Laboratory of
Information Transmission and Control Theory
Head of Laboratory – Full member of
the Russian Academy of Sciences,
Dr.Sc. (Technology), Prof. Nikolai
Kuznetsov
Tel.: (095)
209-42-25, (095) 299-83-54; E-mail: director@iitp.ru
The leading researchers of the
laboratory include:
|
Dr.Sc. (Math.) |
M. Burnashev |
Dr.Sc. (Math.) |
V. Zinovjev |
|
Dr.Sc. (Math.) |
G. Golubev |
Dr. |
E. Asarin |
|
Dr.Sc. (Math.) |
R. Khasminsky |
Dr. |
V. Chepyzhov |
|
Dr.Sc. (Math.) |
A. Krasnosel'skii |
Dr. |
V. Chernorutskii |
|
Dr.Sc. (Math.) |
V. Kozyakin |
Dr. |
R. Izmailov |
|
Dr.Sc. (Math.) |
M. Malyutov |
Dr. |
M. Klepcyna |
|
Dr.Sc. (Math.) |
M. Pinsker |
Dr. |
D. Rachinskii |
|
Dr.Sc. (Math.) |
A. Pokrovskii |
Dr. |
A. Sheverdyaev |
|
Dr.Sc. (Techn.) |
Yu. Sagalovich |
Dr. |
A. Skorobogatov |
|
Dr.Sc. (Techn.) |
Yu. Shtarkov |
Dr. |
A. Vladimirov |
|
Dr.Sc. (Math.) |
M. Vishik |
Dr. |
I. Vladimirov |
|
Dr.Sc. (Techn.) |
K. Zigangirov |
|
|
Directions of Activity:
·
the development of the mathematical models, methods and algorithms for
the protection of the information networks;
·
the development methods of the algebra and information theory for the construction
of the diagnostic built-in system.
·
the study of limit behavior of solutions of non-autonomous non-linear
evolution equations, investigations of trajectory
·
attractors of partial differential equations, their structure and
dependence on parameters, constructions of integral manifolds with exponential
tracing;
·
source coding and data compression;
·
the problem of asymptotically optimal universal coding to relative
redundancy creation;
·
nonparametric estimation: adaptive estimation in partial linear models,
statistical approach to some inverse boundary problems for partial differential
equations, applications of wavelets in nonparametric estimation;
·
algorithmic information theory;
·
codes with iterative decoding, code division multiple access (CDMA) systems;
·
the development of asymptotic theory nonparametric statistic;
·
analysis of systems with complex non-linearities (hysteresis, delays,
round-off and discretization effects);
·
asynchronous systems;
·
hybrid systems;
·
oscillation theory, Hopf bifurcations, stability;
·
network optimization.
The binary
extended nonlinear perfect codes of length 16, which can be obtained by
generalized concatenated construction, were considered and classified.
The coset
weight distribution of several classes of Z_4-linear Goethals codes are
considered. In particular the coset weight distribution is found for Z_4-linear
Goethals codes and also for the binary Goethals-like codes obtained from the last
codes by the Gray map. The exact expressions for the number of code words of
weight four of cosets of weight four are obtained in terms of Kloosterman sums.
This gives some results also for possible values of Kloosterman sums, which
improve some earlier results of Lachaud and Wolfmann. Studying the coset weight
distributions of generalized Z_4-linear Goethals codes, the connection with
Dickson polynomials is also found. We can express the number of code words of
weight four as the number of solutions of some equations for Dickson
polynomials over finite field.
The new
estimates of Kolmogorov e-entropy are
obtained for global attractors for main evolution systems of equations of
mathematical physics, for which we have the uniqueness of solution of the initial
problem.
The global
attractor for 3D Navier-Stokes system is constructed. It was proved that the
global attractors of corresponding Galerkin approximations tend to the global attractor
of 3D Navier-Stokes system.
Probability
theory of low-density parity-check convolutional codes. Asymptotical behavior
of low-density parity-check code (including turbo-codes), both block and
convolutional, was studied when size of interleaver go to infinity.
Particularly, minimal and free distance was studied. New constructive method of
interleaver choice was suggested. It optimizes minimal distance. New bounds for
bit error probability which can be used for turbo-code analysis was derived.
Formula for
forward link other-cell relative interference factor of cellular communication
system was derived. Low rate super-orthogonal turbo-code for using in CDMA
systems was constructed.
Characteristics
of linear decoding methods in multiuser detection systems were investigated. In
particular, estimates for decoding error probabilities, essentially better than
previously known, were obtained.
A new approach
for decoding error probability evaluation was developed.
The main
approach to digital data compression is the universal coding of sources with
memory; it is reduced to the universal coding of the subsequences of independent
symbols. Usually this subsequences are encoded independently one of the another
ones. The method of the joint matrix universal coding is proposed for the increasing
of the compression efficiency for relatively small messages (the ordinary
thing). This matrix coding is compared with the well known and efficient PPM
algorithm.
The checking
matrix of a specific form is constructed for a diagnostic of circuit and
processor nets with regular structure. By means of this matrix The syndrome of
output vector of the net is calculated. The set of syndromes corresponds to the
each single fault of processor. It is proofed that syndromes sets, which
correspond to fault of distinct processors, are disjoint. This fact guarantees
the exact indication the fault processor.
The exceptions
of the including of Kerdock code into the linear subcode of Reed-Muller code of
second order are investigated. Because of this fact the opportunity appears for
the exact indicate the value of main parameter of code as separating systems.
The results are news.
The coincidence
of recent results of other authors in domain of separating systems with old
results of author of this report is disclosed.
The problems of
calculation of the epsilon entropy of ellipsoids in a Hamming space are
investigated. An expression for the main term of the asymptotics of the epsilon
entropy of n-dimensional ellipsoids
as n goes to infinity was obtained.
Upper and lower
bounds of cardinality of codes correcting ordinary and localized errors are
presented.
The main
direction of the researches was related with applications of the principle of
unbiased risk estimation for some inverse problems. It is shown that this
principle gives a solution of the inverse problem with the almost optimal risk.
On the other hand this approach does not use the prior information about the
recovered function.
Within the
frame of "Research on noise-immunity of digital methods of speech
compression and transmission based on autoregressive speech production
model" acoustic noise robustness of pitch estimation procedure of IMBE
codec (TIA/EIA-102.BABA standard) was investigated along with the contribution
of its variance to overall IMBE coding quality. The original algorithm
modifications are offered (in particular look-ahead and look-back tracking
procedures and pitch refinement procedure) that enhance its noise-immunity and
thus improve "voiced/unvoiced segment" decision quality for each of
codec's working frequency band.
A
cross-development system (based on Oberon-2 translators to C), developed and
implemented in 1998-1999 for standard 32 bit CPU (Intel x86, Motorola 680x0,
PPC, etc.) and for modified Harvard architecture DSP (Analog Devices 16 bit
integer ADSP-21xx and 32 bit float ADSP-21xxx) was transferred along with
libraries to POSIX compliant operating systems (BeOS, Linux, QNX, etc).
Unix-dependent modules of OOC project libraries were adapted accordingly.
Translators and libraries manuals were prepared.
Analysis of
existence of attractors of asynchronous systems so as of skew products of
dynamical systems with shadowing base component was fulfilled. New constructions
were proposed which enable the property of algebraic insolubility of the
problem of convergence for infinite products of matrices. The possibility of
prolongation of earlier established results on algebraic insolubility of the
problem of convergence for infinite products of matrices within framework of o-minimality theory was investigated.
The possibility of application of Mane norms for estimating of Lyapunov
exponents of the products of algebraic insolubility of the problem of
convergence for infinite products of matrices was investigated.
New methods for
the study of problems on existence of periodic oscillations in autonomous systems
were developed. Sufficient conditions for the existence of cycles were
suggested for higher order ODEs and equations of control theory. These
conditions use information about two sided sector estimates of the
nonlinearities. The existence of global continuous branches of cycles was
proved for Hamiltonian systems. In periodic problems for PDEs the method leads
to sufficient conditions for the existence of several cycles with different
periods. Lower estimates for the number of cycles and two sided bounds of their
periods were obtained for evolutionary equations with elliptic operators,
parabolic equations with delays in the linear part, etc.
A method to
analyze the structure of solution sets for periodic problems with hysteresis
was developed. New sufficient conditions for the existence of continua of cycles
were suggested for autonomous systems with complex hysteresis nonlinearities
(in particular, Preisach and Ishlinskii hysteresis models, their vector
analogs, etc.). In natural situations, such systems have a curve of equilibria.
It was proved that the standard assumptions of the theorems on Hopf
bifurcations for ODEs (that is assumptions on the linear part of the system)
guarantee the existence of a continuum of cycles in a small neighborhood of the
curve of equilibria for systems with hysteresis. The method can be used in
various other problems on periodic oscillations in autonomous and nonautonomous
systems with complex hysteresis nonlinearities.
The method of
shuttle iterations was modified to construct new approximation procedures that
converge to robust stable solutions or robust stable continuous branches of
solutions of boundary value problems for elliptic equations with nonmonotone
continuous nonlinearities.
Hopf
bifurcations in control systems with smooth nonlinear feedbacks were analyzed
under the conditions of strong 0:1 and 1:1 resonances.
А new type of hysteresis nonlinearities, called a time-dependent Preisach
nonlinearity is analysed. This nonlinearity is described in detail, its basic
properties (monotonicity, continuity, and response to periodic impacts) are
examined, and the possibility of its numerical approximations is explored. The
simplest statements about closed systems with time-dependent Preisach
nonlinearities are formulated. The study of such nonlinearities is motivated by
applied problems arising in mathematical economics in the analysis of
macroeconomic indices and their influence on decision making.
The principal
success was achieved in the applications to rigorous analysis of opto-electronic
phenomena. Here we studied the truncated Lang-Kobayashi equations that describe
the behavior of semiconductor lasers with feedback. For particular values of
parameters we prove rigorously that the system demonstrates chaotic behavior:
there is a compact invariant set with the homoclinic point, there exists infinitely
many unstable periodic modes, etc. The proof is based on computer assisted
computations, where all errors are estimated and taken into account.
The research of
mathematical hysteresis and related topics was continued. The main attention
was payed to sweeping processes (SP). The transversality condition together
with the LCP property of the so-called associated projection system of a
polyhedral SP has been proved sufficient for the Lipschitz continuity of the
input-output operator of this SP in the spaces of regulated functions. One of
the most important areas of application of SPs and related techniques is the
theory of queueing networks. We consider the fluid model of a reentrant line
with FIFO discipline and look for solutions with constant flows (steady
solutions). In the case of constant viscosities we prove the uniqueness of such
a solution. If the viscosities are different we present an example with
multiple steady solutions. It was proved that for some classes of reentrant
lines the uniqueness holds even if the viscosities are different.
We are
interested in the simplest form of explicit solution of the filtering problem
for the first order regression with stationary Gaussian noise observed under
the same noise with the same structure. We propose the technique which gives
the possibility to reduce initial problem to the classical filtering problem of
the component 2-dimensional 1-st order regression under the observation with white
noise and the filtering of the fixed linear functional of the component of this
regression.
Various methods
to derive new formulas for the Laplace transforms of some quadratic forms of
Gaussian sequences are discussed. In the general setting, an approach based on
the resolution of an appropriate auxiliary filtering problem is developed; it
leads to a formula in terms of the solutions of Voterra type recursions describing
characteristics of the corresponding optimal filter. In the case of
Gauss-Markov sequences, where the previous equations reduce to ordinary forward
recursive equations, an alternative approach provides another formula; it
involves the solution of a backward recursive equation. Comparing the different
formulas for the Laplace transforms, various relationships between the
corresponding entries are identified. In particular relationships between the
solutions of matched forward and backward Riccati equations are thus proved
probabilistically; they are proved again directly. In various specific cases, a
further analysis of the concerned equations leads to completely explicit
formulas for the Laplace transform. In the domain of hybrid and timed systems
the influence of noise on the algorithmic decidability of the reachability
problem was explored. A method for automatic computation of phase portraits of
non-deterministic planar hybrid systems was developed. A long-term research was
accomplished, resulting in creation of a theory of timed regular languages.
The work on
administrative weight allocation in PNNI network was completed. Two methods of
administrative weight allocation (for known and unknown traffic matrices,
respectively) have been proposed and analyzed. Both methods can provide significant
performance improvement of PNNIrouting, as compared with default administrative
weight allocation.
The work on
novel hierarchical hybrid optical cross-connects has started. The proposed
approach is based on aggregating of individual wavelengths into wavebands that
can then be routed in transparent optical domain. This hierarchical
architecture can provide significant cost savings in the area of optical
cross-connects. Analysis of combined routing and waveband aggregation
algorithms has been carried out.
GRANTS FROM:
·
Russian
Foundation of Basic Research (No. 99-01-00304): "Trajectory attractors for
equations of mathematical physics";
·
Russian
Foundation of Basic Research (No. 99-01-00828): "Transmission and protection of
information under additional restrictions";
·
Russian
Foundation of Basic Research (No. 00-15-96116): program "Leading research
schools", school by N. A. Kuznetsov;
·
Russian
Foundation of Basic Research (No. 00-01-00571): "Mathematical methods of
investigation and information stability of computer simulation of complex
nonlinear systems";
·
Russian
Foundation of Basic Research (No. 00-01-00266): "Probabilistic methods in
problems of transmission, protection and processing of information";
·
Russian
Foundation of Basic Research (No. 01-01-00146): "Periodic oscillations in
control systems";
·
NSF Grant
(DMS-9971608): "Cooperative research in statistical estimation and asymptotic
analysis", in 1999-2002.
·
Grant TFR
271-198-216: "A probabilistic theory of convolutional low-density parity-check
codes (turbo-codes)";
·
Grant PCC: "Efficient
strategies for wideband CDMA transmission";
·
Grant
SC2000/138: "Mountain pass algorithm in analysis of complex nonlinear
systems";
·
Grant INTAS
2001-265: "Mathematics of stochastic networks";
·
Australian
Research Council Grant A 1002 7063: "Anisotropy-based methods for
filtering and control in stochastic systems".
PUBLICATIONS IN 2001
1. Helleseth T.,
Zinoviev V.A. Codes with the Same Coset Weight Distributions as the Z_4-linear
Goethals Codes // IEEE Trans. On Inform. Theory. 2001. V. 47. № 4. P.
1589-1595.
2. Helleseth T.,
Zinoviev V.A. On coset weight distributions of the Z_4-linear Goethals Codes //
IEEE Trans. on Inform. Theory. 2001. V. 47. № 5. P. 1758-1772.
3. Charpin P.,
Tietavainen A., Zinoviev V.A. Binary cyclic codes with codewords of weight
three and binary sequences with the trinomial property // EEE Trans. on Inform.
Theory. 2001. V. 47. № 1. P. 421-425.
4. Borges J., Rifa
J., Zinoviev V.A. Nonexistence of completely transitive codes with
error-correcting capability e > 3 // IEEE Trans. on Inform. Theory. 2001. V.
47. № 4. P. 1619-1621.
5.
Thomas Ericson, Victor Zinoviev. Codes on Euclidean Spheres //
North-Holland Mathematical Library Elsevier. Amsterdam – London – New York –
Oxford – Paris –Shannon – Tokyo. 2001.
6. Вишик М.И., Чепыжов В.В. Усреднение траекторных аттракторов
эволюционных уравнений с быстро осциллирующими членами // Математический
сборник. 2001. Т. 192. № 1. С. 13-50.
7. Chepyzhov V.V.,
Vishik M.I. Global Attractors and Its Perturbations for a Dissipative
Hyperbolic Equation. Russian Journal of Mathematical Physics. 2001. V. 8. № 3.
P. 311-330.
8. Fiedler B.,
Vishik M.I. Quantitative homogenization of analytic semigroups and
reaction-diffusion equations with diophantine spatial frequencies // Adv. Diff.
Eq. 2001. V. 6. № 11. P. 1377-1408.
9. Chepyzhov V.V.,
Ilyin A.A. A note on the fractal dimension of attractors of dissipative dynamical
systems // Nonlinear Analysis. 2001. V. 44. Р. 811-819.
10. Chepyzhov V.V., Vishik M.I.
Averaging of trajectory attractors of evolution equations with rapidly
oscillating coefficients // Functional Differential Equations. 2001. V. 8. №
1-2. P. 123-140.
11. Engdahl K., Zigangirov K.Sh. Tighter
Bounds on the Error Probability of Fixed Convolutional Codes // IEEE
Transactions on Information Theory. 2001. V. 47. № 4. P. 1625-1629.
12. Wintzell O., Zigangirov D.K.,
Zigangirov K.Sh. On the Capacity of a Pulse Position Hopped CDMA System // IEEE
Transactions on Information Theory. 2001. V. 47. № 6. P. 2639-2943.
13. Beyer B., Engdahl K., Zigangirov
K.Sh. Asymptotical Analysis and Comparison of Two Coded Modulation Schemes
Using PSK Signaling – Part I // IEEE Transactions on Information Theory. 2001.
V. 47. № 7. P. 2782-2792.
14. Beyer B.,
Engdahl K., Zigangirov K.Sh. Asymptotical Analysis and Comparison of Two Coded
Modulation Schemes Using PSK Signaling – Part II // IEEE Transactions on
Information Theory. 2001. V. 47. № 7. P. 2793-2806.
15. Зигангиров К.Ш., Лентмаер М., Трухачев Д.В. Некоторые
результаты конструирования и декодирования турбо-кодов // Проблемы передачи
информации. 2001. Т. 37. № 3. С. 6-23.
16. Зигангиров К.Ш., Лендал М., Трухачев Д.В. К теории
низкоплотностных сверточных кодов II // Проблемы
передачи информации. 2001. Т. 37. № 4. С. 15-35.
17. Amari Sh., Burnashev M.V., Han T.S.
On some estimation problems with information constraints // Theory of
Probabbility and Its Applications. 2001. V. 46. № 2. P. 233-246.
18. Bross Sh.I., Burnashev M.V., Shamai
(Shitz) Sh. Error exponents for the two-user Poisson multiple-access channel //
IEEE Trans. on Inform. Theory. 2001. V. 47. № 5. P. 1999-2016.
19. Burnashev M.V.,
Kutoyants Yu.A. On minimal alpha-mean error parameter transmission over Poisson
channel // IEEE Trans. on Inform. Theory. 2001. V. 47. № 6. P. 2505-2515.
20. Бурнашев М.В. Об оценках сверху для вероятности ошибки
декодирования сверточных кодов // Проблемы передачи информации. 2001. Т. 37. №
4. С. 36-55.
21. Ахкямов А.Р., Курышин С.А., Сагалович Ю.Л. Диагностирование сети процессоров с
закономерной структурой // Автоматика и телемеханика. 2001. № 12. С. 74-82.
22. Бассалыго Л.А., Пинскер М.Ш. Исправление обычных и
локализованных ошибок // Проблемы передачи информации. 2001. Т. 37. № 4. С. 56-59.
23. Golubev G., Khasminskii R.
Statistical approach to Cauchy problem for Laplace equation // IMS Lecture
Notes. Festschrift in honour of W.vanZvet. 2001. V. 36. P. 419-433.
24. Golubev G.,
Lepski O., Levit B. On adaptive estimation for the sup-norm losses // Math
Methods of Stat. 2001. № 1. Р. ?.
25. Голубев Г.К., Еникеева Ф.Н. Асимптотически эффективное
сглаживание в задаче Виксела при квадратичных потерях // Проблемы передачи
информации. 2001. Т. 37. № 1. С. 28-51.
26. Khasminskii R. Limit distributions
of some integral functionals for null-recurrent diffusion // Stochastic
processes and their applications. 2001. V. 92. P. 1-9.
27. Chow P.-L., Khasminskii. R. On
optimal input design for parameter estimation problems in PDE // Proceedings of
38-th Allerton Conference on Communication, Control and Computing. 2001. P.
412-421.
28. Khasminskii R., Milstein Gr. On
estimation of the linearized drift for nonlinear stochastic differential
equations // Stochastics and Dynamics. 2001. V. 1. № 1. Р. 23-43.
29. Khasminskii R., Krylov N. On
averaging principle for diffusion processes with null-recurrent fast component
// Stochastic Processes and their applications. 2001.V. 93. P. 229-240.
30. Asarin E.A., Schneider G., Yovine S.
On the Decidability of the Reachability Problem for Planar Differential
Inclusions // In M. Di Benedetto and A. Sangiovanni-Vincentelli (Eds.) Hybrid
Systems: Computation and Control. LNCS 2034. Springer. 2001. P. 89-104.
31. Asarin E.A., Bansal S., Espiau B.,
Dang T., Maler O. On Hybrid Control of Under-actuated Mechanical Systems // In
M. Di Benedetto and A. Sangiovanni-Vincentelli (Eds.) Hybrid Systems:
Computation and Control. LNCS 2034. Springer. 2001. P. 77-88.
32. Блиман П.-А., Красносельский А.М., Рачинский Д.И. О сильных
резонансах при бифуркациях Хопфа в системах управления // Автоматика и телемеханика.
2001. № 11. С. 29-50.
33. Campillo F., Kleptsyna M.,
Piatnitski A. Homogenization of random parabolic operator with large potential
// Stochastic Processes and their Applications. 2001. V. 93. № 1. P. 57-85.
34. Diamond P., Vladimirov I. Higher
order terms of asymptotic expansion for information loss in quantized random
processes Curcuits // Systems and Signal Processing. 2001. V. 20. № 6. Р. 677-693.
35. Diamond P., Vladimirov I., Kurdjukov
A., Semyonov A. Anisotropy-based performance analysis of linear
discrete-time-invariant control systems // International Journal of Control.
2001. V. 74. № 1. Р. 28-42.
36. Khanin K., Khmelev D., Rybko A.,
Vladimirov A. Steady solutions of fluid dynamics for FIFO networks // Moscow
Mathematical Journal. 2001. V. 1. № 3. Р. 407-419.
37. Klepcyna M.L., Le Breton A. Optimal
linear filtering of general multidimensional Gaussian processes – Application to
Laplace transforms of quadratic functionals // Journal of Applied Mathematics
and Stochastic Analysis. 2001. V. 14. № 3. P. 215-226.
38. Klepcyna M.L., Le Breton A. Some
explicit statistical results about elementary fractional type models //
Nonlinear Analysis. Theory, Methods & Applications. 2001. V. 47. № 7. Р. 4783-4794.
39. Kozyakin V.S., Kloeden P. The
perturbation of attractors of skew-product flows with a shadowing driving
system // Discrete and Continuous Dynamical Systems.2001. V. 7. № 4. P.
883-893.
40. Kozyakin V.S., Kloeden P. Single
parameter dissipativity and attractors in discrete time asynchronous systems //
Journal of Difference Equations and Applications. 2001. № 7. Р. 873-894.
41. Kozyakin V.S.,
Pokrovskii A.V. The asymptotic behavior of elementary symmetric functions on a
probability distribution // Journal of Appl. Math. and Stoch. Anal. 2001. V.
14. № 3. P.
237-248.
42. Красносельский А.М., Кросс Р., Покровский А.В.
Нестационарные модели Прейсаха и их свойства // Доклады Академии наук. 2001. Т. 381. № 2. С. 180-184.
43. Krasnosel'skii
A.M., Pokrovskii A.V. On subharmonics bifurcation in equations with homogeneous
nonlinearities // Discrete and Continuous Dynamical Systems. 2001. № 7. Р. 100-114.
44. Красносельский А.М., Рачинский Д.И. О существовании
континуумов циклов в автономных гамильтоновых системах управления // Автоматика
и телемеханика. 2001. № 2. С. 65-74.
45. Красносельский А.М., Рачинский Д.И. О континуумах циклов в
системах с гистерезисом // Доклады РАН. 2001. Т. 378. № 3. С. 314-319.
46. Красносельский А.М., Рачинский Д.И. О существовании циклов у
квазилинейных обыкновенных дифференциальных уравнений высшего порядка // Известия
РАЕН. Серия МММИУ. 2001. Т. 5. № 1-2. С. 143-151.
47. Krejci P., Vladimirov A. A.
Lipschitz continuity of polyhedral Skorokhod maps // Zeitschrift für
Analysis und ihre Anwendungen. 2001. V. 20. Р. 817-844.
48. Kuznetsov N.A., Mennicken R.,
Rachinskii D.I. The method of potential bounds in periodic nonpotential
problems for control systems // Mathematische Nachrichten. 2001. V. 225. P.
93-121.
49. Pokrovskii A.V., Szybka S.J.,
McInerney J.G. Topological Degree in Locating Homoclinic Structures for
Discrete Dynamical Systems // Institute for Nonlinear Sciences. 2001. Report
01-001.
50. Ott M., Welling G., Mathur S.,
Reininger D., Izmailov R. The Journey Active Network Model // IEEE JSAC. 2001.
V.19. № 3. P. 527-538.
51. Rasskazov O., Huyet G., McInerney
J., Pokrovskii A.V. Rigorous Analysis of Complicated Behaviour in a Truncated
Lang-Kobayashi Model // Institute for Nonlinear Sciences. 2001. Report 11-001.
52. Vladimirov A.
A. Does continuity of convex-valued maps survive under intersection? //
Optimization and Related Topics, Kluwer Academic Publishers, A. Rubinov and B.
Glover (Eds.). 2001. P. 415-428.
53. Кузнецов Н.А., Любецкий В.А., Чернавский А.В. К вопросу о
понятии информационного взаимодействия,2: доречевой интеллект // Труды 3-ей
Международной конференции "Проблемы управления и моделирования в сложных
системах". Самара. 2001. С. 25-42.
54. Кузнецов Н.А. Информационное взаимодействие в технических и
живых системах // Информационные процессы. 2001. Т. 1. № 1. С. 1-9.
55. Кузнецов Н.А., Венец В.И., Вишневский В.М., Морозов Е.В.,
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задач. Понтрягинские чтения – XII", Воронеж, 3-9 мая, 2001.
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conference "Applied Mathematics in our Changing World", Berlin,
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16. Rasskazov O., Pokrovskii A.
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1st SIAM-EMS conference "Applied Mathematics in our Changing World",
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чтения – XII", Воронеж, 3-9 мая, 2001.
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