## Professor of Mathematics

PhD, MSc (Calgary), MSc, BSc (Charles’ University Prague)

Office: Mackenzie Chown J410

905 688 5550 x3298

jvrbik@brocku.ca

**Celestial Mechanics**– perturbed Kepler problem.**Probability and Statistics**– sampling distributions, Normal approximation, parameter estimation, autoregressive models.**Monte Carlo techniques**– applied to Quantum Chemistry**Numerical solution of integral equations**– applied to Mechanical Engineering problems

Representative Publications

- J. Vrbik,

“Solving Lunar problem via perturbed K-S equation”

*New Astronomy***11**#5(2006), 366-373 - J. Vrbik,

“Population moments of sampling distributions”

*Computational Statistics***20**#4(2005), 611-621 - J. Vrbik,

“Finite-n corrections to Normal approximation”

*Communications in Statistics (Simulation and Computation)***34**#4(2005), 827-837 - J. Vrbik,

“Moments of AR(1)-model estimators”

*Communications in Statistics (Simulation and Computation)***34**#3(2005), 595-600 - J. Vrbik,

“Zonal-harmonics perturbations”

*Celestial Mechanics & Dynamical Astronomy***91**(2005), 217-237 - Rokne J, Singh B M, Dhaliwal R S and J. Vrbik,

“The axisymmetric Boussinesq-type problem for half-space under optimal heating of arbitrary profile”

*Int. J. of Math. and Math. Sciences***40**(2004), 2123-2131 - Vrbik J, Singh BM, Rokne J, et al.,

“On the expansion of a penny-shaped crack by a rigid circular disc inclusion in a thick plate”

*ZAMM***84**#8(2004), 538-550 - Rokne J, Singh BM, Dhaliwal RS and Vrbik J,

“The Reissner-Sagoci type problem for a nonhomogeneous elastic cylinder embedded in and elastic non-homogeneous half-space”

*IMA J. Appl. Math.***69**#2(2004), 159-173 - Rokne J, Singh B M, Dhaliwal RS and Vrbik J,

“Mixed boundary value problem in a nonhomogeneous medium under steady distribution of temperature”

*Meccanica***39**#2(2004), 113-123 - J. Vrbik,

“A novel solution to Kepler’s problem”

*European J. of Phys.***24**#6 (2003), 575-583 - Singh BM, Danyluk HT, Vrbik J, et al.,

“The Reisner-Sagoci problem for a non-homogeneous half-space with a surface constraint”

*Meccanica***38**#4 (2003), 453-465 - Singh B M, Rokne, J, Dhaliwal R S and J. Vrbik,

“Contact problem for bonded nonhomogeneous materials under shear loading”

*Int. J. of Math. and Math. Sci.***2003**#29 (2003), 1821-1832 - Vrbik J, Singh B M, Rokne J, at al.,

“The breaking of a non-homogeneous fiber embedded in an infinite non-homogeneous medium”

*Z. Angew Math. Phys.***54**#2 (2003), 212-223 - Vrbik J, Singh B M, Rokne J, et al.,

“The problem of a penny-shaped crack in a nonhomogeneous medium under shear”

*Eur. J. Mech. A-Solid***21**#5 (2002), 773-777 - Vrbik J,

“Erratum: oblateness perturbations to forth order”

*Monthly Notices of the Royal Astronomical Society***331**#4 (2002), 1072 - Vrbik J, Singh B M, Rokne J and Dhaliwal R S,

“Plastic deformation at the tip of an edge crack”

*ZAMM***81**#9 (2001), 642-647 - Singh B M, Danyluk H T, Selvadurai A P S, Dhaliwal R S, Rokne J and Vrbik J, et al.,

“Effects of inclusion in ductile cracks”

*ZAMP***52**(2001), 680-695 - J. Vrbik, Singh B M, Rokne J, Dhaliwal R S,

“External crack in torsion in an infinite nonhomogeneous medium with a non-homogeneous cylindrical inclusion”

*ZAMM***81**#7 (2001), 489-497 - J. Vrbik,

“Quaternionic processo”

*Celestial Mechanics and Dynamical Astronomy***80**#2 (2001), 111-118 - J. Vrbik,

“Perturbative solution of an asteroid’s motion in resonance with Jupiter”

*Monthly Notices of the Royal Astronomical Society*(2000) - J. Vrbik,

“Simple simulation of solar system”

*Astrophysics and Space Science***266**#4 (1999), 557-567. - J. Vrbik,

“Iterative solution to perturbed Kepler problem via Kustaanheimo-Stiefel equation”

*Celestial Mechanics and Dynamical Astronomy***71**(1999), 273-287. - J. Vrbik,

“Novel analysis of tadpole and horseshoe orbits”

*Celestial Mechanics and Dynamical Astronomy***69**(1998), 283-291. - P. Langfelder, S.M. Rothstein, and J. Vrbik,

“Diffusion quantum Monte Carlo calculations of nondifferential properties for atomic ground states”

*J. Chem. Phys.***107**(1997), 8525-35. - J. Vrbik,

“Oblateness perturbations to fourth order”

*Mon. Not. R. Astron. Soc.***291**(1997), 65-70. - J. Vrbik,

“Resonance formation of Kirkwood gaps and asteroid clusters”

*J. Phys. A***29**#12 (1996), 3311-16. - H.T. Danyluk, B.M. Singh, and J. Vrbik,

“A Dugdale-type estimation of the plastic zone for a penny-shaped crack in a thick transversely isotropic layer due to radial shear”

*Engineering Fracture Mechanics***51**(1995), 735-740. - J. Vrbik,

“Perturbed Kepler problem in quaternionic form”

*J. Phys. A***28**(1995), 193-198. - J. Vrbik,

“Dirac equation and Clifford algebra”

*J. Math. Phys.***35**#5 (May 1994), 2309-14. - J. Vrbik,

“Celestial mechanics via quaternions”

*Can. J. Phys.***72**(1994), 141-146. - P. Belohorec, S.M. Rothstein, and J. Vrbik,

“Infinitesimal diffusion quantum Monte Carlo study of CuH spectroscopic constants”

*J. Chem. Phys.***98**#8 (1993), 6401-05. - J. Vrbik,

“A chain sliding off a table”

*Am. J. Phys.***61**#3 (March 1993), 258-261. - H.T. Danyluk, B.M. Singh, and J. Vrbik,

“Ductile penny-shaped crack in a transversely isotropic cylinder”

*Int. J. Fract.***51**#4 (1991), 331-342. - J. Vrbik,

“A simple approximation to the pseudoskin factor resulting from restricted entry”

*SPE Formation Evaluation*(Dec 1991), 444-446. - A.L.L. East, S.M. Rothstein, and J. Vrbik,

“Reply to comment on: ‘Sampling the exact electron distribution by diffusion quantum Monte Carlo”

*J. Chem. Phys.***92**#3 (1990), 2120. - D.A. Lagare, S.M. Rothstein, and J. Vrbik,

“Infinitesimal differential diffusion quantum Monte Carlo: Diatomic molecular properties”

*J. Chem. Phys.***92**(Jan 1990), 1221-27. - M.C. Au, A. Cardou, B.M. Singh, A.P.S. Selvadurai, and J. Vrbik,

“Closed from solution for two finite-length cracks moving in an orthotropic layer under anti-plane loading”

*Theor. Appl. Fract. Mech.***10**#3 (Dec 1988), 197-212. - S.M. Rothstein and J. Vrbik,

“A Green’s function used in diffusion Monte Carlo”

*J. of Compt. Phys.***87**(1987), 1902-03. - J. Vrbik,

“Monte Carlo simulation of general elliptic operator”

*J. of Phys. A.***20**(1987), 2693-98. - J. Vrbik,

“Calculating the pseudo-skin factor due to the partial well completion”

*J. of Canadian Petroleum Technology***25**#5 (1986), 57-61. - J. Vrbik,

“Monte Carlo technique for finding the lowest eigenvalue of a modified Shroedinger equation”

*J. of Phys. A.***18**(1985), 1327-35. - J. Vrbik,

“Asymptotic distribution of the coefficient of cross-association based on a simple Markov-chain model”

*J. of Appl. Prob.***22**(1985), 946-950. - J. Vrbik,

“Statistical properties of the number of runs of matches between two random stratigraphic sections”

*Math. Geol.***17**#1 (1985), 29-40. - R.S. Dhaliwal, B.M. Singh, and J. Vrbik,

“Diffraction of torsional waves by a flat annular crack at the interface of two bonded dissimilar elastic solids”

*Eng. Fract. Mech.***19**#4 (1984), 771-776. - R.S. Dhaliwal, B.M. Singh, and J. Vrbik,

“Torsional impact of a layer or a cylinder bonded to an elastic half-space”

*Int. J. of Eng. Sci.***21**#11 (1983), 1397-1408. - J. Vrbik,

“Test of independence by repeated matching of stratigraphic sections”

*Math. Geol. J.***15**#3 (1983), 427-444. - M. Nosal and J. Vrbik,

“Stratigraphic analysis and the asymptotic distribution of the coefficient of cross-association”

*Math. Geol.***14**#1 (1982), 11-36. - R.S. Dhaliwal, B.M. Singh, and J. Vrbik,

“Semi-infinite medium with a cylindrical inclusion twisted by an annular die”

*J. of Elasticity***10**#2 (1980), 121-134.

**Past Teaching Assignments**

- MATH 1P12 Introductory Linear Algebra
- MATH 1P40 Mathematics Integrated with Computers and Applications I
- MATH 1P97 Differential and Integral Methods
- MATH 1P98 Basic Statistical Methods
- MATH 2P12 Linear Algebra II
- MATH 2P95 Mathematics and Music
- MATH 4/5P96 Technology and Mathematics Education