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V. P. Maslov

Publications and source records attributed to V. P. Maslov.

At least 37 records · Page 2Linked to original sources
arXiv2007

On the superfluidity of classical liquid in nanotubes

In 2001, the author proposed the ultra second quantization method. The ultra second quantization of the Schrödinger equation, as well as its ordinary second quantization, is a representation of the N-particle Schrödinger equation, and this means that basically the ultra second quantization of the equation is the same as the original N-particle equation: they coincide in 3N-dimensional space. We consider a short action pairwise potential V(x_i -x_j). This means that as the number of particles tends to infinity, $N\to\infty$, interaction is possible for only a finite number of particles. Therefore, the potential depends on N in the following way: $V_N=V((x_i-x_j)N^{1/3})$. If V(y) is finite with support $Ω_V$, then as $N\to\infty$ the support engulfs a finite number of particles, and this number does not depend on N. As a result, it turns out that the superfluidity occurs for velocities less than $\min(λ_{\text{crit}}, \frac{h}{2mR})$, where $λ_{\text{crit}}$ is the critical Landau velocity and R is the radius of the nanotube.

math-ph↗
arXiv2006

Rank distributions in semiotics

The notions of real and user cardinality of a sign are introduced. Rank distributions can be extended to arbitrary sign objects, i.e., semiotic systems. The dynamics of the distribution of consumer durables, such as automobiles, is studied.

math.PR↗
arXiv2005

Thermo- and gas-dynamical processes in NPPs after accidents

In the theory of superfluidity and superconductivity, a jump of the free energy was discovered theoretically and was naturally called a {\it zeroth-order phase transition}. We present an example of an exactly solvable problem in which such a phase transition occurs.

cond-mat.supr-con↗
arXiv2005

Nonlinear Averaging in Economics

Kolmogorov nonlinear averaging is complemented by a natural axiom. For this averaging, we prove a theorem on large deviations as well as establish the relationship to the tunnel canonical operator.

physics.soc-ph↗
arXiv2005

Uniformization of Nonlinear Hamiltonian Systems of Vlasov and Hartree Type

Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization of classical systems to arbitrary Hamiltonian (Lie-Jordan, or Poissonian) algebras, in particular to the algebras of operators in indefinite spaces. A functional calculus is developed for the uniformized observables, which unifies the calculi of generating functionals for classical, Bosonian and Fermionian multiparticle variables. The nonlinear kinetic equation of Vlasov and Hartree type are derived for both classical and quantum multiparticle Hamiltonian systems in the mean field approximation. The possibilities for finding approximate solutions of these equations from the solutions of uniformized linear equations are investigated.

math-ph↗
arXiv2004

Design of Optimal Dynamic Analyzers: Mathematical Aspects of Wave Pattern Recognition

We give a review of the most important results on optimal tomography as mathematical wave-pattern recognition theory emerged in the 70's in connection with the problems of optimal estimation and hypothesis testing in quantum theory. In quantum theory such problems are sometimes referred as the problem of optimal measurement of an unknown quantum state, and are the main subject of the emerging mathematical theory of quantum statistics. We develop the results of quantum pattern recognition theory, most of which belong to VPB, further into the direction of wave, rather than particle statistical estimation and hypothesis testing theory, with the aim to include not only quantum matter waves but also classical wave patterns like optical and acoustic waves. We conclude that Hilbert space and operator methods developed in quantum theory are equally useful in the classical wave theory, as soon as the possible observations are restricted to only intensity distributions of waves, i.e. when the wave states are not the allowed observables, as they are not the observables of individual particles in the quantum theory. We show that all characteristic attributes of quantum theory such as complementarity, entanglement or Heisenberg uncertainty relations are also attributes of the generalized wave pattern recognition theory.

quant-ph↗
arXiv2003

Approximation probabilities, the law of quasistable markets, and phase transitions from the "condensed" state

For common people, in contrast to brokers, bankers, and those who play on rising and falling prices of stocks, the stock market law is based on the simple fact that the depositors aim for financial profit at any given concrete stage. The common depositor cannot cause any significant variations in prices. This concept suggests an analogy with the quasistable physics, i.e., thermodynamics, in the situation in which the temperature varies slowly along with the external conditions. Therefore, in the quasistable market, we can see phase transitions similar to those in the situation of the Bose-condesate in thermodynamics. We stress the positive role of information for common depositors and the possibility of changing bonds of large denomination into bonds of small denomination.

math.PR↗
arXiv2001

Unifying Approach to Software and Hardware Design for Scientific Calculations

A unifying approach to software and hardware design generated by ideas of Idempotent Mathematics is discussed. The so-called idempotent correspondence principle for algorithms, programs and hardware units is described. A software project based on this approach is presented. Key words: universal algorithms, idempotent calculus, software design, hardware design, object oriented programming

quant-ph↗