Generalized quantum electrodynamics: One-loop correction

In this paper, we give an update on divergent problems concerning the radiative corrections of quantum electrodynamics in (3[Formula: see text]+[Formula: see text]1) dimensions. In doing so, we introduce a geometric adaptation for the covariant photon propagator by including a higher derivative field. This derivation, so-called generalized quantum electrodynamics, is motivated by the stability and unitarity features. This theory provides a natural and self-consistent extension of the quantum electrodynamics by enlarging the space parameter of spinor-gauge interactions. In particular, Haag’s theorem undermines the perturbative characterization of the interaction picture due to its inconsistency on quantum field theory foundations. To circumvent this problem, we develop our perturbative approach in the Heisenberg picture and use it to investigate the behavior of the operator current at one-loop. We find the two- and three-point correlation functions are ultraviolet finite, electron self-energy and vertex corrections, respectively. On the other hand, we also explain how the vacuum polarization remains ultraviolet divergent only at [Formula: see text] order. Finally, we evaluate the anomalous magnetic moment, which allows us to specify a lower bound value for the Podolsky parameter.

Legal Capacity of an Individual and an Individual Entrepreneur: A Comparative Law Aspect

Purpose. The article is devoted to the consideration of theoretical and practical issues that reflect the legislative requirements and the practice of applying the norms of civil law imposed on the characteristics of the status of an individual entrepreneur in comparison with the status of an individual. Methodology: dialectical method of scientific cognition, system approach, methods of deterministic factor analysis. Conclusions. The author draws attention to a number of theoretical and legal controversial provisions outlined by civil legislation and the practice of its application. The comparative legal study analyzes the characteristics of civil legal personality; and the distinction between the statuses of an individual and an individual entrepreneur in civil relations. The article emphasizes the openness of a number of issues that require legislative solutions and the correct position of the judiciary. In particular, in the theory of civil law, the discussion does not stop about whether all the components of the legal capacity and legal capacity of a citizen as an individual apply to an individual entrepreneur? Substantiates the position that the actions of persons engaged in entrepreneurial activities without forming a legal entity in violation of the requirements of state registration, shall be subject to the legal assessment of the criminal code and administrative code. The author considers it reasonable to disclose the legal personality of an individual entrepreneur as a consistent extension of the general legal personality of a citizen. When forming judicial practice, we consider it correct to clearly adhere to the position that arbitration courts consider only those cases involving individual entrepreneurs in which the disputed legal relations are caused by the implementation of entrepreneurial activities. Scientific and practical significance. Analytical information and conclusions may be of interest to teachers and researchers, business entrepreneurs, legal practitioners accompanying business transactions, as well as to law students.

A NEW ERA OF MEDICAL BY ARTIFICIAL INTELLIGENCE

The multifaceted nature and climb of data in social protection suggest that artificial intelligence (system-based intelligence) will dynamically be applied inside the field. Overall restorative administrations have become components due to the changes in the human future. While attempting to beat repressions normal in the standard system helped investigation, authorities have made tasks that reenact ace human reasoning. A couple of sorts of AI are starting at now being used by payers and providers of care, and life sciences associations. The key classes of usages incorporate end and treatment proposition, calm responsibility and adherence, and definitive activities. The consistent extension of clinical information has made it increasingly hard for the doctor to stay side by side of medication outside a restricted field. There are various models where system-based intelligence can perform therapeutic administration endeavors likewise or better than individuals, execution parts will hinder gigantic degree automation of human administration capable occupations for a broad period. Offering more types of assistance in essential consideration and eventually in patient’s homes could be viewed as a definitive objective for medicinal services conveyance and to a limited extent, this could be encouraged by intelligence.

Distributions as initial values in a triangular hyperbolic system of conservation laws

The present paper concerns the system ut + [ϕ(u)]x = 0, vt + [ψ(u)v]x = 0 having distributions as initial conditions. Under certain conditions, and supposing ϕ, ψ: ℝ → ℝ functions, we explicitly solve this Cauchy problem within a convenient space of distributions u,v. For this purpose, a consistent extension of the classical solution concept defined in the setting of a distributional product (not constructed by approximation processes) is used. Shock waves, δ-shock waves, and also waves defined by distributions that are not measures are presented explicitly as examples. This study is carried out without assuming classical results about conservation laws. For reader's convenience, a brief survey of the distributional product is also included.

PROVABILITY LOGICS RELATIVE TO A FIXED EXTENSION OF PEANO ARITHMETIC

Let T and U be any consistent theories of arithmetic. If T is computably enumerable, then the provability predicate $P{r_\tau }\left( x \right)$ of T is naturally obtained from each ${{\rm{\Sigma }}_1}$ definition $\tau \left( v \right)$ of T. The provability logic $P{L_\tau }\left( U \right)$ of τ relative to U is the set of all modal formulas which are provable in U under all arithmetical interpretations where □ is interpreted by $P{r_\tau }\left( x \right)$. It was proved by Beklemishev based on the previous studies by Artemov, Visser, and Japaridze that every $P{L_\tau }\left( U \right)$ coincides with one of the logics $G{L_\alpha }$, ${D_\beta }$, ${S_\beta }$, and $GL_\beta ^ -$, where α and β are subsets of ω and β is cofinite.We prove that if U is a computably enumerable consistent extension of Peano Arithmetic and L is one of $G{L_\alpha }$, ${D_\beta }$, ${S_\beta }$, and $GL_\beta ^ -$, where α is computably enumerable and β is cofinite, then there exists a ${{\rm{\Sigma }}_1}$ definition $\tau \left( v \right)$ of some extension of $I{{\rm{\Sigma }}_1}$ such that $P{L_\tau }\left( U \right)$ is exactly L.

Generalization of Gravitation Theory

This chapter attempts to formulate a consistent extension of the theory of general relativity. The starting point of the general theory of relativity is the recognition of the unity of gravitation and inertia (principle of equivalence). From this principle, it follows that the properties of “empty space” were to be represented by a symmetrical tensor expressed in the theory. The principle of equivalence, however, does not give any clue as to what may be the more comprehensive mathematical structure on which to base the treatment of the total field comprising the entire physical reality. As such, this chapter considers the problem of how to find a field structure which is a natural generalization of the symmetrical tensor as well as a system of field equations for this structure which represent a natural generalization of certain equations of pure gravitation.

Extending service brands into products versus services

Purpose This paper aims to provide an empirical investigation into extension category effects on service brand extensions, both to other services (service–service extensions) and to products (service–product extensions), and the extension category’s influence on brand/consumer-level success drivers, as well as the perceived quality of the extension. Design/methodology/approach This study included an empirical testing of a conceptual framework using a hierarchical linear modeling approach and testing of hypotheses with a multilevel regression analysis. The data set consisted of 216 respondents reporting on both product and service extensions. Data were collected on three levels, namely, consumer level, parent brand level and extension level. Findings The findings indicate a general and consistent extension category-dependent effect that moderates the importance of brand extension success drivers. The influence of parent brand reliance and perceived parent brand quality were found to have stronger effects, whereas parent brand conviction was weaker in the context of service-to-service extensions. Research limitations/implications The study focuses on two brands with four extensions. Further research could replicate the study with a broader range of brands and extensions. Practical implications The study provides guidance to service managers to enhance consumers’ extension evaluations through better-positioned communication efforts when extending to different categories. Originality/value The study is one of the first empirical investigations into category-extension effects and its moderating role regarding brand and consumer level success drivers. Sparse research has been dedicated to a real-world occurrence of services extending between extension categories; this study thus furthers service brand research in terms of brand management decisions.