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)

Collection of Buddhist philosophical texts written by Mongolian monks and scholars.

في كتابه من نقد العقل إلى هيرمينوطيقا الرموز: بحث في فلسفة الثقافة عند إرنست كاسيرر، الصادر عن المركز العربي للأبحاث ودراسة السياسات، يحاول فؤاد مخوخ التركيز على فلسفة كاسيرر، ساعيًا لإثبات أصالتها وجِدَّتِها في مجال نقد الثقافة. فـ "قراءة كاسيرر فلسفة كانط"، كما يقول مخوخ، "متميزة وأصيلة، ويتجلى ذلك في مشروع تطوير نقد العقل وتمديده إلى نقد الثقافة الذي تجسد في فلسفة الأشكال الرمزية باعتبارها فلسفةً للثقافة، وتقعيدًا نظريًا لإبيستمولوجيا علوم الثقافة، وهيرمينوطيقا لتأويل عالَم الإنسان وفهمه".

Within the framework of the Kershaw approach and of a hypothesis on spatial stochasticity, the relativistic equations of Lehr and Park, Guerra and Ruggiero, and Vigier for stochastic Nelson mechanics are obtained. In our model there is another set of equations of the hydrodynamical type for the drift velocityv i(x j,t) and stochastic velocityu i(x j,t) of a particle. Taking into account quadratic terms in l, the universal length, we obtain from these equations the Sivashinsky equations forv i(x j,t) in (...) the caseu i →0. In the limit l →0, these equations acquire the Newtonian form. (shrink)

In the article the issue of singling out some systemic criteria of differentiation between the fundamental and applied terminologies is considered. The authors point at the fact that each terminology has its own individual peculiarities, which mark it out against a general background of the terminological fund of a certain language. It is asserted that one of the most important and effective criteria that can be the basis of the approach to the study of sublanguages for special purposes is a (...) fundamental or applied character of the sphere of professional or scientific knowledge verbalized by a certain terminology. Such terms, as ‘fundamental terminology‘, ‘applied terminology‘ and ‘terminology of transition type‘, are introduced for scientific use. The fundamental terminology is understood as a sublanguage for special purposes that verbalizes the notions, forming the totality of fundamental knowledge, serving for the description of phenomena and processes in reality and in science, in the framework of which the fundamental research is carried out. The applied terminology is the name for the sublanguage for special purposes representing the notions, in which the results of human being’s practical scientific-industrial activity for changing the reality, forming the artificial habitat, are conceptualized. The terminology of transition type is the terminology that verbalizes the fragments of the field of scientific knowledge in which the research can have both a fundamental and applied character. The authors come to the conclusion that pure applied or fundamental terminologies are quite rare, that it is rational to speak about the degree of manifestation of the applied or fundamental character within the limits of this or that terminological system. (shrink)

There is no unique way to generalize the mass operator 0 2 −p · p to curved spacetimes. The possible generalizations using either an analytic or an algebraic (group-theoretic) approach are discussed. We investigate in detail three possibilities: (i) the generalized D'Alembertian $$- \tilde \square = - (1/\sqrt { - g} )(\partial /\partial x^v )(\sqrt { - g} g^{\mu v} {\text{ }}\partial /\partial x^\mu$$ (ii) the operator ( $- (\tilde \square + \tfrac{1}{6}{\text{R)}}$ , which is conformally invariant in the massless (...) case, and (iii) an operator suggested by Meggs for Robertson-Walker spacetimes. A criterion for choosing among the different possibilities is proposed. It is used to eliminate the Meggs operator, but is not stringent enough to decide between the other two. (shrink)

Rationality - as opposed to 'ad-hoc' - and asymptotics - to emphasize the fact that perturbative methods are at the core of the theory - are the two main concepts associated with the Rational Asymptotic Modeling (RAM) approach in fluid dynamics when the goal is to specifically provide useful models accessible to numerical simulation via high-speed computing. This approach has contributed to a fresh understanding of Newtonian fluid flow problems and has opened up new avenues for tackling real fluid flow (...) phenomena, which are known to lead to very difficult mathematical and numerical problems irrespective of turbulence. With the present scientific autobiography the author guides the reader through his somewhat non-traditional career; first discovering fluid mechanics, and then devoting more than fifty years to intense work in the field. Using both personal and general historical contexts, this account will be of benefit to anyone interested in the early and contemporary developments of an important branch of theoretical and computational fluid mechanics. (shrink)

Islamic philosophy; Arab countries; intellectuals and intellectual life.

The article is devoted to the problem of studying the relationship between language and ethnic culture. It analyzes Bashkir toponyms associated with the cult of fire. The Bashkirs, like many nations, including the Turkic and Mongolian, have thought that fire symbolized home and was the protector of the family. The Bashkirs worshiped fire as cleansing and healing power, while at the same time the fire represented formidable and dangerous force. Fire in the Bashkir mythology is closely related to its opposite (...) element - Water, with the gods of the upper world - the Sun and the Moon and the deity of Earth, geographical names of Bashkortostan testify this. On the material of Bashkir toponymy and related beliefs it was attempted to do a semantic etimological-onomasiological reconstruction of the Bashkir deity of fire Otukan, which dates back to the old Turkic deity Yduk Otuken//Otukan. In Mongolian mythology, it corresponds to the deity Etugen//Otuken, associated with the cult of the mother goddess, earth and fire, and in Japanese mythology - with the god, the owner of the land, - Ootukonu-si-no kami. According to the author, the formation of names connected with ‘fire‘ in the Bashkir toponymy was promoted by the worship of the deity of fire, the tribal fire, the tribal habitat and the family by Tatar-Mongols. Interesting is the fact, that the base ‘ut‘, which is connected with the ancient Turkic beliefs, also builds a theonym, a toponymic term, a geographic name, an ethnonym and anthroponym, i.e. it permeates the entire onomastic and appellative vocabulary. However, at the appellative level, this lexical item has no religious significance. For example, Otukan, TÓ©kÓ©n, Ò®tәgәn, Ò®tәk, otaq in Turkic languages have the meanings of ‘home‘, ‘yurt‘, ‘mountain valley‘, ‘flat place in the mountains on the hillside‘, ‘southern winter quarters‘. This relationship is explained by the fact that, initially, perhaps, yet there was the worship of a female deity Otukan that embodied fire and was associated with the earth, with the habitat and the ancestral hearth, where the original base morpheme was ‘fire‘, then it was associated with the deification of family and tribal territory, and later with the deification of the person of the ruler, this lexic item has spread throughout the onomastic vocabulary and in the appellative lexicon within the meaning of the place of residence. (shrink)