Scientific activity of members of Computer Science and ... · integro-differential systems, Lecture Series on Computer and Computational Sciences, Vol. 8, 2007, pp.493-496. ... Stability

Scientific activity of members of Computer Science and Mathematics Department

in 2007

Grants of the Israel National Science Foundation

1. A. Domoshnitsky. Nonoscillation intervals in the theory of functional differential equations. Application No.: 1002/06 Abstract: Nonoscillation intervals are very important in the theory of the linear thn order

ordinary differential equation

1

0

)()( ],0[),()()()())((n

i

ii

n ttftxtptxtMx . The

problems of existence and uniqueness of solutions of the interpolation boundary value problems for this equation, the problems of positivity (or a corresponding regular behavior) of their Green’s functions, the problems of the Polia-Mammana factorization (i.e. a representation of the operator M as a product of first order differential operators), the problems of Lyapunov’s stability of a second order equation with periodic coefficients, the problem of oscillatory (according to Gantmaher-Krein) Green’s functions and many others are connected with the nonoscillation intervals of the corresponding homogeneous equation

0Mx . In the known monographs on nonoscillation of functional differential equations there is no any connection between these topics. The results on nonoscillation were formulated only as existence of eventually positive solutions of functional differential equations on semiaxis. In this project we try to create a theory of nonoscillation for functional differential equations. We start with a definition of homogeneous equations, preserving their finite dimensional fundamental systems. This allows us to introduce and then to use such standard notions of the theory of ordinary differential equations as the fundamental system, the Wronskian, the Green’s function also in a study of functional differential equations. Note that in our approach many methods of the theory of ordinary differential equations can be applied. We also develop our own procedures reducing problems for functional differential equations to the standard problems of functional analysis. Our nonoscillation theory of functional differential equations consists of two parts: the first is to discover nonoscillation of the interval ],0[ and the second – to find various corollaries and applications of nonoscillation. We obtain results about existence and uniqueness of solutions, positivity/negativity of Green’s functions of boundary value problems as a corresponding corollaries of nonoscillation. In many cases we prove even equivalence of nonoscillation and positivity/negativity of Green’s functions. We find conditions of validity of the maximum principle and the classical Sturm’s separation theorem (between two adjacent zeros of a nontrivial solution there is one and only one zero of each other) for second order functional differential equations. We propose a corresponding analog of the Polia-Mammana factorization and use it to get positivity of Green’s functions in cases of integrals of the solution )(tx in the boundary conditions. We consider the comparison problems for systems of functional differential equations, which are actually the problem of positivity of the elements of the Cauchy and Green’s matrices, and obtain assertions about their positivity. Then we use this fact in study of the exponential stability. We define a principle of partial monotonicity (comparison of only several components of the solution vector), and reduce it to positivity of elements in only several lines of the Green’s matrix and to nonoscillation of several components of the solution vector.

2. T. Shamir, M. Wagner with cooperation of B. Ben-Moshe. Visual evaluation of velocity – Testing a new theory based on a mathematical model. An interdisciplinary research in Applied Mathematics: Mathematical Psychology (Grant number 666/07). Abstract: When we see a moving object, it is often difficult to determine its velocity only by sight. Distant objects seem to move more slowly than they really do, and constant speed does not look constant. It is important to know how we perceive the velocity of an object in order to make appropriate decisions and take action. Visual perception is a complicated process involving many physiological factors besides the reception of external optical information. How do we evaluate what we see? Here we propose a simple mathematical model on visual interpretation of velocity. In order to isolate the basic effect, it pertains to a stationary observer and a single isolated object moving on a blank background, along any smooth and simple trajectory. If the observer is stationary, then an angular velocity vector )(t of the optic flow field is induced, relative to the cyclopean eye of the observer. Denote the position vector relative to the observer by )(tR , and k is a visual scaling coefficient that depends on the frontal distance, on contrast and other stimulus properties, as well as on the individual observer. The model states that the perceived instantaneous velocity vector is estimated approximately as the scaled vector cross product Rv kp . This mathematical model has interesting qualitative consequences, which can explain some familiar phenomena of velocity perception. The purpose of this research is to test this theory by psychophysical experiments.

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).סופית

.ר ניר שוולב"ח בשיתוף ד"ש 200,000, משרד הביטחון: פרויקט רובוטים זעירים .3 .ח"ש 25,000: ובדיקה של מטלות תכנות, נק מחקר בנושא בדיקת העתקותמע: מיטל .4

, )ר מיכאל ווגנר“בשיתוף ד(סימולטורים לנהיגה : שני מענק בנושאים: קרן פנימית בטיחות בדרכים .5 ח "ש 36,000כ "סה: הכללה של אור ברקס

Patents

1. B. Ben-Moshe, L. Serruya and A. Shamir. Image Compression Terrain Simplification, patent pending IL182367

Published books

1. G. Kresin and V. Maz’ya. Sharp Real Part Theorems. A Unified Approach, Lecture Notes in

Mathematics, v. 1903, Springer Verlag, Berlin-Heidelberg-New York, 2007.

Accepted books

1. F. Assous and P. Ciarlet, Jr. Numerical solution Electromagnetics in bounded domains. Mathematical analysis, numerical methods and applications, in preparation for the Scientific Computation series of Springer-Verlag. 2. J. Chaskalovic, To be published in October 2008, Finite element method applied to engineering sciences, Contracted with Springer – Verlag.

3. J. Chaskalovic, To be published in October 2009, Data mining for engineering and marketing applications, Contracted with Springer – Verlag.

Published articles 1. F. Assous and P. Ciarlet, Jr. Numerical solution to Maxwell's equations in singular waveguides, Lecture Note in Engineering and Computer Sciences, O. Castillo, C. Douglas, D.D. Feng, J.-A. Lee (eds), pp. 2366-2371, 2007. 2. A. Domoshnitsky. Maximum principle for functional equations in space of discontinuous functions of three variables, Journal of Mathematical Analysis and Applications, 329 (2007), pp. 238-267. 3. A. Domoshnitsky and Ya. Goltser. Positivity of solutions to boundary value problems for infinite functional differential systems, Mathematical and Computer Modelling, 45, No. 11-12, June 2007, pp. 1395-1404. 4. A. Domoshnitsky and R. Koplatadze. On the Kneser-type solutions for two-dimensional linear differential systems with deviating arguments, Journal of Inequalities and Applications, vol. 2007, article ID 52304, 22 pages, doi: 10.1155/207/52304. 5. A.Domoshnitsky, Ya.Goltser and D.Ophir, Numerical approach to studying stability of integro-differential systems, Lecture Series on Computer and Computational Sciences, Vol. 8, 2007, pp.493-496. 6. L.Berezansky, E.Braverman, A.Domoshnitsky, First order functional differential equations: nonoscillation and positivity of Green's functions, Functional Differential Equations, vol. 15, 2008, No. 1-2, 57-94. 7. R.Yavich, N. Davidovich, B. Starichenko, L. Mahrov, Management of the student's educational activities on the basis of the network information technologies. Education and Science, vol. 6, December 2007, pp 3-15, (the journal is refereed and recognized by the Russian AC) 8. L. S

. Grinblat. On sets not belonging to algebras, The Journal of Symbolic Logic, 72 (2007),

pp. 483-500. 9. G. Kresin and V. Maz’ya. Sharp Bohr’s type real part estimates, Computational Methods and Functions Theory, 7, N. 1 (2007), pp. 151-165.

10. G. Kresin. Hadamard-Borel-Caratheodory and Bohr theorems for non-concentric disks, Functional Differential Equations, 14, N. 2-3-4 (2007), pp. 293-314. 11. G. Kresin and V. Maz’ya. Sharp pointwise estimates for solutions of strongly elliptic second order systems with boundary data from Lp, Applicable Analysis, 8 6 , N o .7 ( 2 007 ) , p p . 7 83 - 805 .

12. Levit, V. E. and Mandrescu, E. (2007). A Family of Graphs whose Independence Polynomials are both Palindromic and Unimodal, Carpathian Journal of Mathematics, Vol. 23, No. 1-2, 108-116. 13. Levit, V. E. and Mandrescu, E. (2007). Triangle-Free Graphs with Uniquely Restricted Maximum Matchings and their Corresponding Greedoids, Discrete Applied Mathematics, Vol. 155, Issue 18, 2414 – 2425. 14. Levit, V.E. and Mandrescu, E. (2007). Matrices and -Stable Bipartite Grap, Journal of Universal Computer Science, Vol. 13, No. 11, 1692-1706. 15. Levit, V. E. and Mandrescu, E. (2007). Some Structural Properties of Very Well-Covered Graphs, Congressus Numerantium, Vol. 186, 97-106. 16. Kempner, Y. and Levit, V. E. (2007). A Geometric Characterization of Poly-Antimatroids, Electronic Notes in Discrete Mathematics Vol. 28, 357-364 17. Levit, V. E. and Mandrescu, E. (2007). The Intersection of All Maximum Stable Sets of a Tree and its Pendant Vertices, Discrete Mathematics, doi: 10.1016/j.disc.2007.10.001 (accepted) 18. M. Radune, D. Ophir. A. Lugovskoy, M. Zinigrad, D. Eliezer. A Sulfur Diffusion Investi-gation in Metal and Oxide Phases, Defect and Diffusion Forum Vols. 258-260, January 2007. 19. E. Shmerling. Stability of Solutions of Linear Systems of Differential Equations with Periodic Coefficients, Functional Differential Equations, 14, No 1, 2007, pp. 117-122. 20. X. L. Nguyen, J. Chaskalovic and al., 2007, Residual subjective daytime sleepiness under CPAP treatment in initially somnolent apnea patients: A pilot study using data mining methods, Sleep medicine. 21. Boaz Ben-Moshe, Paz Carmi, Matthew J. Katz: Approximating the Visible Region of a Point on a Terrain. GeoInformatica 12(1): 21-36 (2008) 22. Boaz Ben-Moshe, Matthew J. Katz, Joseph S. B. Mitchell: A Constant-Factor Approximation Algorithm for Optimal 1.5D Terrain Guarding. SIAM J. Comput. 36(6): 1631-1647 (2007) 23. Boaz Ben-Moshe, Binay K. Bhattacharya, Qiaosheng Shi, Arie Tamir: Efficient algorithms for center problems in cactus networks. Theor. Comput. Sci. 378(3): 237-252 (2007) 24. Boaz Ben-Moshe, Liad Serruya, Ariel Shamir: Image Compression Terrain Simplification. CCCG 2007: 125-128 25. Boaz Ben-Moshe, Matthew J. Katz, Igor Zaslavsky: Distance Preserving Terrain Simplification - An Experimental Study. CCCG 2007: 129-132 26. Boaz Ben-Moshe, Binay K. Bhattacharya, Sandip Das, Daya Ram Gaur, Qiaosheng Shi: Computing a planar widest empty alpha-siphon in o(n3) time. CCCG 2007: 33-36

27. Boaz Ben-Moshe, Yefim Dinitz: Fast Additive Constant Approximation Algorithms for the Safe Deposit Boxes Problem with Two and Three Currencies. CCCG 2007: 53-56 28. Yehuda Ben-Shimol, Boaz Ben-Moshe, Yoav Ben-Yehezkel, Amit Dvir, Michael Segal: Automated antenna positioning algorithms for wireless fixed-access networks. J. Heuristics 13(3): 243-263 (2007)

Accepted articles 1. F. Assous and P. Ciarlet, Jr. Solving Vlasov-Maxwell equations in singular geometries, to appear in Math.and Comput. in Simul. 2. B. Ben-Moshe, B. Bhattacharya, Qiaosheng Shi, A. Tamir. Efficient Algorithms for Cen-ter Problems in Cactus Graphs, to appear in Theoretical Computer Science.

3. B. Ben-Moshe, P. Carmi and M.J. Katz. Approximating the Visible Region of a Point on a Terrain, to appear in GeoInformatica. 4.E. Shmerling and K.J. Hochberg. Stability of Stochastic Jump-Parameter Semi-Markov linear Systems of Differential Equations, to appear in Stochastics : An International Journal of Probability and Stochastic Processes. 5.Levit, V. E. and Mandrescu, E. (2007). The Intersection of All Maximum Stable Sets of a Tree and its Pendant Vertices, Discrete Mathematics, doi: 10.1016/j.disc.2007.10.001 (accepted) 6.A.Domoshnitsky, Maximum principles and nonoscillation intervals for first order Volterra functional differential equations, 47 p., Dynamics of Continuous, Discrete and Impulsive Systems. 7. Goltser Ya. Litsyn E. Non-linear Volterra IDE, infinite systems and normal form of ODE, Nonlinear Analysis, TMA, series A.

Submitted articles 1. E. Shmerling and M. Korenblit. SKoAl Algorithm for Integration over a Convex Polyhed- ron, ACM Transactions on Mathematical Software, 2007. 2. E. Shmerling. Multi-Stage Interval Estimation of Binomial Coefficient, Journal of the American Statistical Association, 2007. 3. T. Shamir, B. Ben Moshe & M. Wagner, Visual distortions of velocity are not all illusions but a result of geometric projection, case of isolated object moving horizontally on the fronto-parallel plane. Accepted (subject to revision), Biological Cybernetics Journal 2008.

Papers published in Proceedings of Conferences

1. F. Assous and M. Mikhaeli. Nitsche type method for approximating boundary conditions in the static Maxwell equations, MIC 2007, L. Bruzzone Ed., pp. 402-407, 2007.

2. M. Barabash, I. Gurevich and L. Yanovsky. Usage of computerized environment in the course "Plane Transformations and Constructions in Geometry", The Proceeding of The Fifth International Conference on Teaching Education at a Crossroads, 2007.

3. B. Ben-Moshe and Y. Dinitz. Fast Additive Constant Approximation Algorithms for Safe Deposit Boxes Problems with Two or Three Currencies, Proc. of the 19th Canadian Conference on Computational Geometry, 2007.

4. B. Ben-Moshe, L. Serruya and A. Shamir. Image Compression Terrain Simplification – An Experimental Study, Proc. of the 19th Canadian Conference on Computational Geometry, 2007.

5. B. Ben-Moshe, M. J. Katz and I. Zaslavsky. Distance Preserving Terrain Simplification –An Experimental Study, Proc. of the 19th Canadian Conference on Computational Geometry, 2007.

6. B. Ben-Moshe, B. K. Bhattacharya, S. Das, D. R. Gaur and Qiaosheng Shi. Computing a planar widest empty α-siphon in O(n3) time, Proc. of the 19th Canadian Conference on Computational Geometry, 2007.

7. E. Shmerling. Algorithm for Defining the Distribution of Zeros of Random Polynomials, Proceedings of the 11-th WSEAS International Conference on Computers, Greece,2007,

pp. 657-660. 8. T Shamir, M Wagner and B. Ben Moshe, Hyperbolic velocity for straight line motion seems constant, ECVP 2007, published in Perception, supplement 2007.

9.E. Shmerling and A. Hirshberg. Two-Stage Binomial Fixed-Width Interval Estimation, to appear in Proceedings of the 56-th Biennial Session of the ISI-2007.

10.Goltser Ya. Singular perturbed Integro-Differential Volterra Equations and Drazin Inverse of Singular Matrices, EQUADIFF 2007, Vienna, Austria, 2007

11.A. Vanheuverzwyn and J. Chaskalovic, Innovation in estimation - A reliable approach for radio audience indicators, International Congress of ESOMAR (Dublin) ,2007.

12.R. Yavich, The efficiency using e-learning technologies in tracing the students' learning processes, Ariel University Center of Samaria Fourth International Conference on Contemporary Issues in Higher Education: Pedagogical Aspects of Emerging Methodologies in Higher Education, September 2007.

13. R. Yavich, COMPUTER AS THE BASIS OF NEW ATTITUDE AND NEW STYLE OF THINKING- Increase the efficiency and preparation of physics and computer science teachers in modern conditions - International scientifically-practical conference, Ural state pedagogical university, Russia, April 2007

14. R. Yavich and L. Mohrova, Inquiries of mathematical pedagogical education «Provision of information of pedagogical education», The materials of the international scientific-practical conference, Part II, Yekaterinburg, Russia, 29-31 January 2007

Participation in Conferences 1. F. Assous. Nitsche type method for approximating boundary conditions in the static Maxwell equations. The 26th International Conference on Modelling, Identification and Control (MIC'07), (February 2007). 2. F. Assous. Numerical solution to Maxwell's equations in singular waveguides. The IAENG Int. Conf. on Computer Science (IMECS07), Hong Kong, China, (March 2007).

3. M. Barabash, I. Gurevich and L. Yanovsky. Usage of computerized environment in the course "Plane Transformations and Constructions in Geometry", The Fifth International Conference on Teaching Education at a Crossroads, 2007. 4. B. Ben-Moshe and Y. Dinitz. Fast Additive Constant Approximation Algorithms for Safe Deposit Boxes Problems with Two or Three Currencies, The 19th Canadian Conference on Computational Geometry, 2007.

5. B. Ben-Moshe, L. Serruya and A. Shamir. Image Compression Terrain Simplification – An Experimental Study, The 19th Canadian Conference on Computational Geometry, 2007.

6. B. Ben-Moshe, M. J. Katz and I. Zaslavsky. Distance Preserving Terrain Simplification –An Experimental Study, The 19th Canadian Conference on Computational Geometry, 2007.

7. B. Ben-Moshe, B. K. Bhattacharya, S. Das, D. R. Gaur and Qiaosheng Shi. Computing a planar widest empty α-siphon in O(n3) time, The 19th Canadian Conference on Computational Geometry, 2007.

8. L. S

. Grinblat. Theorems with uniform conditions on sets not belonging to almost σ -algebras, 22nd Summer Conference on Topology and Its Applications, Castelon, Spain, 2007. 9. G. Kresin. Sharp Real Part Theorems, Sixth Negev Workshop on Applied Mathematics, Sede-Boqer, Israel, 2007.

10. D. Ophir, I. Schlissel and B. Tamir. Body Movement Identification (BMI), Submitted to (ECIW-2007) The 6th European Conference on Information , Warfare and Security, Defence College of Management and Technology, Shrivenham, UK, 2-3 July 2007.

11. E. Shmerling. Algorithm for Defining the Distribution of Zeros of Random Polynomials,11-th WSEAS International Conference on Computers, Greece, 2007. 12. E. Shmerling. Two- Stage Binomial Fixed-Width Interval Estimation, 56-th Biennial Session of the International Statistical Institute, Lisbon, 2007. 13. A. Vanheuverzwyn and J. Chaskalovic, Innovation in estimation - A reliable approach for radio audience indicators, International Congress of ESOMAR, Dublin, 2007.

,השנתי של העוסקים בהוראההכנס , תיאורו הדינאמי והוויזואלי חשבון דיפרנציאלי ואינטגראלי .דן אופיר . 13 cham.technion.ac.il-http://kesher 26.3.2007, לעל יסודי בישראלבמחקר ובפתוח בתחום המתמטיקה

התקבל לכנס !?תורת המשקים ועוד, אלקטרוניקה, מה משותף לכלכלה .גדול. נ, אללי. מ, אופיר. ד .14 John Braude 31.05.07, Development of Initiatives for Promoting Learning in Higher Education,

College ORT Braude College, Karmiel , Israel, May 31, 2007.