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✖We consider the algebras M_p of Fourier multipliers and show that for every bounded continuous function f on R^d there exists a self-homeomorphism h of R^d such that the superposition foh$ is in M_p(R^d) for all p, 1<p<\infty. Moreover, under certain assumptions on a family K of continuous functions, one h will suffice for all f\in K. A similar result holds for functions on the torus T^d. This may be contrasted with the known solution of Luzin's problem related to the Wiener algebra.
This book deals with mathematical modeling, namely, it describes the mathematical model of heat transfer in a silicon cathode of small (nano) dimensions with the possibility of partial melting taken into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type free boundary problems. The approach used is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the mathematical model including its parallel implementation. The results of numerical simulation concludes the book. The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.
The problem of viscous compressible fluid flow in an axially symmetric pipe with small periodic irregularities on the wall is considered for large Reynolds numbers. An asymptotic solution with double-deck structure of the boundary layer and unperturbed core flow is obtained. Numerical investigations of the influence of the density of the core flow on the flow behavior in the near-wall region are presented.
There is a gap in the proof of the main theorem in the article [5] on optimal bounds for the Morse lemma in Gromov-hyperbolic spaces. We correct this gap, showing that the main theorem of [5] is true. We also describe a computer certification of this result.
The mathematical model describing the dynamics of HIV in the human body is a nonlinear system of differential equations. This model takes into account the effect of drugs on the body. Thus, it is possible to obtain ”optimal” treatment regimens for patients, which cause minimal harm to the body. In the work for constructing suboptimal control of the supply of drugs, the method of ”extended linearization” is used, which makes it possible to switch from a nonlinear model to a linear model, but with parameters that depend on the state. To solve the resulting equation Riccati and search for control actions, a method is proposed for the formation of optimization algorithms for nonlinear control systems based on the application of functions of admissible values of control actions.
In this paper, we describe the Desmos supercomputer that consists of 32 hybrid nodes connected by a low-latency highbandwidth Angara interconnect with torus topology. This supercomputer is aimed at cost-effective classical molecular dynamics calculations. Desmos serves as a test bed for the Angara interconnect that supports 3D and 4D torus network topologies, and verifies its ability to unite massively-parallel programming systems speeding-up effectively MPI-based applications. We describe the Angara interconnect presenting typical MPI benchmarks. Desmos benchmarks results for GROMACS, LAMMPS, VASP and CP2K are compared with the data for other HPC systems. Also, we consider the job scheduling statistics for several months of Desmos deployment.
We have measured the ultrafast anisotropic optical response of highly doped graphene to an intense single cycle terahertz pulse. The time profile of the terahertz-induced anisotropy signal at 800 nm has minima and maxima repeating those of the pump terahertz electric field modulus. It grows with increasing carrier density and demonstrates a specific nonlinear dependence on the electric field strength. To describe the signal, we have developed a theoretical model that is based on the energy and momentum balance equations and takes into account optical phonons of graphene and the substrate. According to the theory, the anisotropic response is caused by the displacement of the electronic momentum distribution from zero momentum induced by the pump electric field in combination with polarization dependence of the matrix elements of interband optical transitions.
Formulas for the asymptotics of some class of integrals of rapidly oscillating functions that generalize the well-known stationary phase method, which were obtained in the previous paper of the author, are applied to integrals arising in the well-known tsunami hydrodynamic piston model in the case of a constant pool bottom. As a result, asymptotic formulas are obtained for the head part of the wave for large values of the time elapsed since the occurrence of the tsunami. These formulas contain some special reference integrals and have different forms depending on combinations of wave and time parameters.
We study properties of generalized $K$-functionals and generalized moduli of smoothness in $L_p(\R)$ spaces with $1 \le p \le +\infty$. We obtain the direct Jackson type estimate and the inverse Bernstein type estimate for them. We state equivalence between approximation error of convolution integrals generated by an arbitrary generator with compact support generalized $K$-functionals generated by homogeneous function and generalized moduli of smoothness generated by $2\pi$-periodic generator subject to equivalence of their generators. We show that generalized $K$-functionals and generalized moduli of smoothness contain, as their special cases many well-known constructions of $K$-functionals and moduli of smoothness with an appropriate choice of the generators.
In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a 'central' charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher-Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.
Single-point mutations in the transmembrane (TM) region of receptor tyrosine kinases (RTKs) can lead to abnormal ligand-independent activation. We use a combination of computational modeling, NMR spectroscopy and cell experiments to analyze in detail the mechanism of how TM domains contribute to the activation of wild-type (WT) PDGFRA and its oncogenic V536E mutant. Using a computational framework, we scan all positions in PDGFRA TM helix for identification of potential functional mutations for the WT and the mutant and reveal the relationship between the receptor activity and TM dimerization via different interfaces. This strategy also allows us design a novel activating mutation in the WT (I537D) and a compensatory mutation in the V536E background eliminating its constitutive activity (S541G). We show both computationally and experimentally that single-point mutations in the TM region reshape the TM dimer ensemble and delineate the structural and dynamic determinants of spontaneous activation of PDGFRA via its TM domain. Our atomistic picture of the coupling between TM dimerization and PDGFRA activation corroborates the data obtained for other RTKs and provides a foundation for developing novel modulators of the pathological activity of PDGFRA.
In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (x1, x2) with the constant magnetic field normal to this plane and with the potential V having the form of a harmonic oscillator in the direction x1 and periodic with respect to variable x2. Such a potential can be used for modeling a long molecule. We assume that the magnetic field is quite large, this allows us to make the averaging and to reduce the original problem to a spectral problem for a 1-D Schrödinger operator with effective periodic potential. Then we use semiclassical analysis to construct the band spectrum of this reduced operator, as well as that of the original 2-D magnetic Schrödinger operator.
A stratified liquid with two layers separated by a fast oscillating interface in the case of Raleigh--Taylor instability is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed.
The transmission and the circular transmission are investigated for a ring of quantum dots (in a benzene-type configuration) connected to external leads in the meta-configuration. A computational method utilizing the tight-binding approximation to the Schrödinger equation is used to solve for the transmission probabilities as a function of the electron energy and external magnetic flux. The flux dependence is incorporated into the model using a standard procedure involving the Aharonov–Bohm effect. The positions of the transmission zeros and poles in the complex energy plane, and their possible interference with or even complete cancellation of each other, are shown to correlate with the amplitude and structure of the circular transmission resonances. Large-amplitude resonances of the circular transmission are found to occur when two poles of the transmission are separated along the imaginary axis. These resonances demonstrate a high degree of flux sensitivity at specific energy values and flux ranges. A small change in flux causes the orientation of the resonance poles in the complex energy plane to rotate parallel to the real energy axis, resulting in a concurrent decrease in the circular transmission amplitude. The flux-dependent interference between the transmission poles and zeros in the complex energy plane leads to a decrease of the circular transmission resonance amplitudes. The circular transmission and its corresponding current–voltage characteristic provide more information related to the external flux than can be obtained from the normal transmission alone.
We theoretically study the phase dynamics in Josephson junctions, which maps onto the oscillatory motion of a pointlike particle in the washboard potential. Under appropriate driving and damping conditions, the Josephson phase undergoes intriguing bistable dynamics near a saddle point in the quasienergy landscape. The bifurcation mechanism plays a critical role in superconducting quantum circuits with relevance to nondemolition measurements such as high-fidelity readout of qubit states. We address the question “what is the probability of capture into either basin of attraction?” and answer it concerning both classical and quantum dynamics. Consequently, we derive the Arnold probability and numerically analyze its implementation of the controlled dynamical switching between two steady states under the various nonequilibrium conditions.
The Nevanlinna theory is used to derive the general structure of transcendental meromorphic solutions for a wide class of autonomous nonlinear ordinary differential equations with two dominant monomials. An algebro-geometric method, which enables one to obtain these solutions explicitly, is described. New simply periodic solutions of the Lorenz system are obtained.
An algorithm for the construction of elliptic curves satisfying special requirements is presented. The choice of requirements aims to prevent known attacks on the elliptic curve discrete logarithm problem in special cases. The results of practical experiments are discussed, some parameters of concrete elliptic curves are given.
The project of the standard of neural network biometric containers protection using cryptographic algorithms is analysed. The inconsistency of the suggested combination of password and neural network biometric information protection systems is shown.