Abstract:
The article is devoted to the study of the process of the emergence of rights in the primitive society of the period of savagery and barbarism. The time frame expands from the beginning of the birth of life (about 4.1 – 3.7 billion years ago) to the invention of methods of cultivation of land and the primary division of labor and the invention of ancient civilization of Sumerians of writing (respectively 6,500 years - 3,100 years BC). The social and anthropological reasons for the emergence of law (needs of common habitation, normative consciousness), the world-view basis, the nature of the binding character of the original rules, their interrelation with morality, are substantiated. The original rules of conduct in the form of prohibitions (taboos), custom, rite, worship and ritual were alloy, a mixture of divine and natural, magical and psychological. These mono norms formed the core of primitive law as the form of proper, necessary behavior, the most significant factor of the force of which was the joint residence and the mutual benefit of acting concertedly.
In the absence of political power in the primitive society, they also supported the authority of tribal leaders, elders, healers, healers and sorcerers. With the emergence of religion and systems of morality, these norms receive a new religious and value justification and differentiate from those norms of morality that do not require more stringent, compared with them, sanctions. Thus, the social interaction in the process of living together and the elaboration of the rules of this residence, the improvement of the methods of resolving conflicts and disputes provided the ground on which the archaic right of the primitive society has grown, which in the form reached us in the relevant earliest historical sources, according to the constant scientific tradition, is called customary law.

Abstract:
A method of calculating a possible stability loss by a rotating circular annular disc of variable thickness is suggested within the theory of perfect plasticity with the help of small parameter method. A characteristic equation for a critical radius of a plastic zone is obtained as a first approximation. The formula for the critical angular velocity, determining the stability loss of the disc according to the self-balanced form, is derived. The method using which we can take into account the disc’s geometry and loading parameters is also specified. The efficiency of the proposed method is shown in Section 5 while considering an illustrative example. The values of critical angular velocity of rotating are found numerically for different parameters of the disc.

Structural lesions of
CNS, reported to be associated with torticollis, are mostly restricted to
cerebellum, brain stem and basal ganglia. In fact, we
know only about two documented frontal lobe mass lesions—meningiomas,
associated with torticollis. Our
observation of frontal lobe cavernous angioma associated with clinical
picture of torticollis confirms the role this area could play in
the pathophysiology of involuntary movements.
We report a case of patient with torticollis associated with cavernous angioma
of the right frontal lobe and presuppose causative role of angioma in the development
of our patient’s torticollis.

Abstract:
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions and/or their spectral characteristics, which are measurable experimentally (for example, due to spectroscopy techniques) and accessible from particle dynamics simulations, can be found by means of this approach, the main idea of which is the estimation of the so-called frequency parameters. Model cases with the exact and approximative solutions are given and discussed.

Abstract:
We study the asymptotics of large, moderate and normal deviations for the connected components of the sparse random graph by the method of stochastic processes. We obtain the logarithmic asymptotics of large deviations of the joint distribution of the number of connected components, of the sizes of the giant components, and of the numbers of the excess edges of the giant components. For the supercritical case, we obtain the asymptotics of normal deviations and the logarithmic asymptotics of large and moderate deviations of the joint distribution of the number of components, of the size of the largest component, and of the number of the excess edges of the largest component. For the critical case, we obtain the logarithmic asymptotics of moderate deviations of the joint distribution of the sizes of connected components and of the numbers of the excess edges. Some related asymptotics are also established. The proofs of the large and moderate deviation asymptotics employ methods of idempotent probability theory. As a byproduct of the results, we provide some additional insight into the nature of phase transitions in sparse random graphs.

Abstract:
We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state dependence. The limit stochastic process is a continuous-path reflected process on the nonnegative orthant. We give an application to generalised Jackson networks with state-dependent rates.

Abstract:
We consider two Ito equations that evolve on different time scales. The equations are fully coupled in the sense that all coefficients may depend on both the "slow" and the "fast" processes and the diffusion terms may be correlated. The diffusion term in the "slow" process is small. A large deviation principle is obtained for the joint distribution of the slow process and of the empirical measure of the fast process. By projecting on the slow and fast variables, we arrive at new results on large deviations in the averaging framework and on large deviations of the empirical measures of ergodic diffusions, respectively. The proof of the main result relies on the property that exponential tightness implies large deviation relative compactness. The identification of the large deviation rate function is accomplished by analysing the large deviation limit of an exponential martingale.

Abstract:
The focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers processes under the fluid and diffusion scalings. Other results concern limits for general time-dependent queues and for time-homogeneous queues in steady state.

Abstract:
Results of an exhaustive search for minimum peak sidelobe level binary sequences are presented. Several techniques for efficiency implementation of search algorithm are described. A table of number of non-equivalent optimal binary sequences with minimum peak sidelobe (MPS) level up to length 68 is given. This number can be used in prediction of the longest length for a given sidelobe level of binary sequences. The examples of optimal binary MPS sequences having high merit factor are shown.

Abstract:
The article offers a dynamic model of market price formation and production, which allows identification of general regularities of influence of production and technological specific features upon evolution of an economic system. Balance relations, which unite approaches of L. Walras and A. Marshall for description of dynamics of prices and volumes of industrial production of one commodity in the market, serve as the theoretical basis of building the model. Synthesised mathematical model is a system of two linear differential equations for identifying price and volume of the commodity in discrete time. Conditions of stability of the equilibrium position have been obtained for this dynamic system and a relevant parametric analysis was conducted. The article considers in detail periodical modes of functioning of the studied system from the point of view of the theory of economic cycles. The problem of influence of autonomous fluctuations on the demand side in general upon dynamics of price formation and volume of commodity output are considered as an example. Numerical results, which demonstrate all types of fluctuation behaviour including harmonic beat and resonance, are presented with the help of the means of computer modelling. В настоящей работе предложена динамическая модель рыночного ценообразования и производства, которая позволяет определить общие закономерности производственно-технологической специфики на эволюцию экономической системы. Теоретической основой построения модели являются балансовые соотношения, объединяющие подходы Л.Вальраса и А. Маршалла для описания динамики цен и объемов промышленной продукции на рынке одного товара. Синтезированная математическая модель представляет собой систему двух линейных разностных уравнений для определения цены и объема товара в дискретном времени. Для данной динамической системы получены условия устойчивости равновесного положения и выполнен соответствующий параметрический анализ. В данной статье достаточно подробно