Curriculum Vitae of Robert Pertsch Gilbert

Unidel Chair of Applied AnalysisDepartment of Mathematical Sciences

University of Delaware

February 25, 2008

1 A Short Professional History

Professor Gilbert, an applied analyst, is primarily known for his treatises on function theoreticmethods applied to partial differential equations. He has written four such monographs and theseare listed below As a research mathematician Dr. Gilbert has published 300 articles in profes-sional journals and conference proceedings. He is the Founding Editor of two mathematics journalsComplex Variables and Applicable Analysis. In addition he is on the Editorial Board of adozen mathematics journals plus several book series. He is also the Founding President of ISAAC(International Society for Analysis and Applications).Dr. Gilbert’s current research efforts are in the areas of inverse problems, theory of plasto-elasticity,homogenization, hemivariational inequalities, and the flow of viscous fluids. The work on homoge-nization concentrates on models of biological mechanics.

2 Recent Employment:

1. Unidel Professor of Mathematics, University of Delaware, September 1975 - Present. (MarineStudies 1987 - Present).

2. Professor, Department of Mathematics, Indiana University, September 1966 - August 1975.

3 Editorships:

1. Editor-in-Chief Applicable Analysis: An International Journal, Publisher: Gordon andBreach.

2. Editor-in-Chief Complex Variables: Theory and Application, Publisher: Gordon and Breach.

3. Associate Editor, Acta Applicata Mathematica, Academica Sinica.

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4. Advisory Editorial Board Member, Pitman Press, CRC, Orlando.

5. Editorial Board, Mathematical Methods in Applied Science, Wiley.

6. Editorial Board, Numerical Functional Analysis and Optimization, Dekker.

7. Editorial Board, Journal for Nonlinear Analysis, Elsevier.

8. Editorial Board, Zeitschrift f. Analysis u.i. Anwendungen VEB, Deutscher Verlag d. Wis-senschaft.

9. Editorial Board, Journal Computational Acoustics, World Scientific, Singapore.

10. Series Editor, ISAAC Monograph Series World Scientific.

11. Editorial Board, Communications on Nonlinear Analysis, International Publications, Or-lando, FL.

12. Editorial Board, Communications in Applied Analysis

13. Editorial Board, Journal of Inequalities and Applications, Hindawi.

14. Editorial Board, Boundary Value Problems, Hindawi.

15. Editorial Board, Evolutionary Equations,

4 Prizes and Awards:

1. von Humboldt Foundation, Senior Scientist Award, in 1975 - at the Freie Universitat Berlinand in 1986 at the Freie Universitat Berlin.

2. Oxford University (1981) British Science Council Research Award.

3. Deutsche Forschungsgemeinschaft (German N.S.F.) fellow at the Freie Universitat Berlin,1988-89.

4. von Humboldt Senior scientist Award, 2005 at Universitate Bochum

4.1 Foreign Visiting Appointments:

1. Guest Research Professor: University of Glasgow, May 1972; Universitat a Dortmund, Oc-tober 1972; Hahn-Meitner-Institut Berlin GmbH., March 1974 - June 1974; Guest Professor,Freie Universityat Berlin, September 1974 - February 1975;

2. Guest Research Professor: Technical University, Denmark, May-June 1979; Universitat Karl-sruhe, May-June 1980. Oxford University, 1980-81. Guanzhou University, Canton, Nov. 1985.National Auton. Univ. Mexico, Winter 1985. Freie Universitat Berlin Summer 1985. Uni-versite Jean Monnet de SAINT-ETIENNE, Fall 1993. Univerite Claude Bernard de LYON,Spring 1998 Universitat Bochum, Marh, May 2005 Univerite Claude Bernard de LYON,October-November 2005

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4.2 Listed in the following:

1. American Men of Science

2. World Who’s Who in Science,

3. Who’s Who in Education, Vol., I, Teachers and Volume II, Scientists

4. World Dictionary of Mathematicians,

5. Who’s Who in Midwest,

6. Who’s Who in America.

5 Doctoral Students:

1. Chi Yeung Lo, Univ. Maryland 1966, present position Prof. Michigan State Univ.

2. P. Ramankutty, Indiana University 1968, Senior Lecturer, Aukland University

3. Edward Newberger, Indiana University 1969, ?.

4. Ronald Brown, Indiana University 1970, NRL

5. Dean Kukral, Indiana University 1970, Wichita State University.

6. Gerald Hile, Indiana University 1971, Professor University of Hawaii

7. Satish Bhatnagar, Indiana University 1972, Professor Univ. Nevada

8. Patrick Brown, Indiana University 1973, MITRE

9. James Buchanan, Univ. Delaware 1978, present position Prof. U.S. Naval Academy

10. Peter Shi, Univ. Delaware 1988, present position Assoc. Prof. Oakland Univ.

11. Yongzhi Xu, Univ. Delaware 1990, present position Prof. University of Tennessee

12. Khaldoun Kashanah, University of Delaware, 1994, present position Asst. Prof., Stevens Inst.Technology

13. Zhongshan John Lin, University of Delaware, 1998, present position Associate Professor,Delaware State University

14. Alex Panchenko, University of Delaware, 2001, present position Assistant Prof. WashingtonState University

15. Pingquin Li, University of Delaware, 2000

16. Miao Ou, University of Delaware, 2001, present position Asst. Prof., Florida Central Univer-sity

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17. Fang Ming, University of Delaware, 2003, present position Assistant Prof. Norfork StateUniversity

18. Ningyi Zhang, University of Delaware, 2007,.

19. Robert Ronkese, University of Delaware, 2007, West Point.

20. Ana Vasilic, University of Delaware, 2009.

21. Ying Liu, University of Delaware, 2009.

22. Patrick Rowe, University of Delaware, 2010.

I would also add to this list Rolando Magnanini, Professor University of Florence, who considersme to be his thesis advisor. After completeing the license he worked with me and we wrote threepapers together on three different topics. This constitutes the usual apprenticeship in the Italiansystem prior to the introducing of the Ph.D.

6 Conferences Organized:

1. AFOSR Conference on Analytic Methods in Mathematics Physics co-organized with RogerNewton at Indiana University, Bloomington, Indiana 1968.

2. AFOSR Conference on Constructive Methods for Differential Equations co-organized with D.L. Colton at Indiana University, Bloomington, Indiana, 1974.

3. Special Session on Topics in Plane Analyticity at the AMS Meeting San Francisco, California,1981.

4. Special Session on Inverse Problems in Underwater Acoustics at the IMACS Conference atHarvard University, Cambridge, Mass. 1991.

5. Special Session on Inverse Problems at the IMACS conference to be held at Rutgers in June1992. co-organized with Yongzhi Xu)

6. Minisymposium on Shells and Plates held at the SIAM Conference in Los Angeles July 1992.co-organized with Klaus Hackl

7. Conference on Complex Analysis to be held in Hong Kong Jan 1993 (co-organizer C.C.Yang)

8. First ISAAC Congress, University of Delaware, Summer 1997. (300 attendees)

7 Research Funded:

Since 1962 until 2004 I have been funded by either NSF, AFOSR, ONR, NRL, or DOE for 42years. The other two years were supported by grants from the von Humboldt Foundation, theDFG, and the Australian NSF. Before 1962, while at the Institute for Fluid Dynamics and Applied

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Mathematics I was supported on Alexander Weinstein’s AFOSR grant, and as a graduate studentI was a research associate on Zeev Nehari’s AFOSR grant. I have also consulted for the Bureauof Mines, the Naval Ordinance Lab., and the Naval Underwater Systems Center. I am presentlyfunded by an NSF Internationl US-France grant and a US Civilian Research and Develop. Found.grant. I intend to submit a proposal to Mathematical Biology at NSF in January.

8 Recent Funding

1. NSF BCS-9002866

2. NSF INT-9011085 US-China

3. NSF DMS-9002837

4. NSF DMS-9402539

5. NSF US-Japan INT-960329

6. NATO US-France CRG-970261

7. NSF US-France INT-9726213

8. NSF DMS-9820813 1999, 2000, 2001, 2002

9. COBASE 1999

10. NRL- N00173-99-1-G903

11. ONR-N00014-001-0853, 2001, 2002, 2003

12. Eisenhower Title II 1998, 1999, 2000

13. NSF-CNRS US-France 2006, 2007, 2008

14. US Civilian Research Development Foundation 2007, 2008.

9 Publications

9.1 Books:

1. Function Theoretic Methods in Partial Differential Equations, Academic Press, New York,1969.

2. Constructive Methods for Elliptic Partial Differential Equations, Springer-Verlag, LectureNote Series #365, Heidelberg, 1974.

3. First Order Elliptic Systems: A Function Theoretic Approach, Academic Press, New York,1983 (with J. Buchanan).

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4. Transmutations, Transformations and Reproducing Kernels Vols. I, II (with H. Begehr) Pit-man, London, 1993.

5. Differential Equations, Prentice Hall UK, 1991 (with H. Howard).

6. A Computer Supported Calculus,(with A. Ben Israel) Springer, 2002.

7. From Convexity to Nonconvexity, Kluwer, Dordrecht 2002. (edited with P.D. Panagiotopou-los, and P. M. Pardalos)

8. Partaial Differential and Integral Equations, Kluwer, Dordrecht 1999. H. G. W. Begehr, R.P. Gilbert, Guo-Chen Wen ‘ (editors)

9. Direct and Inverse Problems Robert P. Gilbert, Joji Xu and Yongzhi Xu (editors)

10. Recent Developments in Complex Analysis Robert P. Gilbert, Joji Xu and Yongzhi Xu (edi-tors)

11. Proceedings of the Second ISAAC Congress Volumes I, and II Kluwer, Dordrecht (2000)(editedwith )

12. Proceedings of the Third ISAAC Congress Volumes I, and II Kluwer, Dordrecht (2000)(editedwith H. Begehr )

13. Maple Projects for Differential Equations Prentice Hall 2003 (with George Hsiao)

14. Marine Acoustics: Direct and Inverse Problems SIAM 2004 (with J.L. Buchanan, A. Wirgin,Y. Xu)

9.2 Conferences Edited:

1. Proceedings of the Symposium on Analytic Methods in Mathematics Physics, (edited by R.P.Gilbert and R.G. Newton) Gordon and Breach, London, 1970.

2. Constructive and Computational Methods for Differential and Integral Equations, (edited byR.P. Gilbert and D.L. Colton) Springer-Verlag, Lecture Note Series, Heidelberg, 1975.

3. Function Theoretic Methods in Differential Equations, (edited by R.P. Gilbert and R.J.Weinacht) Research Notes No. 8, Pitman, London, 1977.

4. Direct and Inverse Problems of Mathematical Physicsedited by R. P. Gilbert, J. Kajiwara,and Y. S. Xu, 1999

5. Recent Developments in Complex Analysis and Computer Analysis, Kluwer, Doordrecht, 2000(with H. G. W. Begehr and Joji Kajiwara)

6. Proceedings of the Second ISAAC Congress, Kluwer, Doordrecht, 2000 (with Joji Kajiwaraand Yonzhi Xu)

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7. Direct and Inverse Problems of Mathematical Physics Kluwer, Doordrecht, 2001 (withH. G.W. Begehr and Joji Kajiwara)

8. Analysis and its appliucations Kluwer, Doordrecht, 2001 (withH. G. W. Begehr and M.-W.Wong)

9. Progress in Analysis 2 volumes Proccedings of the third internation ISAAC Congress, WorldScientific, Singapore,2003 (with H. Begehr and M.-W. Wong)

10. Advances in Analysis 2 Proccedings of the third internation ISAAC Congress, World Scientific,Singapore, 2005 (with H. Begehr, M.E. Muldoon and M.-W. Wong)

9.3 Research Papers in Mathematics:

1. Two-dimensional, steady cavity flow about slender bodies in channels of finite breadth, J. Appl.Mechanics 24, 2 (1957), 170-176 (with Hirsch Cohen).

2. Reverse in situ combustion, J. Appl. Mathematics & Physics (ZAMP), X, 6 (1959), 544-551.

3. On a two-dimensional free-boundary problem, J. Appl. Math. & Physics (ZAMP),XI, 5(1960), 341-355 and (ZAMP), XII 1 (1960), 69-70 (with R. J. Bean and H. Kendall).

4. Singularities of three-dimensional harmonic functions, Pacific J. of Mathematics 10, 4 (1960),1243-1255.

5. Singularities of solutions to the wave equations in three dimensions, J. fur die reine undangewandte Mathematik, Band 205, Heft 1/2 (1960), 75-81.

6. On the singularities of generalized axially symmetric potentials, Archive for Rational Mechan-ics & Analysis 6, 2 (1960), 171-176.

7. On the theory of hot water drives, J. Appl. Math. & Physics (ZAMP), XII, (1961), 489-496(with C. Carney).

8. A note on harmonic function in (p+2)−variables, Archive for Rational Mechanics & Analysis9, 3 (1961), 223-227.

9. On geometric character of singularity manifolds for harmonic functions in three variables: I,Archive for Rational Mechanics and Analysis 9

¯, 4 (1962), 352-360.

10. A note on the singularities of harmonic functions in three variables, Proc. of American Math.Soc. 13, 2 (1962), 229-232.

11. On generalized axially symmetric potentials, J. fur die reine und angewandte Mathematik,Band 212, Heft 3/4 (1963), 158-168.

12. Some properties of generalized axially symmetric potentials, Amer. J. of Math. 84, 3 (1962),475-484.

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13. On harmonic functions of four variables with rational P4 associates, Pac. J. Math. 13, 1(1963), 79-96.

14. Poisson’s equation and generalized axially symmetric potential theory, Annali di MatematicaPura ed Applicata, Serie IV. Tome LXI (1963), 337-348.

15. Harmonic functions in four variables with algebraic and rational P4 associates, Ann. PoloniciMath. IX, (1964) 273-287.

16. Composition formulae in generalized axially symmetric potential theory, J. Math. and Mech.13, 4 (1964), 577-588.

17. Operators which generate harmonic functions in three variables, Scripta Math. XXVII, 2(1964), 141-152.

18. Bergman’s integral operator method in generalized axially symmetric potential theory, J. Math.Physics 5, 7 (1964), 983-997.

19. Integral operator methods in generalized bi-axially symmetric potential theory, Contrib. toDifferential Equations II, 3 (1965), 441-456.

20. Some inequalities for generalized axially symmetric potentials with entire and meromorphicassociates, Duke J. Math. 32, 2, (1965), 239-246.

21. Multivalued harmonic functions of four variables, J. d’Analyse Math. XV (1965), 305-323.

22. On certain classes of elliptic partial differential equations, Portugaliae Mathematica 26 (1967),353-373 (with H. C. Howard).

23. On a class of elliptic partial differential equations, Pac. J. Math. 14, 9 (l964), 1223-1236.

24. On the locations of singularities of a class of elliptic partial differential equations in fourvariables, Can. J. Math. 17 (l965), 678-688.

25. Singularities of analytic functions having integral representations with a remark about theelastic unitary integral, J. Math. Physics 6, 7 (1965), 1157-1162 (with S. Aks and H. C.Howard).

26. The analytic properties of the elastic unitary integral, J. Math. Physics 6, 11 (1965), 1626-1634 (with S. Aks and H. C. Howard).

27. On solutions of the generalized axially symmetric wave equation represented by Bergman op-erators, Proc. London Math. Soc. 15, 3 (1965), 346-360 (with H. C. Howard).

28. On solutions of the generalized bi-axially symmetric Helmholtz equation generated by integraloperators, J. fur reine und angewandte Mathematik, 218 (1965), 109-120 (with H. C. Howard).

29. On generalized axially symmetric potentials whose associates are distributions, Scripta Math.XXVII, 3 (1966), 245-256.

30. A generalized Goursat problem for elliptic equations, J. fur reine und angewandte Mathematik,222 (1966) 1013 (with A. K. Aziz).

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31. On the singularities of Sturm-Liouville expansions: II, Applicable Analysis, 2 (1972), 269-282(with H. C. Howard).

32. Integral operator methods for generalized axially symmetric potentials in (n + 1)− variables,J. Australian Math. Soc. 5, 3 (1965), 331-348 (with H. C. Howard).

33. On a non-linear elliptic boundary value problem with generalized Goursat data, Ann. di MathPura ed Appl. IV , 62 (1966), 325-342 (with A. K. Aziz and H. C. Howard).

34. A new method in the theory of potential scattering, J. Math. Physics 7, 3 (1966), 431-433,(with S. Y. Shieh).

35. Role of the integral operator method in the theory of potential scattering, J. Math. Physics 8,1 (1967), 141-148, (with H. C. Howard).

36. An investigation of the analytic properties of solutions to the generalized axially symmetric,reduced wave equation in (n + 1)− variables, with an application to the theory of potentialscattering, SIAM J. on Appl. Math. 16, 1 (1967), 30-50.

37. On the analytic properties of solutions to a generalized reduced Schroedinger equation, J.Differential Equations 3 (1967), 59-77.

38. On the analytic properties of solutions of equation ∆u + xux + yuy + c(r)u = 0, Duke Math.J. 34, 2 (1967), (with G. S. S. Avila).

39. On the singularities of Sturm Liouville expansions for second order, ordinary differentialequations, Proc. of Symposium on Analytic Methods in Math. Physics, Gordonand Breach, New York, 1970, 443-452 (with H. C. Howard).

40. Singularities of solutions to elliptic partial differential equations with analytic coefficients, TheQuarterly J. Math. 19, 76 (1968), 391-396 (with D. L. Colton).

41. Function theoretic methods in the theory of boundary value problems for generalized metahar-monic functions, Bull. of AMS 75, 5 (1969), 948-952 (with D. L. Colton).

42. A method of ascent, Bull. of AMS 75, 6 (1969), 1286-1289.

43. Integral operator methods for approximating solutions of Dirichlet problems, Proc. of Conf.on Numerische Methoden der Approximationstheorie, Oberwolfach, Germany (June 1969),International Series of Numerical Mathematics, Vol. 15, Birkhauser Verlag, Basel, 1970.

44. Generalized Goursat data for analytic nonlinear partial differential equations, Duke Math. J.37, 2 (1970), 367-376.

45. A contribution to the Vekua-Rellich theory of metaharmonic functions, Am. J. Math. XCII,3 (1970), 525-540 (with D. L. Colton).

46. New results on the approximation of solutions to partial differential equations: The methodof particular solutions, Proc. of Conf. on Analytic Theory of Differential Equa-tions, Western Michigan University (May 1970), Springer-Verlag Lecture Note Series #183,Berlin, 1971, (with D. L. Colton).

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47. New results on the approximation of solutions to partial differential equations: Iterative meth-ods, Proc. of Conf. on Analytic Theory of Differential Equations, WesternMichigan University (May 1970), Springer-Verlag Lecture Note Series #183, Berlin, 1971,(with D. L. Colton).

48. On the numerical treatment of partial differential equations by function theoretic methods,Proc. of Symposium on Numerical Solution of Partial Differential Equations, Univ. of Mary-land (May 1970), Academic Press, New York, 1971, (with D. L. Colton).

49. Recent advances in the function theoretic approach to elliptic equations, Proc. of theSymposium on Mechanics and Related Topics in Analysis, Tblisi State University,U.S.S.R.

50. Pseudohyperanalytic function theory, Proc. of Conf. on Function Theoretic Meth-ods in Differential Equations, October 18-21, 1972, Bonn, Germany.

51. The scope of the function theoretic approach for equations permitting a separation of variablesJ. Math. Anal. Appl. 34 (1971), 671-683 (with H. C. Howard).

52. Generalized hyperanalytic function theory, Bull. of AMS 78, 6 (1972), 998-1001 (with G.Hile).

53. The construction of solutions for boundary value problems by function theoretic methods,SIAM J. Math. Anal., 1 (1970) 96-114.

54. An integral operator approach to Cauchy’s problem for ∆p+2u + Fu = D, SIAM J. Math.Anal. 2, 1 (1971), 113-132 (with D. L. Colton).

55. Rapidly convergent approximations to Dirichlet’s problem for semilinear elliptic equations,Appl. Anal., 2 (1972), 229-240 (with D. L. Colton).

56. On the approximation of solutions of elliptic partial differential equations in two and threedimensions, SIAM J. Math. Anal. 2, 1 (1971), 17-30 (with C. Y. Lo).

57. Integral operators and complete families of solutions for ∆2p+2u(x)+A(r2)∆p+2u(x)+B(r2)u(x) =

0, Archive Rat. Mech. and Anal. 43 (1971) 62-78 (with D. L. Colton).

58. Higher order elliptic equations in three independent variables Bull. of AMS 79, 1 (1973),96-99 (with D. Kukral).

59. Initial value problems for fourth order, semilinear elliptic equations, Appl. Anal. 3 (1974),321-331 (with J. Conlan).

60. Reproducing kernels for elliptic systems, Proc. of Conf. on Constructive and Com-putational Methods for Differential and Integral Equations, Springer-VerlagLecture Notes in Mathematics #430, Berlin, 1975, (with R. J. Weinacht).

61. On Dirichlet’s problem for quasilinear elliptic systems Proc. of Conf. on Constructiveand Computational Methods for Differential and Integral Equations, Springer-Verlag Lecture Notes in Mathematics #430, Berlin 1975, (with G. C. Hsiao).

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62. Generalized hyperanalytic function theory, Trans. Amer. Math. Soc., 194 (1975) 1-29 (withG. Hile).

63. Nonlinear initial data for second and higher order semilinear elliptic equations, J. fur reineund angewandte Mathematik, 276 (1975) 1-14 (with J. Conlan).

64. A function theoretic method for ∆3u + F (x1, x2)u = 0, J. Indian Math. Soc., 38 (1974)227-231 (with D. Kukral).

65. A function theory in the sense of L. Bers for hypercomplex functions, Mathematische Nachrichten,72 (1976), 187-200 (with G. Hile).

66. On a normal form for second order elliptic equations and constructive methods for Dirichlet’sproblem, Math. Nach. 67 (1975), 139-143 (with G. C. Hsiao).

67. A function theoretic method for ∆23u + Qxu = 0, Nachrichten 67 (1975), 199-212 (with D.

Kukral).

68. Iterative schemes for almost linear elliptic systems with nonlinear initial data, J. fur reineund angewandte Mathematik, 277 (1975), 193-206 (with J. Conlan).

69. A function theoretic method for ∆24u + Qxu = 0, Annali di Math. Pura ed Appl. IV, c. IV

(1975), 31-42 (with D. Kukral).

70. Reproducing kernels for generalized Hilbert function spaces, Appl. Anal. 6 (1977), 159-161(with G. N. Hile).

71. Function theoretic methods for elliptic equations with more than four variables RendicontiTorino, 31 (1973), 275-285 (with D. Kukral).

72. Iterative schemes for elliptic systems, Proc. Conf. Constructive and ComputationalMethods for Differential and Integral Equations, Springer-Verlag Lecture Notes#430, Heidelberg 1975 (with R. J. Weinacht).

73. Constructive methods for higher order, analytic Sobolev-Galpern equations, Bull. Math. de laSoc.d Math. Roumainie, 19 (67) (1976), 213-225 (with P. M. Brown).

74. Generalized hyperanalytic systems with analytic coefficients, Royal Soc. Edinburgh 73A, 22(1974/75), 317-331 (with W. Wendland).

75. Constructive function theoretic methods for fourth order psuedoparabolic equations in twospace variables, Rendiconti di Matematica Roma (with P. M. Brown and G. C. Hsiao).

76. Higher order pseudo and metaparabolic equations: A function theoretic approach, FunctionTheoretic Methods for Partial Differential Equations, Springer Lecture Note Series #561(1977) (with G. C. Hsiao).

77. Evolution equations with generalized Riemann operators, Appl. Anal. 6 (1977), 75-79 (withM. Schneider).

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78. Bergman type operators for pseudoparabolic equations in several space variables, Math. Nachr.76 (1977) 61-68, (with S. Bhatnagar).

79. Nonlinear boundary value problems for elliptic systems in the plane, Nonlinear Systemsand Applications, ed., V. Lakshmikantham, Academic Press, New York, 1977.

80. Constructive methods for solving ∆24u + A∆4ut + But + C∆4u + Du = 0, Math. Nach. 80

(1977) 105-113 (with S. Bhatnagar).

81. Integral operators generating solutions of ∆23ut + A∆3ut + B∆3u + Cu = 0, Glasnik Matem-

aticui 12 (32) (1977); 31-48 (with S.d Bhatnagar).

82. Hilbert function modules with reproducing kernels, Nonlinear Anal. 1(2) (1977), 135-150(Pergamon Press) (with G. N. Hile).

83. Randwertaufgaben ganzzahliger Charakteristik fur verallgemeinerte hyperanalytische Funkitio-nen, Appl. Anal. 6 (1977), 189-205 (with H. Begehr).

84. Das Randwert-Normproblem fur ein fastlineares elliptisches System und eine Anwendug, An-nales Acad. Scien. Fennicae, Serie A. I Math., Vol. 3 (l977) (with H. Begehr).

85. On Riemann boundary value problems for certain linear elliptic systems in the plane, J.Differential Equations 32 (1979) 1-14, (with H. Begehr).

86. Generalized meta and pseudoparabolic equations in the plane, 70th Anniversary Volume ded-icated to Acad. I. N. Vekua, Moscow, 1979 (with M. Schneider).

87. Uber das Randwert-Normproblem fur ein nichtlineares elliptisches System, Function The-oretic Methods for Partial Differential Equations, Springer Lecture Note Series#561, Berlin, 1977 (with H. Begehr).

88. Piecewise continuous solutions of pseudoparabolic equations in two space dimensions, Proc.Royal Soc. Edinburgh 81A, (1978) 153-173 (with H. Begehr).

89. A method of ascent for a class of sixth order elliptic equations, Bull. Math. de la Soc. Sci.Math. Roumanie 18 (66) (1974), 5-16 (with S. Bhatnagar).

90. On a class of boundary value problems for a composite system of first order differential equa-tions, J. Approx. Theory 25 (1979) 105-119 (with M. Schneider).

91. Shock development prior to detonation in a shaped layered nonlinear elastic medium withstochastic variability, AMI Technical Report 67A (1979) (with A. Jeffrey).

92. Constructive methods for meta and pseudoparabolic systems, Bull Soc. Sci. Math. R. S.Roumanie 20, (68) (1976) 97-109 (with G. F. Roach).

93. The linear anisotropic plate, J. Composite Materials, 15 (1981), 71-78, (with M. Schneider).

94. On the numerical solution of pseudoparabolic equations, (with L.R. Lundin) Zeitschrift f.Analysis u.i. Anwendungen 2 (1983), 25-36.

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95. A Lewy-Type reflection principal for pseudoparabolic equations, J. Differential Equations 37(2) (l980), 261-284.

96. Riemann Hilbert problems for generalized hyperanalytic functions with distributions data,(with J. Buchanan) Appl. Anal. 11 (1981), 303-323.

97. A computational approach for constructing singular solutions of one-dimensional pseudoparabolicand metaparabolic equations, SIAM J. Sci. Stat. Comput. 3 (1) (1982), 111-125 (with J.Jensen).

98. A reactive shock in a polytropic gas, J. Math. Analysis & Applications 89 (1982), 193-202(with A. Jeffrey).

99. A boundary-layer theory for the orthotropic plate, ZAMM 63 (1983), 229-237 (with M. Schnei-der).

100. Generalized hyperanalytic function theory, in Proc. of the Dundee Conf. on Differ-ential Equations, 1980, Springer, Berlin.

101. Verallgemeinerte hyperanalytische Funktionen theorie, in Komplexe Analysis und ihre An-wendungen auf partielle Differentialgleichungen, Teil 2, 124-145, Wissenschaftliche Beitrage1980/81 (M 18), Halle (Salle).

102. Finite element representations for classical functionals, Appl. Anal. (14) (1983), 259-274.

103. Generalized meta and pseudoparabolic equations in the plane, in Memorial Issue for Acad.I. N. Vekua, Moscow, 1979 (with M. Schneider).

104. Recent results and developments in hyperanalytic function theory, in Complex Analysis:Methods, Trends, and Application, Akademie Verlag, Berlin, 1983.

105. Boundary value problems associated with first order elliptic systems in the plane, Contempo-rary Mathematics Series Vol. 11, A.M.S., Providence (1982).

106. Reverse in situ combustion in oil reservoirs, ZAMM 64 (1984) 124-127 (with A. Jeffrey).

107. An analytical approach to the hot water drive, ZAMM 64 (1984), p. 7, (with A. Jeffrey).

108. Degenerate elliptic systems whose coefficient matrix is a group inverse, Complex Variables 1(1982), 61-87.

109. The two dimensional linear orthotropic plate, Appl. Anal. 15 (1983), 147-170 (with G. Hsiaoand M. Schneider).

110. Algorithms for generalized Cauchy kernels, Complex Variables 2 (l983) 103-124 (with LinWei).

111. The asymptotics of reverse in situ combustion to appear Porous Media (1988) (with A. Jef-frey).

112. Function theoretic solutions to problems of orthotropic elasticity J. Elasticity 15 (1985), 143-154.

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113. Constructive methods for fourth-order elliptic equations, J. Approximation Theory, 44 (1985)55-68 (with Lin Wei).

114. Hele-Shaw type flows in Rn, J. Nonlinear Analysis, 10 (1986) 65-85 (with H. Begehr).

115. Non-Newtonian Hele-Shaw flows in n > 2 dimensions, J. Nonlinear Analysis, 11 (1987),17-47. (with H. Begehr).

116. Pure bending problem for a vibrating elastic plate with non-uniform temperature, J. Elasticity(with J. Buchanan and R. Magnanini).

117. A transmutational approach to underwater sound propagation, Wave Motion 8 (1986) 383-397.(with D. H. Wood)

118. Direct generations of normal modes by transmutation theory, Computational Acoustics, Else-vier (1988), 389-402. (with M.D. Duston, G.R. Verma and D.H. Wood).

119. Transmutations occurring in ocean acoustics, in Proceedings of the Conference onPartial Differential Equations and Applied Mathematics, Oakland University May17, 1986, Pitman, London.

120. Pseudohyperanalytic functions, Complex Analysis, 9 (1988) 343-357 (with H. Begehr).

121. A moving boundary problem associated with flow through a porous medium J. Nonlinear Anal-ysis 12(2) (1988) 109-119 (with R. Magnanini).

122. The boundary integral method for two dimensional orthotropic materials, Journal of Elasticity(with R. Magnanini) J. Elasticity 18 (1987) 61-82.

123. Some initial boundary value problems for nonlinear pseudoparabolic systems, Mathem. Nachrichten163 (1993) 27-34 (with Guo-chun Wen).

124. Integral and boundary value problems for nonlinear systems of composite type, Jour. Analysisand Applications, 12 (1993) 343-352.

125. The two-dimensional nonlinear orthotropic plate Jour. Elasticity 26 (1991) 147-167 (with H.Begehr and C.Y.Lo).

126. On the approximation of acceleration waves (with A. Jeffrey) Int. J. Nonlinear Mech. 22(1987), 209-215.

127. A wave propagation computation technique using function theoretic representation (with M.D.Duston and D.H. Wood) Num. Math. Applications XIth IMACS World Cong..

128. Free and moving boundary problems in fluid dynamics J. Nonlinear Analysis 13 (3) (1989),285-303 (with Wen G.).

129. A function theory for thin elastic shells, J. Elasticity 22 (1989), 81-03 (with Xu, Yongzhi).

130. The use of Macsyma for solving elliptic boundary value problems (to appear) ZAMM (withPeter Thejll).

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131. Starting fields and far fields in ocean acoustics, Wave Motion 11 (1989), 507-524 (with Xu,Yongzhi)

132. Anisotropic Hele Shaw Flows, Math. Methods Applied Sciences, 11 (1989), 417-429 ( withPeter Shi).

133. An inverse problem for harmonic acoustics in stratified oceans, J. Math. Anal. Appl.176(1)(1993),121-137 (with Y. Xu).

134. Vekua theory in higher dimensional complex spaces: the Π-operator in Cn, Complex Variables,21(1993),99-106 (with Z. Y. Hou and X. W. Meng).

135. Hypermembrane shells, Trends in Applications of Mathematics to Mechanics, Springer, 261-272, 1988.

136. A solution of the equations of elastic shell theory, Math. Meths. Applied Scis. (withJ.Buchanan) 12 (1990), 341-363.

137. Free boundary problems occuring in planar fluid dynamics Nonlinear Analysis 13 (1989) 285-303.

138. The weak solution for the generalized hyperanalytic equations of thin elastic shells, TechnicalReport (to appear) (with Guo-chun Wen).

139. Construction of approximations to acoustic Green’s functions for nonhomogeneous oceansusing transmutations, Wave Motion 10 (1988), 285-297 (with Xu, Yongzhi and Wood, D.H.).

140. Dense sets and the projection theorem for acoustic harmonic waves in homogeneous finitedepth ocean, Math. Meth in Applied Sciences 12 (1992), 69-76 (with Xu, Yongzhi).

141. Harmonic representation of the Hele-Shaw free boundaries, Applicable Analysis (with P. Shi).

142. Hyperanalytic, Riemann Boundary value problems on rectifiable, closed curves (to appear)(with Zeng Yuesheng).

143. The propagation problem and far field patterns in a stratified finite depth ocean, Math. Meth.Applied Sciences, 12 (1990), 199-208. (with Xu, Yongzhi)

144. An approximation scheme for the three-dimensional scattered wave and its propagating far-field pattern in a finite depth ocean, ZAMM, 72 (with Y. Xu, and P. Thejll)(1992), 459-480.

145. Underwater acoustics for submersibles, in Ocean Resources, ed. D. A. Ardus and M. A.Champ, Vol. 2, 135-146 (with Wood, D. H.and Xu, Yongzhi).

146. A class of nonlinear Riemann-Hilbert problems for the second order elliptic systems, ComplexVariables 32 (1997) 105-129.(with Li Mingzhong).

147. Modeling acoustic waves by transmutation, in Progress in Underwater Acoustics, Plenum,New York, (1987),389-393, (with Wood, D.H.)

148. The irregular oblique derivative problem for quasilinear parabolic equations of second order,(to appear) (with Guo Chun Wen).

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149. Generalized Herglotz functions and inverse scattering problems in a finite depth ocean inInvariant Imbedding Problems ed Corones, Kristensson, Nelson, Seth, SIAM 1992(withY. Xu)

150. An approximation scheme for the three-dimensional scattered wave and its propagating far-field pattern in a finite depth ocean , ZAMM 72(1992), 459-480.

151. Acoustic waves and farfield patterns in two dimensional oceans with porous elastic-seabeds,Results in Mathematics, 22(with Y. Xu)(1992) 685-700.

152. Approximate solutions for some free boundary problems occurring in planar fluid dynamicsin Integral Equations and Boundary Value Problems World Scientific, Singapore(1991) (with Guo-chun Wen).

153. Numerical solutions for some free boundary problems occurring in planar fluid dynamics,Zeitschrift f. Analysis u. Anwend.,11(with G.C. Wen)(1992) 531-537.

154. On the conditions for uniqueness and existence of solutions to an inverse problem: I, Jour.Comp. Acoustics 1 (1993) (with Zhongyan Lin).

155. Initial and boundary value problems for nonlinear systems of composite type, (to appear) (withGuo-chun Wen).

156. Scattering of acoustic waves by an ellipse in a shallow ocean in Advances in ComputerMethods for Partial Differential Equations-VII ed. Vichnevetsky, Knight, Richter(with Y. Xu)(1993)

157. A quasi-static contact problem in linear thermoelasticity, Rendiconti di Matematica, VII(10)(1990), 785-808.(with P. Shi and M. Shillor).

158. Two free boundary problems occuring in planar filtrations, Nonlinear Analysis 21 (1993) 859-868 (with Guo Wen).

159. Non-isothermal, non-Newtonian, Hele-Shaw flows- Part I: Mathematical formulation.in Pro-ceedings of the First International Conference on Transport Phenomena,(with P. Shi)(1992), 1067-1088.

160. An unidentified inclusion problem for a shallow ocean I: Construction of the Green’s func-tionin Computational Acoustics ed. Lee, Vichnevetsky, Robinson (1993) 1-19. (with K.Khashanah, and Y. Xu)

161. Theory of thermo-elastic plates Modern Theories of Plates and Shells (1994) Longman(with K. Hackl)

162. Theory of elastic-plastic plates, Modern Theories of Plates and Shells (1994) Longman(with K. Hackl)

163. Moving boundary value problems in injection molding, Proc. Conference on ComplexAnalysis, Hong Kong Jan. 1993 (with Zhenyuan Xu)

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164. Some initial value problems for a nonlinear pseudoparabolic equation, Math. Nachrichten,163(1993)27-34. (with G.C. Wen)

165. Wavelet solutions for time harmonic acoustic waves in a finite ocean, J. Comp. Acous-tics,1(1)(1993), 31-61. (with W. Lin)

166. Nonlinear boundary value problems for certain second-order, overdetermined, elliptic systems,Complex Variables, 22(1993), 11-22.

167. Transition loss in the farfield for the Biot sediment model , Computational Acoustics (toappear) (with J. Buchanan).

168. Computation of the acoustic modal solutions in a shallow ocean with an elastic seabed, Bull.Tech. University Istanbul 47(43-60), (1994)(with K. Khashanah, and B. Swart).

169. Wave propagation in a system: porous media with Dirichlet’s condition on the boundary-continuous media Proc.Third Int. Congr. Acoustics ed. Gary Cohen, INRIA andSIAM Publ. (1995), 449-455. (with S. Gnelecoumbaga, and G. Panasenko).

170. Acoustic waves in a shallow inhomogeneous ocean with a layer of sediment,Acta Acustica,82,(1996) (with Johny Zhongyan Lin).

171. Green’s function for acoustic pressure over a poroelastic seabed Proc. Second Int. Conf.Theoretical and computational Acoustics (1996).

172. Acoustic waves in shallow inhomogeneous oceans with a poro-elastic seabed , ZAMM 79(4)(1997),1-12 (with John Z. Lin)

173. Transition loss in the farfield for an ocean with a Biot sediment over an elastic substrate,ZAMM 77(1997), 121-135 (with J. Buchanan).

174. Inverse problems in a shallow ocean with an interactive seabed, ZAMM 76 (1996) S4, 57-60(with John Z. Lin)

175. A sea-mount problem SIAM special issue on the occasion of Professor Ivar Stakgold’s 70thbirthday, Nonlinear Problems in Applied Mathematics, Editor T. Angell et al, (1996), 140-149.(with Steve Y. Xu)

176. Analytical methods for acoustic seabed exploration, Oceans ’95 MTS/IEEE Proceedings (1996)(with M. Gaer and Y. Xu)

177. Scattering in a shallow ocean with an elastic seabed, Computational Acoustics, 5(1997) 403-431.

178. Comparison of the solution to a problem in ocean acoustics by parabolic approximation withthe exact solution obtained by the residue calculus, in Generalized Analytic Functions, Kluwer,Amsterdam, 241-253, 1998. (with J. L. Buchanan )

179. Underwater Acoustics,in Generalized Analytic Functions, Kluwer, Amsterdam, 215-228, 1998(with Z. J. Lin).

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180. The coefficient problem for a shallow ocean with an unknown inhomogeneity and an elasticseabed, Applicable Analysis 63 (1996) 77-86.(with Yongzhi S. Xu)

181. The unidentified object problem in a shallow ocean J. Acoust. Soc. America 103 (1998),1320-1327. (with T. Scotti, A. Wirgin, and Yongzhi S. Xu)

182. The fundamental singularity in a shallow ocean with an elastic seabed (to appear) ApplicableAnalysis (with John Lin)

183. Determination of the coefficients of an elastic seabed Applicable Analysis 68 (1998), 75-86.(with J. Buchanan)

184. Green’s function representation for acoustic pressure over a poroelastic seabed, ApplicableAnalysis, 65 (1996) 57-68. (with J. Buchanan, and Y.Xu)

185. Identification of a 3D object in a shallow sea from scattered sound Ondes et vibrations/ Wavesand Vibrations,C. R. Sci. Paris, 325 (1997) 383-389. (with T. Scotti, A. Wirgin, and Y. Xu)

186. Application of reproducing kernels to partial differential systems ,Proc.Conf. on GeneralizedAnalytic Functions, Kluwer, (1998)

187. Underwater acoustics Generalized Analytic Functions ,Kluwer, Amsterdam, 215-228, 1998.(withJohn Lin)

188. Transition loss in a depth-varying ocean over a poroelastic seabed, Generalized Analytic Func-tions , Kluwer, (1998). (with J. Buchanan)

189. Transmission loss in a depth-varying ocean over a poroelastic seabed, in Proceedings ofthe First ISSAC Conference, Kluwer, Amsterdam, 1998. (with J. Buchanan)

190. The intersecting canonical domain approximation for a shallow ocean with poro-elastic seabeds,SIAM/INRIA Conference Proceedings, Golden, Colorado (to appear)(with Klaus Hackl, andA. Wirgin).

191. Transition loss in the farfield over a one-layer seabed assuming the Biot sediment model ,ZAMM, 77(1997) 2, 121-135 (with J. Buchanan).

192. A class of nonlinear Riemann-Hilbert problems for second order elliptic systems, ComplexVariables 32(1997) 105-129 (with Mingzhong Li).

193. Acoustic waves in a shallow inhomogeneous ocean with a layer of sediment,Acta Acustica,82,(1996)(with Zhongyan Lin).

194. Nonisothermal, nonnewtonial Hele-Shaw flows, Part II: Asymptotics and existence of weaksolutions, Nonlinear Analysis 27(1996) 539-559. (with P. Shi).

195. Inverse problems in a shallow ocean with an interactive seabed ICIAM Conference Proceedings,ZAMM 76 (1996) S4, 57-60, (with Zhongyan Lin)

196. Non-isothermal, non-Newtonian, Hele-Shaw flows- Part II: Asymptotics and existence of weaksolutions, Nonlinear Analysis 27 5 (1996) 539-559.

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197. The coefficient problem for a shallow ocean with an unknown inhomogeneity and an elasticseabed, Applicable Analysis, 63 (1996), 77-86.(with Yongzhi Xu)

198. Transition loss in the farfield for an ocean with a Biot sediment over an elastic substrate,ZAMM 77(1997), 121-135 (with J. Buchanan).

199. Acoustic field in a shallow, stratified ocean with a poro-elastic seabed , ZAMM 77, 9, 677-688,(1997), (with Zhongyan Lin).

200. Wave propagation in a system: porous media with Dirichlet’s condition on the boundary-continuous media Proc.Third Int. Congr. Acoustics ed. Gary Cohen, INRIA andSIAM Publ. (1995), 449-455 (with S. Gnelecoumbaga, and G. Panasenko).

201. Direct and inverse problems in ocean acoustics Nonlinear Analysis, 30 3 (1997), 1535-1546.(with J. Buchanan, and John Lin)

202. Scattering in a shallow ocean with an elastic seabed, Computational Acoustics 5 4 (1997),403-431. (with John Lin )

203. Comparison of the parabolic approximation with residue calculus in ocean acoustics, in An-alytic Functions, K. Florian, K. Hackl and W. Tutschke (eds.), pages 241–253, Dordrecht,1998. Kluwer Acad. Publ.(with J. Buchanan).

204. Simplex-based algorithms for determining the coefficients of an elastic seabed, in AnalyticFunctions, K. Florian, K. Hackl and W. Tutschke (eds.), Kluwer, Amsterdam (1998), (withJ. Buchanan).

205. Finding an inclusion in a shallow ocean using a canonical domain method, in Proc. FourthEuropean Conf. Underwater Acoustics, ed. A. Alippi and G.B. Canneli, Rome (1998)pp389-394. (with Buchanan, J.L.,and Wirgin,A.) 389-394

206. Determination of the coefficients of an elastic Seabed Applicable Analysis 68 (1998), 75-86(with James Buchanan).

207. Green’s function representation for acoustic pressure over a poroelastic seabed,ApplicableAnalysis 65 (1996) 57-68 (with J. Buchanan, and Y.Xu).

208. Application of reproducing kernels to partial differential systemsUnderwater Acoustics in An-alytic Functions, K. Florian, K. Hackl and W. Tutschke (eds.), Kluwer, Amsterdam,41-54(1998).

209. Transmission loss in a shallow ocean over a two-layer seabed, Int J. of Solids, Structures35,(1998) 4779-4801. (with J. L. Buchanan)

210. The fundamental singularity in a shallow ocean with an elastic seabed, Applicable Analysis,68(1998), 87-107.(with Zhongyan Lin)

211. Propagation in an acoustic waveguide containing a soft body of revolution , Rept. PI/LMA11/98-4, LMA, Marseille, 1998. (with Buchanan J.L., Cristini P., Wirgin A. and Xu Yongzhi)

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212. The unidentified object problem in a shallow ocean with a fluid-like sediment layer overlayinga rigid seabed, Applicable Analysis, 73(1-2) (1999) 5-17. (with Buchanan J.L., Wirgin A. andXu Yongzhi S.)

213. Acoustics of a stratified poroelastic composite, Zeit. f. Analysis u. i. Anwendungen 184(1999), 977-1001. (1999)977-1001. (with A. Panchenko)

214. Acoustic Green’s function approximations Computational Acoustics, 6(1998),435-452 (withK. Hackl, and John Lin).

215. Direct and inverse problems in ocean acoustics, Nonlinear Analysis,30 3 (1997), 1535-1546.(with J. Buchanan, and John Lin)

216. The unidentified object problem in a shallow ocean, J. Acoust. Soc. Amer. 103 (1998), 1-8.(with T. Scotti, A. Wirgin, and Yongzhi S. Xu)

217. Green’s function representation for acoustic pressure over a poroelastic seabed, ApplicableAnalysis, 65 (1996) 57-68. (with J. Buchanan, and Y. Xu)

218. Finding an inclusion in a shallow ocean using the ICBM method, Applicable Analysis, 71(1-4), (1999) 347-378 (with J.L. Buchanan and A. Wirgin).

219. Propagation in an acoustic waveguide containing a soft body of revolution , Rept. PI/LMA11/98-4, LMA, Marseille, 1998. (with Buchanan J.L., Cristini P., and Xu Yongzhi)

220. Identification, by the intersecting canonical domain method, of the size, shape and depth ofa soft body of revolution located within an acoustic waveguide, Inverse Problems 16 (2000)1709-1726. (with Buchanan J.L., Wirgin A. and Xu Yongzhi)

221. Acoustics of a Stratified Poroelastic Composite, Zeit. f. Analysis u. i. Anwendungen, (toappear) (with A. Panchenko)

222. Implementation of the ICBA method for solids of revolution, Problemi Atuali dell’Analisi edella Fisica Matematica, 41-57 Aracne Press, Rome (2000). (with Buchanan J.L.,and WirginA.)

223. A two-dimensional nonlinear theory of anisotropic plates, Mathematical and Computer Mod-eling 32 (2000) 855-857, (with T. S. Vashakmadze)

224. Acoustic imaging in a shallow ocean with a thin ice cap,Inverse Problems 16 (2000) 1799-1811,(with Yongzhi Xu).

225. Homogenizing the acoustic properties of the seabed: Part I, Nonlinear Analysis 40, 185-212,(2000), (with A. Mikelic)

226. Homogenizing the acoustic properties of the seabed, Part II,(with Th. Clopeau, J.L. Ferrın,and A. Mikelic), Mathematical and Computer Model. 33 (2001) 821-841.

227. Vibration of two bonded composites: effects of the interface and distinct periodic struc-tures,Int. J. Solids and Structures, 40 (2003), 3177-3193, (with Michael Harik and AlexanderPanchenko)

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228. Implementation of the method of variation of boundaries for three-dimensional objects in awaveguide, (with J. L. Buchanan, and M. Ou)

229. Near field representations of the acoustic Green’s function in a shallow ocean with a fluid-likeseabed , Georgian Mathematical Journal, 14 (2007) 109-122(with M. Ou)

230. Identification of a 3D void or inclusion in a plate by inversion of the diffracted wavefield,Ultrasonics, 36, 1998, 115-119, Actes du colloque: Ultrasonics International 97, Delft, 2-4/7/97, (with SCOTTI T., WIRGIN A. et XU Y.S.)

231. A mode-matching method for forward and inverse scattering from an object in a shallow-waterwaveguide, Theoretical and Computational Acoustics 99 (Actes du colloque: 4th Intl. Conf.Theoret.Computat.Acoustics, Trieste, 10-14/5/1999).(with BUCHANAN J., CRISTINI P.,WIRGIN A. et XU Y.).

232. Unambiguous reconstruction of the 2D boundary of a half-space probed by acoustic waves,in Proceedings of 3rd International ISAAC Congress, Actes du colloque: 3rd InternationalISAAC Congress, Berlin, 20/8-25/8/01 (with BUCHANAN J., WIRGIN A. et XU Y.).

233. Finding an inclusion in a shallow ocean using the ICBA method, Appl. Analysis 71 (2000)347-378.

234. Imaging floating objects from underwater, in Proceedings of 3rd International ISAAC Congress,3rd International ISAAC Congress,(2003) 1369-1376, World Scientific, Berlin, (with XU Y.,et WIRGIN A.)

235. Unambiguous identification of the rough boundary of a half space probed by acoustic or electro-magnetic waves, in Mathematical and Computer Modelling, (with BUCHANAN J., WIRGINA. et XU Y.)

236. Determination of a distributed inhomogeneity in a two-layered waveguide from scatteredsound in Direct and Inverse Problems of Mathematical Physics, 107-124, Kluwer,Dordrecht, 2000. (with C. Mawata and Yongzhi Xu)

237. A two-dimensional, non-linear theory of anisotropic plates. Math. Computer Modeling 32(2000), 855-875.

238. The seamount on a sloping seabed problem in Differential Equations and Nonlinear Mechanics,Chapter 9, Edited by K. Vajravelu, Kluwer, Dordrecht. (with Miao-Jung Ou, and YongzhiXu )

239. Low shear asymptotics for elastic seabeds, Math. and Computer Model. 33 (2001) 877-882,(with G. N. Makrakis).

240. The unknown object problem in a sea with sloping bottom, Applicable Analysis 78, (2001),1-15, (with Miao-Jung Ou, and Yongzhi Xu).

241. Determination of a buried object in a two-layered shallow ocean, Comp. Acoustics, 9 (3)(2001) 1025-1037, (with Michael Werby, and Yongzhi Xu)

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242. Transmission loss in a depth-varying ocean over a poroelastic seabed 2nd ISSAC procedings.

243. The Seamount on a Sloping Seabed Problem, Communication on Applied Nonlinear Analysis,2000 .(with M. Y. Ou and Y. S. Xu)

244. Acoustic Wave Propagation in a Composite of Two Different Poroelastic Materials with aVery Rough Periodic Interface: a Homogenization Approach in Acoust. Mechan. andRelated Top. Analysis, (2002) 157-1163, (with (with M. Y. Ou).

245. Transient Reflection and Transmission of Ultrasonic Wave in Cancellous Bone, to appearin Mathematical and Computer Modelling,142 (2003) 561-573. (joint with J. Buchanan, A.Wirgin and Y. Xu)

246. Nonlinear systems arising from nonisothermal, non-Newtonian, Hele-Shaw flows in the pres-ence of body forces and sources, Mathematical and Computer Modeling, 35 (2002) 1425-1444(with M. Fang).

247. An integral equation method for generalized analytic functions in Quaderni di Mathematica7(2002)161-175 (with G. Hsiao)

248. Depth sounding: an illustration of some of the pitfalls of inverse scattering problems, Math.Comp. Modeling 35, 2002, 1315-1354.

249. Unambiguous identification of the unevan boundary of a half-space probed by acoustic orelectromagnetic waves Math. Comp. Modeling 36, 2002, 13-31.(joint with J. Buchanan, A.Wirgin, and Yongzhi Xu)

250. Extremal solutions of a class of dynamic boundary hemivariational inequalities, J. Inequalitiesand Applications, 7 2002, 479-502.

251. Ultrasonic characterization of bone tissue, (preprint) (with Z. Fellah, E. Ogam, A. Wirgin,Yonghi Xu)

252. A note on generalized Cesaro operators, in Acoust. Mechan. and Related Top. Anal-ysis, (2002) 92-99 (with. D.C. Chang and G. Wang)

253. Effective acoustic equations for a nonconsolidated medium with microstructure, in Acoust.Mechan. and Related Top. Analysis, (2002) 164-170, (with A. Panchenko).

254. Identification of distant soft solids of revolution in a wave guide using the ICBA method (toappear) Applicable Analysis (with J. Buchanan, A. Wirgin, and Yongzhi Xu)

255. Acoustic Wave Propagation in a Composite of Two Different Poroelastic Materials with aVery Rough Periodic Interface: a Homogenization Approach, Int. Jour. Multiscale Comp.Engin. 1 (4) (2003)(with M. Ou)

256. A Uniqueness Theorem of the 3-dimensional Acoustic Scattering Problem in a Two-layeredWaveguide with Fluid-like Seabed, Computational Acoustics, 11 (4) (2003) 535-549 (with M.Y. Ou).

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257. Focused ultrasonic wave in submerged cancellous bone (to appear) Computational Acoustics(with Wei Lin and Yongzhi Xu)

258. Imaging floating objects from underwater, in Proceedings of 3rd International ISAAC Congress,3rd International ISAAC Congress,(2003) 1369-1376, World Scientific, Berlin, (with XU Y.,et WIRGIN A.)

259. Computationmal results for seamount imaging in a water waveguide (with Yongzhi Xu) Ap-plicable Analysis 82 (2003) 619-628.

260. Ultrasound as a Diagnostic Tool to Determine Osteoporosis, in Advances in Analysis,World Scientific (2005) 345-354 (with J. Buchanan and Yongzhi Xu)

261. Bergman projection and weighted holomorphic functions, Operator Theory, 143 (2003), 147-169 (with Der-Chen Chang and Jingzhi Tie)

262. Measuring Osteoporosis Using Ultrasound, in Advances in Scattering and BiomedicalEngineering eds. D. I. Fotiadis, C. V. Massalas, World Scientific, (2004) 484-494. (with J.Buchanan)

263. Some mathematical and numerical aspects of acoustic scattering in recent researchdevel-opments in acoustics, Vol. 1 (2003) Transworld research network (with I. V. Andronov,V. A. Fock, B. P. Belinsky, Y. Xu)

264. Compression moulding I: a generalized non-isothermal, non-Newtonian Hele Shaw flow, Non-linear Analysis, Kluwer, Dordrecht, (2004), 513-530.

265. Compression moulding II: Existance of a solution for a Hele Shaw type model, Jour. Analysisand Applications 23 783–807 (2004).(with M. Fang)

266. Effective acoustic equations for a two-phase medium with microstructure, Mathematical andComputer Model., 39, (2004) 1431-1448. (with A.Panchenko )

267. Numerical algorithm based on transmutation for solving the inverse wave equation Mathemat-ical and Computer Model., 39, (2004) 1467-1476. (with Z. Lin)

268. An obstacle problem in non-isothermal and non-Newtonian Hele-Shaw flows Comm. AppliedAnalysis 8 (4) (2004) 459-489.

269. A prototype homogenization model for acoustics of granular materials, (2004) (submittedRoyal Society) (with A.Panchenko (with A.Panchenko and X. Xie)

270. Homogenization of viscoelastic matrix in linear frictional contact, Math. Methods in theApplied Sciences 28 (2005) 309-328. (with A.Panchenko and X. Xie.

271. Vibration of an elastic plate under action of an incompressibel fluid in the case of n = 0 ap-proximation of I. Vekua’s heirarchical models 85 (9)1177-1187(2006) (with N. Chinchiladze).

272. Viscosity dominated flows with temperature-dependent thermal conductivity Math. Methodsin the Applied Sciencess, Math. Methods Appl. Sci. 28 (2005), no. 10, 1201–1217 (withMing Fang and Yongzhi Xu).

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273. Cylindrical vibration of an elastic cusped plate under action of an incompressible fluid in caseof N = 0 approximation of I. Vekua’s heirarchical models, Complex Variables 50 (2005),479-496. (with N. Chinchaladze)

274. Marine Acoustics: Direct and Inverse Problems SIAM, Philadelphia (2004) (with J. Buchanan,A. Wirgin and Y. Xu).

275. A uniqueness theorem of the 2-dimensional acoustic scattering problem in a shallow oceanwith a fluid-like seabed. Computational Acoust. 11 (2003), 535-549.

276. Nonlinear systems arising from nonisothermal, non-Newtonian Hele-Shaw flows in the pres-ence of body forces and sources, Math. and Computer Modeling bf 35 (2002), 1425-1444.(withMing Fang)

277. Vibrations of an elastic plate under action of an incompressible fluidin the case of N = 0approximation of I. Vekua’s hierarchial models, (to appear) (with N. Chinchaladze)

278. Determination of the parameters of cancellous bone using high frequency acoustic measure-ments, Mathematical and Computer Model.45 (2007) 281-308 (with J. Buchanan).

279. Deriving the effective ultrasound equations for soft tissue (to appear) Computers and Math-ematics with Applications, Comput. Math. Appl. 49 (2005), no. 7-8, 1069–1080.(with MingFang and Xuming Xie

280. Homogenization of a viscoelastic matrix in linear frictional contact, Math. Methods in Appl.Scis. 28, 2005, 309-328.

281. Computing porosity of cancellous bone using ultrasound waves proceedings ISAAC 2005 meet-ing in Catania. (with Yongzhi Xu and Shamgyou Zhang)

282. identification of object in an acoustic wave guide inversion II: Robin-Dirichlet conditions,Math. Methods. Appl. Scis. bf 14(2)185-199 (2006). (with Doo-Sung Lee)

283. 2D mode excitation in a porous slab saturated with air in the high frequency approximation*:SAPEM 2005, (with J.-P. Groby, E. Ogam, A. Wirgin, Z.E.A. Fellah, W. Lauriks, J.-Y.Chapelon, C. Depollier, L. DeRyck, N. Sebaa, Y. Xu)

284. Recovery of the mechanical parameters of long bones from their vibroacoustic impulse response: SAPEM 2005, (with Erick Ogam, Armand Wirgin, Z.E.A Fellah, J.-P Groby, Walter Lau-riks, Jean-Yves Chapelon,Claude Depollier, Laurent DeRyck, Naima Sebaa, Yongzhi Xu)

285. Acoustic identification of a poroelastic cylinder:SAPEM 2005,(with Laurent DeRyck Zine Fel-lah, Jean-Philippe Groby, Erick Ogam, Naima Sebaa Jean-Yves Chapelon, Claude Depollier,Thierry Scotti, Armand Wirgin, Yongzhi Xu)

286. Nonexistence of Solutions to Hele-Shaw Equations, is in press by Nonlinear Analysis, TMA.(with Ming Fang).

287. A prototype homogenization model for acoustics of granular materials, Inter, Journ. Multi-scale Comput. Eng. 4(5), XX-XX (2006). (with A. Panchenko and Xuming Xie)

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288. Determination of the parameters of cancellous bone using high frequency acoustic measure-ments II: Inverse Problems, J. Comput. Acoustics, 15 (2) (2007), 199-220. (with J. Buchanan)

289. Nonisothermal, non-Newtonian Hele-Shaw flows witin Cattaneo’s heat flux law, Mathematicaland Computer Modelling, 46 (2007), 765-775. ( with Ming Fang )

290. Homogenization in time-harmonic acoustics of bone: The monophasic case, Mathematicaland Computer Modelling, 46 (2007), 331-340 with M. Fang, A Panchenko and A. Vasilic).

291. Near field representations of the acoustic Green’s function in a shallow ocean with infiniteelastic seabed, Georgian Journal of Mathematics (with Miao Ou

292. Asymptotic model of a nonlinear adaptive visco-elastic rod, Chapter 2, Discrete and Compu-tational Mathematics, 17-30, Nova Science Publishers, Inc., 2008. (Book) (Editors: FengshanLiu, Gaston M. N’Guerekata, Drajoljub Pokrajac, Xiquan Shi, Jiguang Sun, Xianggen Xia)ISBN: 1-60021-810-5, (with Xuming Xie)

293. An asymptotic model of a nonlinear Kelvin-Voight Viscoelastic plate (to appear) EvolutionaryEquations, Int. Jour. Evolutionary Equats. 2 (3) (2007), 235-253. (wth R. Ronkese).

294. Use of specific Green’s functions for solving direct problems involving a heterogeneous rigidframe porous medium slab solicited by acoustic waves Mathem. Methods Applied Sciences(2008)

295. A mathematical model for the evaluation of osteoporosis , Chapter 1, Discrete and Compu-tational Mathematics, 1-16, Nova Science Publishers, Inc., 2008. (Book) (Editors: FengshanLiu, Gaston M. N’Guerekata, Drajoljub Pokrajac, Xiquan Shi, Jiguang Sun, Xianggen Xia)ISBN: 1-60021-810-5 (with Yongzhi Xu and Shangyou Zhang)

296. Computing porosity of cancellous bone using ultrasonic waves, Journal of Applied FunctionalAnalysis. 2 (2) 185-195 (2007) (with Y. Xu and S. Zhang).

297. Modeling the Acoustic Behavior of Cancelleous Bone, in Solution methods by computersed. S. Saitoh, Research Insitute for Mathematical Scienes, Kyoto University, Kyoto, Japan(2007).

298. Existence and uniqueness theorems fror cusped prismatic shells in the nth hierarchial model.Math. Methods Applied Scis. (20080 (to appear) (with N. Chinchaladze, G. Jainini, S.Kharibegashvili, D. Natroshvili).

299. Homogenization in time-harmonic acoustics of bone: The monophasic case II: NumericalExperiments, Int. Journal Multiscale Comp. Engineering (with M. Fang, P. Guyenne and A.Vasilic).

300. Some inverse problems raised from a mathematical model of ductal carcinoma in situ Math-ematical and Computer Modelling (2008) (to appear) ( with Yongzhi Xu).

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