For a sufficiently large class of formal systems a duality theorem is proved. We consider such formal set theories $\widetilde{\scr{T}}$ [2] which, at least, satisfy the following conditions: 1. The theory $\widetilde{\scr{T}}$ contains its own (either bounded or introduced by a definition) substantive constant U, for which $\vdash \forall x[x\in U]$ or $\vdash \forall x[x\subset U]$ . 2. The operation of "complement", denoted by C, is defined with respect to U. 3. For any formula (resp. a term), A ⊦ A (...) ↔ ⅂⅂ A (resp. ⊦ CCA = A), and some basic conclusions follow. (shrink)

In this paper, the authors have detected a new effect in the area of geomagnetism, related to the behavior of a magnetic dipole freely floating on water surface. An experiment is described in the present paper in which a magnetic dipole fixed upon a float placed on non- magnetized water surface undergoes displacement along with reorientation caused by fine structure of the earth's magnetic field. This fact can probably be explained by secular decrease of the earth's major dipole moment. Further, (...) a detailed study of the phenomenon may create interesting premises for its practical use, particularly for the analysis of fine structure of geomagnetic field and its time-dependent anomalies. A strange behavior of some sea fish species prior to strong earthquakes may be explained if the fish are assumed as 'live magnetic dipoles'. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called 4/3-problem (...) without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

From the Editors:Such was the topic considered by members of a new discussion club, "The Free Word" [Svobodnoe slovo] , along with specialists from the Institute of Philosophy, USSR Academy of Sciences.

Islamic philosophy; Arab countries; intellectuals and intellectual life.

Hegel, Georg Wilhelm Friedrich; 1770-1831; criticism and interpretation; history; philosophy.

al-juzʼ 1. al-Alfāẓ wa-madhāhib -- al-juzʼ 2. al-Mafāhīm wa-al-uṣūl.

Islam and politics in Iran; and on philosophy of political science.

Juzʼ 1. al-Muqaddimāt. ʻIlm al-kalām. al-Falsafah al-Islāmīyah. al-Murājiʻ wa-al-maṣādir (p. 483-489). --.

Kitāb-i avval. Falsafah-i qadīm -- Kitāb-i duvvum. Falsafah-ʼi Qurūn-i Vusṭá -- Kitāb-i sivvum. Falsafah-ʼi jadīd.

Medicine; religious aspects; laws and legislations.