# 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:**

**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.**S. Avdonin and B. Belinskiy,**On controllability of a non-homogeneous string with memory,*J. Math. Anal. Appl.,*(2013), vol. 398, 254--269.**M. Sherman and R. Smith,**Principally normal matrices.*Linear Algebra and its Applications*438 (2013) 2617-2627.**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.**Qingkai Kong and Min Wang,**Eigenvalue approach to even order system periodic boundary value problems,*Canad. Math. Bull.*56 (2013), 102--115.**John R. Graef, Shapour Heidarkhani, and Lingju Kong,**Multiple solutions for systems of multi-point boundary value problems,*Opuscula Math.*33 (2013), 293--306.**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.**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.**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 Computation*3 (2013), 21--35.**Serguei Naboko, Roger Nichols, and Gunter Stolz,**Simplicity of eigenvalues in Anderson-type models.*Ark. Mat.51,*157-183 (2013).**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 Theory*12B (2013), 1--8.**Ron Smith and Michael Sherman.**Principally Normal Matrices. (joint with Michael D. Sherman),*Linear Algebra and Its Applications,*438 (2013) 2617-2627.**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.**Xuhua (Roy) Liu, Tin-Yau Tam.**Gradient Flows for the MInimum Distance to the Sum of Adjoint Orbits*.**Linear and Multilinear Algebra*, Vol.61 (2013), No.5, 678-696.**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).**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.**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.**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.**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.**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.**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.**John R. Graef, Lingju Kong, Qingkai Kong,****and****Min Wang**, Fractional boundary value problems with integral boundary conditions,*Appl. Anal.*, 92 (2013), 2008--2020.**J. R. Graef**,**L. Kong**,**Q. Kong**,**and****M. 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.**J. R. Graef**,**L. Kong**,**Y. Tian**,**and****M. Wang**, On a discrete fourth order periodic boundary value problem,*Indian Journal of Mathematics*55 (2013), 163--184.**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.**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.**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.**Sumith Gunasekera,**Inferences on the Common Scale Parameter of Several Exponential Populations based on the Generalized Variable Method.*M**odel Assisted Statistics and Applications,*8 (2013), 205-214.**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.**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.**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.**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.**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.**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).**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.**John R. Graef, Lingju Kong, and Qingkai Kong,**Infinitely many solutions for a discrete fourth order boundary value problem,*Nonlinear Dyn. Syst. Theory***13**(2013), 400–411.**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.**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.**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.**S. R. Grace, John R. Graef, and A. Zafer,**Oscillation of integro-dynamic equations on time scales, Applied Mathematics Letters 26 (2013), 383--386.**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.**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.**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.**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.**John R. Graef and S. Saker,**Oscillation theory of third-order nonlinear functional differential equations, Hiroshima Mathematical Journal 43 (2013), 49--72.**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.**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.**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.**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.**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.**A. Benmezai, John R. Graef, and Lingju Kong,**Positive solutions for abstract Hammerstein equations and applications, Communications in Mathematical Analysis 16 (2013), 47--65.**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.**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.