scholarly journals An Extension Theorem for a Sequence of Krein Space Contractions

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Gerald Wanjala
Keyword(s):  
Krein Space ◽  
Extension Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Krein Spaces ◽  
Kreĭn Space ◽  
Necessary And Sufficient ◽  
The Way

Consider Krein spaces U and Y and let Hk and Kk be regular subspaces of U and Y, respectively, such that Hk⊂Hk+1 and Kk⊂Kk+1  (k∈N). For each k∈N, let Ak:Hk→Kk be a contraction. We derive necessary and sufficient conditions for the existence of a contraction B:U→Y such that BHk=Ak. Some interesting results are proved along the way.

Hilbert rings and G(oldman)-rings issued from amalgamated algebras

2018 ◽  
Vol 17 (02) ◽  
pp. 1850023 ◽  
Author(s):  
L. Izelgue ◽  
O. Ouzzaouit
Keyword(s):  
New York ◽  
Commutative Algebra ◽  
Quotient Ring ◽  
Sufficient Conditions ◽  
Ring Homomorphism ◽  
Necessary And Sufficient Conditions ◽  
Local Rings ◽  
Finitely Generated ◽  
Necessary And Sufficient ◽  
The Way

Let [Formula: see text] and [Formula: see text] be two rings, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] be a ring homomorphism. The ring [Formula: see text] is called the amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text]. It was proposed by D’anna and Fontana [Amalgamated algebras along an ideal, Commutative Algebra and Applications (W. de Gruyter Publisher, Berlin, 2009), pp. 155–172], as an extension for the Nagata’s idealization, which was originally introduced in [Nagata, Local Rings (Interscience, New York, 1962)]. In this paper, we establish necessary and sufficient conditions under which [Formula: see text], and some related constructions, is either a Hilbert ring, a [Formula: see text]-domain or a [Formula: see text]-ring in the sense of Adams [Rings with a finitely generated total quotient ring, Canad. Math. Bull. 17(1) (1974)]. By the way, we investigate the transfer of the [Formula: see text]-property among pairs of domains sharing an ideal. Our results provide original illustrating examples.

Exploitation

2018 ◽  
Author(s):  
Benjamin Ferguson
Keyword(s):  
Sufficient Conditions ◽  
Social Contexts ◽  
Necessary And Sufficient Conditions ◽  
Welfare Gains ◽  
Unfair Advantage ◽  
Necessary And Sufficient ◽  
Normative Status ◽  
The Way

The concept of exploitation is often invoked in situations where relatively impoverished people are treated unfairly in economic and social contexts. While the claim that exploitation involves taking unfair advantage is broadly accepted, there is little consensus about what fairness requires and whether unfairness is seriously wrong in the context of exchanges. One family of accounts claims that exploitation involves the maldistribution of resources, either because exploitative transactions result in distributions that violate substantive norms of fairness, or because procedural flaws in the way exploitative transactions come about entail that their outcomes are unfair.A second, domination-based approach to exploitation claims that the moral flaw embodied by exploitative relations is the exploiter’s disrespectful use of his power over the exploitee. While exploiters’ domination of others may lead to maldistributions, defenders of the domination-based approach argue that distributive unfairness is neither necessary nor sufficient for exploitative relations.These approaches both face two kinds of challenges. The first concerns the scope. Neither appears to provide necessary and sufficient conditions that are adequate to capture all and only cases commonly described as exploitation. The second concerns the normative status. Exploitation is typically assumed to be morally impermissible, yet neither approach seems to satisfactorily explain how exploitations that nevertheless generate significant welfare gains for both parties can be wrong.

Personal Identity

2017 ◽  
Author(s):  
Galen Strawson
Keyword(s):  
Personal Identity ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Human Being ◽  
Individual Substance ◽  
Past Time ◽  
Necessary And Sufficient ◽  
The Way

This chapter examines John Locke's idea of personal identity by focusing on the canonical personal identity question: What are the necessary and sufficient conditions of the truth of the claim that a person considered now at time t₂, whom we may call [P], is the same person as a person considered at a different past time t₁, whom we may call [Pₓ]? What has to be true if it is to be true that [Pₓ] is the same person as [P]? The canonical question assumes that “person” denotes a thing or object or substance that is a standard temporal continuant in the way that a human being or person1 is (or an immaterial soul, on most conceptions of what an immaterial soul is). The chapter considers how Locke's person differs both from human being (man) and from (individual) substance, material or immaterial, on the same ground, as well as his concept of the field of consciousness in relation to personhood.

Applications of the GapSpace Model for Multidimensional Mechanical Assemblies

2003 ◽  
Vol 3 (1) ◽  
pp. 22-30 ◽  
Author(s):  
Zhihua Zou ◽  
Edward P. Morse
Keyword(s):  
Sufficient Conditions ◽  
Tolerance Analysis ◽  
Necessary And Sufficient Conditions ◽  
Important Task ◽  
Assembly Model ◽  
Worst Case ◽  
Mechanical Assemblies ◽  
Necessary And Sufficient ◽  
The Way

The most fundamental, and perhaps most important, task in the tolerance analysis of assemblies is to test whether or not the components with tolerances are actually able to fit together (called assembleability). Another important task of tolerance analysis is to check how the tolerances affect the quality or functionality of a product when they are assembled together. This paper presents the way the tolerance analyses are implemented by an assembly model, called the GapSpace model. The model can not only capture the necessary and sufficient conditions for assembleability analysis, but also transfers the functionality into the modeling variables (gaps). The assembleability analyses based on the GapSpace model for nominal components and those with worst case or statistical tolerances are introduced through an example. The problems of testing the quality of assemblies and calculating sensitivities are solved quickly and precisely using the model. The GapSpace model is more suitable for certain GD&T tolerancing methods than for parametric plus/minus tolerancing.

scholarly journals Epistemic Injustice

2021 ◽  
Author(s):  
◽  
Hannah Simpson
Keyword(s):  
Sufficient Conditions ◽  
Social World ◽  
Necessary And Sufficient Conditions ◽  
Epistemic Injustice ◽  
Small Section ◽  
Extensive Analysis ◽  
The Social ◽  
Necessary And Sufficient ◽  
Key Terms ◽  
The Way

<p>“Epistemic injustice” is a fairly new concept in philosophy, which, loosely speaking, describes a kind of injustice that occurs at the intersection of structures of the social world and knowledge. While the concept was first put forward in the 1990’s, the most significant publication on the topic is Miranda Fricker’s book Epistemic Injustice: Power and the Ethics of Knowing, which was published in 2007. Since then, there has been something of an explosion of literature on the topic of epistemic injustice. However, the concept of epistemic injustice is one that is poorly understood.  While Epistemic Injustice offers extensive analysis of some aspects of epistemic injustice, it does a poor job of explaining, overall, what epistemic injustice actually is, limiting most of that explanation to a small section in the introduction of the book. The way that epistemic injustice is presented in this section is highly ambiguous, with key terms being loosely defined (if at all), and the necessary and sufficient conditions of something being an epistemic injustice are left unclear. This remains unresolved in the literature beyond Fricker’s account: while there has been some progression in how we think about epistemic injustice beyond what Fricker’s work provides us with, there has been a general failure to adequately recognize and address the ambiguities of the Frickerian account of epistemic injustice.  In this thesis, I aim to show that, despite superficial impressions to the contrary, the Frickerian account is fundamentally ambiguous and incomplete. Moreover, later attempts to address these issues by subsequent theorists have failed. This project, however, is not in vain. I conclude by proposing a new account of epistemic injustice that overcomes these problems with the Frickerian account, offering a way of understanding epistemic injustice that is both philosophically satisfying and practically useful.</p>

scholarly journals Epistemic Injustice

2021 ◽  
Author(s):  
◽  
Hannah Simpson
Keyword(s):  
Sufficient Conditions ◽  
Social World ◽  
Necessary And Sufficient Conditions ◽  
Epistemic Injustice ◽  
Small Section ◽  
Extensive Analysis ◽  
The Social ◽  
Necessary And Sufficient ◽  
Key Terms ◽  
The Way

<p>“Epistemic injustice” is a fairly new concept in philosophy, which, loosely speaking, describes a kind of injustice that occurs at the intersection of structures of the social world and knowledge. While the concept was first put forward in the 1990’s, the most significant publication on the topic is Miranda Fricker’s book Epistemic Injustice: Power and the Ethics of Knowing, which was published in 2007. Since then, there has been something of an explosion of literature on the topic of epistemic injustice. However, the concept of epistemic injustice is one that is poorly understood.  While Epistemic Injustice offers extensive analysis of some aspects of epistemic injustice, it does a poor job of explaining, overall, what epistemic injustice actually is, limiting most of that explanation to a small section in the introduction of the book. The way that epistemic injustice is presented in this section is highly ambiguous, with key terms being loosely defined (if at all), and the necessary and sufficient conditions of something being an epistemic injustice are left unclear. This remains unresolved in the literature beyond Fricker’s account: while there has been some progression in how we think about epistemic injustice beyond what Fricker’s work provides us with, there has been a general failure to adequately recognize and address the ambiguities of the Frickerian account of epistemic injustice.  In this thesis, I aim to show that, despite superficial impressions to the contrary, the Frickerian account is fundamentally ambiguous and incomplete. Moreover, later attempts to address these issues by subsequent theorists have failed. This project, however, is not in vain. I conclude by proposing a new account of epistemic injustice that overcomes these problems with the Frickerian account, offering a way of understanding epistemic injustice that is both philosophically satisfying and practically useful.</p>

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

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
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&gt; 0 for eachj&gt; 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.

Nonlinear boundary-value problems for degenerate differential-algebraic systems

2020 ◽  
Vol 17 (3) ◽  
pp. 313-324
Author(s):  
Sergii Chuiko ◽  
Ol'ga Nesmelova
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Algebraic System ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weakly Nonlinear ◽  
Differential Algebraic System ◽  
Linear Differential ◽  
Necessary And Sufficient

The study of the differential-algebraic boundary value problems, traditional for the Kiev school of nonlinear oscillations, founded by academicians M.M. Krylov, M.M. Bogolyubov, Yu.A. Mitropolsky and A.M. Samoilenko. It was founded in the 19th century in the works of G. Kirchhoff and K. Weierstrass and developed in the 20th century by M.M. Luzin, F.R. Gantmacher, A.M. Tikhonov, A. Rutkas, Yu.D. Shlapac, S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko, O.A. Boichuk, V.P. Yacovets, C.W. Gear and others. In the works of S.L. Campbell, L.R. Petzold, Yu.E. Boyarintsev, V.F. Chistyakov, A.M. Samoilenko and V.P. Yakovets were obtained sufficient conditions for the reducibility of the linear differential-algebraic system to the central canonical form and the structure of the general solution of the degenerate linear system was obtained. Assuming that the conditions for the reducibility of the linear differential-algebraic system to the central canonical form were satisfied, O.A.~Boichuk obtained the necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and constructed a generalized Green operator of this problem. Based on this, later O.A. Boichuk and O.O. Pokutnyi obtained the necessary and sufficient conditions for the solvability of the weakly nonlinear differential algebraic boundary value problem, the linear part of which is a Noetherian differential algebraic boundary value problem. Thus, out of the scope of the research, the cases of dependence of the desired solution on an arbitrary continuous function were left, which are typical for the linear differential-algebraic system. Our article is devoted to the study of just such a case. The article uses the original necessary and sufficient conditions for the solvability of the linear Noetherian differential-algebraic boundary value problem and the construction of the generalized Green operator of this problem, constructed by S.M. Chuiko. Based on this, necessary and sufficient conditions for the solvability of the weakly nonlinear differential-algebraic boundary value problem were obtained. A typical feature of the obtained necessary and sufficient conditions for the solvability of the linear and weakly nonlinear differential-algebraic boundary-value problem is its dependence on the means of fixing of the arbitrary continuous function. An improved classification and a convergent iterative scheme for finding approximations to the solutions of weakly nonlinear differential algebraic boundary value problems was constructed in the article.

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