ◽  
Sufficient Condition ◽  
Conceptual Scheme ◽  
Necessary And Sufficient Condition ◽  
Definition Of ◽  
Necessary And Sufficient

In the last two decades, there has been a great deal of interest in providing an intentional criterion of the psychological. Of the various ones proferred, it seems to me that the best was the earliest, which was Chisholm’s initial criterion in his 1955 essay “Sentences about Believing.” In this present paper I first single out a basic misconception pervading the recent literature on intentionality and suggest that a consequence of this misconception has been the futile attempt to use the notion of intentionality to provide a kind of definition of “mind”; that is, to use intentionality to provide a necessary and sufficient condition for the psychological. Secondly, I point out how intentionality as captured by my own criterion is indispensable in that it is an essential property of certain particulars (persons) which are basic to our conceptual scheme and apparently basic to any conceptual scheme whatsoever.

scholarly journals On the Geometrical Representation of Classical Statistical Mechanics

2018 ◽  
Author(s):  
Georgios C. Boulougouris
Keyword(s):  
Statistical Mechanics ◽  
Parametric Representation ◽  
Gauss Map ◽  
Inner Product ◽  
Necessary And Sufficient Condition ◽  
Thermodynamic State ◽  
Classical Statistical Mechanics ◽  
Geometrical Representation ◽  
Definition Of ◽  
Necessary And Sufficient

In this work a geometrical representation of equilibrium and near equilibrium statistical mechanics is proposed. Using a formalism consistent with the Bra-Ket notation and the definition of inner product as a Lebasque integral, we describe the macroscopic equilibrium states in classical statistical mechanics by “properly transformed probability Euclidian vectors” that point on a manifold of spherical symmetry. Furthermore, any macroscopic thermodynamic state “close” to equilibrium is described by a triplet that represent the “infinitesimal volume” of the points, the Euclidian probability vector at equilibrium that points on a hypersphere of equilibrium thermodynamic state and a Euclidian vector a vector on the tangent bundle of the hypersphere. The necessary and sufficient condition for such representation is expressed as an invertibility condition on the proposed transformation. Finally, the relation of the proposed geometric representation, to similar approaches introduced under the context of differential geometry, information geometry, and finally the Ruppeiner and the Weinhold geometries, is discussed. It turns out that in the case of thermodynamic equilibrium, the proposed representation can be considered as a Gauss map of a parametric representation of statistical mechanics.

Notes on mildly distributive semilattices

2017 ◽  
Vol 67 (5) ◽  
Author(s):  
Sergio Arturo Celani ◽  
Luciano Javier González
Keyword(s):  
Prime Ideals ◽  
Distributive Semilattice ◽  
Definition Of ◽  
Distributive Semilattices ◽  
Distributive Extension

AbstractIn this paper we shall investigate the mildly distributive meet-semilattices by means of the study of their filters and Frink-ideals as well as applying the theory of annihilator. We recall some characterizations of the condition of mildly-distributivity and we give several new characterizations. We prove that the definition of strong free distributive extension, introduced by Hickman in 1984, can be simplified and we show a correspondence between (prime) Frink-ideals of a mildly distributive semilattice and (prime) ideals of its strong free distributive extension.

scholarly journals On Aggregation and Computation on Domain Values

1992 ◽  
Vol 21 (414) ◽  
Author(s):  
Kim Skak Larsen
Keyword(s):  
Query Languages ◽  
Relational Algebra ◽  
Way Of Thinking ◽  
Definition Of ◽  
Almost All ◽  
Natural Way

<p>Query languages often allow a limited amount of anthmetic and string operations on domain values, and sometimes sets of values can be dealt with through aggregation and sometimes even set comparisons. We address the question of how these facilities can be added to a relational language in a natural way. Our discussions lead us to reconsider the definition of the standard operators, and we introduce a new way of thinking about relational algebra computations.</p><p>We define a language FC, which has an iteration mechanism as its basis. A tuple language is used to carry out almost all computations. We prove equivalence results relating FC to relational algebra under various circumstances.</p>

scholarly journals Some results concerning frames in Banach spaces

2007 ◽  
Vol 38 (3) ◽  
pp. 267-276 ◽  
Author(s):  
S. K. Kaushik
Keyword(s):  
Finite Number ◽  
Banach Spaces ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linearly Independent ◽  
Banach Frame ◽  
Minimal Sequence ◽  
Definition Of ◽  
Necessary And Sufficient

A necessary and sufficient condition for the associated sequence of functionals to a complete minimal sequence to be a Banach frame has been given. We give the definition of a weak-exact Banach frame, and observe that an exact Banach frame is weak-exact. An example of a weak-exact Banach frame which is not exact has been given. A necessary and sufficient condition for a Banach frame to be a weak-exact Banach frame has been obtained. Finally, a necessary condition for the perturbation of a retro Banach frame by a finite number of linearly independent vectors to be a retro Banach frame has been given.

Global Economic History: A Survey

2018 ◽  
Author(s):  
Peer Vries
Keyword(s):  
Economic Development ◽  
Economic History ◽  
Adam Smith ◽  
Market Mechanism ◽  
Necessary And Sufficient Condition ◽  
Historical Experience ◽  
Economic Discourse ◽  
Theoretical Support ◽  
Almost All ◽  
Necessary And Sufficient

This chapter studies global economic history. Until quite recently, two perspectives have almost monopolized thinking about economic development: ‘Smithian’ and ‘Marxian’. They functioned as explanatory framework and theoretical support for almost all master narratives in global economic history. The first perspective is called after Adam Smith and covers the views of all those who regard the market mechanism as the necessary and sufficient condition for economic development. Meanwhile, the second perspective has been inspired by Karl Marx’s ideas on economic development. However, the hitherto dominant approaches of Marx and Smith have recently been challenged. Economic historians, stimulated by the successive economic miracles that have occurred in East Asia, are now more than ever taking non-European historical experience into account, while developing new models that are better contextualized and themselves have the potential to influence the Western economic discourse.

scholarly journals On the Hurwitz action in finite Coxeter groups

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Barbara Baumeister ◽  
Thomas Gobet ◽  
Kieran Roberts ◽  
Patrick Wegener
Keyword(s):  
Parabolic Subgroup ◽  
Coxeter Group ◽  
Coxeter Groups ◽  
Coxeter Element ◽  
Necessary And Sufficient Condition ◽  
Reduced Decompositions ◽  
Finite Coxeter Group ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Hurwitz Action

AbstractWe provide a necessary and sufficient condition on an element of a finite Coxeter group to ensure the transitivity of the Hurwitz action on its set of reduced decompositions into products of reflections. We show that this action is transitive if and only if the element is a parabolic quasi-Coxeter element. We call an element of the Coxeter group parabolic quasi-Coxeter element if it has a factorization into a product of reflections that generate a parabolic subgroup. We give an unusual definition of a parabolic subgroup that we show to be equivalent to the classical one for finite Coxeter groups.

SYSTOLIC TREE WITH BASE AUTOMATA

1991 ◽  
Vol 02 (03) ◽  
pp. 221-236 ◽  
Author(s):  
A. MONTI ◽  
D. PARENTE
Keyword(s):  
Sufficient Condition ◽  
Tree Automata ◽  
Necessary And Sufficient Condition ◽  
The Family ◽  
Emptiness Problem ◽  
Necessary And Sufficient ◽  
Natural Way

Different systolic tree automata (STA) with base (T(b)−STA) are compared. This is a subclass of STA with interesting properties of modularity. We give a necessary and sufficient condition for the inclusion between classes of languages accepted by T(b)− STA, (L(T(b)−STA)), as b varies. We focus on T(b)−STA obtained by varying the base b in a natural way. We prove that for every base b within this framework there exists an a such that L(T(a)−STA) is not contained in L(T(b)−STA). We characterize the family of languages accepted by T(b)−STA when the input conditions are relaxed. Moreover we show that the emptiness problem is decidable for T(b)−STA.

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