The combinatorics of the splitting theorem

1997 ◽  
Vol 62 (1) ◽  
pp. 197-224
Author(s):  
Kyriakos Kontostathis

The complexity of priority proofs in recursion theory has been growing since the first priority proofs in [1] and [11]. Refined versions of classic priority proofs can be found in [18]. To this date, this part of recursion theory is at about the same stage of development as real analysis was in the early days, when the notions of topology, continuity, compactness, vector space, inner product space, etc., were not invented. There were no general theorems involving these concepts to prove results about the real numbers and the proofs were repetitive and lengthy.The priority method contains an unprecedent wealth of combinatorics which is used to answer questions in recursion theory and is bound to have applications in many other fields as well. Unfortunately, very little progress has been made in finding theorems to formulate the combinatorial part of the priority method so as to answer questions without having to reprove the combinatorics in each case.Lempp and Lerman in [10] provide an overview of the subject. The entire edifice of definitions and theorems which formulate the combinatorics of the priority method has acquired the name Priority Theory. From a different vein, Groszek and Slaman in [2] have initiated a program to classify priority constructions in terms of how much induction or collection is needed to carry them out. This program studies the complexity of priority proofs and can be called Complexity Theory of Priority Proofs or simply Complexity.

1. Comparatively little progress has been made in the mathematical study of the general motion of the aeroplane. Lanchester’s phugoids, steady motion, and the small deviations obtained when an aeroplane has an actual motion differing slightly from the steady motion appropriate to the conditions of the controls and engines, represent almost the whole of the mathematics of the rigid dynamics of the aeroplane in the present stage of development of the study of the subject. Interesting results have been obtained by L. Hopf and his collaborators ( Aerodynamik . by L. Hopf, Springer, Berlin, 1934); but general solutions in explicit form are rarely given. Thus the only information of a general character concerning the dynamics of the aeroplane, i.e. unassociated with steady motion,is the theory of Lanchester’s phugoids; and although Lanchester published this in 1908, reference to the literature on the subject shows that not only has practically no advance been made on Lanchester’s work, but that its significance as a first approximation under certain conditions is not yet fully understood. It is stated by Hopf ( ibid .p. 231), but he does not specify the exact conditions, and does not study further developments.


Think India ◽  
2019 ◽  
Vol 22 (3) ◽  
pp. 72-83
Author(s):  
Tushar Kadian

Actually, basic needs postulates securing of the elementary conditions of existence to every human being. Despite of the practical and theoretical importance of the subject the greatest irony is non- availability of any universal preliminary definition of the concept of basic needs. Moreover, this becomes the reason for unpredictability of various political programmes aiming at providing basic needs to the people. The shift is necessary for development of this or any other conception. No labour reforms could be made in history till labours were treated as objects. Its only after they were started being treating as subjects, labour unions were allowed to represent themselves in strategy formulations that labour reforms could become a reality. The present research paper highlights the basic needs of Human Rights in life.


2018 ◽  
Vol 11 (2) ◽  
pp. 41-51 ◽  
Author(s):  
I. Ya. Lukasevich

The subject of the research is new tools for business financing using the initial coin offering (ICO) in the context of the development of cryptocurrencies and the blockchain technologies as their basis. The purpose of the work was to analyze the advantages and disadvantages of the ICO in comparison with traditional financial tools as well as prospects, limitations and problems of using digital financial tools. Conclusions are made in relation to possibilities, limitations and application areas of digital business financing tools, particularly in the real sector, taking into account the specifics of the Russian economy and legislation. It is shown that the main problems of using the digital financial tools are related to the economic sphere and caused by the lack of adequate approaches to evaluation of assets as well as the shortage of objective information. The problems and new tasks of corporate finance in the digital economy are defined.


1983 ◽  
Vol 22 (1) ◽  
pp. 57-61
Author(s):  
Shahrukh Rafi Khan

The book under review is a compilation of the author's articles and lectures that highlight the prominent developments in the literature on the subject of Islamic banking and inform the reader of the current state of debate on it. One of the earliest and main contributors to this topic is the author himself. The focus of this review will mainly be on "Economics of Profit-Sharing", which is the title of the fourth chapter of the book and is among his latest contributions. This chapter is a significant contribution as it is the first attempt to formalise the concept of profit sharing into an analytical model and, therefore, demands closer scrutiny. However, in the remaining chapters of the book, the author has drawn attention to some of the fine points made in the literature on this topic. Since some of these points appear to be controversial to me, I will briefly discuss them before moving on to the analytical chapter of the book.


2020 ◽  
Vol 22 (2) ◽  
pp. 1-27
Author(s):  
João Carlos Brum Torres

O artigo tem por objeto o exame de três registros de gritantes e distintos paradoxos na Doutrina do Direito de Kant. Registros feitos em tempos e contextos históricos diferentes por Friedrich Bouterwek, Marcus Willaschek e Balthazar Barbosa Filho. Bouterwek atribuiu a Kant a mais paradoxal das proposições jamais enunciadas por qualquer autor, a de que a mera ideia de soberania deve obrigar-nos a obedecer como a nosso inquestionável senhor a quem quer que se haja estabelecido como tal, sem que caiba indagar quem lhe deu o direito de comandar-nos. Willaschek aponta a incompatibilidade de duas teses centrais da doutrina kantiana: a do caráter externo dos vínculos jurídicos e a da incondicionalidade obrigacional do direito positivo, pois não é possível entender como é possível termo-nos como obrigados por imperativos jurídicos e, ao mesmo, vermo-nos internamente isentados do dever de obedecê-los. O ponto crítico de Balthazar é alegar que não pode haver na filosofia kantiana uma crítica da razão político e jurídica, simplesmente porque o conceito de imputação, base da normatividade própria dessas esferas, pressupõe uma pluralidade de agentes livres que, justamente, só pode ser uma pressuposição, pois nosso acesso à normatividade prática só pode ter lugar em primeira pessoa. No exame a que o artigo submete essas alegações, o artigo argumenta, em objeção à tese de Balthazar, que o caráter universal e categórico da força que vincula o sujeito quando confrontado com a lei moral em primeira pessoa necessariamente se desvaneceria se, ao mesmo tempo, ele não fosse tomado pela evidência de que a realidade objetiva dos princípios morais é não só instanciável, mas assegurada pela múltipla instanciação. Com relação às dificuldades levantadas por Willaschek e Bouterwek, o artigo argumenta que o princípio exeundum e statu naturali, enquanto norma metapositiva, anterior à divisão do domínio prático entre doutrina do direito e doutrina da virtude, permite ao mesmo tempo compreender a exigência de obediência ao poder constituído e a restrição das obrigações jurídico-políticas exclusivamente ao foro externo.AbstractThe object of the article is to examine three claims about three distinct and allegedly blatant paradoxes in Kant's Doctrine of Right. These three critical points had been made in distinct times and contexts by Friedrich Bouterwek, Marcus Willaschek e Balthazar Barbosa Filho. Bouterwek attributed to Kant the most paradoxical of all paradoxical propositions, the statement that by the mere idea of sovereignty we are obliged to obey as our lord who has imposed himself upon us, without questioning from where he got such right. Willaschek points out the incompatibility of two main theses of Kantian doctrine of right: the claims that the legal bounds are of external character and that they are the source of unconditional obligations, since it seems impossible to understand how it would be possible to be obliged by juridical norms and decisions and at the same time to be exempted of the internal duty of compliance. The radical objection of Professor Balthazar is the claim that in the context of Kantian Philosophy it is impossible to admit a critique of the juridical and political reason because the concept of imputation, ground of the normativity in these domains, requires not only the presupposition of free agents, but a true and secure epistemic access to them, which is, according to him, impossible considering that the moral law and the other practical principles are accessible for us only in the first person. In the course of the appraisal of such claims, the article contest that objection arguing that the universal and categorical force of the normative bound experienced by the subject when confronted with the moral law in the first person would ineluctably vanish if, at the same time, he had not been taken by the evidence that the objective reality of the moral principles is secured by multiple instancing. Regarding the difficulties raised by Willaschek and Bouterwek, the article argues that the principle exeundum e statu naturali, as a norm of meta-positive character, prior to the division of practical domains between the doctrine of right and the doctrine of virtue, is the cue both to the understanding of the requirement of unquestioning obedience to the constituted power and to the restriction of the validity of this requirement only in foro externo.


2020 ◽  
Vol 2 (3) ◽  
pp. 12-32
Author(s):  
E. V. Burdina ◽  

Introduction. The article is devoted to the problems of the essence and content of judicial ethics in the new conditions of the technical revolution and with other social needs for legal regulation. Theoretical Basis. Methods. The work used a systematic, activity-personal approach to the study of moral and ethical standards of the conduct of judges. This made it possible to reveal a new and broader view on judicial ethics, which is not simply a set of moral restrictions and obligations imposed on a judge. Results. The work has identified and analysed the signs of judicial ethics at the current stage of development. It is argued that ethical regulation is precautionary in relation to the legal regulation of the independence of judges, for they complement ethical rules and reinforce legal norms. The ethical conduct of judges is an instrument guaranteeing judicial independence in all of its manifestations, including in organisational and judicial relations. The new realities of our time recognise the expansion of boundaries and the subject area itself of ethical regulation. A broader view on judicial ethics, which differs from the traditional one, is hereby justified. The latter is defined in two ways – namely both as a system of professional values, as well as a means of judicial administration based on the principle of self-regulation. By its very nature, judicial ethics is the result (and the way) of judicial self-governance, developed on the basis of the experience of functioning bodies of the judicial community. Discussion and Conclusion. Conclusions are drawn on both the instrumental and the managerial impact of the categories of ethics. The subject of judicial ethics has been defined, which constitutes the rules of conduct of judges in the performance of their professional duties and beyond – namely the set of general principles of work of a judge, as well as the personal qualities of a judge personifying the judicial power. Proposals on the optimisation of the mechanism of ethical influence, differentiation of ethical and disciplinary norms have also been substantiated.


Author(s):  
Steven J. R. Ellis

This chapter examines the socio-economic motivations behind the shaping of retail landscapes in Roman cities. It is about who opened retail outlets, as well as why and where. After critiquing some of the normal methods for illustrating the locations of shops and bars, including the conventional distribution plan itself, as well as questioning the economic rationality of operating tabernae, this chapter argues for the value in complicating our otherwise basic understanding of why urban investments were made in the places we find them. Rather than accepting profit as the single motivation to urban investment, a range of social, economic, and political motivations are considered as an explanation for the ultimate shape of Roman retail landscapes. Thus beyond discussions of space and urban topography, the subject of this chapter is investment.


Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.


Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.


2002 ◽  
Vol 9 (1) ◽  
pp. 83-112
Author(s):  
S. Kwapień ◽  
V. Tarieladze

Abstract Problems of the Mackey-continuity of characteristic functionals and the localization of linear kernels of Radon probability measures in locally convex spaces are investigated. First the class of spaces is described, for which the continuity takes place. Then it is shown that in a non-complete sigmacompact inner product space, as well as in a non-complete sigma-compact metizable nuclear space, there may exist a Radon probability measure having a non-continuous characteristic functional in the Mackey topology and a linear kernel not contained in the initial space. Similar problems for moment forms and higher order kernels are also touched upon. Finally, a new proof of the result due to Chr. Borell is given, which asserts that any Gaussian Radon measure on an arbitrary Hausdorff locally convex space has the Mackey-continuous characteristic functional.


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