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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.
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.
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.
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.
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 prove that the affine-triangular subgroups are the Borel subgroups of the Cremona groups
We report isolation, sequencing, and electrophysiological characterization of OSK3 (α-KTx 8.8 in Kalium and Uniprot databases), a potassium channel blocker from the scorpion Orthochirus scrobiculosus venom. Using the voltage clamp technique, OSK3 was tested on a wide panel of 11 voltage-gated potassium channels expressed in Xenopus oocytes, and was found to potently inhibit Kv1.2 and Kv1.3 with IC_{50 values of ~ 331 nM and ~ 503 nM, respectively. OdK1 produced by the scorpion Odontobuthus doriae differs by just two C-terminal residues from OSK3, but shows marked preference to Kv1.2. Based on the charybdotoxin-potassium channel complex crystal structure, a model was built to explain the role of the variable residues in OdK1 and OSK3 selectivity.}
We consider the problem of a viscous compressible subsonic fluid flow along a flat plate with small periodic irregularities on the surface for large Reynolds numbers. We obtain a formal asymptotic solution with double-deck structure of the boundary layer. We present the results of numerical simulation of flow in the thin boundary layer (i.e., in the near-boundary region).
The problem of flow of a viscous incompressible fluid in an axially symmetric pipe with small irregularities on the wall is considered. An asymptotic solution of the problem with the double-deck structure of the boundary layer and the unperturbed flow in the environment (the “core flow”) is obtained. The results of flow numerical simulation in the thin and “thick” boundary layers are given.
This is a preface to the paper A. Borel, "Mathematics: Art and Science" reprinted in EMS Newsletter, No. 103, March 2017.
Dusty plasma structures in glow discharge in helium in the temperature range of 5–300 K are investigated experimentally. We have described the experimental setup that makes it possible to continuously vary the temperature regime. The method for experimental data processing has been described. We have measured interparticle distances in the temperature range of 9–295 K and compared them with the Debye radius. We indicate the ranges of variations in experimental parameters in which plasma–dust structures are formed and various types of their behavior are manifested (rotation, vibrations of structures, formation of vertical linear chains, etc.). The applicability of the Yukawa potential to the description of the structural properties of a dusty plasma in the experimental conditions is discussed.
By the example of the RNGAVXLIB random number generator library, this paper considers some approaches to employing AVX vectorization for calculation speedup. The RNGAVXLIB library contains AVX implementations of modern generators and the routines allowing one to initialize up to 10^19 independent ran-dom number streams. The AVX implementations yield exactly the same pseudorandom sequences as the orig-inal algorithms do, while being up to 40 times faster than the ANSI C implementations.
We studied the quantum correlations between the nodes in a quantum neural network built of an array of quantum dots with dipole–dipole interaction. By means of the quasiadiabatic path integral simulation of the density matrix evolution in a presence of the common phonon bath we have shown the coherence in such system can survive up to the liquid nitrogen temperature of 77 K and above. The quantum correlations between quantum dots are studied by means of calculation of the entanglement of formation in a pair of quantum dots with the typical dot size of a few nanometers and interdot distance of the same order. We have shown that the proposed quantum neural network can keep the mixture of entangled states of QD pairs up to the above mentioned high temperatures.
Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example with the Metropolis algorithm. It is hence interesting to see whether such transitions can be more easily studied using population annealing. We report here our preliminary observations from population annealing runs for the two-dimensional Potts model with q>4, where it undergoes a first-order transition.
The study of filtration of the suspension in a porous medium is a vital problem in the design and construction of tunnels and hydraulic structures. An exact solution is constructed for an unsteady flow of a monodisperse suspension in a homogeneous porous medium with sizeexclusion mechanism for particle retention. The concentrations of suspended and precipitated particles are calculated in case of a linear blocking filtration coefficient.