Existence of a supersymmetric massless ground state of the SU(N) matrix model globally on its valleys

In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensions D = 4, 5, 7 and 11, or equivalently the SU(N) Matrix Model. That is, the 0+1 reduction of the 10-dimensional SU(N) Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given value V0, which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of the SU(N) constraint. We first show that their Lebesgue measure is finite, subject to restrictions on D in terms of N. We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions.

Pluralistic Virtue Ethics

This chapter advocates a pluralistic form of virtue ethics according to which there are several ultimate grounds of virtue, features which make traits of character excellences as opposed to deplorable or bad. These are fundamental evaluatively significant features in objects to which virtue is characteristically responsive (such as the value of those items). We call these fundamental features bases of ethical response. We could say then that virtues have but one ultimate general ground if there is but one basis of ethical response and a plurality of ultimate grounds if there are several (such as value, status, and the good for an individual). Thus, according to a monistic form of virtue ethics, for all traits, what makes that trait a virtue is that it is a disposition of (basically) correct responsiveness to the fundamental basis of ethical response (such as value, or the good for an agent), whereas for a pluralistic virtue ethics for any virtue what makes that trait a virtue is that it is a disposition of characteristically good or correct responsiveness to any or all of a number of fundamental bases of ethical response (such as value, considerations of status, and the good for).

Culpa in Contrahendo as the General Ground for Precontractual Liability in Polish Civil Code

The justified and legally relevant relationship between contracting partners acting together in order to conclude a contract along with a comprehensive system of precontractual liability have been recognized in Poland at least since the enter into force of the Code of Obligations in 1933. Nevertheless until 2003 there wasn’t any specific legislative enactment of general duty of fair dealing in the precontractual stage. This article sheds light on the legal concept of culpa in contrahendo, with particular emphasis on questions of tort, contract or tertium genus, the objective character of precontractual liability, the scope of protected precontractual interest, and the adequate causal link and the moment of breaking off negotiations. The article concludes with an overview of the perspectives of culpa in contrahendo in the new Civil Code in Poland.

Grounding Obligations

Grice has been an unjustly neglected thinker. His version of contract theory offers a distinctive approach combining deliberative rationality with a non-moralized conception of motivation. He is particularly noteworthy for his early attempt to distinguish motive and reason. His attempt to ground moral reasoning is presented as part of a general scheme of reasoning in which there are different forms of reasons: prudential; obligatory; and super-obligatory. Each depends on how human interests and goals are understood. There are some particular difficulties with his theory. However, the principal difficulty is that, in order to derive a general ground of obligation, he has to assume that reasons are intrinsically agent-neutral, having universal scope, and there is no reason to think this thesis true. There can be agent-relative reasons, and Grice does not provide us with an argument to move beyond those.

Intellectual Analysis For Educational Path’ Cognitive Modeling

Regulative models based on the human cognitive systems and the ethics are embodied in the educational processes and social institutions for training and socialization. The intellectual potential of an organization, region and country forms the general ground for the competitiveness in the context of the global knowledge economy. The intellectual analysis is directed to solving the essential uncertainties of the knowledge – anticipation for the future (basic uncertainty) and the personal character of knowledge and competence (relating the personality, individual conscience and acting capacity). The widespread interest towards the intellectual systems and intelligence for any sphere of the social life is based, first of all, on the practice of the professional and educational path, the self-realization trajectory and strategic choice of the specialists in different industries. The paper presents the longitude results obtained in 2005-2018 of the values that determine the choice of the educational trajectory on the level of the second degree of higher education – Master programs, which are not necessary for the majority of the corporate positions, that allows scholars to analyze this choice as reflecting the free interest of the potential students for their personal cognitive growth.

Las dificultades prácticas de la determinación del tribunal competente en el proceso monitorio europeo = Practical difficulties in determining the competent court of the European order for payment procedure

Resumen: La STJUE de 10 de marzo de 2016, Flight Refund Ltd. vs. Deutsche Lufthansa AG, versa sobre el procedimiento a seguir cuando se ha formulado oposición contra un requerimiento europeo de pago expedido por un órgano o autoridad de un Estado miembro, en este caso, Hungría, cuyos tribunales no son competentes para conocer de la reclamación formulada en el requerimiento, siendo que el Reglamento (CE) nº 1896/2006 no establece criterio de competencia para tales supuestos. En esta sentencia, el Tribunal de Justicia trata de determinar, de forma algo confusa, las facultades del tribunal encargado de designar el órgano jurisdiccional competente para conocer del proceso contencioso derivado de la oposición al requerimiento de pago.Palabras clave: Proceso monitorio europeo, Reglamento (CE) nº 1896/2006, oposición del demandado al requerimiento europeo de pago, competencia internacional.Abstract: CJEU´s decision on the 10th of March 2016, Case Flight Refund Ltd. vs. Deutsche Lufthansa AG analyses the contentious proceeding after the presentation of the statement of opposition to an European order for payment issued by an organ or authority without international jurisdiction (in this case, the Hungarian Courts), taking into consideration that the Regulation (EC) nº 1896/2006 does not establish the general ground of jurisdiction. The CJEU´s decision deals, in a confusing manner, with the power of the competent Court to issue the contentious proceedings arising from the defendant´s opposition to the European order for payment.Keywords: European order for payment procedure, Regulation (EC) nº 1896/2006, defendant´s opposition to the European order for payment, international judicial competence

The Non-Identical Twins in UK Public Law: Reasonableness and Proportionality

Ever since the Wednesbury decision in 1947 (Associated Provincial Picture Houses Ltd v Wednesbury Corporation [1948] 1 KB 223) courts and public law scholars in the United Kingdom (UK) have been struggling to comprehend the meaning of ‘reasonableness’ and its relation to ‘proportionality’. The main purpose of this article is to promote conceptual clarity in UK public law by describing the nature of reasonableness and proportionality as grounds of judicial review and by highlighting the overlooked similarities and differences between them.The main arguments of this article are that: (i) reasonableness is, in essence, an exercise in balancing and weighing; (ii) proportionality adds very little to the existing grounds of judicial review in UK public law; (iii) this addition is not necessarily focused on the administrative weighing and balancing process; and (iv) since proportionality adds very little to the existing grounds of judicial review, there is no conceptual or normative reason to prevent having proportionality as a general ground of judicial review in UK public law.