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Published Research by Mathematics Faculty

The Department of Mathematics prides itself on a tradition of active and productive research. Recent published research by UTC Department of Mathematics faculty members of the department are listed below.

 

Published in 2013:

 

  1. John R. Graef,  Shapour Heidarkhani, and Lingju Kong,  Multiple solutions for a class of $(p_1,...,p_n)$-biharmonic systems, Commun. Pure Appl. Anal.  12  (2013), 1393--1406.
  2. S. Avdonin and B. Belinskiy,  On controllability of a non-homogeneous string with memory, J. Math. Anal. Appl.,(2013),  vol. 398, 254--269.
  3. M. Sherman and R. Smith, Principally normal matrices. Linear Algebra and its Applications 438 (2013) 2617-2627.
  4. John R. Graef, Lingju Kong, and Min Wang, Solutions of a nonlinear fourth order periodic boundary value problems for difference equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.20 (2013), 53--63.
  5. Qingkai Kong and Min Wang, Eigenvalue approach to even order system periodic boundary value problems,Canad. Math. Bull. 56 (2013), 102--115.
  6. John R. Graef, Shapour Heidarkhani, and Lingju Kong,  Multiple solutions for systems of multi-point boundary value problems,  Opuscula Math.33 (2013), 293--306.
  7. John R. Graef, Lingju Kong, and Bo Yang, Positive solutions for boundary value problems of discrete and continuous beam equations, J. Appl. Math. Comput.41 (2013), 197--208.
  8. Aditya H. Gaur, Cuilan Gao and et al., Surveillance of Hospital-Acquired Central Line–Associated Bloodstream Infections in Pediatric Hematology-Oncology Patients: Lessons Learned, Challenges Ahead. Infection Control and Hospital Epidemiology, Vol. 34, No. 3, (2013), pp. 316-320.
  9. John R Graef, Lingju Kong, Qingkai Kong, and Min Wang, Uniqueness and parameter dependence of positive solutions to higher order boundary value problems with fractional q-derivatives, Journal of Applied Analysis and Computation3 (2013), 21--35.
  10. Serguei Naboko, Roger Nichols, and Gunter Stolz, Simplicity of eigenvalues in Anderson-type models.  Ark. Mat.51, 157-183 (2013).
  11. D. A. Goldston and A. H. Ledoan. On the differences between consecutive prime numbers, I (Proceedings of the Integers Conference 2011), INTEGERS: Electronic Journal of Combinatorial Number Theory12B (2013), 1--8.
  12. Ron Smith and Michael Sherman. Principally  Normal Matrices. (joint with Michael D. Sherman),  Linear Algebra and Its Applications, 438 (2013) 2617-2627.
  13. Xuhua Liu, Brice M. Nguelifack, Tin-Yau Tam. Unitary Similarity to a Complex Symmetric Matrix and its Extension to Orthogonal Symmetric Lie Algebras. Linear Algebra and Its Applications, Vol.438 (2013) No.10, 3789-3796.
  14. Xuhua (Roy) Liu, Tin-Yau Tam. Gradient Flows for the MInimum Distance to the Sum of Adjoint OrbitsLinear and Multilinear Algebra, Vol.61 (2013), No.5, 678-696.
  15. Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols, and Gerald Teschl,  Weyl--Titchmarsh theory for Sturm--Liouville operators with distributional potentials.  Opuscula Math. 33, no. 3, 467-563 (2013).
  16. Lingju Kong, Existence of solutions to boundary value problems arising from the fractional advection dispersion equation, Electron. J. Differential Equations, Vol. 2013 (2013), No. 106, pp. 1--15.
  17. John R. Graef, Shapour Heidarkhani, and Lingju Kong,  A variational approach to a Kirchhoff-type problem involving two parameters, Result. Math.  63 (2013), 877--889.
  18. Lingju Kong, Qingkai Kong, Man K. Kwong, and James S. W. Wong, Linear Sturm-Liouville problems with multi-point boundary conditions, Math. Nachr.286 (2013), 1167—1179.
  19. John R. Graef and Lingju Kong, Existence of positive solutions to higher order singular boundary value problems with fractional $q$-derivatives,  Fract. Calc. Appl. Anal.  16  (2013), 695—708.
  20. John R. Graef, Lingju Kong, Min Wang, and Bo Yang, Uniqueness and parameter dependence of positive solutions of a discrete fourth order problem, J. Difference Equ. Appl.19  (2013), 1133—1146.
  21. D. A. Goldston and A. H. Ledoan, On the differences between consecutive prime numbers, I, Combinatorial Number Theory (Proceedings of the “Integers Conference 2011,” Carrollton, Georgia, October 26-29, 2011), De Gruyter Proceedings in Mathematics, 2013, 37--44.
  22. John R. Graef, Lingju Kong, Qingkai Kong, and Min Wang, Fractional boundary value problems with integral boundary conditions, Appl. Anal., 92 (2013), 2008--2020. 
  23. J. R. Graef, L. Kong, Q. Kong, andM. Wang, Existence and uniqueness of solutions for a fractional boundary value problem with Dirichlet boundary condition, Electronic Journal of Qualitative Theory of Differential Equations 2013 (2013), No. 55, 1--11.
  24. J. R. Graef, L. Kong, Y. Tian, andM. Wang, On a discrete fourth order periodic boundary value problem, Indian Journal of Mathematics 55 (2013), 163--184.
  25. Aditya Gaur and Cuilan Gao et al, Evaluating application of the National Healthcare Safety Network Central Line-Associated bloodstream Infection Surveillance Definition: A Survey of Pediatric Intensive Care and Hematology /Oncology Units, Infection Control and Hospital Epidemiology, Vol.34 No. 7 July 2013.
  26. John R. Graef, Shapour Heidarkhani, and Lingju Kong, Infinitely many solutions for systems of multi-point boundary value problems, Topol. Methods Nonlinear Anal.42(2013), 105—118.
  27. Sumith Gunasekera, Statistical Inferences for Availability of a Series System with Pareto Failure and Repair Times. Model Assisted Statistics and Applications, 8 (2013), 51-60.
  28. Sumith Gunasekera, Inferences on the Common Scale Parameter of Several Exponential Populations based on the Generalized Variable Method. Model Assisted Statistics and Applications, 8 (2013), 205-214.
  29. Zengji Du, Zhengmin Fu, and Lingju Kong, Existence of solutions for a class of fourth-order multi-point boundary value problems on time scales, Nonlinear Oscil.16 (2013), 336—349.
  30. John R. Graef, Lingju Kong, Qingkai Kong, and Min Wang, Positive solutions of nonlocal fractional boundary value problems, Discrete Contin. Dyn. Syst., suppl. 2013, 283--290.
  31. John R. Graef, Lingju Kong, and Min Wang, Existence of multiple solutions to a discrete fourth order periodic boundary value problem, Discrete Contin. Dyn. Syst., suppl. 2013, 291--299.
  32. Yu Tian, John R. Graef, Lingju Kong, and Min Wang, Existence of solutions to a multi-point boundary value problem of second order differential systems via the dual least action principle, Discrete Contin. Dyn. Syst., suppl. 2013, 759--769.
  33. Lucas Van der Merwe, Terry Walters, Ossama Saleh, and Johannes Hattingh. Nordhaus-Gaddum type results for the induced path number with relative complements in Km;n. JCMCC, 85 (2013), 365-377. 
  34. Fritz Gesztesy, Steve Hofmann, and Roger Nichols.  On square root domains for non-self-adjoint Sturm--Liouville operators.  Methods Funct. Anal. Topology, 19, No. 3, 227-259 (2013).
  35. Jonathan Eckhardt, Fritz Gesztesy, Roger Nichols and Gerald Teschl. Inverse spectral theory for Sturm-Liouville operators with distributional potentials  J. London Math. Soc. doi:10.1112/jlms/jdt041   John R. Graef, Shapour Heidarkhani, and Lingju Kong, Existence of nontrivial solutions to systems of multi-point boundary value problems, Discrete Contin. Dyn. Syst. suppl. (2013), 273–281.
  36. John R. Graef, Lingju Kong, and Qingkai Kong, Infinitely many solutions for a discrete fourth order boundary value problem, Nonlinear Dyn. Syst. Theory13 (2013), 400–411.
  37. John R. Graef, Lingju Kong, and Min Wang, Multiple solutions to a periodic boundary value problem for a nonlinear discrete fourth order equation, Adv. Dyn. Syst. Appl. 8 (2013), 203 -- 215.
  38. John R. Graef, S. Heidarkhani and L. Kong, Multiple solutions for a class of (p_1, ... ,p_n)-biharmonic systems, Communications on Pure and Applied Analysis 12 (2013), 1393--1406.
  39. John R. Graef, S. Padhi, and S. Pati, Existence and nonexistence of multiple positive periodic solutions of first order differential equations with unbounded Green's kernel, PanAmerican Mathematical Journal 23 (2013), 45--55.
  40. S. R. Grace, John R. Graef, and A. Zafer, Oscillation of integro-dynamic equations on time scales, Applied Mathematics Letters 26 (2013), 383--386.
  41. John R. Graef and B. Yang, Upper and lower estimates of the positive solutions of a higher order boundary value problem, Journal of Applied Mathematics and Computing 41 (2013), 321--337.
  42. John R. Graef, S. Panigrahi, and P. R. Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Communications in Mathematical Analysis 15 (2013), 11--28.
  43. John R. Graef, T. Li, E. Thandapani, and E. Tunc, Oscillation of second-order Emden-Fowler neutral differential equations, Nonlinear Studies 20 (2013), 1--8.
  44. S. R. Grace, John R. Graef, S. Panigrahi, and E. Tunc, On the oscillatory behavior of Volterra integral equations on time-scales, PanAmerican Mathematical Journal 23 (2013), 35--41.
  45. John R. Graef and S. Saker, Oscillation theory of third-order nonlinear functional differential equations, Hiroshima Mathematical Journal 43 (2013), 49--72.
  46. V. Balasubramanian, John R. Graef, and E. Thandapani, Oscillation criteria for second order neutral difference equations with negative neutral term, International Journal of Pure and Applied Mathematics 87 (2013), 283--292.
  47. M. Bartusek and John R. Graef, Limit-point/limit-circle results for super-linear damped equations, Abstract and Applied Analysis, 2013 (2013), Article ID 784761, 10 pages.
  48. John R. Graef, S. Padhi, and S. Pati, Multiple positive periodic solutions of first order ordinary differential equations with unbounded Green's kernel, Communications in Applied Analysis 17 (2013), 319--330.
  49. John R. Graef, S. Heidarkhani and L. Kong, Existence of nontrivial solutions to systems of multi-point boundary value problems, Discrete and Continuous Dynamical Systems, Supplement (2013), 273--281.
  50. John R. Graef, Lingju Kong, and Q. Kong, Infinitely many solutions for a discrete fourth order boundary value problem, Nonlinear Dynamics and Systems Theory 13 (2013), 400--411.
  51. A. Benmezai, John R. Graef, and Lingju Kong, Positive solutions for abstract Hammerstein equations and applications, Communications in Mathematical Analysis 16 (2013), 47--65.
  52. John R. Graef, P. K. Kar, S. Padhi, and S. Pati, Periodic solutions of a single species renewable resources under periodic habitat fluctuations with harvesting and Allee effect, Communications on Applied Nonlinear Analysis 20 (2013), 1--16.
  53. John R. Graef, Lingju Kong, and Min Wang, Multiple solutions to a periodic boundary value problem for a nonlinear discrete fourth order equation, Advances in Dynamical Systems and Applications 8 (2013), 203--215.

 

 

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