Let A be a n-homogeneous $(n \geqslant 4)$ C*-algebra. Further, suppose the space
primA of primitive ideals for the algebra A is homeomorphic to a two-dimensional oriented
manifold. In this case, the algebra A can be generated by three idempotents. The algebra A can
not be generated by two idempotents.
Keywords: C*-algebra, primitive ideals, base space, algebraic bundle, operator algebra,
irreducible representation
Assume that a viscous stratified fluid partially fills an arbitrary container and, in the unperturbed state, uniformly rotates with angular velocity
${\vec w_0 = \omega_0 \vec e_3}$, where ${\vec e_3}$ is the axial vector of rotation axis ${Ox_3}$ (assume that ${\omega_0>0}$).
In a state of relative equilibrium, the fluid occupies the region ${\Omega \in \Bbb R^3}$ bounded by solid wall $S$ and the equilibrium surface ${\Gamma}$.
We consider the energy operator of two-magnon systems with four-spin exchange
Hamiltonian and investigated the structure of essential spectra and discrete spectrum of the
system. It is known that the continuous spectrum of the energy operator of two-magnon systems
for an arbitrary spin value in the Heisenberg model is consists of the segment [mmin, Mmax],
and the discrete spectrum of the system is consists of no more than 2ν eigenvalues, lying in the
A completely controlled linear stationary dynamical system is considered. The
problem of program motion stabilization is solved for the system.
The article deals with an initial-boundary value problem for a nonlinear
functional-differential equation (FDE) of parabolic type with transformation of the unknown
function arguments. It describes the phenomenon of structure formation in an optical system,
consisting of a thin layer of a nonlinear Kerr-type medium and a differently organized twodimensional feedback external contour. The dynamics of the system depends on the change in
the parameters of the optical signal at the input or the parameters of the system itself.
One specialist in the field of operations research decided to use optimization methods to solve a very important problem for him - getting rid of extra fullness. He formalized this problem according to established rules just chosen the target function - weight, restrictions - the minimum of proteins, carbohydrates, fats, etc., then he solved the mathematical problem of minimization under restrictions. The optimal solution was to restrict the ration of food by using vinegar more than three hundred liters per day (the American philosopher Ch. Hitch).
In n-dimensional unitary space
Mathematical formalization of various natural processes leads to models that
are described by nonlinear differential equations (ordinary, in partial derivatives and functionaldifferential equations) or nonlinear integral equations.
Their research takes place within the framework of applied non-linear dynamics. The issues
of stability, bifurcation of solutions, the emergence of spatially inhomogeneous structures, quasiperiodic solutions, etc. are considered. Various theories, methods and algorithms are used (for
Nonlinear ordinary differential equations and partial differential equations have
found application in many sections of physics: photonics and plasmonics, nonlinear optics, gasfree combustion theory, hydrodynamics and electrodynamics; biophysics; nonlinear population
dynamics; nonlinear wave theory, etc. In terms of system analysis, the considered models contain
evolutionary blocks, diffusion, diffraction, blocks of interaction, nonlinear blocks and others.
As you know, a network model is a plan for performing some complex of
interrelated operations, given in the form of a network, the graphical representation of which is
called a network graph. At the same time, all the interrelationships of the work to be performed
require a clear definition. Network planning is one of the most well-known applications of graph
theory and is widely used in practice.
The paper studies perturbed initial-boundary value problems of conjugation generated by a sesquilinear form. The principle of superposition allows us to represent the solution of the original problem as a sum of solutions of auxiliary problems containing inhomogeneity either in the equation or in one of the boundary conditions. The original initial-boundary value problems are reduced to Cauchy problems for first-order integro-differential and differential operator equations in a Hilbert space.
For large systems expected to come, such as, for example,
long beam with a payload at the end, control modes are proposed
active vibration damping. Self extinguishing turn
internal mass (damper) along the guide, vertical beam. Control
consists in choosing the coefficients of a linear function, which is combined for
rejection of the absorber and payload.
In this paper, we consider a model spectral problem that preserves all the features of the real problem of normal oscillations of the hydrodynamic
a system consisting of two incompressible homogeneous liquids placed in an arbitrary vessel. In this case, a liquid of higher density is viscous,
and the smaller one is ideal. The study of the spectrum of the problem was carried out on the basis of the study of the transcendental characteristic equation with respect to
complex damping decrement of normal oscillations.
Let $\mathcal H$~--- be an infinite-dimensional complex Hilbert space, let $(\mathcal B(\mathcal H), \|\cdot\|_\infty)$~--- $C^\star$ - algebra of all bounded linear operators acting in $\mathcal H$, and let \ $\mathcal C_E$ \ l be the symmetric
The problems with changing phase space are a subclass of the so-called hybrid (composite)
systems. They are characterized by the fact that at different time intervals they are described by
different differential systems and certain links for the connection of the trajectories. The systems
can have the similar dimensionality and also the transfer both from the dimension with the higher
dimensionality to the lower dimensionality and vice versa. The original source of such problems
were the multistage processes of space flights.
The paper considers a problem of competition between three manufacturing firms in the
market of homogeneous infinitely divisible products. It is assumed that the nature of the
interaction of manufacturing firms in the market has a hierarchical structure. Namely, one of
the companies, the leader company, is the leading manufacturer and is the first to decide on the
volume of product deliveries to the market. While the other two firms decide on the number of
The low-pressure RFI model is considered as a nonlinear eigenvalue problem with a parameter for a system that includes the electron balance equations and the Maxwell equations with mixed boundary conditions. The free parameter of the problem is the value of the electron density at the center of the plasma bunch $n_{e0}$.
The problem of stability of stationary solutions of traditional initial-boundary value problems for systems of equations describing the growth and distribution of a substance is considered. A positive effect of migration (diffusion) processes on stability in small areas is noted.
Keywords: diffusion model, initial boundary value problem, stationary solution (state), stability, sufficient stability condition.
The article presents the method of generalized powers (OS) for constructing a sequence of basic solutions for a system of linear differential equations of the first order, known as the Moisil-Teodorescu systems. To accomplish this task, the quaternion form of the Moisil-Teodorescu equation is translated into a matrix form. With the help of a certain operation called joining, the system is reduced to a form that allows the use of the OS method.
In this paper, we consider the class $G$ of orientation-preserving Morse-Smale diffeomorphisms defined on a closed 3-manifold whose nonwandering set consists of exactly four points of pairwise distinct Morse indices. It is known that the two-dimensional saddle separatrices of any such diffeomorphism always intersect, and their intersection necessarily contains non-compact heteroclinic curves, but can also contain compact ones.
It is known that the contemporary approach in the theory of control systems and mathematical physics leads to models that are conveniently described by using differential equations and inclusions. Recently, the attention of many researchers (see [1]–[3] and the references therein) was attracted to generalizations of differential and functional differential equations and inclusions, namely to the class of functional equations and inclusions with causal operators. The term causal operator or Volterra operator in the sense of A. N.
The paper considers the dynamics and stability of homogeneous equilibrium states of a mathematical model of a nonlinear generator of optical radiation with a stretching operator for the spatial coordinates of a light wave and a time delay in the feedback loop. The mathematical model is an initial-boundary value problem for a parabolic type equation in a circle with a spatial argument stretching operator and a time delay in a nonlinear feedback functional.
The stability of rotation of a symmetrical rigid body on a vertical flexible rod (shaft) is investigated. Both ends of the shaft are secured from offsets. The lower end of the shaft is supported by a bearing, and the bearing of the upper end is attached to an elastic ring plate, pinched along the outer diameter. This is one of the designs of a real-life centrifuge. The shaft material is considered inherently viscoelastic. The equations of motion of the flexible shaft are constructed within the framework of the linear Euler–Bernoulli model.
In the paper, one constructs the examples of polar Morse–Smale systems (diffeomorphisms and flows) with a sink fixed point, source fixed point and two saddles fixed points on n-dimensional sphere \(S^n\),\(n ≥ 3\). To prove this result, we construct different decompositions of the n-dimensional sphere \(S^n\). Moreover, the Morse index of a saddle fixed point can be any value between \(1\) and \(n − 1\), and the Morse indexes of the saddles fixed points are always different.
The paper presents a method for constructing point and interval estimates of the regression coefficient (RC) of nonlinear regression in a passive, in a certain sense, experiment. Passivity is understood through the role of the experimenter regarding the content of the initial data. The role is passive and does not affect the method of collecting information. The initial data for the experimenter is an unchangeable given.
Applied network tasks of multiagent routing or (applied network tasks of multiagent routing или \(mTSP\)) arise in many application areas and lead to various models of pseudo-Boolean optimization. Such problems, as a rule, are \(NP\)--hard, for them exact algorithms are applicable only in the case of a small dimension of the original network (graph). Multiagency can be contained in the initial formulation or arise as a result of simplifying and reducing the dimension of the problem (decomposition, clustering).
A sufficient condition for the consistency of nonparametric estimator for regression function based on the partial Fourier–Lagrange sums is proved.
Keywords: nonparametric regression, consistency, estimator, orthogonal series.
The article explores the practical necessity of using elliptic functions. The history
of the origin of the concept of an elliptic function is considered in detail. Clear conclusions on
the formation of the apparatus of the theory of elliptic functions in the works of Abel, Jacobi,
Weierstrass and Somov are proposed. Based on the proof of Abel’s theorem, a representation of
elliptic functions in terms of theta functions is shown.
The introduction and use of elliptic and hyperelliptic functions bring the problems of control
In a $n$-dimensional unitary space $ \mathrm{U}_{}^{n} $ $(n > 4)$ there are three series of regular polytopes: the regular simplex $ \mathrm{\alpha}_{n}^{} $ , the generalized cross polytopes $ \mathrm{\beta}_{n}^{m} $ and the generalized $n$-cube $ \mathrm{\gamma}_{n}^{m} $. The generalized $n$-cube has $ m^{n} $ vertices:
$ (\mathrm{\Theta}_{}^{\mathrm{k}_{1}^{}}, \mathrm{\Theta}_{}^{\mathrm{k}_{2}^{}}, ..., \mathrm{\Theta}_{}^{\mathrm{k}_{n}^{}} ) $,