SIMPLE SET GAME PROOF STUNS MATHEMATICIANS

Keyword(s):  
2020 ◽  
Vol 19 (6) ◽  
pp. 1173-1188
Author(s):  
A.B. Kogan ◽  
A.N. Pristavka

Subject. The article presents various definitions of the efficiency concept, their changes as the economic science evolves, and describes various methods to measure company performance efficiency, ranging from a simple set of financial indicators to comprehensive systems for effectiveness evaluation. Objectives. The purpose of the study is to systematize the said definitions and identify a category that will meet the current condition of business environment. Methods. The study rests on the retrospective and comparative analysis of interpretations of the efficiency concept in the economic science. We also employ the historical and logical methods of general theoretical research. Results. We identify three approaches to the interpretation of the efficiency concept. Within the selected approaches, we consider the main methods for company performance measurement that have emerged since 1914. The paper formulates criteria, which were used to carry out the comparative analysis of these methods. The analysis enabled to trace all changes in the methods. Conclusions. We propose to use the term Integrated Company Efficiency and to develop methodological framework for measuring the comprehensive efficiency of companies operating in various industries.


Author(s):  
Garrett Cullity

Three things often recognized as central to morality are concern for others’ welfare, respect for their self-expression, and cooperation in worthwhile collective activity. When philosophers have proposed theories of the substance of morality, they have typically looked to one of these three sources to provide a single, fundamental principle of morality—or they have tried to formulate a master-principle for morality that combines these three ideas in some way. This book views them instead as three independently important foundations of morality. It sets out a plural-foundation moral theory with affinities to that of W. D. Ross. There are major differences: the account of the foundations of morality differs from Ross’s, and there is a more elaborate explanation of how the rest of morality derives from them. However, the overall aim is similar. This is to illuminate the structure of morality by showing how its complex content is generated from a relatively simple set of underlying elements—the complexity results from the various ways in which one part of morality can derive from another, and the various ways in which the derived parts of morality can interact. Plural-foundation moral theories are sometimes criticized for having nothing helpful to say about cases in which their fundamental norms conflict. Responding to this, the book concludes with three detailed applications of the theory: to the questions surrounding paternalism, the use of others as means, and our moral responsibilities as consumers.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.


2016 ◽  
Vol 34 (11) ◽  
pp. 961-974 ◽  
Author(s):  
Lukas Maes ◽  
Romain Maggiolo ◽  
Johan De Keyser

Abstract. The cold ions (energy less than several tens of electronvolts) flowing out from the polar ionosphere, called the polar wind, are an important source of plasma for the magnetosphere. The main source of energy driving the polar wind is solar illumination, which therefore has a large influence on the outflow. Observations have shown that solar illumination creates roughly two distinct regimes where the outflow from a sunlit ionosphere is higher than that from a dark one. The transition between both regimes is at a solar zenith angle larger than 90°. The rotation of the Earth and its orbit around the Sun causes the magnetic polar cap to move into and out of the sunlight. In this paper we use a simple set-up to study qualitatively the effects of these variations in solar illumination of the polar cap on the ion flux from the whole polar cap. We find that this flux exhibits diurnal and seasonal variations even when combining the flux from both hemispheres. In addition there are asymmetries between the outflows from the Northern Hemisphere and the Southern Hemisphere.


2019 ◽  
Vol 305 ◽  
pp. 83-90 ◽  
Author(s):  
Kristoffer Arnsfelt Hansen ◽  
Mikhail Raskin

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