2,716 research outputs found
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations
In this paper we consider three-dimensional quantum q-oscillator field theory
without spectral parameters. We construct an essentially big set of eigenstates
of evolution with unity eigenvalue of discrete time evolution operator. All
these eigenstates belong to a subspace of total Hilbert space where an action
of evolution operator can be identified with quantized discrete BKP equations
(synonym Miwa equations). The key ingredients of our construction are specific
eigenstates of a single three-dimensional R-matrix. These eigenstates are
boundary states for hidden three-dimensional structures of U_q(B_n^1) and
U_q(D_n^1)$.Comment: 13 page
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
Topological insulators and geometry of vector bundles
For a long time, band theory of solids has focused on the energy spectrum, or
Hamiltonian eigenvalues. Recently, it was realized that the collection of
eigenvectors also contains important physical information. The local geometry
of eigenspaces determines the electric polarization, while their global
twisting gives rise to the metallic surface states in topological insulators.
These phenomena are central topics of the present notes. The shape of
eigenspaces is also responsible for many intriguing physical analogies, which
have their roots in the theory of vector bundles. We give an informal
introduction to the geometry and topology of vector bundles and describe
various physical models from this mathematical perspective.Comment: v2: revised and extended version, submission to SciPos
On invariance of specific mass increment in the case of non-equilibrium growth
It is the first time invariance of specific mass increments of crystalline
structures that co-exist in the case of non-equilibrium growth is grounded
using the maximum entropy production principle. Based on the hypothesis of the
existence of a universal growth equation, with the use of dimensional analysis,
an explicit form of the dependence of specific mass increment on time is
proposed. Applicability of the obtained results for describing growth in
animate nature is discussed.Comment: 5 page
The method of restoring the musculoskeletal system after physical activity with relaxation
The paper discusses the theme of the restoration of the musculoskeletal system in athletes, engaged in physical activity with relaxation. The relevance of the chosen topic in that people after exercise pay little time for recovery and relaxation method few people know, this method is a good helper in the recovery of the bodyΠ ΡΠ°Π±ΠΎΡΠ΅ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Π° ΡΠ΅ΠΌΠ° Π²ΠΎΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΠ΅ ΠΎΠΏΠΎΡΠ½ΠΎ-Π΄Π²ΠΈΠ³Π°ΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ° Ρ ΡΠΏΠΎΡΡΡΠΌΠ΅Π½ΠΎΠ², Π·Π°Π½ΠΈΠΌΠ°ΡΡΠΈΡ
ΡΡ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΠΌΠΈ Π½Π°Π³ΡΡΠ·ΠΊΠ°ΠΌΠΈ ΠΏΡΠΈ ΠΏΠΎΠΌΠΎΡΠΈ ΡΠ΅Π»Π°ΠΊΡΠ°ΡΠΈΠΈ. ΠΠΊΡΡΠ°Π»ΡΠ½ΠΎΡΡΡ Π²ΡΠ±ΡΠ°Π½Π½ΠΎΠΉ ΡΠ΅ΠΌΡ Π² ΡΠΎΠΌ, ΡΡΠΎ Π»ΡΠ΄ΠΈ ΠΏΠΎΡΠ»Π΅ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΈΡ
Π½Π°Π³ΡΡΠ·ΠΎΠΊ ΠΌΠ°Π»ΠΎ ΡΠ΄Π΅Π»ΡΡΡ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Π²ΠΎΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ, Π° ΠΌΠ΅ΡΠΎΠ΄ ΡΠ΅Π»Π°ΠΊΡΠ°ΡΠΈΠΈ ΠΌΠ°Π»ΠΎ ΠΊΠΎΠΌΡ Π·Π½Π°ΠΊΠΎΠΌ, ΠΈΠΌΠ΅Π½Π½ΠΎ ΡΡΠΎΡ ΠΌΠ΅ΡΠΎΠ΄ Ρ
ΠΎΡΠΎΡΠΈΠΉ ΠΏΠΎΠΌΠΎΡΠ½ΠΈΠΊ ΠΏΡΠΈ Π²ΠΎΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΠ΅ ΠΎΡΠ³Π°Π½ΠΈΠ·ΠΌ
Evolutionary Synthesis of Dynamical Object Emulator Based on RBF Neural Network
The combination of Genetic Algorithms (GAs) and Artificial Neural Networks (ANNs) has already resulted in researchers advancing in quite a few real world applications but it is in control that this alliance yields much appreciable benefit. The paper reports a Radial Basis Function (RBF) network training technique which joins together global strategy of GAs and a local adjusting procedure typical for RBF networks. While activation function window centres and widths are processed via a "slow" numeric GA, output-layer neurone synaptic weights are defined by a "fast" analytical method. The technique allows to minimize not only the network hidden-layer size but also the pattern set required for training the adequate dynamical object neuroemulator
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