scholarly journals XVI. Functions of positive and negative type, and their connection the theory of integral equations

1909 ◽  
Vol 209 (441-458) ◽  
pp. 415-446 ◽  
Keyword(s):  
Continuous Function ◽  
Early Stage ◽  
Sufficient Conditions ◽  
Slight Modification ◽  
Negative Type ◽  
Original Plan ◽  
Definition Of ◽  
Almost All ◽  
Necessary And Sufficient

The present memoir is the outcome of an attempt to obtain the conditions under which a given symmetric and continuous function k ( s, t ) is definite, in the sense of Hilbert. At an early stage, however, it was found that the class of definite functions was too restricted to allow the determination of necessary and sufficient conditions in terms of the determinants of § 10. The discovery that this could be done for functions of positive or negative type, and the fact that almost all the theorems which are true of definite functions are, with slight modification, true of these, led finally to the abandonment of the original plan in favour of a discussion of the properties of functions belonging to the wider classes. The first part of the memoir is devoted to the definition of various terms employed, and to the re-statement of the consequences which follow from Hilbert’s theorem.

Additivity of the Pn-Integral

1978 ◽  
Vol 30 (4) ◽  
pp. 783-796 ◽  
Author(s):  
George Cross
Keyword(s):  
Sufficient Conditions ◽  
Slight Modification ◽  
Necessary And Sufficient Conditions ◽  
Definition Of ◽  
Necessary And Sufficient

It is known that the Pn-tegral as originally defined is not additive on abutting intervals. This paper offers a slight modification in the definition of the integral and develops necessary and sufficient conditions for the integral to be additive.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

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.

Arithmetical Semigroup Rings

1980 ◽  
Vol 32 (6) ◽  
pp. 1361-1371 ◽  
Author(s):  
Bonnie R. Hardy ◽  
Thomas S. Shores
Keyword(s):  
Principal Ideal ◽  
Sufficient Conditions ◽  
Forthcoming Paper ◽  
Semigroup Ring ◽  
Necessary And Sufficient Conditions ◽  
Semigroup Rings ◽  
Principal Ideal Ring ◽  
Arithmetical Semigroup ◽  
Necessary And Sufficient

Throughout this paper the ring R and the semigroup S are commutative with identity; moreover, it is assumed that S is cancellative, i.e., that S can be embedded in a group. The aim of this note is to determine necessary and sufficient conditions on R and S that the semigroup ring R[S] should be one of the following types of rings: principal ideal ring (PIR), ZPI-ring, Bezout, semihereditary or arithmetical. These results shed some light on the structure of semigroup rings and provide a source of examples of the rings listed above. They also play a key role in the determination of all commutative reduced arithmetical semigroup rings (without the cancellative hypothesis on S) which will appear in a forthcoming paper by Leo Chouinard and the authors [4].

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.

Empathy, Honesty, and Integrity in the Therapist

2020 ◽  
Author(s):  
Jeffrey H. D. Cornelius-White ◽  
Gillian Proctor
Keyword(s):  
Sufficient Conditions ◽  
Therapist Attitudes ◽  
Carl Rogers ◽  
Empathic Understanding ◽  
Unconditional Positive Regard ◽  
Therapy Relationship ◽  
Necessary And Sufficient ◽  
Fully Functioning

Empathy, honesty, and integrity are essential concepts to ensure the quality of the therapy relationship and the client’s trust in the therapist. This chapter situates these concepts in relation to the necessary and sufficient conditions for therapy proposed by Carl Rogers in the late 1950s, and particularly in relation to the therapist attitudes of empathic understanding, unconditional positive regard, and congruence. In person-centered therapy (PCT), empathy is a moral, not instrumental, practice that nondirectively protects the self-determination of the client. It exemplifies power with others, avoiding power over others, and facilitating power from within, by providing a conduit for non-possessive love, the active ingredient in PCT. Honesty in PCT involves the sincerity of the therapist’s unconditional empathy and the transparence to be a full person in relation to a client. Integrity refers not only to the disciplined moral practice of empathy, but an extensional, fully functioning maturation.

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

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