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Tuesday, August 16, 2011 - 02:20
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Abstract We establish the dependence of the critical exponent of the nonlinear heat equation on the initial function and derive an
estimate for the blow-up time of the solution of this problem depending on the nonlinearity exponent and the initial function.
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Tuesday, August 16, 2011 - 02:20
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Abstract We consider the problem of constructing a common controller stabilizing a finite family of linear dynamic plants with respect
to state in a given neighborhood of the zero equilibrium. To this end, we use nonlinear control algorithms leading to the
formation of sliding modes in the closed systems. This approach permits using much smaller gain factors than in linear algorithms.
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Tuesday, August 16, 2011 - 02:20
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Yurii Sergeevich Osipov (a tribute in honor of his seventy-fifth birthday)
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Tuesday, August 16, 2011 - 02:20
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Abstract We solve the problem of optimal boundary force control at one end of a string for the case of a given displacement mode at
the other end. The problem is studied in the sense of a generalized solution of the corresponding mixed initial-boundary value
problem in the Sobolev space. We also solve the problem of choosing an optimal boundary control from infinitely many feasible
controls. The generalized solution of the mixed initial-boundary value problem is constructed in closed form, and the uniqueness
of the solution is proved.
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Tuesday, August 16, 2011 - 02:20
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Abstract We suggest several notions of optimality (equilibrium), which replace the notion of A-equilibrium in conflict problems in the case of its emptiness (this is possible only in problems with side interests of participants)
and are also useful in arbitrary game problems in connection with their Pareto properties.
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Tuesday, August 16, 2011 - 02:20
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Abstract We establish a relationship between the canonical form of a linear differential system and the canonical form of its discrete
approximation based on the replacement of the derivative by Euler’s finite difference. We prove that if there exist limits
of certain sequences of discrete functions constructed with the use of coefficients of the canonical form of the discrete
system, then these limits define the canonical form of the differential system.
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Tuesday, August 16, 2011 - 02:20
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Abstract We present a class of bounded control inputs that permits one to solve target control synthesis problems for linear systems
with geometric (“instantaneous”) constraints on the perturbations by reduction to simpler programmed control problems.
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Tuesday, August 16, 2011 - 02:20
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Abstract A functional method for the localization of invariant compact sets in discrete autonomous systems is generalized to discrete
systems with uncertainty. We describe the properties of the corresponding localizing sets. By using this method, we construct
localizing sets for positively invariant compact sets of the discrete Henon system with uncertainty.
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Tuesday, August 16, 2011 - 02:20
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Abstract We consider a scalar singularly perturbed nonlinear delay differential-difference equation modeling an individual neuron.
We study the existence, asymptotics, and stability of its relaxation cycle.
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Tuesday, August 16, 2011 - 02:20
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Abstract We consider the problem on the infinite-duration tracking of a prescribed trajectory of an inaccurately observed control system
subjected to an unobservable dynamic disturbance. We construct a solution algorithm that is resource-saving in the sense that
the control resources used for solving the problem for small noise values in the state observation channel are little different
from the corresponding resources in the “ideal case” where the current values of the dynamic disturbance are available to
direct observation.
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Tuesday, August 16, 2011 - 02:20
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Abstract We obtain a generalization of the complete Perron effect whereby the characteristic exponents of all solutions change their
sign from negative for the linear approximation system to positive for a nonlinear system with perturbations of higher-order
smallness [Differ. Uravn., 2010, vol. 46, no. 10, pp. 1388–1402].
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Tuesday, August 16, 2011 - 02:20
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Abstract We consider the properties of generalized elements in the problem of compliance to constraints of asymptotic character; these
elements are identified with ultrafilters of special families of sets in the space of ordinary solutions.
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Tuesday, August 16, 2011 - 02:20
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Abstract We study the stability property in a game-theoretic problem on the approach of a conflict control system to an objective set
at a fixed time.
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Tuesday, August 16, 2011 - 02:20
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Abstract For control systems with deviating argument, we consider basic problems of qualitative control theory such as problems of
stabilization and modal control in scales of linear controllers with respect to the type of feedback, from the simplest difference
controllers to integral controllers of general form. We analyze the results obtained in this direction. Special attention
is paid to the stabilization of two-dimensional systems by feedback in the form of difference controllers. For the case in
which the construction of a difference controller is impossible or too difficult, an integral feedback is used. Unlike the
well-known Krasovskii-Osipov method for the construction of integral feedback in delay systems, the suggested method is based
on the Paley-Wiener theorem for entire functions of exponential type.
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Tuesday, August 16, 2011 - 02:20
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Abstract We optimize the boundary displacement control that is applied at one end of a rod consisting of two dissimilar parts and brings
the rod vibrations from a given initial state to a given terminal state for the case in which the other end of the rod is
fixed.
The following two problems are special cases of this general problem: (i) the vibration excitation problem, i.e., the problem
of bringing an originally quiescent rod to a given terminal state; (ii) the vibration damping problem, i.e., the problem of
bringing the rod vibrations from a given initial state to the completely quiescent terminal state.
We find the relationship between the optimal boundary controls in the general problem and the above-mentioned special problems;
finding the optimal boundary control of vibrations of a heterogeneous rod is reduced to the earlier-solved problem on the
optimization of the boundary control of vibrations of a homogeneous
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Friday, July 15, 2011 - 12:02
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Kamil’ Basirovich Sabitov (A tribute in honor of his sixtieth birthday)
- Content Type Journal Article
- Pages 765-765
- DOI 10.1134/S0012266111060012
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Friday, July 15, 2011 - 12:02
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Abstract We show that the trajectories of all points of a stable compact invariant set of a holomorphic mapping are Poisson stable
(recurrent).
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Friday, July 15, 2011 - 12:02
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Abstract We state and prove a theorem on the equality of the real part of the generalized Schwarzian derivative computed along a bifurcating
limit cycle of a family of vector fields defined in ℝ
n
to the first Lyapunov quantity of the corresponding Poincaré map.
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Friday, July 15, 2011 - 12:02
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Abstract The solution of a convolution-type equation for two unknown compactly supported functions for the case in which the kernel
of the integral operator has Fourier transform in the form of the ratio of two polynomials of exponentials and the right-hand
side satisfies additional conditions like the evenness-oddness, absence of zeros, etc. is reduced to the solution of a system
of difference equations. We suggest a solution method for that system.
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Friday, July 15, 2011 - 12:02
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Abstract We consider nonlocal operators generated by pseudodifferential operators and the operator of shift along the trajectories
of an arbitrary diffeomorphism of a smooth closed manifold. We introduce the notion of symbol of such operators acting in
Sobolev spaces. As examples, we consider specific diffeomorphisms, namely, isometries and dilations.
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Friday, July 15, 2011 - 12:01
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Abstract We consider a one-dimensional quasilinear eigenvalue and eigenfunction problem. The simplification of the problem by replacing
a second-order elliptic operator by a one-dimensional one permits carrying out an efficient and unified study of the structure
of the spectrum and the multiplicity of eigenvalues for a wide range of functions specifying the nonlinearity. This opens
up the possibility of preliminarily analyzing specific properties of solutions of such problems for partial differential equations,
in particular, the equilibrium of a toroidal plasma, since the spectrum of the problem and its multiplicity depend only weakly
on the space dimension.
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Friday, July 15, 2011 - 12:01
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Abstract We develop a unified approach to the investigation of invariant properties of Euler and non-Euler functionals and establish
a relationship of variational symmetries with first integrals of a given evolution operator equation of second order with
respect to t. In addition, we investigate the properties of the generators of divergence symmetries.
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Friday, July 15, 2011 - 12:01
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Abstract We study the solvability of a boundary value problem for a quasilinear partial differential equation of the second kind. To
this end, we use a variational method; namely, we prove the existence of a point of absolute minimum of a functional, and
this point is a solution of the original problem.
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Friday, July 15, 2011 - 12:01
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Abstract We obtain sufficient coefficient conditions for the unique solvability of a multipoint boundary value problem for the Lyapunov
matrix differential equation in the case of strong degeneration of the boundary conditions. We suggest an efficient algorithm
for constructing the solution.
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Friday, July 15, 2011 - 12:01
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Abstract In a Hilbert space, we study the well-posedness of the Cauchy problem for a second-order operator-differential equation with
a singular coefficient.
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