VERLAN A.F., SIZIKOV V.S., MOSENTSOVA L.V.

ABSTRACT

An algorithm for solving a system of linear integral equations I kind of multidimensional ill-posed increase the resolving power the antenna by modeling experiments. The algorithm is implemented and analyzed by a program on Matlab.

KEYWORDS

system of linear integral equations, regularization, Tikhonov method, the regularization parameter. 

REFERENCES

1. Tikhonov, A.N., Goncharskiy, A.V., Stepanov, V.V. and  Yagola, A.G. (1990), Chislennye metody resheniya nekorrektnykh zadach  [Numerical methods for solving ill-posed problems],  Nauka, Moscow, Russia.
2. Morozov, V.A. and  Grebennikov, A.I.(1992),  Metody resheniya nekorrektno postavlennykh zadach: algoritmicheskiy aspekt  [Methods for solving ill-posed problems: algorithmic aspects], Izd-vo MGU, Moscow, Russia.
3. Lavrentyev, M.M. (1962), O nekotorykh nekorrektnykh zadachakh matematicheskoy fiziki  [Some ill-posed problems of mathematical physics], Izd-vo AN SSSR,Novosibirsk, Russia.
4. Engl, H.W., Hanke, M. and  Neubauer, A. (1996), Regularization of Inverse Problems, Kluwer,   Dordrecht. 
5. Nashed, M.Z. and  Scherzer, O. (1998), “Least Squares and Bounded Variation Regularization with Non-differentiable Functional”,  Numer. funct. anal. and optimiz, Vol. 19, no. 7, 8, pp. 873-901.
6. Vasin, V.V. (2001), “Regularization and discrete approximation of ill-posed problems in the space of functions of bounded variation”, DAN, Vol. 376, no. 1, pp. 6-11.
7. Antonova, T.V. (2002), “Recovery of Function with Finite Number of Discontinuities by Noised Data”, J. Inverse and Ill-Posed Problems,  Vol. 10, no.  2, pp. 1-11.
8. Starkov, V.N.(2002), Konstruktivnyye metody vychislitelnoy fiziki v zadachakh interpretatsii [Constructive methods of computational physics in problems of interpretation], Naukova dumka,Kiev, Ukraine.
9. Verlan, A.F. and  Sizikov, V.S. (1986), Integralnyye uravneniya: metody, algoritmy, programmy  [Integral equations: methods, algorithms, programs], Naukova  dumka, Kiev, Ukraine.
10. Kojdecki, M.A. (2000), “New criterion of regularisation parameter choice in Tikhonov's method”, Biuletyn WAT (Biul. Mil. Univ. Technol.),  Vol. 49, no. 1 (569), pp. 47-126.
11. Sizikov, V.S. (2011), Obratnyye prikladnyye zadachi i MatLab  [Inverse application tasks and MatLab], Lan, St. Petersburg, Russia.
12. Mosentsova, L.V. (2009), “Implementation of modeling method for solving Fredholm equations of type I in the MATLAB”, Integralnyye uravneniya.  Sb. tezisov konf. [Integral equations.  Proc. Theses Conf.], Kiev, Izd. IPME, 2009, pp. 110-112.

Full text: PDF (in Russian)

EVDOKIMOV V.F., PETRUSHENKO E.I., KUCHAEV V.A.

ABSTRACT

The scalar system of integral equations (ScSIE) obtained in [1—3] will be transformed taking into account symmetries on Y coordinate in the projections of stator magnetic-field sources density k SC. The range of obtained ScSIE definition is part of stator magnetic core surface, lying higher than symmetry plane XOY and at the right of coordinate plane XOZ. This circumstance reduces considerably the calculations volume, related to matrix drafting of the approximating algebraic
system and its decision, substantially.

KEYWORDS

integral model, three-dimensional rotating magnetic field, symmetrical components, symmetry relations, electromagnetic stirrer, magnetic wire, a scalar system of integral equations. 

REFERENCES

1. Evdokimov, V.F., Kuchaev, A.A., Petrushenko, E.I. and Kuchaev V.A. (2012), “Model of  three-dimensional  magnetic field of the stator of cylindrical electromagnetic stirrer with allowance for magnetization  currents  distribution  on the magnetic circuit surface. I”, Elektronnoe modelirovanie, Vol. 34, no.  1, pp. 48-51.

2. Evdokimov, V.F., Kuchaev, A.A., Petrushenko, E.I. and Kuchaev V.A.  (2012), “Model of three-dimensional  magnetic field of the stator of cylindrical electromagnetic stirrer with allowance for magnetization  currents  distribution  on the magnetic circuit surface. II”, Elektronnoe modelirovanie, Vol. 34, no.  2, pp. 51-75.

3. Evdokimov, V.F., Petrushenko, E.I. and  Kuchaev V.A. (2012),  “Integral model  of three-dimensional  rotating magnetic field of the stator of cylindrical EMF on the basis of  symmetric components. I”, Elektronnoe modelirovanie, Vol. 34, no. 6, pp. 3-15.

Full text: PDF (in Russian)

K.N. Murty 1, M.V. Krishna, P. Ramesh
Department of Science and Humanities,
Sreenidhi Institute of Science and Technology
(Yamnampet, Hyderabad — 501301 (A.P.) India,
This email address is being protected from spambots. You need JavaScript enabled to view it.)

ABSTRACT

In the present article, Sylvester matrix first order differential system and matrix first order integro-differential system are studied. A set of sufficient conditions for controllability and complete controllability of the system is presented. As a necessary tool, a variation of parameter formula is developed for the non-linear Sylvester system.

KEYWORDS

control function, resolvent matrix, sylvester system, integro-differential equation, Fubini’s theorem, Volterra integro-differential equation, nonlinear systems. 

REFERENCES

1. Murty K.N., Howell G., Sivasundaram S. Two multi-point nonlinear Lyapunov systems. Existence and uniqueness // J. Math. Anal. Appl. — 1992. —167. — P. 505—512.
2. Lakshmikantham V., Deo S.G. Method of Variation of Parameters for Dynamic Systems.—Vol. 1. — Gordon and Breach Science Publishers, 1998.
3. Yamamoto Y. Controllability of nonlinear systems// J. of Optim. Theory and Appl.—1977.—22. — P. 41—49.
4. Miller R.K. On the linearization of Volterra integral equations// J. Math. Anal. Appl. —1968.— 23. — P. 198—206.
5. Barnett S. Matrix differential equations and Kronecker product//SIAM Appl. Math. —1973.— 14. — P. 1—5.

Full text: PDF (in Russian)

TIMCHENKO L.I., SHPAKOVICH V.V., KOKRYATSKAYA N.I.

ABSTRACT

The authors of the article consider conditions, necessary for development of the method and computer facilities for parallel-hierarchical image transformation, using highly productive GPUadapters. The mathematical models for the parallel-hierarchical (PH) network and a method for PH network training to recognize dynamic patterns have been developed.

KEYWORDS

parallel-hierarchical transformation, training on the network, moving images, normalizing equation, classification, laser lines.

REFERENCES

1. Adinets, A. and  Voevodin, Vl. (2008), “Graphic challenge supercomputers”, Otkrytye sistemy, no.  4. available at: http://www.osp.ru/os/2008/04/5114497/.
2. Skribtsov, P.V. and  Dolgopolov, A.V. (2007), “Performance comparison of graphics cards and CPU in the calculations for large volumes of data to be processed”,  Neyrokompyutery: razrabotka, primenenie,    no. 9, pp. 421-425.
3.“Acceleware released the world's first commercially available cluster based on GPU NVIDIA”, (2009),  Zhurnal iXBT.com.,  № 10, available at: http://www.ixbt.com/news/all/index.shtml?10/63/33.
4. Chitty, D.M. (1991), “A data parallel approach to genetic programming using programmable graphics hardware”, Proc. of the 9th annual conf. on genetic and evolutionary computation, “GECCO 07”, Vol. 2, pp. 1566-1573.
5. Luo, Z., Liu, H. and  Wu, X. (2005), “Artificial neural network computation on graphic process unit”,   Proc. of the IEEE International Joint Conf. on Neural Networks, IJCNN '05,  Vol. 1, pp. 622-626.
6. Li, J.M., Wan, D.L., Chi, Z.X. and  Hu, X.P. (2006), “A parallel particle swarm optimization algorithm based on fine-grained model with GPU accelerating”,  J. of Harbin Institute of Technology, Vol. 38, no.  12, pp. 2162-2166.
7. Xu, R. and  Wunsch, II D.C. (2008), Clustering,  IEEE-Hoboken, Wiley Press, NJ.
8. Everitt, D., Landau, S. and  Leese, M. (2001), Clustering analysis. 4th edition, Arnold, London, UK.
9. Wunsch, II D.C. (2009), “ART properties of interest in engineering applications”, Proc. IEEE. INNS International Joint Conf. on Neural Networks, Atlanta, GA, 2009.
10. Knuth, D. (1997), The Art of Computing Programming: Fundamental Algorithms. 3rd Edition, Vol. 1. Addison-Wesley.
11. Martnez-Zarzuela, M., Pernas, F., de Pablos, A. and et al. (2009), “Adaptative Resonance Theory Fuzzy Networks Parallel Computation Using CUDA”, Bio-Inspired Systems: Computational and Ambient Intelligence, Vol. 5517, pp. 149-156.
12. Gorchetchnikov, M., Ames, H. and  Versace, M. (2008), “Simulating Biologically Realistic Neural Models on Graphics Process Units”,  ICCNS, Boston, MA.
13. Meuth, R.J. (2007), “GPUs surpass computers at repetitive calculations”, Potentials, IEEE,  Vol. 26, no.  6, pp. 12-23.
14. Martin, A.J., Burns, S.M., Lee, T.K. and et al. (1986), “The design of an asynchronous microprocessor”, Advanced Res, VLSI: Proc. Decennial Caltech Conf., MIT Press Cambridge, MA.
15. Sejun, Kim. (2003), A GPU based Parallel Hierarchical Fuzzy ART Clustering, Advanced Res.
16. Prett, U. (1982), Tsifrovaya obrabotka izobrazheniy. V 2-kh kn. [Digital Image Processing. In 2 Vol.], Mir, Moscow, Russia.
17. Primeneniye tsifrovoy obrabotki signalov. Pod red. Oppengeyma, E. (1980), [The use of digital signal processing. Ed. Oppenheim, E.],   Mir, Moscow, Russia.
18. Pogrebnoy, V.A. (1984), Bortovye sistemy obrabotki signalov [On-board signal processing system], Naukova dumka, Kiev, Ukraine.
19. Timchenko, L.I., Melnikov, V.V. and  Kokryatskaya, N.I.(2011), “Method of organizing parallel hierarchical network for pattern recognition”,  Kibernetika i sistemnyy analiz, no. 1, pp. 152-163.

Full text: PDF (in Russian)