## Dr. Kenneth S. BerenhautAssociate Professor of Mathematics &Z. Smith Reynolds Foundation Faculty Fellow

 Office Manchester 331 Phone (336) 758-5922 Home Page http://www.math.wfu.edu/Faculty/berenhaut.html Email berenhks 'at' wfu.edu Degrees Ph. D. Statistics, The University of Georgia, 2000 M.A. Mathematics, The University of Georgia, 1997 M.Sc., Mathematics, The University of Manitoba, 1994 B.A., Mathematics (Emphasis: Analytic Number Theory), The University of Manitoba, 1991 Research Interests Applied probability; discrete dynamics; multi-agent systems; convergence rates; mathematical inequalities; mathematical and statistical models; difference equations; statistical methodology; matrix inequalities; analytic, probabilistic and combinatorial number theory; discrete structures. A recent vitae is available here. Additionally, please see Dr. Berenhaut's biography at Hindawi. Check out Involve, A Journal of Mathematics (MSP, UC Berkeley). See also this article in the February 2011 issue of Math Horizons (MAA). Editorial Activities Founding Editor, Involve - A Journal of Mathematics Editor, Australian Journal of Mathematical Analysis and Applications Editorial Board, International Journal of Mathematics and Mathematical Sciences Editorial Board, Communications in Mathematical Analysis Member, Publications Committee, Mathematical Sciences Publishers, Berkeley, CA Editorial Board, Symmetry Editorial Board, Axioms: Mathematical Logic and Mathematical Physics Editorial Board, Annals of Functional Analysis Editorial Committee, Journal of Mathematical Analysis Editorial Committee, Journal of Inequalities and Special Functions Editorial Board, International Mathematical Forum Editorial Board, International Journal of Contemporary Mathematical Sciences Editorial Board, International Journal of Mathematical Analysis Editorial Board, Applied Mathematical Sciences Editorial Advisory Board, The Open Operational Research Journal Editorial Advisory Board, The Open Applied Mathematics Journal Editorial Board, Journal of Statistics: Advances in Theory and Applications Publications in print/in press [1]  Berenhaut, K. S., Baxley, J. V. and Lyday, R. G.*  (2011). Deviations of discrete distributions and a question of Mori. Statistics and Probability Letters, 81 (2011)(12), 1940- -1944. (S, P, I, PS) [2]  Berenhaut, K. S. and Bergen, L. D.* (2011). Stochastic orderings, folded beta distributions and fairness in coin flips. Statistics and Probability Letters, 81 (2011)(6), 632--638. (S, P) [3]  Berenhaut, K. S., Guy, R. T.** and Vish, N. G.** (2011). An optimal bound for inverses of triangular matrices with monotone entries. Linear and Multilinear Algebra, 59 (2011)(4), 475–-481. (LA, M, I, LR) [4]  Berenhaut, K. S. and Vish, N. G.** (2011). Equations of convolution type with monotone coefficients. Journal of Difference Equations and Applications, 17 (2011)(4), 555--566. (M, LR, D, P, LA) [5]  Crouse, M. B.**, White, J. L.**, Fulp, E. W., Berenhaut, K. S., Fink, G. A. and Haack, J. (2011). Using swarming agents for scalable security in large network environments. Circuits and Systems (MWSCAS), 2011 IEEE 54th International Midwest Symposium on, 1--4. (N) [6]  Berenhaut, K. S., Magargee, E. M.* and Stancil, B. J.*, (2011) Fibonacci-type piecewise linear recurrences and generalized Ramanujan-Nagell equations, Proceedings of The Fourteenth International Conference on Fibonacci Numbers and Their Applications, Accepted. (LR, D) [7]  Berenhaut, K. S. and Jones, A. H.**, (2012) A part-metric variant of Newton's inequalities, Mathematical Inequalities and Applications, Volume 15, Number 2 (2012), 353–359. (D, I, SY) [8]  Berenhaut, K. S., Magargee, E. M.* and Rabidoux, S. M..*, (2011) Asymptotic behavior of solutions to minimum-maximum delay recurrences of higher order, Proceedings of The Fourteenth International Conference on Fibonacci Numbers and Their Applications, Accepted. (LR, D) [9]  Berenhaut, K. S., Guy, R. T.**, and Barrett, C. L.* (2011). Global asymptotic stability for minimum-delay difference equations. Journal of Difference Equations and Applications, 17 (2011) (11), 1581--1590. (LR, D, SY) [10] Berenhaut, K. S. and  Jones, A. H.**, (2012) Asymptotic behavior of solutions to rational difference equations involving elementary symmetric polynomials, Journal of Difference Equations and Applications, 18, No. 6, June 2012, 963--972. (I, SY, D) [11] Berenhaut, K. S., and Guy, R. T.** (2010). Periodicity and boundedness for the integer solutions to a minimum-delay difference equation. Journal of Difference Equations and Applications, 16 (2010) (no. 8), 895–-916. (D) [12] Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2010). Boundedness character of positive solutions of a higher order. International Journal of Computer Mathematics, 87 (2010)(no. 7). (D) [13] Berenhaut, K. S., O’Keefe, A. B.** and Saidak, F. (2010). Remarks on linear recurrences of the form $y_n=y_{n-1}+a_{n-1}y_{n-2}$. Congr. Numer., 200, 141-151. (LR, I) [14] Berenhaut, K. S., Stancil, B. J.* and Newman, J. H.** (2009), On some piecewise-linear difference equations with Mersenne-type periodic solutions, Journal of Difference Equations and Applications 15 (2009),  no. 7, 729--733. (LR, D) [15] Berenhaut, K. S., Morton, D. C.* and Fan, Y. W.** (2009). Bounds for second order recurrences in terms of maximal products over integer partitions. Congr. Numer., 194 (2009), 59--66. (LR, I) [16] Berenhaut, K. S., Chen D.** and Tran, V.** , (2008) On the Dyson condition for sums of independent random variables, Statistics and Probability Letters 78(17), 3110--3113.  (P, S) [17] Berenhaut, K. S., Guy, R. T.** and Vish, N. G.**, (2008) A 1-Norm Bound for Inverses of Triangular Matrices with Monotone Entries, Banach J. Math. Anal., 2 (2008), no. 1, 112—- 121. (LA, I, LR, M) [18] Berenhaut, K. S. and Guy, R. T.** (2009), Symmetric functions and difference equations with asymptotically period-two solutions, International Journal of Difference Equations, 4, no. 1, 43--48. (SY, D) [19] Berenhaut, K. S. and Chen D.**, (2008) Inequalities for functions with convex logarithmic derivative, Journal of Inequalities in Pure and Applied Mathematics 9(4), 9 pp.  (I, M) [20] Berenhaut, K. S. and Chen D.**, (2008) Moment generating functions, local approximations and one-step conditioning, Pan American Mathematical Journal 18(4), 1-- 10. (P, S) [21] Berenhaut, K. S., Donadio, K. M.* and Foley J. D.**, (2008) On a rational recursive sequence with parameter near the boundary, In press, International Journal of Difference Equations 3(1), 53--59.  (D) [22] Berenhaut, K. S. and Chen D.** (2009), Inequalities for convolution ratios under local approximation, In press, Applied Mathematical Sciences 3 (2009) (33-36), 1699--1714. [23] Berenhaut, K. S., Donadio, K. M.* and Foley J.D.** (2008) On the rational recursive sequence $y_n=A+\frac{y_{n-1}}{y_{n-m}}$ for small $A$, Applied Mathematics Letters, 21 (2008), 906--909. (D) [24] Berenhaut, K. S. (2009) On some systems of difference equations with periodic solutions, Dynamics of Continuous, Discrete and Impulsive Systems 16, no.5 (2009), 755—758. (D) [25] Berenhaut, K. S. and Saidak, F. (2007) A note on the maximal coefficients of squares of Newman polynomials, Journal of Number Theory, 125 (2), 285--288.  (R, PS) [26] Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2007) The periodic character of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$, Proceedings of the American Mathematical Society, 135 (2007), 1133-1140. (D) [27] Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2008) The global attractivity of the rational difference equation $y_n=A+\left(\frac{y_{n-k}}{y_{n-m}}\right)^p$, Proceedings of the American Mathematical Society 136 (2008), no. 1, 103--110. (D) [28] Berenhaut, K. S.; O'Keefe, A. B.** Recursive sequences of the form $y_n=a_{n}y_{n- 1}+y_{n-3}$ with integer coefficients. Indian J. Math. 49 (2007), no. 2, 189--209. (LR, I) [29] Stevic, S. and Berenhaut, K. S., (2008) The behavior of the positive solutions of the difference equation $x_n=\frac{f(x_{n-2})}{g(x_{n-1})}$, Abstract and Applied Analysis, 2008 (2008) ID 653243, 8 pp. (D) [30] Berenhaut, K. S., Gibson, B. G.*, Newman, J. H.* and Anderson, J. F. ‡, (2007) Bounds for fourth-order [0,1] difference equations, Computers and Mathematics with Applications, 54 (2007), no. 9--10, 1250--1259. (LR, D, M, I) [31] Berenhaut, K. S., Abernathy, Z. J.*, Fan, Ying Wai** and Foley, J. D.** (2007) Inequalities for coefficients of reciprocals of power series, Appeared, Advances in Inequalities for Series (Edited by S.S. Dragomir & A. Sofo). (M, PS, LR, I) [32] Berenhaut, K. S., Saidak, F. and O’Keefe, A. B.** (2007) Bounds for recurrences on ranked posets, International Journal of Contemporary Mathematical Sciences, Volume 2, no. 19, 929--942. (LA, I, M, LR) [33] Berenhaut, K. S. and Foley, J. D.** (2007) The Periodic Character of the Rational Difference Equation $y_n = (y_{n-m}+y_{n-m-k})/y_{n-k}$, International Mathematical Forum, Vol. 2, 2007, no. 41-44, 2065-2077. (D) [34] Berenhaut, K. S. and Foley, J. D.** (2007) Product difference equations approximating rational equations, Differential & Difference Equations and Applications, Hindawi Publ. Corp., New York, 2006, 159--168.  (D) [35] Berenhaut, K. S. and Stevic, S. (2007) The global attractivity of a higher order rational difference equation, Journal of Mathematical Analysis and Applications, Volume 326, Issue 2, 15 February 2007, Pages 940--944. (D, SY) [36] Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2007) The global attractivity of the rational difference equation $y_{n}=\frac{y_{n-k}+y_{n-m}}{1+y_{n-k}y_{n-m}}$, Applied Mathematics Letters, Volume 20, Issue 1, January 2007, Pages 54--58. (D, SY) [37] Berenhaut, K. S. and Stevic, S. (2007) The difference equation $x_{n+1}=\a+\frac{x_{n- k}}{\sum_{i=0}^{k-1}c_ix_{n-i}}$ has solutions converging to zero, Journal of Mathematical Analysis and Applications, Volume 326, Issue 2, 15 February 2007, Pages 1466-1471. (D) [38] Berenhaut, K. S., Foley, J. D.** and Bandyophadyay, D.†  (2006) Inequalities for inner products under some monotonicity constraints, Journal of Inequalities in Pure and Applied Mathematics, Volume 7, Issue 5, Article 158. (LA, M, I) [39] Berenhaut, K. S., Allen E. E and Fraser, S. J.* (2006), Bounds on coefficients of reciprocals of formal power series with rapidly decreasing coefficients, Discrete Dynamics in Nature and Society Volume 2006 (2006), Article ID 40270, 18 pages.  (PS, M, P, I, LR) [40] Berenhaut, K. S., Dice, J. E.*, Foley, J. D.**, Iricanin, B. and Stevic, S., (2006) Periodic Solutions of the Rational Difference Equation $y_{n}=\frac{y_{n-3}+y_{n-4}}{y_{n- 1}}$, J. Difference Equ. Appl. 12, no. 2, 183--189. (D) [41] Berenhaut, K. S., Saidak, F. and O’Keefe, A. B.** (2006) Recursive sequences of the form $y_n=a_{n}y_{n-1}+y_{n-2}$ with integer coefficients, Indian Journal of Mathematics, Vol. 48, no. 1, 39-54. (I, LR) [42] Berenhaut, K. S. and Stevic, S. (2006) On positive nonoscillatory solutions of the difference equation $x_{n+1}=\alpha + \frac{{x_{n-k}}^p}{{x_n}^p}$, Journal of Difference Equations and Applications, Volume 12, Number 5 May 2006,  Pages  495-- 499. (D) [43] Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2006) Boundedness character of positive solutions of a max difference equation, Journal of Difference Equations and Applications, 12, no. 12, 1193--1199.  (LR, D) [44] Berenhaut, K. S. and Foley, J. D.** (2006) Explicit bounds for multi-dimensional linear recurrences with restricted coefficients, Journal of Mathematical Analysis and Applications, Volume 322, Issue 2, 15 October 2006, Pages 1159-1167. (PS, M, I) [45] Berenhaut, K. S. and Stevic, S. (2006) The Behaviour of the Positive Solutions of the Difference Equation $x_n=A+\left(\frac{x_{n-2}}{x_{n-1}}\right)^p$, Journal of Difference Equations and Applications, 12,  no. 9  (2006), 909-918. (D, M) [46] Berenhaut, K. S. and Foley, J. D.** (2006) Applications of recurrence bounds to networks and paths, International Journal of Applied Mathematics, 19 (2006), 4, 461--470. (I, LR, M, N) [47] Berenhaut K. S. and Goedhart, E. G.**, Stević, S. (2006), Explicit bounds for third-order difference equations, ANZIAM J.  47, 359-366. (I, D, M) [48] Berenhaut, K. S., Foley, J. D.** and Stevic, S. (2006) Quantitative bounds for the recursive sequence $y_n=A+\frac{y_{n-1}}{y_{n-k}}$, Applied Mathematics Letters, Volume 19, Issue 9, September 2006, Pages 983-989. (I, D) [49] Berenhaut K. S. and Goedhart, E. G.**. (2006) Second-order linear recurrences with restricted coefficients and the constant (1/3)1/3 , Mathematical Inequalities & Applications, Volume 9, 445--452. (I, M, LR) [50] Berenhaut, K. S. and Stevic, S. (2005) On the difference equation $x_{n+1}=\frac{1}{x_n x_{n-1}+\frac{1}{x_{n-3} x_{n-4}}$, Journal of Difference Equations and Applications, 11, no. 14, 1225--1228. (D) [51] Lewis, J.†, Berenhaut, K. S., Souter, R. and Daniels, R. F. (2005), Completely compatible taper, whole tree and merchantable volume models based on the gamma and inverse gamma probability functions, Forest Science, 51, No. 6., pp. 578-584.  (O) [52] Fan, Y. W.** and Berenhaut, K. S. (2005), A bound for linear recurrence relations with unbounded order, Computers and Mathematics with Applications, Volume 50, Issue 3/4, Pages 509--518. (LR, I, M) [53] Thul, C., Choi, H. S., Suerken, C. K. , Berenhaut, K. S. and Norris, J. (2005), A comprehensive survey of school psychologists' attitudes, feelings, and professional services offered to gay male and/or lesbian parents and their children, Journal of Applied School Psychology, Volume 22, Issue 1, pages 89-109. (O) [54] Mallakin A., Mezey, P. G., Zimpel, Z., Berenhaut, K. S., Greenberg, B. M. and Dixon, D. G. (2005), Use of molecular shape similarity to model the photoinduced toxicity of anthracene and oxygenated anthracenes, QSAR & Combinatorial Science, Volume 24, Issue 7, page 844-852. (O) [55] Berenhaut, K. S. and Fletcher, P. T.* (2005), On inverses of triangular matrices with monotone entries, Journal of Inequalities in Pure and Applied Mathematics, Volume 6, Issue 3. (I, LA, LR) [56] Berenhaut, K. S. and Morton, D. C.*  (2005), Second-order bounds for linear recurrences with negative coefficients, Journal of Computational and Applied Mathematics, Volume 186, 2, pp 504-522. (PS, M, LA, LR, I) [57] Berenhaut, K. S., Morton D. C.* and Fletcher, P. T.* (2005), Bounds for inverses of triangular Toeplitz matrices, SIAM Journal on Matrix Analysis, Volume 27, Number 1, pp. 212-217. (M, LA, LR, I) [58] Berenhaut, K. S. and Bandyopadhyay D.† (2005), Monotone convex sequences and Cholesky decomposition of symmetric Toeplitz matrices, Linear Algebra and its Applications, Volume 403, 1 July 2005, Pages 75-85. (M, LA, I, LR, SY) [59] Berenhaut, K. S. and Goedhart, E. G.** (2005), Explicit bounds for second-order difference equations and a solution to a question of Stević, Journal of Mathematical Analysis and Applications, Volume 305, Issue 1, 1 May 2005, Pages 1-10. (I, D) [60] Berenhaut, K. S. (2004), Review of Advanced Calculus with Applications in Statistics by André I Khuri, Journal of the American Statistical Association, 99, No. 467, 903--904. (S, LA) [61] Berenhaut, K. S. and Lund, R. B. (2003), Bounds for linear recurrences with restricted coefficients, Journal of Inequalities in Pure and Applied Mathematics, 4, 2, Article 26, 15 pp. (LR, M, I, PS, LA) [62] Hall, D. B. and Berenhaut, K. S. (2002), Score tests for heterogeneity and overdispersion in zero-inflated poisson and binomial regression models, Canadian Journal of Statistics, 30, 3, 415--430. (P, S) [63] Berenhaut, K. S. and Lund, R. B. (2002), Renewal convergence rates for DHR and NWU lifetimes, Probability in the Engineering and Informational Sciences, 16, 1, 67--84. (P, PS, M, I) [64] Berenhaut, K. S., and Lund, R. B. (2001), Geometric renewal convergence rates from hazard rates, Journal of Applied Probability, 38, 180--194. (P, PS, M, I) [65] Berenhaut, K. S. (2000), Geometric Renewal Convergence Rates and Discrete Lifetime Distribution Classes, Ph.D. Dissertation, Department of Statistics, University of Georgia. [66] Berenhaut, K. S.  (1994), The Siegel-Walfisz Condition for Almost Completely Multiplicative Functions, Master’s Thesis, Department of Mathematics and Astronomy, The University of Manitoba. Manuscripts under review, under revision and current can be found *here*. Classes Elementary Probability and Statistics, Statistical Methods, Mathematical Statistics I and II, Stochastic Processes, Multivariate Analysis, Calculus, Elementary Theory of Numbers. Personal Interests Swimming, Rollerblading, Hockey, Canada, Radio and Budgerigars