The mathematical and physical aspects of the conformal symmetry of space-time and of physical laws are analyzed. In particular, the group classification of conformally flat space-times, the conformal compactifications of space-time, and the problem of imbedding of the flat space-time in global four-dimensional curved spaces with non-trivial topological and geometrical structure are discussed in detail. The wave equations on the compactified space-times are analyzed also, and the set of their elementary solutions constructed. Finally, the implications of global compactified space-times for (...) cosmology are discussed. It is argued that the recent discovery of periodic structure of matter distribution on large distances strongly suggests that the global cosmological space-time should be close. Next we analyze the inflation scalar field in the inflationary model of universe evolution considered on the spatially compact Robertson-Walker space-time. It is shown that the energy distribution in this model is periodic and the periods and density decrease with increasing distance, in striking agreement with experimental data. Our model of the universe also provides a definite predictions for the energy distribution, polar and azimuthal, considered as a function of angles θ and φ. These predictions should be tested with the new astronomical data. (shrink)

We use joint probabilities to analyze the EPR argument in the Bohm's example of spins.(1) The properties of distribution functions for two, three, or more noncommuting spin components are explicitly studied and their limitations are pointed out. Within the statistical ensemble interpretation of quantum theory (where only statements about repeated events can be made), the incompleteness of quantum theory does not follow, as the consistent use of joint probabilities shows. This does not exclude a completion of quantum mechanics, going beyond (...) it, by a more general theory of single events, using hidden variables, for example. (shrink)

Greek literature embodies a number of instances of the optative in main clauses that are acknowledged either definitely or probably to have a reference to past time. These are mostly well known, but the object of this article is to reconsider them and to attempt an explanation. They are certainly commonest in the Homeric period, but later examples are by no means wanting.

The use of with the future indicative is admittedly rare in post-Homeric Greek. In the passages concerned many deny the usage completely and either omit the particle or resort to emendation, or dismiss the construction as a mere ana-colouthon. In an instructive article in the Classical Quarterly, xl , Moorhouse argues in favour of retaining many of the readings, and it is only his interpretation that is in question here. His main thesis is that in Homeric Greek, where the usage (...) is common enough, κ or with the future means either ‘in that case’ or ‘probably’ . The latter usage, however, he regards as sometimes assuming a tone of dogmatic certainty , and this ‘emphatic future’ came to be the regular and literal meaning of the later idiom, without any irony being involved. (shrink)

Purpose. Based on actualization of gender discursive features, the current piece aims to clarify and accentuate the manifestation of gender-philosophical ideas interaction: feminism in the framework of objectivism. The source material for the current article is a novel by Ayn Rand "Atlas Shrugged", which is a philosophical work on objectivism. Theoretical basis. The development of the gender discourse, in particular the discourse of feminism is researched from the retrospective angle. This piece is an attempt to underline peculiarities of female artistic (...) images representation in Rand’s work and the way Rand’s novel influenced the logical development of feminist discourse. Discourse of feminism is a rather peculiar notion for Objectivism, where the notion of gender is, theoretically, annihilated as far as gender is irrelevant for both personal and professional growth, however, practically, gender representation and actualization is ubiquitous in Rand’s philosophy. Originality. The distinctive features of gender discourse in Objectivism are highlighted in this piece; the results are based on the application of comparative analysis. It is argued that philosophy itself may well be perceived through a literary work of fiction, thus making artistic images prototypes of philosophy functionaries. Conclusion. "Atlas Shrugged" is not merely a literary fiction, but rather a philosophical treatise on Objectivism, which is a philosophy of individual struggle and achievement. The main female protagonist of "Atlas Shrugged", Dagny Taggart, is a staunch supporter of Objectivism. In Rand’s opinion Dagny Taggart is a prototype of a true woman of utopian American capitalist society, and it is her artistic image that was misinterpreted by supporters of feminist movement ideas and Dagny Taggart became an icon of feminism, whereas in reality Dagny’s discourse is rather a discourse of femininity, for Dagny despises everything that is connected with feminist ideas and practices, and, it is an error to weave her discourse into a much wider feminist discourse. (shrink)

A model representing isotope separation during water evaporation in plants was constructed. The model accounts for substance diffusion, convective transfer and evaporation from the surface of the leaves. The dependence of the system’s separation and enrichment coefficients on various parameters was determined. A comparison was made between the enrichment coefficients calculated from experimental data from different plants and those based on the model. Qualitative agreement between the experimental and theoretical values was obtained for the case of $$\frac{uh}{D} {\gg} 1$$ uh (...) D ≫ 1, where u is the average velocity of water in the plant, h is the height of the plant, and D is the diffusion coefficient of the substance. (shrink)

Vagueness in law leads to indeterminacies in legal rights and obligations in many cases. The book defends that claim and explains its implications for legal theory. Vague language is the book's focus, but vagueness is not merely a linguistic feature of law. Law is necessarily vague. That fact seems to threaten the coherence of the ideal of the rule of law. The book defends a new, coherent articulation of that ideal.

We show that it is possible to consider parity and time reversal, as basic geometric symmetry operations, as being absolutely conserved. The observations of symmetry-violating pseudoscalar quantities can be attributed to the fact that some particles, due to their internal structure, are not eigenstates of parity or CP, and there is no reason that they should be. In terms of a model it is shown how, in spite of this, pseudoscalar terms are small in strong interactions. The neutrino plays an (...) essential role in these considerations. (shrink)

The single postulate of Coulomb-Clausius potential between charges allows one to derive all of Maxwell's equations with an explicit form for polarizability.

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x μ,p μ,v μ,S μv). The only difference is in the normalization of the Dirac velocities γμγμ=4 which has significant consequences.

Open peer commentary on the article “Designing Academic Conferences in the Light of Second-Order Cybernetics” by Laurence D. Richards. Upshot: I propose that a lack of a common ground or culture of understanding is a design flaw in academic conferences that creates opportunities for violent reactions. I suggest that an additional or revised design principle or praxis should be considered through application of second-order cybernetics.

Recent assertions that the present particle physics is on the path of a “final theory” which cannot be reduced to more fundamental ones is critically examined and confronted with a counter-thesis.

Pauli's five-dimensional Dirac equation in projective space, which results in an anomalous magnetic moment term in four dimensions, is related to the Schuster-Blackett law of the magnetic field of rotating bodies and to the recent results on the gyromagnetic ratio in Kaluza-Klein theories.