Professor Peter A. McCoy

"He who waits for roast duck to fly into his mouth must wait a very long time."

-Chinese Proverb


Research Interests: Electromagnetics, Wavelets, Approximation and Computational Methods, Signal and Image Processing, Directed Energy, Orthogonal Polynomials and Special Functions


Ph.D.: University of Wisconsin-Milwaukee


Phone: 410-293-6748 Email: pam@usna.edu

Brief Research Biography

My research interests are in Electromagnetics and related Computational and Approximation methods. I have over 60 publications and have made numerous presentations. I have organized and chaired many sessions, special sessions and minisymposia on partial differential equations and their applications at national meetings of the American Mathematical Society and of the Society for Industry and Applied Mathematics. I received research support from the Radar Division, Naval Research Laboratory (Radar Analysis & Target Characteristics), Washington, D.C., Summers FY 1992-1998. I was funded by the ONR, Code 313, Antennas, Propagation and Electromagnetic Interactions, Summer 1999. I was funded by the Materials Science and Technology Division (Directed Energy Effects), Naval Research Laboratory, Summer FY 2000. Support for Summers FY 2001 and 2002 was through ONR's Applied Analysis Program (H-Infinity Methods for Antennas and Electromagnetic Systems DRI). FY 03-05 funding was through the DOD-Navy High Energy Laser/Free Energy Laser Modeling and Simulation Program under the JTO. The FEL is being designed as a weapon for the Navy's new all-electric ship DD(X).

 

My research activities include applications of Orthogonal Polynomials and Special Functions in the area of electromagnetics and Signal Processing. I am also interested in the application of Wavelets to Image Reconstruction and Electromagnetic Scattering. I peer review for the American Mathematical Reviews in the areas of Wavelets, Signal Processing, and Hele-Shaw Flow (over 160 articles and books). I frequently review for Zentralblatt fur Mathematik in the areas of Orthogonal Polynomials and Special Functions, Signal and Image Processing, and Electromagnetics. I referee for the National Science Foundation, the Army Research Office, National Academy of Sciences (Cobase Grants) and consult for the Office of Naval Research.

 

In 1989, I was awarded the Alumni Association Civilian Faculty Award for Excellence in Research. This is an academy wide competition among all faculty. I was also awarded Researcher of the Year by the Academic Dean and Provost, the Department of the Navy medal for exceptionally meritorious service and I was a member of the Navy Meritorious Unit Commendation in 1998.

I have been onboard or underway on over 40 vessels covering virtually every class of ships in the U.S. Navy. I have made site visits to numerous laboratories and government facilities.

Offices

President of the Washington-Baltimore Section of the Society for Industry and Applied Mathematics (SIAM) which includes NOVA, DC, MD & SoDE). The Wash-Balto section has a mailing list of 1,000 and is SIAM's second most active section. Program Director of the SIAM Special Interest Activities Group on Orthogonal Polynomials & Special Functions.


Senator at Large for the Math-Science Division, Faculty Senate, and a member of the Faculty Senate Executive Committee.

Professional Service (2000-Present)

  1.  SIAM Minisymposium ''Special Functions and Orthogonal Polynomials," Chair and co-organizer with Francisco D. Marcellan (Vice President for Research, Univ. Carlos III de Madrid) SIAM annual mtg, Westin Rio Mar Beach Resort and Country Club, Rio Grande, Puerto Rico, July 10-14, 2000.

  1.  SIAM Minisymposium & Panel Member ''Grand Challenges in Electromagnetics,'' as ONR Representative I presented ''Problems in Electromagnetics of Interest to the Navy," Society for Industry & Applied Mathematics (SIAM) annual mtg, San Diego, CA, July 8, 2001.

  2. AMS Special Session ''Partial Differential Equations and Their Applications,'' co-organizer and co-chair with Reza Malek-Madani and John W. Neuberger, American Mathematical Society (AMS) annual mtgs, San Diego, CA, January 6-9, 2001.

  3. Applied Computational Electromagnetics Society (ACES) Special Session on ''H-Infinity Methods for Antennas,'' Chair, ACES 17th annual mtg, USNPGS, Monterey, CA, March 19-23, 2001.

  4.  SIAM Session ''Remote Sensing and Inverse Problems,'' Chair, SIAM annual mtg, San Diego, CA, July 8, 2001.

  5.  SIAM Minisymposium ''H-Infinity Methods for Antennas & Electromagnetic Systems," co-organizer and co-chair with Reza Malek-Madani, SIAM 50th anniversary mtg, Philadelphia, PA, July 8-12, 2002.

  6.  AMS-SIAM Joint Special Session ''Dynamical Systems and Oceanography,'' co-organizer and co-chair with Reza Malek-Madani, AMS annual mtgs, Baltimore, MD, January 15-18, 2003.

  7. AMS Special Session ''Analytic and Computational Methods in Electromagnetics," co-organizer and co-chair with Alexander Stone, AMS East Coast Section mtg, NYU-Courant Institute of Mathematical Sciences, New York, New York, April 12-13, 2003.

  8. AMS-SIAM Joint Special Session "Classical and Nonlinear Special Functions and their Applications," corresponding organizer and co-chair with Peter Clarkson, Univ. of Kent, Canterbury, U.K. and Franciso Marcellan, Univ. Carlos III de Madrid. AMS annual meetings, Phoenix, Arizona, January 7-10, 2004.

  9. AMS Session Partial Differential Equations, Co-Chair with Danny Arrigo, AMS-MAA Joint meetings, Atlanta, GA, Jan 06, 2005.

  10. “Special Functions: Asymptotic Analysis & Computation in Honor of Nico Temme's 65th Birthday, SIAM Representative (by title), Santandar, Spain, July 4-6, 2005.

  11. “N-Star Symposium on Naval Science & Engineering, ONR-USNA Co-sponsored meetings, Chair of Session 5, Annapolis, Sept 20-24, 2005.

  12. AMS-SIAM Joint Special Session Time Reversal Methods: Analysis & Applications, Co-Chair and Co-responding organizer with Reza Malek-Madani, AMS-MAA annual meetings, San Antonio, TX, Jan 12-15, 2006.

International Service: Workshops/Symposia/Conferences (1997-Present)

  1.  NATO Four Power Air Senior National Representatives Workshop ''High Power Microwave Technology,'' USNA,  Local Host.  In addition, I gave a Lecture on the ''History and Function of the U.S. Naval Academy." May 1997.

  1.  AMEREM 2002 Steering Cmte Member (USNA Liasion) and Ultrawide Band Cmte Member, Annapolis, MD, June 2-7, 2002.

  2.  ''High Power Microwave Technology,'' HPEM Special Sessions 9.1 and 9.2 (Antennas), co-chair with Everett Farr, AMEREM 2002, June 4, 2002.

Selected Publications:

  1. "Near-Circularity of the Error Curve in Chebyshev Approximation of Solutions to a Class of Elliptic PDE's in the Complex Plane," Journal of Computational & Applied Mathematics, Special Issue on Computational Complex Analysis, E.B. Saff & N. Papamichael (Guest Editors), vol. 46, nos. 1-2, (1993) 315-326.

  2. "Interpolation & Approximation of Solutions to a Class of Linear Partial Differential Equations in Several Variables," Complex Variables, Morris Marden Memorial Volume, G. G. Walter and P. A. McCoy (Guest Editors), vol. 26, no. 3 (1994) 213-233.

  3. "Solving Boundary Value Problems with 'Average' Data Sampled on an Arc," Zeitschrift fur Analysis und ihre Anwendungen, vol. 14, no. 3, June-July (1995) 623-635.

  4. "A Classical Theorem on the Singularities of Legendre Series in C3 and Associated System of Hyperbolic Partial Differential Equations," SIAM Journal of Mathematical Analysis vol. 28, no. 3 (1997) 704-714.

  5. "Sampling Theorems for Higher Order Elliptic Boundary Value Problems," Applicable Analysis, vol. 61 (1996) 149-161.

  6. "The Singularities of Legendre Series in Cn," Complex Variables, vol. 34 (1997) 231-245.

  7. "Multi-Power Legendre Series in Cn," Kernel Functions & Their Applications, S. Saito, ed., Kluwer Pub., Boston (1999) 133-140.

  8. "A Function Theoretic Approach to Multivariable Sampling," Applicable Analysis, H. Begehr Special Issue, G.N. Hile (Guest Editor) vol. 73, nos. 1-2 (1999) 153-165.

  9. "On the Singularities of Rational Legendre Series," Complex Variables, vol. 42 (2000) 369-374.

  10. "On the Structure of Multivariable Sampling Series," Complex Variables, vol. 41, no.1 (2000) 1-15.

  11. "On Radiating Solutions to the Helmholtz equation and Inverse Scattering," Applicable Analysis, vol. 77 (2001) 319-326.

  12. "Electromagnetic Scattering in Three Dimensions," Proc. IMACS 2000, D. Schultz, B. Wade, J. Vigo-Aguiar & S.K. Dey, editors, May (Y2K) 334-337.

  13. "Zonal Harmonics," Encyclopaedia of Mathematics, Kluwer Academic Publishers, Supplemental Vol. III, Prof. dr. M. Hazewinkel, managing editor (2001) 464-465.

  14. "Electromagnetic Field Singularities," J. of Math Analysis & Applications, vol. 275 (2002) 761-770.

  15. "On the Singularities of Fractionalized Potentials," Complex Variables, vol. 47, no. 6 (2002) 507-513, Erwin O. Kreyszig 80th Birthday Issue.

  16. An Analysis of the Paraxial Wave Equation, with Reza Malek-Madani (submitted).

  17. Laguerre-Gauss Normal Mode Study of the Paraxial Wave Equation, with Reza Malek-Madani.

  18. "Analysis of a Paraxial Wave Functions via Ince-Gauss Normal Modes, with Reza Malek-Madani (writing up).

  19. "Sampling of Functions Band-Limited to 'Unusual' Domains" (writing up).



Book Reviews:

  1. "Wavelets, Algorithms & Applications," Yves Meyer, CEREMADE (Trans. by John D. Ryan, Office of Naval Research) SIAM, Philadelphia, 1993; American Mathematical Reviews 95f:94005, June 1995.

  2. "Wavelets and their Application," Stefan Goedecker, Cahiers de Physique, Presses Polytechniques et Universitaires Romandes, Lausanne, 1998; American Mathematical Reviews 99m:00014.

  3. "Practical Time-Frequency Analysis," Gabor and Wavelet transforms with an implementation in S. With preface by Ingrid Daubechies. R. Carmona, Wen-Liang Hwang, and B. Torresani, Wavelet Analysis and its Applications, 9, Academic Press, Inc., San Diego, CA, 1998; American Mathematical Reviews 2000a:42050.

  4. "Wavelets," J. Bergh, F. Ekstedt and M. Lindberg, Studentlitteratur, Lund, 1998; American Mathematical Reviews 2000a:42001.

  5. "Wavelet Analysis: The Scalable Structure of Information," Howard L. Resnikoff and Raymond O. Wells, Jr., Springer, New York, 1998, American Mathematical Reviews 1-712-468 (2000j:94001).

  6. "Plane-Wave Theory of Time Domain Fields," Thorkild B. Hansen and Arthur D. Yaghjian, IEEE Series on Electromagnetic Wave Theory, 1999, Zentralblatt fur Mathematik (DE 015152760) 2001.

  7. "Wavelets, Tools for Science and Technology," Stephane Jaffard, Yves Meyer & Robert D. Ryan, SIAM, Philadelphia, 2001. American Mathematical Reviews (1-827-998; 2002).

Additional Professional Activities (2000-Present)

Wavelets Workshop: Gilbert Strang and Truong Nguyen, University of St. Thomas, St. Paul, MN, August, 1999, participant.

Image Processing Workshop: sponsors IPAM-ONR, UCLA, Sept 6-8, 2000, participant.

Workshops: "Image Processing and Low Level Vision" and "Image Processing and High Level Vision," Institute for Mathematics and its Applications, University of Minnesota, 15-20 Oct 00 and 12-17 Nov 00, IMA-ONR sponsors, participant.

ACES-2001 Short Course "Overview of Numerical Computational Methods in Electromagnetics," Dr. Janice Karty, The Boeing Company-Phantom Works, ACES 17th annual mtg (USNPGS), March 19-13, 2001.

Navy-Industry R&D Partnership Conference 2002, Washington, D.C., August 2002, participant.

High Energy Laser Program, Joint Technology Office, Annual Program Review, Albuquerque, NM, May 7-9, 2003 and May 5-6, 2004.

Third Annual Navy Workshop on "Applications of Free Electron Lasers," Johns Hopkins Univ.-Applied Physics Laboratory, July 2003.

JTO Meetings at Albuquerque and Dayton, July 2004 -present.

Miscellaneous Administrative and Teaching Duties at USNA:

  1. Organized and ran the Academic portion of the Naval Academy Summer Seminar for the first four years of the program (formally the Naval Academy Science Seminar and Workshop; and, the Naval Academy Engineering Science Seminar). The NASS has become a major recruiting program for the Naval Academy.

  2. Command and Seamanship Training Squadron: USS 211 AMERICAN PROMISE, NAS-2 COURAGEOUS, NAS-4 VALIANT, NAS-7 DAUNTLESS

  3. Middle Atlantic States 10 Year Accreditation Review (1994-1996) Commission on Higher Education Middle Atlantic States Association of Colleges and Schools. Yard Wide Steering Committee Member: I had Oversight of Chairs for Finance, Long Range Planning & Resource Allocation, Computer Services, Educational Resources, Library & Information Services.

4. President: For 14 years of The Honor Society of Phi Kappa Phi (Chapter #196) www.phikappaphi.org and Phi Kappa Phi Foundation Fellowship Program Manager (9 Foundation Fellows, 1 Marjorie Schoch Fellow  and 1 Award for Excellence: Stanford University (4), M.I.T. (1), Univ. Texas-Austin (2), Carnegie Mellon University (1), Imperial College University of London (1), Oxford University (2) and Corpus Cristi College Cambridge University (1))

5. USNA Protestant Chapel Council Faculty Representative (1994-2002) and USNA Protestant Chapel Contributions Committee Member (1996-2000).

  1. Faculty - Alumni Relations Committee (2 years - Faculty Senate)

7. Math Tutor Navy Football Team (3.5 years)

8. Faculty Representative: Women's Varsity Basketball Team (1994-1996)

  1. Course Coordinator: Engineering Mathematics, and, Engineering Mathematics with Statistics, 1978-2003, (SM 311, 312 & 314) (known as the "Blackboard Samurai" by his students)

  2. Math Dept Awards Committee (principal editor & strategist) math faculty won Apgar, Clements, Teaching (2), Research (2) and Service Awards (1) and two honorable mentions (teaching & research)  in Yard Wide Competitions

  3. USNA Yard Wide Subcommittee on Financial Integrity (NCAA Self-Study, Division I Certification 1995-96).

  4. Normal teaching load: 3 courses Fall/ 2 courses Spring Sabbatical Leaves taken (None).

 

Professional Memberships:

  1. The Society for Industry & Applied Mathematics, and, SIAM Orthogonal Polynomials & Special Functions and Analysis of Partial Differential Equations www.siam.org.

  2. Directed Energy Professional Society www.deps.org .

  3. American Mathematical Society www.ams.org .

Additional Memberships

  1. U.S. Naval Academy Alumni Association (Faculty Associate Member)

  2. Sigma Alpha Epsilon Fraternity Alumni (Phoenix Society Founder Member)

  3. University of Wisconsin-Milwaukee Alumni Foundation

  4. Miles River Yacht Club, St. Michael's, MD

"Each morning in Africa a gazelle awakes and knows it must run faster than the fastest lion or be killed. And each morning a lion awakes and knows it must outrun the slowest gazelle or starve to death. It doesn't matter if you're a lion or a gazelle; when the sun comes up you'd better be running."  Herb Caen.

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last modified 1-3-2006.