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In this paper a multi-server queueing system with regenerative input flow and independent service times with finite means is studied. We consider queueing systems with various disciplines of the service performance: systems with a common queue and systems with individual queues in front of the servers. In the second case an arrived customer chooses one of the servers in accordance to a certain rule and stays in the chosen queue up to the moment of its departure from the system. We define some classes of disciplines and analyze the asymptotical behaviour of a multi-server queueing system in a heavy-trac situation (trac rate is more or equals 1). The main result of this work is limit theorems concerning the weak convergence of scaled processes of waiting time and queue length to the process of the Brownian motion for the case when the traffic rate is more then one and its absolute value for the case when the traffic rate equals one.
In this Review, we present a critical analysis of various applications of the Flory-type theories to a theoretical description of the conformational behavior of single polymer chains in dilute polymer solutions under a few external stimuli. Different theoretical models of flexible polymer chains in the supercritical fluid are discussed and analysed. Different points of view on the conformational behavior of the polymer chain near the liquid–gas transition critical point of the solvent are presented. A theoretical description of the co-solvent-induced coilglobule transitions within the implicit-solvent-explicit-co-solvent models is discussed. Several explicit-solvent-explicit-co-solvent theoretical models of the coil-to-globule-to-coil transition of the polymer chain in a mixture of good solvents (co-nonsolvency) are analysed and compared with each other. Finally, a new theoretical model of the conformational behavior of the dielectric polymer chain under the external constant electric field in the dilute polymer solution with an explicit account for the many-body dipole correlations is discussed. The polymer chain collapse induced by many-body dipole correlations of monomers in the context of statistical thermodynamics of dielectric polymers is analysed.
We present a classical course of lectures on mathematical analysis for the first and second modules for departments of applied mathematics. Practical exercises and preparation for colloquiums is analyzed in detail. Numerous examples are analyzed and problems for individual student work are put. Particular attention is paid to the use of equivalences of elementary functions and the simplest asymptotic formulas for them.
We consider the notion of number of degrees of freedom in number theory and thermodynamics. This notion is applied to notions of terminology such as terms, slogans, themes, rules, and regulations. Prohibitions are interpreted as restrictions on the number of degrees of freedom. We present a theorem on the small number of degrees of freedom as a consequence of the generalized partitio numerorum problem. We analyze the relationship between thermodynamically ideal liquids with the lexical background that a term acquires in the process of communication. Examples showing how this background may be enhanced are considered. We discuss the question of the coagulation of drops in connection with the forecast of analogs of the gas-ideal liquid phase transition in social-political processes.
We propose deterministic and stochastic models of clock synchronization in nodes of large distributed network locally coupled with a reliable external exact time server.
This book explores the theory and application of locally nilpotent derivations, a subject motivated by questions in affine algebraic geometry and having fundamental connections to areas such as commutative algebra, representation theory, Lie algebras and differential equations.
The author provides a unified treatment of the subject, beginning with 16 First Principles on which the theory is based. These are used to establish classical results, such as Rentschler's Theorem for the plane and the Cancellation Theorem for Curves.
More recent results, such as Makar-Limanov's theorem for locally nilpotent derivations of polynomial rings, are also discussed. Topics of special interest include progress in classifying additive actions on three-dimensional affine space, finiteness questions (Hilbert's 14th Problem), algorithms, the Makar-Limanov invariant, and connections to the Cancellation Problem and the Embedding Problem.
A lot of new material is included in this expanded second edition, such as canonical factorization of quotient morphisms, and a more extended treatment of linear actions. The reader will also find a wealth of examples and open problems and an updated resource for future investigations.
A one-dimensional flow of suspension with two types of solid particles moving with different velocities in a porous medium is considered. A mathematical model of deep bed filtration which generalizes the known equations of mass balance and particle capture kinetics for a flow of fluid with identical particles is developed. The exact solution is evaluated at the filter inlet and on the concentration front of fast suspended and retained particles, asymptotic solutions are provided in certain vicinities of these lines. A global asymptotic solution to the problem with a small limit deposit is constructed. The asymptotics rapidly converges to the numerical solution.
We study several Russian key-agreement cryptographic protocols for compliance with specified security properties in view of possible adoption of these protocols as standardized solutions intended to be used in the Russian Federation. We have used a number of automatic cryptographic protocol verification tools available in the Internet such as Proverif, AVISPA-SPAN and Scyther, to simulate examined protocols. We find a number of vulnerabilities and propose ways to fix them.
A method for determining pore size distribution for a porous medium from long-time straining-dominant mono-sized suspension injection is proposed. The aim is avoiding using multiple-size particle suspensions in short-term challenge tests. We derive an exact solution for long-time non-linear injection of particles with the same size, where the non-linearity is determined by accumulation of strained particles and alternation of porous medium properties. The exact downscaling procedure, determining the evolution of pore size distribution from an exact solution of large-scale equations is developed. It shows the preferential plugging of large pores during mono-sized particle transport, explaining well-posed formulation of pore-size distribution tuning from breakthrough concentrations and retention profiles. The laboratory tests on long-term mono-sized injections, where straining dominance has been monitored by DLVO-repulsion between particles and porous media, have been performed. High quality match of the breakthrough concentrations by the analytical model has been observed. The tuned-model-based prediction of the retained profiles also shows close agreement with the experimental data, which validates the proposed method.
We consider a periodic sequence { ck }k=0 ∞ and investigate a numerical properties of an irrational number α =σk=0 ∞ ck/k!. As an application of our results we present a simple transformation of periodic sequence { ck }k=0 ∞ into aperiodic sequence.
We study anisotropies of the helicity modulus, excitation spectrum, sound velocity, and angle-resolved luminescence spectrum in a two-dimensional system of interacting excitons in a periodic potential. Analytical expressions for anisotropic corrections to the quantities characterizing superfluidity are obtained. We consider particularly the case of dipolar excitons in quantum wells. For GaAs/AlGaAs heterostructures as well as MoS2/hBN/MoS2 and MoSe2/hBN/WSe2 transition-metal dichalcogenide bilayers estimates of the magnitude of the predicted effects are given. We also present a method to control superfluid motion and to determine the helicity modulus in generic dipolar systems.
The electron self-energy and anomalous magnetic moment in (2 + 1) QED with a Chern-Simons term are investigated at finite temperature and density in an external magnetic field. In the limiting case of a relatively weak magnetic field, the exact expression for the vacuum anomalous magnetic moment (AMM) has been found at zero temperature and density of the medium. The energy shift and AMM of an electron are analyzed as a function of the temperature and Chern-Simons parameter in the charge-symmetric case. We obtained the new asymptotic expression for the AMM in the high-temperature region. The electron AMM has been calculated also in the case of a completely degenerate magnetized electron gas.
It is well--known that certain properties of continuous functions on the circle T, related to the Fourier expansion, can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the results in this area is the Jurkat--Waterman theorem on conjugate functions, which improves the classical Bohr--P\'al theorem. In the present work we propose a short and technically very simple proof of the Jurkat--Waterman theorem. Our approach yields a stronger result.
Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.
We consider the eigenvalue problem for a two-dimensional perturbed resonance oscillator. The role of perturbation is played by an integral Hartree type nonlinearity, where the selfaction potential depends on the distance between points and has logarithmic singularity. We obtain asymptotic eigenvalues near the upper boundaries of spectral clusters appeared near eigenvalues of the unperturbed operator.
Exploring Bass’ Triangulability Problem on unipotent algebraic subgroups of the affine Cremona groups, we prove a triangulability criterion, the existence of nontriangulable connected solvable affine algebraic subgroups of the Cremona groups, and stable triangulability of such subgroups; in particular, in the stable range we answer Bass’ Triangulability Problem in the affirmative. To this end we prove a theorem on invariant subfields of 1-extensions. We also obtain a general construction of all rationally triangulable subgroups of the Cremona groups and, as an application, classify rationally triangulable connected one-dimensional unipotent affine algebraic subgroups of the Cremona groups up to conjugacy.
Quantum violation of Bell inequalities is now used in many quantum information applications and it is important to analyze it both quantitatively and conceptually. In the present paper, we analyze violation of multipartite Bell inequalities via the local probability model—the LqHV (local quasi hidden variable) model (Loubenets in J Math Phys 53:022201, 2012), incorporating the LHV model only as a particular case and correctly reproducing the probabilistic description of every quantum correlation scenario, more generally, every nonsignaling scenario. The LqHV probability framework allows us to construct nonsignaling analogs of Bell inequalities and to specify parameters quantifying violation of Bell inequalities—Bell’s nonlocality—in a general nonsignaling case. For quantum correlation scenarios on an N-qudit state, we evaluate these nonlocality parameters analytically in terms of dilation characteristics of an N-qudit state and also, numerically—in d and N. In view of our rigorous mathematical description of Bell’s nonlocality in a general nonsignaling case via the local probability model, we argue that violation of Bell inequalities in a quantum case is not due to violation of the Einstein–Podolsky–Rosen (EPR) locality conjectured by Bell but due to the improper HV modelling of “quantum realism”.
We introduce a notion of semiclassical bi-states. They arise from pairs of eigenstates corresponding to tunnel-splitted eigenlevels and generate 2-level subsystems in a given quantum system. As an example, we consider the planar Penning trap with rectangular electrodes assuming the 3:(-1) resonance regime of charge dynamics. We demonstrate that under small deviation of the rectangular shape of electrodes from the square shape (symmetry breaking), there appear instanton pseudoparticles, semiclassical bi-states and 2-level subsystems in such a quantum trap.