Basic Axioms Research Articles

Bilateral redistribution

We explore the implications of three basic and intuitive axioms for income redistribution problems: continuity, no transfer paradox and stability. The combination of the three axioms characterizes in the two-agent case a large family of rules, which we call threshold rules. For each level of total income in society, a threshold is considered for each agent. It is impossible for both agents to be below their respective thresholds. If an agent’s income is below the threshold, the difference is redistributed from the other agent; otherwise, the rule imposes laissez-faire.

A unified construction of product formulas and convolutions for Sturm–Liouville operators

We establish a positive product formula for the solutions of the Sturm–Liouville equation $$\ell (u) = \lambda u$$ , where $$\ell $$ belongs to a general class which includes singular and degenerate Sturm–Liouville operators. Our technique relies on a positivity theorem for possibly degenerate hyperbolic Cauchy problems and on a regularization method which makes use of the properties of the diffusion semigroup generated by the Sturm–Liouville operator. We show that the product formula gives rise to a probability preserving convolution algebra structure on the space of finite measures which satisfies the basic axioms for developing harmonic analysis on the convolution algebra. Unlike previous works, our framework includes a subfamily of Sturm–Liouville operators for which the support of the convolution of Dirac measures is noncompact. The connection with hypergroup theory is discussed. Convolution-type integral equations on weighted Lebesgue spaces are also discussed, and a solvability condition is established.

The Gravity Funnels, formed by the longitudinal vortices, according to the new Axioms and Laws

In the age of information, it is no secret that the modern science is in a very difficult position. On the one hand, it has high hopes for solving the problems of modern humanity and very practical tasks. On the other hand, science shows limited potential and difficulty in carrying out the tasks. Beyond scientific theory remain such phenomena as gravity and gravitational waves and other unexplored and very useful phenomena. Obviously, the reason for these limited capabilities of modern science is its limited foundation. The foundation of science is determined by its basic axioms. If we expand the foundation of science, we will be able to build a more comprehensive, perfect and voluminous theory. In two monographs and a series of articles the author offers a system of extended axioms (with two new axioms) and a more extended theory (with eight new laws). To the great surprise of even the author, this new theory turned out to be extensive enough to cover and explain and the gravity. Moreover, the extended axioms and theory directly and naturally outlined the algorithm in the explanation of the so-called Gravity Funnels. According to the new axioms and laws, Gravity Funnels are both for suction (accelerating) and for expansion (decelerating). Expansion Gravity Funnel decelerates along its longitudinal direction as emits the matter in the transverse direction. In this way it consumes energy and generates matter. Suction Gravity Funnel accelerates along its longitudinal direction as sucks the matter in transverse direction. In this way it consumes matter and generates energy. The both of Funnels are situated in a new Space-time. The Space-time of decelerating and accelerating Funnels is packed by longitudinal vortices, in which the Space (S) is constant. It is radically different of the Space-Time where we live now. The Space-time where we live now is packed by cross vortices, where the time (T) is constant. According the new Axioms and Laws the two described Space- times are mutually orthogonal.

Compromising to share the revenues from broadcasting sports leagues

Abstract We study the problem of sharing the revenues raised from the collective sale of broadcasting rights for sports leagues. We characterize the sharing rules satisfying three basic and intuitive axioms: symmetry, additivity and maximum aspirations. They convey a natural compromise between two focal rules, arising from polar estimations of teams’ loyal viewers. We also show that these compromise ruleshave further interesting properties, such as allowing for the existence of a majority voting equilibrium. We bring some of the testable implications from our axiomatic analysis to the real case of European football leagues.

Firm performance and market expansion from the point of view of resources

Resource-based theory has been widely employed in the research of various marketing and management topics to facilitate explanation and prediction of competitive advantages and performance outcomes. This paper establishes a cohesive theory of resources, starting from several basic axioms, by using systems science and the systemic yoyo model so that organisations and interactions between organisations can be well modelled. Specifically, we show, among others, when a firm develops a competitive advantage, why each capability is a resource, how dynamic capabilities are derivable from capabilities, when firm's performance can be improved, and why expanding into new markets can be risky but beneficial. Because of the approach taken in this paper, results and conclusions established herein are not subject to limitations and uncertainties of empirical analyses and can be generally employed in practical applications.

Дираковский синтез квантовой механики и специальной теории относительности: интертеоретический контекст

One of the key episodes of the history of modern physics – Paul Dirac’s 1928 contrivance of the relativistic theory of the electron – in the context of lucid epistemological model of mature theory change is elicited. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s methodology of the Gen- eral Relativity creation. The structure of Dirac’s scientific research programme and first and foremost the three pivotal principles that put up its heuristics is scrutinized with special emphasis on the “mathematical beauty”. It is contended that it was the general relativity genesis elicited in Eddington’s masterpiece “The Mathematical Theory of Relativity” that constituted Dirac’s synthetic paradigm with its emphasis on mathematical speculation, continual modification and generalization of the basic axioms and with the Clifford algebra and Weyl’s bispinors playing the dual lead of Riemannian geometry and Einstein’s metrical tensor. It is punctuated that in spite of the relentless Dirac’s remarks underestimating the role of philosophy one can trace its indirect influence through Arthur Eddington’s whimsical philosophy of science grounded on Hermann Weyl’s quasi-Husserlian epistemology. The basic stages of realization of Dirac’s research programme are elicited with a special emphasis on the crossbred (dual) objects’ construction.

Foundations of Utilitarianism Under Risk and Variable Population

Utilitarianism is the most prominent family of social welfare functions. We present three new axiomatic characterizations of utilitarian (that is, additively separable) social welfare functions in a setting where there is risk over both population size and the welfares of individuals. First, we show that, given uncontroversial basic axioms, Blackorby et al.'s (1998) Expected Critical-Level Generalized Utilitarianism (ECLGU) is equivalent to a new axiom holding that it is better to allocate higher utility-conditional-on-existence to possible people who have a higher probability of existence. The other two novel characterizations extend classic axiomatizations of utilitarianism from settings with either social risk or variable-population, considered alone. By considering both social risk and variable population together, we clarify the fundamental normative considerations underlying utilitarian policy evaluation.

A particular upper expectation as global belief model for discrete-time finite-state uncertain processes

To model discrete-time finite-state uncertain processes, we argue for the use of a global belief model in the form of an upper expectation that is the most conservative one under a set of basic axioms. Our motivation for these axioms, which describe how local and global belief models should be related, is based on two possible interpretations for an upper expectation: a behavioural one similar to Walley's, and an interpretation in terms of upper envelopes of linear expectations. We show that the most conservative upper expectation satisfying our axioms, that is, our model of choice, coincides with a particular version of the game-theoretic upper expectation introduced by Shafer and Vovk. This has two important implications: it guarantees that there is a unique most conservative global belief model satisfying our axioms; and it shows that Shafer and Vovk's model can be given an axiomatic characterisation and thereby provides an alternative motivation for adopting this model, even outside their game-theoretic framework. Finally, we relate our model to the upper expectation resulting from a traditional measure-theoretic approach. We show that this measure-theoretic upper expectation also satisfies the proposed axioms, which implies that it is dominated by our model or, equivalently, the game-theoretic model. Moreover, if all local models are precise, all three models coincide.

Reflections on happiness and a happy life

Abstract The main objective of the following text is to focus on and exemplify the basic axioms of theories of happiness that come from historical and philosophical tradition and are still, at least in some cases, relevant nowadays. As philosophers claim, the longing for happiness is a naturally human desire that has taken various forms in their thinking: happiness was connected with beatitude (Aristotle), with self-preservation (Spinoza), social helpfulness (Hume), living in the present moment without expostulations or false illusions (Comte-Sponville), and others. The desire for happiness means the main aim of a human life drives particular life goals and the values of individuals. Concepts of happiness have accrued in diachronic and synchronic cross-sections. The Aristotelian/Spinozan conception or Kantian, modern and postmodern traditions formed in a diachronic cross-section. Those that accrued in a synchronic cross-section segregated themselves on the basis of an individual’s spiritual and bodily aspect. Spiritual happiness (spiritual bliss, and inner equilibrium, ataraxis) was preferred by the eudaimonic (ευδαιμονία) tradition (Democritus, Socrates, Aristotle, Hellenism, French materialism and others); bodily pleasures were accentuated by the hedonistic traditions (Lipovetsky, Bauman, Keller). Some conceptions examined the problem of happiness through the optics of society and the individual, stressing general goodness and helpfulness (Plato, Aristotle, Kant); or personal goodness, pleasure and benefit – the contemporary hedonistic concepts (Lipovetsky, Maffesoli, Comte-Sponville) All these conceptions of happiness are united by the common desire of people to live happily; however, their means and ways to reach such a goal are different.

Tinjauan Etika Bisnis Islam dalam Corporate Social Responsibility PT. Garudafood Kabupaten Pati

Corporate Social Responsibility (CSR) is a positive image for companies to stakeholders in a business. Business ethics is very necessary, because business ethics is a values about good, bad, right and wrong in business. Meanwhile, business ethics in Islam like trust, fairness and honesty are essential elements in achieving the success of a business. CSR of PT.Garudafood is realized through Garudafood Sehati which is focused on social activities. The research objectives are to explain 1) Islamic business ethics; 2) CSR; and 3) CSR management of PT GarudaFood in Islamic business ethics. This research is a qualitative research. Primary data obtained from interviews and documentation. Secondary data were obtained from books and internet sites containing economics, Islamic business ethics, and CSR. The results of this study are 1) Islamic business ethics has basic axioms, namely unity, equilibrium, free will, benevolence, responsibility, shiddiq, istiqamah, fathanah, amanah, and tablig. 2) PT. Garuda Food has got CSR in the social, economic, and environmental fields. 3) The application of a form of social responsibility in accordance with Islamic business ethics, namely a form of business responsibility between man and God, man and the universe, and man and man.

Определение цитокинового статуса у больных с псориазом на фоне стандартного лечения

Обследовано 54 больных с распространенным вульгарном псориазом в возрасте от 17 до 58 лет. При обследовании больных в крови повышается содержание каждого из обследованных цитокинов, после проведения стандартного лечения нами было проведено повторное обследование крови больных было выявлено увеличения уровня цитокинов. Данное исследование может свидетельствовать о том, что у донной группы больных после поведенного стандартного лечения псориаза риск развития рецидивов крайне высок, а также эти изменения в иммунном статусе больного приводят в большинстве случаев к удлинению клинического течения и хроническому течению заболевания.

Generalized dice similarity measures for complex q-Rung Orthopair fuzzy sets and its application

Complex q-rung orthopair fuzzy set (Cq-ROFS) is an extension of Complex fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, to cope with complicated and inconsistence information in the environment of fuzzy set theory with a wider domain. In Cq-ROFS, each attribute is characterized by the degree of membership and non-membership degree over the unit-disc of the complex plan. Keeping the advantages of Cq-ROFSs, in this manuscript, we present a concept of the dice similarity and generalized dice similarity measures between the pairs of the sets. The basic axioms and properties are also stated. Further, we extend the proposed measures to weighted dice similarity measures and investigated their properties. The certain properties and the special cases of the proposed work are also derived. The applicability of the proposed measures is demonstrated with some numerical examples related to medical diagnoses and pattern recognition. The superiority and advantages of the measures over the existing ones are also illustrated with certain numerical examples.

Investigation of Technological Parameters for Machining Toroidal Section of Solid Ceramic End Mills

Solid ceramic mills are a promising technological solution for cutting heat-resistant materials. Although nanostructured cutting ceramics has a number of valuable physical and mechanical properties providing high operational performance of mills, it has low strength. The design of a solid ceramic mills is formed by smooth surfaces without stress concentrators to ensure operability and to reduce the probability of failure. The most important structural element of solid ceramic end mill is a helical groove with a negative rake angle needed to increase surface strength. This groove can be machined with standard grinding wheels of type 1A1 or 1V1. However, the application of grinding wheels of a standard shape requires the use of reduced cutting parameters to prevent chipping on the forming sections of the cutter. Chipping can be caused by too short length of the contact line and the stress concentration at the end point of the profile of the grinding wheel, which is typically fully responsible for shaping the front surface and its transition to the tooth back. In this paper, in order to increase the contact line, we develop a new approach to designing grinding wheels for machining helical grooves of solid mills and determining rational technological and operational parameters for there use. A new approach is developed based on the fundamental principles of analytical geometry and linear algebra, numerical methods and basic axioms of the shaping theory. In this study, we have identified the key relationships between parameters determining the position of the grinding wheel relative to the workpiece and the geometrical parameters of a solid ceramic mills. The developed approach allowing to determine the specific design of the grinding wheel, depending on the initial parameters of the mill and the trajectory of the axis of the wheel relative to the mill, was implemented in the MathCAD environment.

Fuzzy control under uncertainty in machine building

This report addresses the aspects of decision-making problems during asset management in cases when there is an uncertainty of the situation that can be caused by complexity of an asset or insufficient information about it. In last decades, the fuzzy logic proposed by Lotfi Zadeh has been successfully used in such cases. This report also considers positive and negative aspects of this form of logic and proposes using fuzzy converse logic (antonyms-related), which is free from weaknesses of fuzzy-related concepts proposed by Zadeh. We outline the basic axioms of converse logic and its application for decision-making problems during asset management under uncertainty.

Hjelmslev's geometry of reality

During the first half of the 20th century the Danish geometer Johannes Hjelmslev developed what he called a geometry of reality. It was presented as an alternative to the idealized Euclidean paradigm that had recently been completed by Hilbert. Hjelmslev argued that his geometry of reality was superior to the Euclidean geometry both didactically, scientifically and in practice: Didactically, because it was closer to experience and intuition, in practice because it was in accordance with the real geometrical drawing practice of the engineer, and scientifically because it was based on a smaller axiomatic basis than Hilbertian Euclidean geometry but still included the important theorems of ordinary geometry. In this paper, I shall primarily analyze the scientific aspect of Hjelmslev's new approach to geometry that gave rise to the so-called Hjelmslev (incidence) geometry or ring geometry.

Internalisasi Nilai-Nilai Macca na Malempu' dalam Etika Bisnis Islam sebagai Upaya Meningkatkan Kepuasan Pelanggan CV. Idlan Waranie Perkasa (Mabello Indonesia)

This study aims to describe the realization of the values of macca na malempu 'and Islamic business ethics in an effort to increase customer satisfaction and the process of internalizing the values of macca na malempu' in Islamic business ethics as an effort to increase customer satisfaction of Mabello Indonesia. This research uses field research methodology and library research with descriptive qualitative methods and analysis with a normative theology approach and literature study. The result of the research is that Mabello Indonesia in an effort to increase customer satisfaction has realized the values of macca na malempu ', such as in product innovation and product quality control, Mabello Indonesia has also implemented Islamic business ethics in an effort to increase customer satisfaction by implementing 5 basic axioms, among others; unity, equilibrium, responsibility, free will, and benevolence, and the values of macca na malempu 'are internalized in the 5 basic axioms of Islamic business ethics. The implications of research on business activities must uphold the value of regional local wisdom and for Muslim businessmen, the application of Islamic business ethics is absolutely necessary so that business activities are oriented to the world and the hereafter.

An Axiom-Based Comparison of the Core and Other Core Extensions

We propose an axiomatic framework that allows a unified analysis of the core and three other related cooperative solution concepts that are applicable even when the core itself is empty. Existing axiomatizations of the core and similar concepts of a cooperative game include the desired form of feasibility (or efficiency) in the generic definition of a solution concept and/or are restricted to the domain of games for which existence is guaranteed. We dispense of both practices, thus opening up the possibility of comparing, via basic axioms, solution concepts that have different feasibility constraints and domains. Our characterization of the core can be adapted to axiomatize extensions of the core concept that generate predictions for games with empty cores. We use this avenue to provide new axiomatizations of the aspiration set, the aspiration core, and the c-core.

Discounted Markov decision processes with fuzzy costs

Fuzzy theory is a discipline that has recently appeared in the mathematical literature. It generalizes classic situations. Therefore, its success continues to increase and to keep going up from time to time. In this work, we consider the model of Markov decision processes where the information on the costs includes imprecision. The fuzzy cost is represented by the fuzzy number set and the infinite horizon discounted cost is minimized from any stationary policy. This paper presents in the first part the notion of fuzzy sets and some axiomatic basis and relevant concepts with fuzzy theory in short. In second part, we propose a new definition of total discounted fuzzy cost in infinite planning horizon. We will compute an optimal stationary policy that minimizes the total fuzzy discounted cost by a new approach based on some standard algorithms of the dynamic programming using the ranking function concept. The last adapted criterion has many applications in several areas such that the forest management, the management of energy consumption, the finance, the communication system (mobile networks).

Combining absolute and relative poverty: income poverty measurement with two poverty lines.

I study income poverty indices in a framework considering two poverty lines: one absolute line capturing subsistence and one relative line capturing social exclusion. In this framework, a set of basic axioms a la Foster and Shorrocks (Econometrica 59(3): 687–709, 1991) characterizes the class of hierarchical indices. This is a class of additive indices for which the poverty contribution of any individual depends on both her income and the income standard in her society. The key feature of hierarchical indices is to grant some form of precedence to absolutely poor individuals. These indices always consider that an absolutely poor individual is poorer than an individual who is only relatively poor, regardless of the income standard in their respective societies. Classical indices are not hierarchical, except in trivial cases. As a result, they yield debatable poverty comparisons of societies having different income standards.

Sparse representations in reproducing kernels of operator equations

In a Hilbert space a linear operator defined through an inner product kernel hasa natural reproducing kernel structure. In the present paper we first define what we call the $\\HH$ formulation that stands as an axiomatic basis of the study. There is a built-in mechanism in the $\\HH$ formulation that can straightforwardly solve three basic type problems, namely, the image function identification, inverse problem, and Moore-Penrose pseudo-inverse problem. After a summary on the classical basis method we introduce the POAFD (pre-orthogonal adaptive Fourier decomposition) $\\lq\\lq$non-basis method in the $\\HH$ formulation. We give historical notes, theoretical foundations, as well as algorithm principles of POAFD. The maximal selection principle of POAFD makes itself be the best among all the existing matching pursuit methods in the one-step-optimal-selection category. It, therefore, can be used to give fast converging sparse numerical solutions of approximation, ordinary and partial differential equations, and optimization problems.