The Department of Mathematics at the University of Tennessee at Chattanooga offers the Bachelor of Arts (B.A.) and the Bachelor of Science in Applied Mathematics (B.S.) degrees. There are several different options under the B.S. in Applied Mathematics program not commonly found at all undergraduate institutions including concentrations in Actuarial Science, Computer Science, Corporate Science, and Systems Science. These concentrations require that the student take specific courses in disciplines outside the Department in addition to their Mathematics courses. For example, under the Corporate Science option, students must take courses in Accounting, Economics, Finance, Management, and Marketing.

The Department is the second largest credit hour producer in the University. During the 1999 Summer, 1999 Fall, and 2000 Spring Semesters the Department generated a total of 15,782 Semester Credit Hours (SCH). In order to put this figure in perspective, it should be noted that this represents 7.1% of the University total SCH and 12.4% of the College of Arts and Sciences SCH during the same time period. Moreover, this level of SCH production represents 53.4% of the SCH produced by the College of Business Administration, 45.8% of the SCH produced by the College of Education & Applied Professional Studies, 148.8% of the SCH produced by the College of Engineering & Computer Science, and 84.6% of the SCH produced by the College of Health & Human Services in this same time period.

This year saw many changes in the Mathematics Department the most significant of which were in the area of curriculum. Beginning with the 1999 Fall Semester, the new University General Education requirements went into effect. In preparation for these changes, the Department spent many months during the 1998--99 Academic Year revising several lower level service courses including the Calculus sequence. Changes were also made in other introductory level courses that resulted in the introduction of the new courses Math 123, 131, and 144. More details can be found in the section on Curriculum.

A new Department Head was hired in August of 1999 and some new activities in the areas of student relations were initiated. In addition, new efforts were made to attract more Mathematics majors and minors (see the section on Students below).

The Department had an outstanding year in research: 3 books appeared in print, 76 papers appeared in print or were accepted for publication in refereed journals, and another 15 papers were submitted for publication. Even when adjusted to account for some of the papers being jointly authored by more than one member of the Department, the numbers (67 and 15) are still quite impressive for a Department the size of the one at UTC. Of the twenty-four full time faculty members in the Department, thirteen had at least one paper appear in print or be accepted for publication during 1999-2000. In addition, faculty delivered a total of 24 presentations at professional meetings and invited colloquium lectures. Such a research output compares very favorably with Mathematics Departments at other universities that offer graduate programs.

The Department has been very active in its outreach activities. As can be seen from the sections on Grants and Contracts and Other Professional Activities below, faculty in the Department of Mathematics conduct workshops and provide other support activities for area school teachers. Some of these activities have received funding from outside agencies. It should be kept in mind that such activities also serve as valuable recruiting techniques for the Department and the University.

Personnel:

In 1999-2000 there were twenty-four full time faculty in the Department of whom 20 hold the Ph.D. degree. One faculty member, Kozubowski, was on leave-without-pay the whole year and Miller was on educational leave for the Spring Semester. John Gordon, Martha Wayland, and Terry Williams were hired on one year appointments. Pete Caithamer was reappointed as an Assistant Professor, Chris Mawata was promoted from Associate Professor to Professor, and Tom Kozubowski and Steve Xu were awarded tenure. Steve Kuhn's application for Sabbatical Leave for the 2001 Spring Semester was approved. John Graef was appointed Professor and Head of the Department effective August 1, 1999. A complete list of faculty and staff is as follows:

• Professors: Boris Belinskiy, Jerald Dauer, Billy Edwards, John Graef (Head), Stephen Kuhn, Christopher Mawata, Harry Miller, Edward Rozema, Eugene Schlereth, Ronald Smith.

• Associate Professors: Stan Byrd, Betsy Darken, Aniekan Ebiefung, Tomasz Kozubowski, Irene Loomis, Ossama Saleh, Terry Walters, Yongzhi Xu.

• Assistant Professors: Peter Caithamer.

• Instructors: Aimee Ellington, John Gordon, Martha Wayland, Terry Williams, Robert Wynegar (Director of Developmental Mathematics).

• Laboratory Staff: Mayme Kay Banasiak, Connie Boroughs.

• Staff: Karen Young (Administrative Secretary).

  In addition, the following adjunct faculty taught for the Department in 1999--2000: Dorothy Beach, Mayme Banasiak, Shukri Dalloul, Roland Fanselau, Thomas Fox, Samuel Ofori, Thomas Orofino, Walton Powers, Robert Reker, George Taylor, John Squires, Juanita Woods.

Awards and Honors:

• Ron Smith received the College of Arts and Sciences Outstanding Research Award .

• Boris Belinskiy, Bob Wynegar, and Steve Xu and Bob Wynegar were awarded Exceptional Merit for their activities during the 1998-99 Academic Year.

• Billy Edwards and Ron Smith successfully completed their Cumulative Performance Review.

• Several faculty members received Service Awards; these include:
  • Billy Edwards -- 30 years
  • Betsy Darken -- 20 years
  • Irene Loomis -- 10 years
  • Boris Belinskiy -- 5 years
  • Aimee Ellington -- 5 years
  • Harry Miller -- 5 years

The Department currently has 36 undergraduate majors enrolled in either the B.S. or B.A. program. There are also 35 Mathematics Education majors, and 14 Post-baccalaureate students are pursuing licensure in Secondary Mathematics. These last two groups are particularly important because Mathematics Education majors take the same courses designed for Mathematics majors but only three fewer hours. There are also currently 29 undergraduate students who are minoring in Mathematics.

Recruiting: Additional efforts were made this year to attract more Mathematics Majors and Minors. A flier describing the additional requirements needed for Engineering, Computer Science, Chemistry, and Physics majors to minor in Mathematics was circulated to those respective departments as well as to students currently enrolled in Mathematics courses. A copy of this flier appears as Appendix A in this report.

For more than 25 years the Mathematics Department has been administering the regional test for the Tennessee Mathematics Teachers Association's (TMTA) annual mathematics contest. This year the contest took place on March 21. More than 350 of the brightest students from Hamilton and five neighboring counties competed at five levels of mathematical ability: Algebra I, Algebra II, Geometry, Advanced Topics I, and Advanced Topics II. The top ten finishers in the region in each of the five levels, and the top ten finishers in Advanced Topics I and Advanced Topics II at the state level, were sent letters informing them of some of the opportunities available at UTC and inviting them to visit the campus.

Advising: At the beginning of the 1999 Fall Semester, letters were written to all undergraduate Mathematics majors informing them of the name of their advisor for the 1999--2000 Academic Year. A list of Mathematics Education majors and a list of students who are pursuing licensure in Secondary Mathematics were obtained from the College of Education and Applied Professional Studies. All of these students were also assigned a Mathematics advisor, and letters were written to inform them of the name of their assigned advisor. This procedure will continue to be used in the future.

Student Activities: In an effort to more actively involve undergraduate majors in the both the social and academic life of the Department, the Department Student Relations Committee, Chaired by Irene Loomis and composed of faculty members ( Mayme Kay Banasiak, Pete Caithamer, Billy Edwards, Aimee Ellington, Stephen Kuhn, Marti Wayland, Terry Williams and students (Jeremy Higdon, Eric Rymer, Jud Laman) sponsored several activities for students this year. These included hosting a pizza party at the start of the Fall Semester and inviting the students to a holiday luncheon in the Department at the end of the Fall Semester. The Committee also hosted a reception in honor of the graduating seniors at the end of the Spring 2000 Semester. Students were appointed to other committees in the Department including the Colloquium Committee (Yung-Ju Jeong ) and the Curriculum committee (Oloko Akintoye).

Student Awards and Honors:
Each year the Department makes a number of awards to deserving undergraduate students. These awards are presented at Honors Day. The recipients for 2000 are:

• Ruth Clark Perry Memorial Mathematics Award -- Kristen Clounch
• Winston Massey Memorial Mathematics Award -- Ryan Chamberlain and Yung Ju Jeong
• John W. Jayne Mathematics Award -- Jonathan McGlumphy and Kelly Ray Walker
• Pi Mu Epsilon Freshman Mathematics Award -- Sonja Petrovic
• James G. Ware Mathematics Education Award -- Kendal Eren Shipley

A Mathematics major, Ryan Chamberlain, passed the first actuarial exam on his first attempt; this is a significant accomplishment. Ryan is enrolled in the Actuarial Science Concentration in the B.S. in Applied Mathematics program.

Student Research::

• Boris Belinskiy sponsored Akintoye Oloko for a Provost Undergraduate Student Research Award on the "Investigation of the cross product in four dimensional space" which he received for Summer 2000.
• Steve Xu sponsored Yeon Whang for a Provost Undergraduate Student Research Award on "Inverse scattering" which he received for the Spring 2000 Semester.

Degrees Awarded:
The following students were awarded degrees in Secondary Mathematics Education during 1999--2000: Lakesha Carson, Kristen Clounch, Kellye Creech, Charlotte Purkey, Kendal Shipley, Erika Vonpeters, and Karen Wolfe.

Alumni Notes:

• Debbie Troutman Cantrell (B.S. Ed. 1982) is on the faculty at Chattanooga State (CSTCC).
• Gladys Crates (B.S. 1971, M.S. 1973) is the Dean of Mathematics and Science at Chattanooga State (CSTCC).
• John Gordon (B.A. 1997) is an Instructor of Mathematics at the University of Tennessee at Chattanooga.
• Pam Grimes Poland (B.S. 1983) is an Ophthalmologist practicing in Oklahoma.
• Marsha Schoonover (M.S. Ed. 1981) is a member of the Mathematics faculty at Chattanooga State (CSTCC).
• David Scott (B.S. 1993) is working at Blue Cross and Blue Shield of Tennessee.

Among the many changes in lower level course offerings, the most significant one is the Calculus sequence. The new courses Math 151: Calculus I and Math 152: Calculus I Laboratory correspond to the previous Math 150: Calculus and Analytic Geometry. Math 151 is a three hour lecture course while Math 152 is a two contact hour one credit hour laboratory.Similar statements hold for Math 161/162, i.e., Calculus II. The laboratory courses Math 152 and 162 are taught in the Department's computer lab and make extensive use of the software package Maple. The laboratory projects are designed by the faculty members teaching the courses; this requires a great deal of time and effort on their part.

Changes were also made in a number of other Mathematics courses in order to ensure that they satisfy the requirements to be a General Education course. These courses are Math 123, 131, 136, 144, 145, and 210.

The Department Curriculum Committee (Boris Belinskiy, Betsy Darken, Steve Kuhn (Chair) , Chris Mawata, Gene Schlereth, Oloko Akintoye (student)) are charged with reviewing and making recommendations for possible changes in the undergraduate curriculum for both the B.A. and B.S. degrees. This review is expected to take two years.

The research interests of the faculty span the range from abstract to applicable to applied. The faculty collaborate with other mathematicians from the United States as well as from China, the Czech Republic, France, Hungary, India, Japan, Russia, and Slovakia. Models describing the growth of certain animal populations, the spread of infectious diseases, wave phenomena, acoustic scattering, underwater imaging, manufacturing systems, industrial pollution emission control, random oscillations of mechanical systems, and financial data are among the many applications studied by members of the Department. The remainder of this section documents the various research activities of the Department in 1999--2000.

Books:

A. Jerald P. Dauer

1. "Elements of Control Theory," with K. Balachandran, Narosa Publishing House, London, 1999.

2. "Recent Developments in Complex Analysis and Computer Algebra," with R. P. Gilbert and J. Kajiwara, Kluwer Academic, 1999.
3. "Direct and Inverse Problems of Mathematical Physics," with R. P. Gilbert and J. Kajiwara, Kluwer Academic, 2000.

Papers Appeared in Print:

A. Boris Belinskiy

1. Wave phenomena in a wave guide with elastic walls: abstract differential equation formulation, with J. P. Dauer, in: Volterra Equations and Applications, ed. C. Corduneanu and I. W. Sandberg, Gordon and Breach Science Publishers, Amsterdam, 1999, 149--155.
2. Existence and uniqueness for boundary value contact problems, with I. V. Andronov, in: Partial Differential and Integral Equations, H. G. W. Begehr et al. (eds.), Kluwer Academic Publishers, 1999, 287--301.
3. Eigenvalue problems for elliptic type partial differential operators with spectral parameter contained linearly in boundary conditions, in: Partial Differential and Integral Equations, H. G. W. Begehr et al. (eds.), Kluwer Academic Publishers, 1999, 319--333.
4. The reality of fluid wave resonance frequencies on a cylindrical shell , with J. P. Dauer and H. Uberall, Acta Mechanica 141 (2000), 117--123.
5. Exponential mixture representation of geometric stable densities , with T. Kozubowski, Journal of Mathematical Analysis and Applications 246 (2000), 465--479.

6. On the distribution of self-similar stochastic processes defined by double Wiener-Ito integrals , Radovi Matematicki 9 (1999).

7. Wave phenomena in a wave guide with elastic walls: abstract differential equation formulation , with B. Belinskiy, in: Volterra Equations and Applications, ed. C. Corduneanu and I. W. Sandberg, Gordon and Breach Science Publishers, Amsterdam, 1999, 149--155.
8. Bicriteria programming with several modern applications , with Y. H. Liu, Computers and Industrial Engineering 37 (2000), 563--580.
9. The reality of fluid wave resonance frequencies on a cylindrical shell , with B. Belinskiy and H. Uberall, Acta Mechanica 141 (2000), 117--123.
10. Controllability of neutral functional integrodifferential systems in Banach spaces , with K. Balachandran, Computers and Mathematics with Applications 39 (2000), 117--126.

11. Information technology outsourcing decision analysis: analytic hierarchy approach , with G. Udo, in: Information Technology Outsourcing Decision Analysis: Analytic Hierarchy Approach, Proceedings of the 30th Annual Meeting of the Decision Sciences Institute.
12. The vertical linear complementarity problem associated with po-matrices , Optimization Methods and Software 10 (1999), 747--761.
13. Human factors affecting the success of advanced manufacturing systems , with G. Udo, Computers and Industrial Engineering 37 (1999), 297--300.
14. An industrial pollution emission control model , with G. Udo, Computers and Industrial Engineering 37 (1999), 371--374.

15. The research backs calculators , with D. J. Dessart and C. M. DeRidder, Mathematics Education Dialogues, National Council of Teachers of Mathematics 2 (1999), 6.

16. Oscillation of a higher order neutral difference equation with a forcing term}, with M. M. S. Manuel, P. W. Spikes, and E. Thandapani, International Journal of Mathematics and Mathematical Sciences 22 (1999), 147--154. *
17. Oscillatory behavior of solutions of Volterra summation equations , with E. Thandapani, Applied Mathematics Letters 12 (1999), 79--84.*
18. On a nonlinear boundary value problems for fourth order equations , with B. Yang, Applicable Analysis 72 (1999), 439--448.*
19. Global dynamics of a SEIR model with varying total population size , with J. Karsai, M. Y. Li, and L. Wang, Mathematical Biosciences 160 (1999), 191--213.*
20. Review of "Global Behavior of Nonlinear Difference Equations of Higher Order with Applications" by V. L. Kocic and G. Ladas , Mathematical Intelligencer 21 (1999), 60--61.*
21. Global stability in a nonlinear difference equation , with C. Qian, Journal of Difference Equations and Applications 5 (1999), 251--270.*
22. Oscillation of two dimensional difference systems , with C. Qian and E. Thandapani, Computers and Mathematics with Applications 38 (1999), 157--165.*
23. Oscillatory and asymptotic behavior of solutions of third order delay difference equations , with E. Thandapani, Funkcialaj Ekvacioj 42 (1999), 355--369.*
24. Existence and nonexistence of positive solutions of fourth order nonlinear boundary value problems , with B. Yang, Applicable Analysis 74 (2000), 201--214.
25. On the phase volume method for nonlinear difference equations , with J. Karsai and M. Y. Li, International Journal of Differential Equations and Applications 1 (2000), 17--35.*
26. Behavior of solutions of impulsively perturbed non--halflinear oscillator equations , with J. Karsai, Journal of Mathematical Analysis and Applications 244 (2000), 77--96.
27. Global attractivity in differential equations with variable delays , with C. Qian, Journal of the Australian Mathematical Society Series B: Applied Mathematics 41 (2000), 568--579.*
28. A note on the existence of oscillatory solutions of higher order neutral differential equations , with B. Yang and B. G. Zhang, Acta Scientiarum Mathematicarum, 66 (2000), 63--70.
29. Behavior of solutions of perturbed quasilinear difference equations , with R. Arul, P. W. Spikes, and E. Thandapani, Communications in Difference Equations (2000), 45--58.*
30. A generalization of the Milloux--Hartman theorem for nonlinear systems , with J. Karsai and M. Y. Li, Communications in Difference Equations (2000), 203--214.*

31. Tails of Levy measure of geometric stable random variables , with K. Podgorski and G. Samorodnitsky, Extremes 1 (1998), 367--378.
32. Univariate geometric stable distributions , with S. T. Rachev, Journal of Computational Analysis and Applications 1 (1999), 177--217.
33. Multivariate geometric stable distributions , with S. T. Rachev, Journal of Computational Analysis and Applications 1 (1999), 349--385.
34. Multivariate geometric stable distributions in financial applications , with A. K. Panorska, Mathematical and Computer Modeling 29 (1999), 83--92.
35. Geometric stable laws: estimation and applications , Mathematical and Computer Modeling 29 (1999), 241--253.
36. Simulation of geometric stable and other limiting multivariate distributions arising in random summation scheme , with A. K. Panorska, Mathematical and Computer Modeling 29 (1999), 255--262.
37. A class of asymmetric distributions , with K. Podgorski, ARCH Research Clearing House 1 (1999), 113--134.
38. Geometric stable laws through series representations , with K. Podgorski, Serdica Mathematical Journal 25 (1999), 241--256.
39. Asymmetric Laplace distributions , with K. Podgorski, Mathematical Scientist, 25 (2000), 36--45.
40. Computer simulation of geometric stable distributions , Journal of Computational and Applied Mathematics 116 (2000), 221--229.
41. Exponential mixture representation of geometric stable densities , with B. P. Belinskiy, Journal of Mathematical Analysis and Applications 246 (2000), 465--479.

42. Determination of a distributed inhomogeneity in a two-layered waveguide from scattered sound , with R. P. Gilbert and Y. Xu, in: "Direct and Inverse Problems of Mathematical Physics," edited by R. P. Gilbert, J. Kajiwara, and Y. Xu, Kluwer Academic Publishers, 2000, 107--123.

43. Path Product Matrices , with C. R. Johnson, Journal of Linear and Multilinear Algebra 46 (1999), 177--191.
44. The general totally positive matrix completion problem with few unspecified entries , with S. M. Fallat and C. R. Johnson, Electronic Journal of Linear Algebra 7 (2000), 1--20.
45. The positive definite completion problem relative to a subspace , with C. R. Johnson, Linear Algebra and Its Applications 307 (2000), 1--14.

46. Inverse acoustic scattering problems in ocean environments , Journal of Computational Acoustics 7 (1999), 111--132.
47. Inverse scattering method for imaging objects in ocean environments , in: Proceeding of PIEMA99, Clermont-Ferrand, France, (1999).
48. An inverse problem for the quasistatic thermoelastic system on the unit disk , Applicable Analysis (Special Issue on Dr. H. Begehr's 60th Birthday), 73 (1999), 295--305.
49. The unidentified object problem in a shallow ocean with a fluid-like sediment layer overlying a rigid seabed , with J. Buchanan, R. P. Gilbert, and A. Wirgin, Applicable Analysis (Special Issue on Dr. H. Begehr's 60th Birthday), 73 (1999), 5--17.
50. Identification of acoustically soft solids of revolution in a waveguide using the ICBA method , with J. Buchanan, R. P. Gilbert, and A. Wirgin, in: Analytical and Computational Methods in Scattering Theory and Applied Mathematics, F. Santosa and I. Stagold (eds.), CRC Press LLC, 1999, 27--36.
51. Determination of a distributed inhomogeneity in a two-layered waveguide from scattered sound , with R. P. Gilbert and C. Mawata, in: "Direct and Inverse Problems of Mathematical Physics," edited by R. P. Gilbert, J. Kajiwara, and Y. Xu, Kluwer Academic Publishers, 2000, 107--123.

A. Boris Belinskiy

1. Heat distribution in a room with partially insulated walls , with J. Hiestand, Applicable Analysis, to appear.
2. Wave propagation in the ice-covered ocean wave guide and operator polynomials , Proceedings of the Second ISAAC Congress, to appear.
3. Mathematical aspects of wave phenomena in a wave guide with elastic walls and operator polynomials , with J. Dauer, Chapter 5 in Festschrift Volume II: Propagations, Ocean Acoustics and Scattering, dedicated to H. Uberall, World Scientific Publishing Company, to appear.

4. Evaluating calculus reform: a review and a longitudinal study , with S. Kuhn and R. Wynegar, Research in Collegiate Mathematics Education, CBMS Issues in Mathematics Education, American Mathematical Society, Providence, to appear.

5. Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces , Journal of Mathematical Analysis and Applications, to appear.
6. Mathematical aspects of wave phenomena in a wave guide with elastic walls and operator polynomials , with B. Belinskiy, Chapter 5 in Festschrift Volume II: Propagations, Ocean Acoustics and Scattering, dedicated to H. Uberall, World Scientific Publishing Company, to appear.

7. Asymptotic behavior of solutions of differential equations with variable delays , with C. Qian and B. Zhang, Proceedings of the London Mathematical Society, to appear.*
8. On L² solutions of third order nonlinear differential equations , with M. Bartusek, Dynamic Systems and Applications, to appear.*
9. Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations , with E. Thandapani, Fasciculi Mathematici, to appear.*
10. Oscillation theorems for general quasilinear second order difference equations , with E. Thandapani and K. Ravi, Computers and Mathematics with Applications, to appear. An invited paper for the special issue: "Advances in Difference Equations III."*
11. Nonoscillation results for nonlinear systems with nondecreasing energy , with J. Karsai and B. Yang, Dynamics of Continuous, Discrete and Impulsive Systems, to appear.*
12. Global attractivity of the equilibrium of a nonlinear difference equation , with C. Qian, Czechoslovak Mathematical Journal, to appear.*
13. On the oscillation of impulsively damped halflinear oscillators , with J. Karsai, Electronic Journal of Qualitative Theory of Differential Equations, to appear.

14. Asymmetric Laplace laws and modeling financial data , with K. Podgorski, Stable Models in Finance, Vol 2, (eds. S. Mittnik and S. T. Rachev), Pergamon Press, to appear.
15. A multivariate and asymmetric generalization of Laplace distribution , with K. Podgorski, Computational Statistics, to appear.

16. Evaluating calculus reform: a review and a longitudinal study , with B. Darken and R. Wynegar, Research in Collegiate Mathematics Education, CBMS Issues in Mathematics Education, American Mathematical Society, Providence, to appear.

17. Generalized dual space indicator method for underwater imaging , with W. Lin and Y. Xu, in Inverse Problems, (Special Issue for Inverse Problems in Underwater Acoustics), to appear.
18. Generalized dual space indicator method for imaging obstacles in a homogeneous medium , with W. Lin and Y. Xu, Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers, to appear.

19. Line insertions in totally positive matrices , with C. R. Johnson, Journal of Approximation Theory, to appear.

20. Evaluating calculus reform: a review and a longitudinal study , with B. Darken and S. Kuhn, Research in Collegiate Mathematics Education, CBMS Issues in Mathematics Education, American Mathematical Society, Providence, to appear.

21. A mode-matching method for forward and inverse scattering from an object in a shallow-water waveguide , with J. Buchanan, P. Cristini, R. P. Gilbert, and A. Wirgin, Proceeding of ICTCA'99, to appear.
22. Generalized dual space indicator method for underwater imaging , with C. Mawata and W. Lin, in Inverse Problems, (Special Issue for Inverse Problems in Underwater Acoustics), to appear.
23. Generalized dual space indicator method for imaging obstacles in a homogeneous medium , with C. Mawata and W. Lin, Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers, to appear.
24. Continuity and determination of parameters for quasistatic thermoelastic system , with M. He, Proceedings of the Second ISAAC Congress, Kluwer Academic Publishers, to appear.
25. Determination of a buried object in a two-layered shallow ocean , with R. P. Gilbert and M. Wirby, J. of Computational Acoustics, to appear.

A. Boris Belinskiy

1. Optimal control of an elastic string with a viscous damping, with S. Lenhart, to appear.
2. On uniqueness of the solution for the diffraction problem on an infinite plate with local non-homogeneities, with I. V. Andronov, to appear.
3. Acoustic scattering from an elastic plate supported by a rigid narrow rib, with I. V. Andronov, to appear.
4. Uniqueness and non-uniqueness for boundary contact value problems, with I. V. Andronov, to appear.
5. Asymptotics of eigenfrequencies and eigenmodes of non-homogeneous in-extensible filament loaded at one end, with M. A. Shubov, to appear.

6. Positive solutions of a boundary value problem for fourth order nonlinear differential equations, with B. Yang, to appear.*
7. Some new results and open problems on oscillation of nonlinear difference equations, with L. Ramuppillai and E. Thandapani, to appear.*
8. Forced oscillation of second order linear and half-linear difference equations, with O. Dovsly and J. Jarovs, to appear.

9. An Asymmetric multivariate Laplace distribution, with K. Podgorski, to appear.
10. A new measure of local dependence, with I. Bairamov and S. Kotz, to appear.
11. Maximum entropy characterization of asymmetric Laplace distribution, with S. Kotz and K. Podgorski, to appear.
12. On the vertical density of the multivariate exponential power distribution, to appear.

13. A simple method for object detection in a shallow water waveguide, to appear.
14. A mode-matching method for forward and inverse scattering from an object in a shallow-water waveguide, with J. Buchanan, P. Cristini, R. P. Gilbert, and A. Wirgin, to appear.
15. Generalized dual space indicator method for inverse scattering problems in underwater acoustics, to appear.

A. Boris Belinskiy

1. Acoustic excitation of Scholte-Stoneley and Lamb waves on a reinforced cylindrical shell, with J. Dauer, A. Gerard, O. Poncelet, and H. Uberall, an invited talk presented at the Fourth International Conference on Theoretical and Computational Acoustics, in Stazione Marittima, Trieste, Italy, 1999.
2. Stochastic integral equations and random oscillations of mechanical systems, with P. Caithamer, presented at the 105th Annual Meeting of the American Mathematical Society, in Washington, D. C., January 19--22, 2000.
3. Uniqueness and non-uniqueness for boundary-contact value problems of acousto-elastic scattering, with I. V. Andronov, presented at the symposium ``Theory of Partial Differential Equations and Special Topics of Theory of Ordinary Differential Equations, dedicated to the 150-th anniversary of the birthday of Sofia V. Kovalevskaya, in St. Petersburg, Russia, 2000.
4. Energy of a mechanical system driven by gaussian noise white in time, with P. Caithamer, presented at the Year 2000 International Conference on Dynamical Systems and Differential Equations, held at Kennesaw State University, Kennesaw, Georgia, May 18--21, 2000.

5. Stochastic integral equations and random oscillations of mechanical systems, with B. Belinskiy, presented at the 105th Annual Meeting of the American Mathematical Society, in Washington, D. C., January 19--22, 2000.
6. Energy of a mechanical system driven by gaussian noise white in time, with B. Belinskiy, presented at the Year 2000 International Conference on Dynamical Systems and Differential Equations, held at Kennesaw State University, Kennesaw, Georgia, May 18--21, 2000.

7. Acoustic excitation of Scholte-Stoneley and Lamb waves on a reinforced cylindrical shell, with B. Belinskiy, A. Gerard, O. Poncelet, and H. Uberall, an invited talk presented at the Fourth International Conference on Theoretical and Computational Acoustics, in Stazione Marittima, Trieste, Italy, 1999.

8. Information Technology Outsourcing Decision Analysis: Analytic Hierarchy Approach presented at the 30th Annual Meeting of the Decision Sciences Institute, in New Orleans, Louisiana, November 20--23, 1999.

9. Nonoscillatory behavior of solutions of impulsive systems with increasing energy, with J. Karsai and B. Yang, to be presented at the Sixth Colloquium on the Qualitative Theory of Differential Equations, held at the Bolyai Institute of Mathematics of the University of Szeged, Szeged, Hungary, August 10--14, 1999.*
10. Existence of solutions for boundary value problems of a sixth order differential equation, with B. Yang, presented at the Twenty--fourth Annual Meeting of the Society for Industrial and Applied Mathematics Southeastern Atlantic Section, held at the University of Georgia, Athens, Georgia, March 24--25, 2000.
11. Some integrability properties of solutions of nonlinear third order differential equations, with M. Bartusek, an invited address presented in the Special Session ``Differential Inequalities and Applications" at the 953rd Meeting of the American Mathematical Society, held at Notre Dame University, Notre Dame, Indiana, April 8--9, 2000.
12. Some limit-point/limit-circle results for third order differential equations, with M. Bartusek, presented at the Year 2000 International Conference on Dynamical Systems and Differential Equations, held at Kennesaw State University, Kennesaw, Georgia, May 18--21, 2000.
13. Oscillation and nonoscillation in a nonlinear impulsive system with increasing energy, with J. Karsai, presented at the Year 2000 International Conference on Dynamical Systems and Differential Equations, held at Kennesaw State University, Kennesaw, Georgia, May 18--21, 2000.

14. Almost principal minors of inverse M-matrices, with C. R. Johnson, presented at the Thomas L. Markham Matrix Theory, Symposium in Columbia, South Carolina, December, 1999.

15. A regularized acoustic inverse scattering method for underwater imaging, an invited talk in the special session ``Inverse Problems in Acoustics" at the Second Congress of International Society of Analysis, its Applications and Computations (ISAAC'99), in Fukuoka, Japan, August 16-22, 1999.
16. Generalized dual space indicator method for inverse scattering problems in underwater acoustics, presented at the conference ``Inverse Problems and Nonlinearity, Theory and Applications" held at the Université Montpellier II, Montpellier, France, June 20-24, 2000.

A. John R. Graef

1. The limit-point/limit-circle problem: a survey, presented at Mississippi State University, Mississippi State, Mississippi, June 26, 2000.

2. Laplace distributions and their generalizations, presented at the University of California at Santa Barbara, October 19, 1999.

3. A generalized dual space indicator method for inverse problems in underwater acoustics, presented at Mississippi State University, Mississippi State, Mississippi, April 5, 2000.
4. Inverse scattering problems in underwater acoustics, presented at City University of Hong Kong, May 4, 2000.
5. A generalized dual space indicator method for inverse scattering problems in ocean acoustics, presented at Zhongshan University, Guangzhou, China, May 8, 2000.
6. A new method for inverse scattering problems in underwater acoustics, presented at Ningxia University, Yinchuan, China, May 25, 2000.
7. Applied mathematics and mathematics education in the U.S., presented at Ningxia University, Yinchuan, China, May 25, 2000.
8. Some new results of the generalized dual space indicator method, presented at CNRS Lab of Mechanics and Acoustics, Marseille, France, June 16, 2000.

• Boris Belinskiy was named a CECA Scholar for the 1999--2000 academic year.
• Boris Belinskiy applied for a Faculty Development Grant to support his trip to the University of Texas at Lubbock to give an invited Colloquium Lecture and collaborate on a research paper with M. A. Shubov. The proposal was not funded.
• Boris Belinskiy received a $1,500 Faculty Development Grant for 2000--01 to conduct the Department Colloquium Series.
• Boris Belinskiy received a $1300 Grant from the Speakers and Special Events Committee to invite three distinguished speakers to the UTC campus.
• Boris Belinskiy and Peter Caithamer received a UTC Library Enhancement Grant in the amount of $386.
• Betsy Darken and Bob Wynegar were awarded the THEC/Eisenhower Grant Standards Based Mathematics in the Middle School in the amount of $27,000. They worked with 19 middle school teachers from 6 different regional school systems.
• Jerry Dauer and Linda Collins (UTC Biological and Environmental Sciences) received the three year National Science Foundation Course, Curriculum and Laboratory Improvement grant Sunlight, Science and Understanding: A Theme Based Interdisciplinary Course in the amount of $150,000 ($37,885 for 1999--2000) to develop and implement an interdisciplinary course to satisfy the new General Education Requirements in the natural sciences.
• Jerry Dauer and Phil Kazemersky (UTC College of Engineering and Computer Science) applied for a NASA grant to fund UTC's Saturday School for introducing high school students to mathematics and science. The proposal was not funded.
• Aniekan Ebiefung was named a Research Associate for the 2000 Spring Semester by the Office of Grants and Research.
• Aniekan Ebiefung applied for a UTC Summer Fellowship The vertical complementarity problem. The proposal was not funded.
• Aniekan Ebiefung applied for a Faculty Research Grant Production equilibrium point in multi--units manufacturing systems. The proposal was not funded.
• Aniekan Ebiefung applied for a CECA CCI Grant Discovering statistics and probability through exploration. The proposal was funded for the 2000 Fall Semester.
• Aniekan Ebiefung applied for CECA Scholarship The vertical nonlinear complementarity problem. The funding is pending.
• John Graef and Phil Kazemersky (UTC College of Engineering and Computer Science) received a $2300 grant from the UTC Center of Excellence for Computer Applications to purchase a one year site license for the software MINITAB to be used in Statistics courses.
• John Graef received a UTC Library Enhancement Grant in the amount of $470.
• Steve Kuhn and Bob Wynegar received the Goals 2000 Grant Priming the Algebra One Pump with Content and Technology in the amount of $194,000. They worked with 47 Algebra One teachers from 12 regional school systems.
• Steve Kuhn, Chris Mawata, and Bob Wynegar submitted the grant proposal Putting Mathematics on the Web to the American Honda Foundation in the amount of $41,708; the grant was not funded.
• Chris Mawata and Bob Wynegar submitted the Proof of Concept proposal Putting Mathematics on the Web to the National Science Foundation in the amount of $75,000; the funding is still pending.
• Ron Smith was named a CECA Scholar for the 1999--2000 academic year.
• Bob Wynegar receives a Faculty Development Grant to attend the International Conference on Technology in Collegiate Mathematics on November 4 --7, 1999; the grant was in the amount of $1,174.
• Steve Xu received a CECA Research Grant for Spring 2000 and a CECA CCI Grant also for Spring 2000.
• Steve Xu received a Faculty Summer Research Fellowship for the Summer of 2000.

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  OTHER PROFESSIONAL ACTIVITIES

  Editing and Reviewing Activities:

  • Several members of the Department serve as referees for journals in the Mathematical Sciences and several are reviewers for Mathematical Reviews.
  • The following faculty members serve on Editorial Boards for professional journals:
    • Jerry Dauer: Journal of Mathematical Analysis and Applications
    • John Graef: Dynamic Systems and Applications; Electronic Journal of Qualitative Theory of Differential Equations; Nonlinear Studies.
    • Steve Xu: Applicable Analysis

  Workshops Conducted:

  The Mathematics Department has a very active program of outreach activities including conducting workshops for various groups. Faculty members presented the following workshops during the time period of this report.

  • Aniekan Ebiefung conducted the workshop Action Plan for Integrating the Web into the Classroom for Hamilton County School teachers on August 28, 1999.
  • Aniekan Ebiefung conducted the workshop Teaching and Sharing Internet Resources in the Mathematics Department on September 11, 1999.
  • Billy Edwards conducted the Mathematics Study Section for prospective engineers in preparation for their Fundamentals of Engineering Exam (FE) in the Spring 2000 Semester.
  • Steve Kuhn and Bob Wynegar conducted a Content (Algebra I) and Technology (TI-83Plus) Workshop for a total of 70 area teachers over an eight day period.
  • Steve Kuhn and Bob Wynegar conducted a Technology Training (TI-83Plus) Workshop for Hamilton County Schools; they gave four days of training for two groups of teachers.
  • Bob Wynegar conducted technology, content, and curriculum training for Education Edge/CESME; this provided three days of training for regional teachers.

  Other Activities:

  • Boris Belinskiy prepared a Special Issue of the journal Applicable Analysis containing the Proceedings of the Special Session on Differential Equations/Dynamical Systems at the SIAM/SEAS Meeting on Control that he organized in May 1999).
  • Boris Belinskiy organized a Special Session on Mathematical Aspects of Wave Propagation Theory at the International Conference on Dynamical System and Differential Equations held at Kennesaw State University, Kennesaw, Georgia, on May 18--21, 2000.
  • Stan Byrd organized a STUDENT PROBLEM COMPETITION where each month a different problem was posed and the persons submitting correct solutions were recognized. He is trying to obtain external sources of funds to provide a small reward to the monthly winners.
  • The Department served as a testing site for the Society Of Actuaries examinations. Pete Caithamer administered the exams in Fall 1999 and Ossama Saleh administered them in Spring 2000.
  • Jerry Dauer attended the 105th Annual Meeting of the American Mathematical Society, in Washington, D. C., January 19--22, 2000.
  • Jerry Dauer is a member of the Scientific Committee for the International Conference on Acoustics, Noise and Vibrations which will be held at McGill University in August, 2000.
  • Billy Edwards was selected to attended a NSF Workshop at Appalachian State University on Pre-Statistics teacher preparation in July, 1999; only a total of 20 participants were chosen from a variety of national geographical regions.
  • Billy Edwards is the higher education member of an advisory committee to the Discovery Museum; they are planning a Math theme for Summer, 2000.
  • Aimee Ellington received the Outstanding Achievement Award in Mathematics Education at the University of Tennessee at Knoxville, in April 2000.
  • John Graef served on the Praxis Task Force for the College of Education and Applied Professional Studies (CEAPS) and a subcommittee of NCATE 2000 for CEAPS.
  • John Graef served as an external reviewer for a Ph.D. student at the University of Madras, Madras, India.
  • Dr. Janos Karsai, Senior Research Associate at the Department of Medical Informatics of Albert Szent-Gyorgyi Medical University in Szeged, Hungary, visited UTC from May 1 to June 1, 2000 to conduct joint research with John Graef.
  • Tom Kozubowski wrote a test unit for the Society of Actuaries Exam 1 to be used in the new actuarial examination system; this work was done for the American College Testing Program.
  • Tom Kozubowski was invited to serve as a consultant on initiating an actuarial science program in the Department of Mathematics at Indiana University-Purdue University at Indianapolis, on December 7-10, 1999.
  • Irene Loomis was asked to serve on the Advisory Board for Women's Studies.
  • Irene Loomis participated on a panel on Women's Studies in Mathematics and Science.
  • Ron Smith together with C. R. Johnson (College of William and Mary) organized the Thomas L. Markham Matrix Theory Symposium held in Columbia, South Carolina, in December, 1999.
  • Again this year, Bob Wynegar} ran the Tennessee Early Mathematics Placement Test (TEMPT) Program that was used by 30 schools statewide involving more than 3,200 students.
  • Bob Wynegar conducted the Tennessee Mathematics Teachers' Association's Annual Mathematics Competition which hosted 160 students from 8 schools from the greater Chattanooga area here at UTC.
  • Bob Wynegar serves on the Advisory Board for PRISM (Promoting Resolve in Science and Mathematics), a UTC College of Education and Applied Professional Studies project.
  • Steve Xu served on the Examination Panel for a Ph.D. thesis defense at the CNRS Lab of Mechanics and Acoustics, in Marseille, France.
  • Steve Xu organized a special session on Inverse Problems in Acoustics at the Second Congress of the International Society of Analysis, its Applications and Computations (ISAAC'99), held in Fukuoka, Japan, on August 16-22, 1999.
  • Several members of the Department (Billy Edwards, Steve Kuhn, Chris Mawata, Ed Rozema, Terry Walters, Marti Wayland and Bob Wynegar) were selected to participate in the ``Guide to Success" program at UTC. This program concerns the use of technology in the classrooms, and these faculty will act in an advisory capacity to other faculty on campus.

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  OTHER DEPARTMENT ACTIVITIES

  The Department has had a very active Colloquium Lecture Series in the past and this year was no exception. The Colloquium Committee (Boris Belinskiy (Chair), The Department has had a very active Colloquium Lecture Series in the past and this year was no exception. The Colloquium Committee (Boris Belinskiy (Chair), Aniekan Ebiefung, Harry Miller, Yongzhi Xu, Yung-Ju Jeong} (student) arranged for twenty-seven Colloquium Lectures to be presented on a variety of topics dealing with pure and applied mathematical research, mathematics education, grant writing, and changes in the Hamilton County Schools Mathematics courses. These lectures were presented by mathematicians from the U.S., Bosnia, China, Germany, Hungary, and New Zealand. Boris Belinskiy obtained a grant from the Speakers and Special Events Committee to support three of the speakers, namely, Janos Karsai (University of Szeged, Hungary), John Kenelly (Clemson University), and John Neuberger (North Texas University). A complete listing of presenters, titles, and dates of their lectures can be found in APPENDIX B.

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  SERVICE

  Faculty members in the Department of Mathematics serve on Masters Degree examination committee for students in other departments and colleges. They also serve on a variety of committees at all levels in the University. A complete list of committee assignments is as follows.

  Department Committees:

  1. Colloquium Committee: Boris Belinskiy (Chair), Aniekan Ebiefung, Harry Miller, Yongzhi Xu, Yung-Ju Jeong (student)
  2. Curriculum Committee: Boris Belinskiy, Betsy Darken, Stephen Kuhn (Chair), Chris Mawata, Gene Schlereth, Oloko Akintoye (student)
  3. Hiring Committee: Stan Byrd, Ossama Saleh, Gene Schlereth (Chair), Terry Walters, Steve Xu
  4. Library Committee: Pete Caithamer, Aniekan Ebiefung, Ron Smith (Chair)
  5. Rank, Tenure, and Reappointment Committee: All tenured faculty; Chris Mawata was elected Chair
  6. Scheduling Committee: Stan Byrd, Edward Rozema (Chair), Ron Smith
  7. Student Relations Committee: Mayme Kay Banasiak, Pete Caithamer, Billy Edwards, Aimee Ellington, Stephen Kuhn, Irene Loomis (Chair), Marti Wayland, Terry Williams, Jeremy Higdon (student), Eric Rymer (student), Jud Laman (student)
  8. Technology Committee:} Jerry Dauer, Chris Mawata, Terry Walters (Chair), Steve Xu
  9. Testing Committee: Mayme Kay Banasiak, John Gordon, Edward Rozema, Bob Wynegar (Chair)
  10. Course Coordinator for Math 105 & 106: Robert Wynegar
  11. Course Coordinator for Math 116: Billy Edwards
  12. Course Coordinator for Math 123: Gene Schlereth
  13. Course Coordinator for Math 131: Boris Belinskiy
  14. Course Coordinator for Math 136: Harry Miller (Fall Semester), Marti Wayland (Spring Semester)
  15. Course Coordinator for Math 144: Steve Xu
  16. Course Coordinator for Math 145: Stan Byrd
  17. Course Coordinator for Math 151 & 152: Stephen Kuhn
  18. Course Coordinator for Math 160: Edward Rozema
  19. Course Coordinator for Math 210: Pete Caithamer
  20. Course Coordinator for Math 212: Aniekan Ebiefung
  21. Course Coordinator for Math 245: Irene Loomis

  College of Arts and Sciences Committees:

  1. College Council: John Graef, Gene Schlereth

  University Committees:

  1. Academic Standards Committee: Terry Walters
  2. Admissions Committee: Ed Rozema
  3. Athletics Committee (Chair): Billy Edwards
  4. Bookstore Committee: Gene Schlereth
  5. Classroom Technology Committee: Chris Mawata
  6. Curriculum Committee: Boris Belinskiy
  7. Dean of Arts and Sciences Search Committee: Boris Belinskiy
  8. Departmental Honors Committee: Ossama Saleh
  9. Faculty Council: Irene Loomis, Edward Rozema
  10. Faculty Rating of Administration Committee: Aniekan Ebiefung
  11. Dean of Arts and Sciences Search Committee: Boris Belinskiy
  12. Faculty Research: Pete Caithamer, Jerry Dauer
  13. General Education Committee (Chair): Betsy Darken
  14. Handbook Committee: Ed Rozema
  15. Library Committee: Ron Smith
  16. Petitions Committee: Bob Wynegar
  17. SACS Accreditation Library Subcommittee: Gene Schlereth
  18. Scholarship Committee: Steve Kuhn
  19. Speakers and Special Events Committee: Stan Byrd

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  SOME NOTES ON ASSESSMENT

  One measure of assessment common to many universities is the use of student evaluations. On the question "The Instructor of this class is an effective teacher," the Mathematics Department average in Fall 1999 computed from data provided by the UTC Office of Planning, Evaluation, and Institutional Effectiveness is 5.14, which compares favorably with the average for the College of Arts and Sciences (5.34) and the entire University (5.33) for the same time period.

  Another measure of assessing a degree program is how successful its graduates are in attaining the next step in their career plans. Of the five Mathematics majors who graduated in 1999--2000, and in fact, they all received their degree in May 2000, Ryan Chamberlain and Jud Laman are now working at Unum-Provident, Yung Ju Jeong has been accepted to graduate school at the University of Connecticut, Eric Rymer has accepted a teaching position at Silverdale Baptist School, and Amy Handzo has returned to Florida and has not yet indicated where she is employed.

  Departments with large service loads such as the Mathematics Department are often criticized by students for their courses being too difficult, etc.. However, one very reassuring factor is the overwhelming number of written comments on the student evaluations attesting to the fact that faculty in the Mathematics Department are always willing and available to help students.