scholarly journals Theoretical Analysis for a Class of Rheonomous Affine Constraints on Configuration Manifolds—Part I: Fundamental Properties and Integrability/Nonintegrability Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-32 ◽  
Author(s):  
Tatsuya Kai
Keyword(s):  
Theoretical Analysis ◽  
Sufficient Conditions ◽  
Complete Integrability ◽  
Geometric Representation ◽  
Fundamental Properties ◽  
Affine Constraints ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Partial Integrability ◽  
Configuration Manifolds

We analyze a class of rheonomous affine constraints defined on configuration manifolds from the viewpoint of integrability/nonintegrability. First, we give the definition ofA-rheonomous affine constraints and introduce, geometric representation their. Some fundamental properties of theA-rheonomous affine constrains are also derived. We next define the rheonomous bracket and derive some necessary and sufficient conditions on the respective three cases: complete integrability, partial integrability, and complete nonintegrability for theA-rheonomous affine constrains. Then, we apply the integrability/nonintegrability conditions to some physical examples in order to confirm the effectiveness of our new results.

Semi-invariant submanifolds of a normal almost paracontact manifold

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4875-4887 ◽  
Author(s):  
Mehmet Atçeken ◽  
Siraj Uddin
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fundamental Properties ◽  
Invariant Submanifolds ◽  
Normal Almost Paracontact Manifold ◽  
Necessary And Sufficient

In this paper, we introduce the notion of semi-invariant submanifolds of a normal almost paracontact manifold. We study their fundamental properties and the particular cases. The necessary and sufficient conditions are given for a submanifold to be invariant or anti-invariant. Also, we give some results for semi-invariant submanifolds of a normal almost paracontact manifold with constant c and we construct an example.

scholarly journals Generalized Timelike Mannheim Curves in Minkowski Space-Time

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. Akyig~it ◽  
S. Ersoy ◽  
İ. Özgür ◽  
M. Tosun
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Space Time ◽  
Necessary And Sufficient Conditions ◽  
Minkowski Space Time ◽  
Mannheim Curve ◽  
Definition Of ◽  
Necessary And Sufficient

We give the definition of generalized timelike Mannheim curve in Minkowski space-time . The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations of generalized Mannheim curve.

Equivalent norms on Banach Jordan algebras

1979 ◽  
Vol 86 (2) ◽  
pp. 261-270 ◽  
Author(s):  
M. A. Youngson
Keyword(s):  
Jordan Algebra ◽  
Sufficient Conditions ◽  
Equivalent Norm ◽  
Jordan Algebras ◽  
The Self ◽  
Equivalent Norms ◽  
Positive Elements ◽  
Definition Of ◽  
Necessary And Sufficient

1. Introduction. Recently Kaplansky suggested the definition of a suitable Jordan analogue of B*-algebras, which we call J B*-algebras (see (10) and (11)). In this article, we give a characterization of those complex unital Banach Jordan algebras which are J B*-algebras in an equivalent norm. This is done by generalizing results of Bonsall ((3) and (4)) to give necessary and sufficient conditions on a real unital Banach Jordan algebra under which it is the self-adjoint part of a J B*-algebra in an equivalent norm. As a corollary we also obtain a characterization of the cones in a Banach Jordan algebra which are the set of positive elements of a J B*-algebra.

scholarly journals Translation and the Dialectics of Difference and Equivalence: Some Theoretical Propositions for a Redefinition of the Source-Target Text Relation

2002 ◽  
Vol 45 (2) ◽  
pp. 210-227 ◽  
Author(s):  
Lieven Tack
Keyword(s):  
Social Relations ◽  
Communication Theory ◽  
Sufficient Conditions ◽  
General Question ◽  
Source Text ◽  
The Social ◽  
The One ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Level Of Analysis

Abstract At which level of analysis (descriptivist, empirical, epistemological), and along which perspective (sociological, linguistical, communicative), should we locate the distinctive criteria for the definition of translation? In other words, what are the necessary and sufficient conditions which constitute the object « translation,» exclusively this object and not any other object? This is the general question of this article. It will be developped in two steps. First, we shall try to demonstrate that the perspective adopted by translatology, in defining translation by its semantical and fonctional equivalence relation with a source text, is congenetically determined by the discursive exclusion of the theorisation of that which is the very condition of possibility of each translation: the disrupture and distancing by which humans structure their social relation. Consequently, it is by the critique of communication theory, where a large part of translatology has drawn its scientific foundations, that we can deliver sound arguments for the assessing of translation in the structure of social relations. A second step consists in the formulation of a working hypothesis: if translation may be caused by the social dialectics of distancing and negociation of meaning, it is not sufficiently specified by this logic. It could be hypothesized that translation finds its specificity in the hybridity of the linguistic referential relation it instaures with the mute universe to be conceptualized on the one hand, and with the source text to be reformulated on the other.

On isotropic rank 1 convex functions

1999 ◽  
Vol 129 (5) ◽  
pp. 1081-1105 ◽  
Author(s):  
Miroslav Šilhavý
Keyword(s):  
Arbitrary Dimension ◽  
Sufficient Conditions ◽  
Singular Values ◽  
Invariant Function ◽  
Two Dimensional ◽  
Rank 1 Convexity ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Rotationally Invariant ◽  
Positive Determinant

Let f be a rotationally invariant function defined on the set Lin+ of all tensors with positive determinant on a vector space of arbitrary dimension. Necessary and sufficient conditions are given for the rank 1 convexity of f in terms of its representation through the singular values. For the global rank 1 convexity on Lin+, the result is a generalization of a two-dimensional result of Aubert. Generally, the inequality on contains products of singular values of the type encountered in the definition of polyconvexity, but is weaker. It is also shown that the rank 1 convexity is equivalent to a restricted ordinary convexity when f is expressed in terms of signed invariants of the deformation.

Fair bets and inductive probabilities

1955 ◽  
Vol 20 (3) ◽  
pp. 263-273 ◽  
Author(s):  
John G. Kemeny
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Inductive Probability ◽  
Other Hand ◽  
Frequency Interpretation ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Degree Of Confirmation

The question of what constitutes fairness in betting quotients has been studied by Ramsey, deFinetti, and Shimony. Thanks to their combined efforts we now have a satisfactory definition of fairness.On the other hand, the explication of the concept of degree of confirmation (inductive probability) has progressed rapidly in recent years, thanks primarily to Carnap. This explication has usually proceeded by laying down the axioms for frequency-probabilities, and elaborating on these. While in the case where a frequency interpretation is intended these axioms are clearly justified, in our case they have been laid down without any justification. Carnap's presentation has been criticized for just this reason.The purpose of this paper is to show that the probability axioms are necessary and sufficient conditions to assure that the degrees of confirmation form a set of fair betting quotients. In addition it will be shown that one additional, highly controversial, axiom is precisely the condition needed to assure that not only deFinetti's weaker criterion but Shimony's criterion of fairness is also satisfied.

THE INDEPENDENCE OF FUZZY VARIABLES WITH APPLICATIONS TO FUZZY RANDOM OPTIMIZATION

2007 ◽  
Vol 15 (supp02) ◽  
pp. 1-20 ◽  
Author(s):  
YIAN-KUI LIU ◽  
JINWU GAO
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Possibility Distribution ◽  
Fuzzy Variables ◽  
Fundamental Properties ◽  
Random Optimization ◽  
Fuzzy Random Programming ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Fuzzy Random

This paper presents the independence of fuzzy variables as well as its applications in fuzzy random optimization. First, the independence of fuzzy variables is defined based on the concept of marginal possibility distribution function, and a discussion about the relationship between the independent fuzzy variables and the noninteractive (unrelated) fuzzy variables is included. Second, we discuss some properties of the independent fuzzy variables, and establish the necessary and sufficient conditions for the independent fuzzy variables. Third, we propose the independence of fuzzy events, and deal with its fundamental properties. Finally, we apply the properties of the independent fuzzy variables to a class of fuzzy random programming problems to study their convexity.

scholarly journals On the Option Pricing by the Binomial Model

2021 ◽  
Author(s):  
Nikos Halidias
Keyword(s):  
Sufficient Conditions ◽  
Fair Value ◽  
Point Of View ◽  
Binomial Model ◽  
No Arbitrage ◽  
Mathematical Arguments ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Probabilistic Point ◽  
Absence Of Arbitrage

In this note we study the binomial model applied to European, American and Bermudan type of derivatives. Our aim is to give the necessary and sufficient conditions under which we can define a fair value via replicating portfolios for any derivative using simple mathematical arguments and without using no arbitrage techniques. Giving suitable definitions we are able to define rigorously the fair value of any derivative without using concepts from probability theory or stochastic analysis therefore is suitable for students or young researchers. It will be clear in our analysis that if $e^{r \delta} \notin [d,u]$ then we can not define a fair value by any means for any derivative while if $d \leq e^{r \delta} \leq u$ we can. Therefore the definition of the fair value of a derivative is not so closely related with the absence of arbitrage. In the usual probabilistic point of view we assume that $d < e^{r \delta} < u$ in order to define the fair value but it is not clear what we can (or we can not) do in the cases where $e^{r \delta} \leq d$ or $e^{r \delta} \geq u$.

scholarly journals On the Main Eigenvalues of Universal Adjacency Matrices and U-Controllable Graphs

2015 ◽  
Vol 30 ◽  
pp. 812-826
Author(s):  
Alexander Farrugia ◽  
Irene Sciriha
Keyword(s):  
Adjacency Matrix ◽  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Simple Graph ◽  
Identity Matrix ◽  
The Matrix ◽  
Vertex Degrees ◽  
Definition Of ◽  
Main Eigenvalues ◽  
Necessary And Sufficient

A universal adjacency matrix U of a graph G is a linear combination of the 0–1 adjacency matrix A, the diagonal matrix of vertex degrees D, the identity matrix I and the matrix J each of whose entries is 1. A main eigenvalue of U is an eigenvalue having an eigenvector that is not orthogonal to the all–ones vector. It is shown that the number of distinct main eigenvalues of U associated with a simple graph G is at most the number of orbits of any automorphism of G. The definition of a U–controllable graph is given using control–theoretic techniques and several necessary and sufficient conditions for a graph to be U–controllable are determined. It is then demonstrated that U–controllable graphs are asymmetric and that the converse is false, showing that there exist both regular and non–regular asymmetric graphs that are not U–controllable for any universal adjacency matrix U. To aid in the discovery of these counterexamples, a gamma–Laplacian matrix L(gamma) is used, which is a simplified form of U. It is proved that any U-controllable graph is a L(gamma)–controllable graph for some parameter gamma.

scholarly journals An algorithm for the anchor points of the PPS of the FRH models

2020 ◽  
Author(s):  
Dariush Akbarian
Keyword(s):  
Decision Making ◽  
Sufficient Conditions ◽  
Data Envelopment ◽  
Proposed Model ◽  
Decision Making Unit ◽  
Production Possibility Set ◽  
Anchor Points ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Decision Making Units

In this paper we deal with a variant of non-convex data envelopment analysis, called free replication hull model and try to obtain their anchor points. This paper uses a variant of super-efficiency model to characterize all extreme efficient decision making units and anchor points of the free replication hull models. A necessary and sufficient conditions for a decision making unit to be anchor point of the production possibility set of the free replication hull models are stated and proved. Since the set of anchor points is a subset of the set of extreme units, a definition of extreme units and a new method for obtaining these units in non-convex technologies are given. To illustrate the applicability of the proposed model, some numerical examples are finally provided.

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