Families:
Littlewood and Paley wavelet
Haar wavelet
Shannon wavelet
Mexican Hat wavelet

Applications:
Wavelet solution of differential equations,
Solitary waves evolution,
Sequence analysis,
Multifractal analysis
Refinable integrals, Connection coefficients

Books

C.Cattani,M. Li, C. Toma, (Eds.) Short Range Phenomena: Modeling, Computational Aspects,and Applications”Specialissue of the journal Mathematical Problems in Engineering, Hindawi, Article ID 761081,(2008). http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/761081

C. Cattani,J.J.Rushchitsky, Wavelet and Wave Analysis as applied to Materials with Micro or Nanostructure, Series on Advances in Mathematics for Applied Sciences,World Scientific, Singapore, 74 (2007). 456 pp. http://www.worldscibooks.com/mathematics/6497.html , Review [1]

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Journals

C. Cattani, “Wavelet analysis of Prime Numbers Distribution”, to appear on NBU-Math Journal,
(2011).

C. Cattani, “Wavelet analysis of Self Similar Functions”,
Journal of Dynamical Systems and Geometric Theories, vol. 8 (2) (2010).

C.Cattani, “Shannon Wavelets for the solution of Integro-Differential Equations”, Mathematical Problems in Engineering, vol. 2010, Article ID 408418, (2010), 1–22. doi:10.1155/2010/408418

C. Cattani, A. Kudreyko, “Application of periodized harmonic wavelets towards
solution of eigenvalue problems for integral equations”, MPE Special Issue NVASC (2010).

C. Cattani, A. Kudreyko, “Harmonic wavelet method towards
solution of the Fredholm type integral equations of the second
kind”, Applied Mathematics and Computation 215 (2010) 4164-4171.

C. Cattani, A. Kudreyko,
“Application of wavelet-basis for solution of the Fredholm type integral equations”, Computational Science and its Applications, D. Taniar et Al.(Eds.) ICCSA, Lecture Notes in Computer Science, Springer-Verlag Berlin Heidelberg, LNCS 6017, Part 2, (2010), 155-163.

C. Cattani, “Wavelet Based Approach to Fractals and Fractal Signal Denoising”, Transactions on Computational Sciences Journal VI, LNCS 5730 (2009) 143-162.

C.Cattani, “Harmonic Wavelet Analysis of a Localized Fractal”, International Journal of Engineering and Interdisciplinary Mathematics 1 (1) (2009), 35-44. Download

C.Cattani, “Wavelet Analysis of Fractals”, Bulletin of the Chelyabinsk State University 8 (146) (2009) 25-27.

C.Cattani, “Harmonic Wavelet Approximation of Random, Fractal and High Frequency Signals”, Telecommunication Systems (2009) 207–217..

C.Cattani, “Harmonic wavelet analysis of nonlinear waves”,Technische Mechanik, 28 (2), (2008) 166–181.
http://www.uni-magdeburg.de/ifme/zeitschrift_tm/2008_Heft2/07_Cattani.pdf

C.Cattani,“Harmonic Wavelet Solution of Poisson’s Problem”,Balkan Journal of Geometry and its Applications 13, No. 1 (2008) 27-37. http://www.mathem.pub.ro/bjga/v13n1/v13n1.htm

C.Cattani, “Harmonic Wavelet Solution of Poisson’s Problem with a localized source”, Atti dell’Accademia Peloritana dei Pericolanti, Classe di Scienze, Matematiche e Naturali, Vol. LXXXVI (2008).
http://antonello.unime.it/atti/2008_2/c1a0802003.pdf

List of Pubblications

* WAVELETS
* NONLINEAR AND SOLITARY WAVES
* BIOMATHEMATICS
* HISTORY OF SCIENCE
* RELATIVITY
* OTHER

C.Cattani, “Shannon Wavelets Theory”,Mathematical Problems in
Engineering, vol. 2008, Article ID 164808, 24 pages, (2008).
http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/164808

J.J.Rushchitsky, C.Cattani, E.V. Terletska, Y.Symchuk, “Elastic
Wavelets and their Application to Solitary Wave Propagation”,
Rendiconti Accademia Peloritana dei Pericolanti,LXXXVII,1(2008) 1-17.
http://antonello.unime.it/atti/2008_1/c1a0801004.pdf

C.Cattani, “On the scale dependence of the structural models for
nanocomposite materials”,Materiale Plastice 44(4),(2007), 269–272.
Download

C.Cattani, “Connection Coefficients of Shannon Wavelets”,Mathematical
Modelling and Analysis, vol. 11 (2),(2006), 1–16.
http://inga.vgtu.lt/~art/k_m11_fileslist.php?key_m=832

C.Cattani,“Wavelet approach to Stability of?Orbits
Analysis”,International Applied Mechanics, 42,6,(2006),136-142.
http://www.springerlink.com/content/f07l68h15j272j0n/?p=3cdb608c818c49869ed7e30a766ac734π=17

C.Cattani,I. Bochicchio,“Wavelet Analysis of Chaotic Systems”,Journal of ?Interdisciplinary Mathematics, 9, 3, (2006) 445-458.

C.Cattani,“Harmonic Waveletstowards Solution of Nonlinear PDE”,Computers and Mathematics with Applications, 50, 8-9
(2005), 1191-1210. doi:10.1016/j.camwa.2005.07.001

C.Cattani, A.Ciancio,“Wavelet Clustering in? Time Series Analysis”,Balkan Journal of Geometry and Its Applications (BJGA), 10, 2, (2005), 33-44. http://ftp.fi.muni.cz/pub/muni.cz/EMIS/journals/BJGA/10.2/b10-cb.pdf

C.Cattani and S. V. Rogosin, “Harmonic Wavelets and their certain properties”,Izv. Nat. Akad. Nauk ?Belarusi (Proceedings
of the Belarussian Academy of Science), ser. Physical-Mathematical Sciences, 2 (2005), 35-41 (in Russian). Download

C.Cattani, “Haar Wavelet based Technique for Sharp Jumps Classification”,Mathematical and Computer Modelling 39, (2004)
255-279. clear doi:10.1016/S0895-7177(04)90010-6

C.Cattani, “Haar wavelets based technique in evolution problems”,Proc. Estonian Acad. of Sciences, Phys. Math., 53, 1 (2004) 45-63. http://www.kirj.ee/public/va_fm/s04-1-fm.htm , Download

C.Cattani and L.M. Sanchez Ruiz, “Discrete Differential Operators in Multidimensional Haar Wavelet Spaces”,International Journal of Mathematics and Mathematical Sciences, No. 44, (2004) 2347-2355.
http://www.emis.de/journals/HOA/IJMMS/2004/41-442347.pdf

C.Cattani, “Harmonic Wavelet Solutions of the Schr dinger Equation”,International Journal of Fluid Mechanics Research 5,(2003), 1-10. http://www.begellhouse.com/journals/71cb29ca5b40f8f8,3002b98831d48002.html

C.Cattani, “Multiscale Analysis of Wave Propagation in Composite Materials”,Mathematical Modelling and Analysis, vol. 8, Nr. 4 (2003) 267-282. http://inga.vgtu.lt/~art/k_m08_fileslist.php?key_m=750

C.Cattani, “The Wavelet-based technique in dispersive wave propagation”,International Applied Mechanics, 39, no. 4 (2003), 493-501. http://www.springerlink.com/content/u81865p0217×5075/?p=3cdb608c818c49869ed7e30a766ac734π=10

C.Cattani, “Wavelet Analysis of Dynamical Systems”,Electronics and Communications, 17, (2002), 115-124.

C.Cattani, “Wavelet Solutions of Evolution Problems”,Atti Accademia Peloritana dei Pericolanti, Classe I, Scienze Fis.Mat. e Nat., vol. LXXX (2002), 21-34.

C. Cattani and A. Ciancio, “Wavelet analysis of linear transverse acoustic waves”,Atti Accademia Peloritana dei Pericolanti, Classe I, Scienze Fis.Mat. e Nat., vol. LXXX (2002), 83-104.

C. Cattani and E.Laserra, “Wavelets in the Transport Theory of Heterogeneous Reacting Solutes”,Applied Hydromechanics, vol. 4 (76), n.3 (2002), 75-77,

C. Cattani,“Wavelet-Ritz Discretization of Variational Problems”,Researches on Numerical Methods of Analysis and Optimization, Vol. 3, nr.1(5), (2001), 3-5.

C. Cattani,“Haar Wavelet Spline”, Journal of Interdisciplinary Mathematics vol.4, No. 1, (2001), 35-47.

Proceedings

C. Cattani “Wavelet Extraction of a Pulse from a Periodic Signal”, ICCSA 2008, June 30-July 3, 2008, Perugia, M. Gavrilova et al.(Eds.), Lecture Notes in

Computer Science,LNCS 5072, Part I,Springer-Verlag Berlin Heidelberg (2008) 1202-1211.
http://www.springerlink.com/content/c171563l57mv5qn1/

C. Cattani and A. Kudreyko,“Mutiscale Analysis of the Fisher Equation”, ICCSA 2008, June 30-July 3, 2008, Perugia, M. Gavrilova et al.(Eds.), Lecture Notes in
Computer Science, LNCS 5072, Part I, Springer-Verlag Berlin Heidelberg (2008) 1171-1180.
http://www.springerlink.com/content/38xj6×88877l6802/

C. Cattani, “Wavelet solution for the momentless state equations of an hyperboloid shell with localized stress”, Proceedings of the International Conference on Computational Science and Application, (ICCSA 2007), August 26-30, 2007, Kuala Lumpur, Malaysia, M. Gavrilova et al. (Eds.), Lecture Notes in Computer Science, LNCS 3980, Springer-Verlag Berlin Heidelberg (2007) 490-499.
http://www.springerlink.com/content/x578107657641k3n/

C. Cattani, “Shannon Wavelet Analysis”, Proceedings of the International Conference on Computational Science, ICCS 2007, May 27-30, 2007, Beijing, China, Y. Shi et Al. (Eds.),Lecture Notes in Computer Science, LNCS 4488, Part II, Springer-Verlag Berlin Heidelberg (2007) 982-989. http://www.springerlink.com/content/22634wk7p632307m/

C.Cattani, L.M. Sanchez Ruiz, “On the differentiable structure of Meyer wavelets” Proceedings of the International Conference on Computational Science, ICCS 2007, May 27-30, 2007, Beijing, China, Y. Shi et Al. (Eds.),Lecture Notes in Computer Science, LNCS 4488, Part II, Springer-Verlag Berlin Heidelberg (2007). http://www.springerlink.com/content/3045500614p36333/

C.Cattani, L.M. Sanchez Ruiz, “Revisiting Meyer wavelets” Workshop on Applications of Wavelets to real world problems-IWW 2007, 7-9 June 2007, Istanbul, p.51-57.

C. Cattani and I. Bochicchio, “Wavelet analysis of bifurcation in a competition model”, Proceedings of the International Conference on Computational Science, ICCS 2007, May 27-30, 2007, Beijing, China, Y. Shi et Al. (Eds.), LNCS 4488, Part II, Springer-Verlag Berlin Heidelberg (2007) 990-996. http://www.springerlink.com/content/jk512g84pk73×65g/

C. Cattani, “Multiscale approach to evolution problems”, Proceedings of the International Conference 4th Polyakhov Readings, February 5-9, 2006, St. Petersburg,E. Kustova, A. Polyansky (Eds.), (2006), 55-64.

C.Cattani, “On the optimal wavelet representation of sequences”, International Conference “Potential Theory and Complex Analysis”, May 8-11, 2006 Kiev, O. Limarchenko et al.(Eds.),?Institute of Mathematics of the Ukrainian Academy of Science (2006) 52-59.

C. Cattani, “Wave Propagation of Shannon Wavelets”, International Conference on Computational Science and its Applications (ICCSA 2006), May 8-11, 2006 Glasgow, M.Gavrilova et al.(Eds.), LNCS 3980, Springer-Verlag Berlin Heidelberg (2006), 785-793.
http://www.springerlink.com/content/w73n5xk432276w24/

C. Cattani, “Wavelets in Jumps detection”, International Workshop on Applications of Wavelets to Real World Problems (IWW2005) 17-18 JULY 2005, ITICU, Istanbul, TURKEY, A.H. Siddiqi, S. Alsan, M. Rasulov, O. Oguz and Z. Aslan (Eds.), Istanbul Commerce University Publication, (2005) 121-132.

C.Cattani, “Wavelet solution of Fredholm integral equations”, Proceedings of the International Conference on “Differential Equations and Computer Algebra System”(DE&CAS’2005), Brest October 5-8, Belarus, Part 1, BSTU (2005), 242-249.

C.Cattani, “Wavelet Analysis of Solitary Wave Evolution”,International Conference on Computational Science and its Applications (ICCSA 2005), May 9-12, 2005 Singapore, O. Gervasi et al. (Eds.), Springer-Verlag Berlin Heidelberg (2005), 604-613.
http://www.springerlink.com/content/rl5dkbcm9qe824ph/

C.Cattani, A.Ciancio, “On the Haar Wavelet Analysis of Jumps”, Proceedings of the the 3-rd International Colloquium“Mathematics in Engineering and Numerical Physics” (MENP-3) October 7-9, 2004 Bucharest, Romania, BSG Proceedings 12, C.Udriste and V.Balan (Eds), Balkan Society of Geometers, Geometry Balkan - Press, 2005, 72-81. http://www.mathem.pub.ro/proc/colloq04/M-CAT.PDF

C. Cattani, “Noise Sorting? by a Wavelet Based Technique”, Proceedings of the 7th International Workshop on Complex Systems in Natural and Social Sciences (CSNSS’02), Matrafured, Hungary September 26-29, 2002, E.Hideg, K.Martinas, M.Moreau and D.Meyer Eds., (2003) 47-56.

C.Cattani, “Spike detection and sorting by wavelets”, Mechanics, Mechatronics and Structronics: Proceedings of the First International Congress on Mechatronics - Johannes Kepler University of Linz, Austria, July 3-7, 2002 Ardeshir Guran Ed., World Scientific (2003) 75-80.

C.Cattani, “Wavelets Solving Variational Problems”, Proceedings of the VIII Erouguine Readings, International Conference, Brest (Bielorussia), May 20-23, (2002), 79.