A Note on harmonic maps of semi-Riemannian manifold,
Proceedings of the Workshop on Global Analysis, Differential
Geometry and Lie Algebras (Thessaloniki, 1995), 33-37, BSG Proc.,1.
(with Ianus, S.)--Abstract
2. Geodesics on a certain step 2 sub-Riemannian
manifold, Annals of Global Analysis and Geometry, Vol.22,
No.4, pp. 317-339, (2002).-Abstract
3. Variational calculus on sub-Riemannian
manifolds, Balcan Journal of Geometry and Applications,
vol. 8, 2003 (with Mangione, V.)--Pdf.file
4. Geodesics with constraints on Heisenberg
manifolds, Results in Mathematics, 44, 2003, p. 44-53 (with
Mangione, V.).--Pdf file.
5. Some PDE's from the geometric point
of view, Bulletin Mathematique de la Societé des
Sciences Mathematiques de Roumanie, 47 (95), no. 3-4, (2004),
pp. 159-165. (with Mangione, V.).--Abstract
6. Some results on Heisenberg manifolds,
published in Quaderni del Dipartimento di Matematica, Univ.
Parma, 282, 2002. (with Mangione, V.).
7. Invariant formulas for the Euler-Lagrange
equation associated to sub-Riemannian geodesics, Quaderni
del Dipartimento di Matematica, Univ. Parma, 290, 2002. (with
8. On sub-Riemannian geodesics, Analysis
and Its Applications, vol 1,issue 3, 2003, pp. 289-350 (with
Greiner, P). -Abstract
9. The Missing Direction and Differential
geometry on Heisenberg Group, Ph.D. thesis, University
of Toronto, 2000.--Pdf.file
10. Real and complex Hamiltonian mechanics
on some SubRiemannian manifolds, Asian Journal of Mathematics,
vol 18, no.1, pp. 137-160 (with Chang, D.C., Greiner, P.C.--Abstract,
11. On a Step 2(k+1) Sub-Riemannian manifold,
Journal of Geometric Analysis, vol 14, no.1, 2004, pp.1-18.
(with Chang, D.C., Greiner, P.C.) --Pdf.file
12. Geometric Mechanics on a step 4 subRiemannian
manifold, Taiwanese Journal of Mathematics, June 2005,
vol. 9, No. 2, pp. 261-280. (with Chang, D.C.)--Pdf.file
13. Geometric Analysis on SubRiemannian
Manifolds, Advances in Analysis: Proceedings of the 4th
ISAAC Congress, World Scientific, (ed. by M.W. Wong), 17-38,
2005 (with Chang, D.C., Greiner, P.C.).-book
14. The Geometry on a Step 3 Grusin Model,
Arbeitsgruppe Partielle Differentialgleichungen und komplexe
Analysis, Universitat Postdam, Institut fur Mathematik, April
2004 (with Chang, D.C.)
15. Geometric mechanics on the Heisenberg
group, Bulletin of the Institute of Mathematics, Academia
Sinica, vol.33, no.3, Sep., 2005 (with Chang, D.C.)--Pdf.file
16. The geometry on a step 3 Grushin model,
Applicable Analysis,Vol. 84, Issue 2, February 2005, pages
111-129(with Chang, D.C.).--Pdf.file
17. The Geometry of a step two Grushin
operator, Proceedings of International Conference on Complex
Analysis and Dynamical Systems, (ed. by L. Karp and L. Zalcman),
Contemporary Math., Amer. Math. Soc., vol. 382, pp. 89-111,
2005(with Chang, D-C, and Greiner, P., Kannai, Y.).--Abstract
18. Hermite operator on the Heisenberg
group, Harmonic Analysis, Signal Proceedings and Complexity,
(ed. by D. Walnut and D. Struppa), Birkhauser, Boston, Massachusetts,
pp. 37-54, 2005 (with D.C. Chang and J. Tie). --Pdf.file
19. Solving Asset Pricing Models when the
Price-Dividend Function is Anaytic, Econometrica, vol.
73, pp. 961-982, 2005 (with Yu Chen, T. F. Cosimano and A. Himonas)--Abstract,Pdf.file
20. Geometric Analysis on a Family of Pseudoconvex
Hypersurfaces, Complex Variables,
Theory and Applications, vol. 50, no 7-11, pp. 803-835, 2005
(with D.C. Chang).--Pdf.file
21. Fundamental solutions for Hermite and
subelliptic operators, J. d'Analyse Math., Vol. 100, 2006
(with D.C. Chang and J. Tie). --Abstract,
22. Fundamental solutions for a family
of sub-elliptic PDEs, Pure and Applied Mathematics Quarterly,
vol. 3, no. 2, pp. 1-23, 2007 (with D.C. Chang and S. Fricke).--Abstract
23. Periodic solutions for a family of
Euler-Lagrange systems, Asian J. Math., vol. 11, no. 1,
pp. 69-88, March 2007 (with D.C. Chang and Yau, S. T). --Pdf.file
24. SubRiemannian geometry on S^3,
Canadian J. of Math., Vol. 61, no.4, pp. 721-739, 2009 (with
D.C. Chang and Markina, I). --Pdf.file
25. Isometric Embeddings of SubRiemannian
Manifolds in R^n, Advanced Studies in Contemporary Mathematics,
Vol. 15, No.1, pp. 21-36, July 2007 (with D.C. Chang). --Pdf.file
26. Geometric Analysis on H-type groups
related to division algebras, Math. Nachr. 282, nr. 1,
2009 (with D.C. Chang, Markina, I.).--Pdf.file
27. SubRiemannian geometry, a variational
approach, Journal of Differential Geometry, vol. 80, #1,
pp. 23-43 (with D.C. Chang).--Abstract
28. Generalized Hamilton-Jacobi Equation
and Heat Kernel on Step Two Nilpotent Lie Groups, Analysis
and Mathematical Physics. New Trends in Mathematics, Birkhauser,
2009, pp. 49-76 (with D.C. Chang, I. Markina)-Pdf.file
29. Heat kernels for Kolmogorov-type operators
and its applications, Journal of Fourier Analysis and Applications,
Vol. 15, Issue: 6, Publisher: Birhauser, Boston,INC, pp. 816-838,
2009 (with D.C. Chang).--Abstract,
30. Heat kernels for operators with gravitational
potential operators in one and two variables, Pure and
Applied Mathematics Quarterly, vol. 6., no.3, 2010, pp.677-692
(with D.C. Chang).--Pdf.file
31. Non-Connectivity Example in SubRiemannian
Geometry, Complex Variables and Elliptic Equations,Vol.
56 Issue 1-4, p.35-47, 2011 (with D.C. Chang).--
32. Generalizations of conjugate connections,
Trends in Diff. geometry, complex analysis, and mathematical
physics, 26-34, World Sci. Publ., Hackensack, NJ, 2009 (with
Matsuzoe, H., Zhang, J.).--Pdf.
33. Stochastic regression in terms of Brownian
motion, (with D.C. Chang and J. Hu), Applicable Analysis,
Volume 90, Issue 6, pp. 899-919, June 2011--Pdf
34. Stochastic Trigonometry and Stochastic
Invariants (with D.C. Chang), Journal of Nonlinear and
Convex Analysis, Vol. 11, No.1, 2010 --Pdf
35. Non-holonomic system and sub-Riemannian
geometry, (with D.C. Chen and S.T. Yau), Comm. Informations
and Systems, vol. 10, No.4, pp. 293-316, 2010.Abstract
36. On a Class of Nilpotent Distributions
(with DC Chang), Taiwanese Journal of Math., Vol. 15, No. 2,
pp. 875-881, April 2011-- Pdf.file
37. Heat Kernels for differential operators
with radical function coefficients, (with D.C. Chang),Taiwanesse
Journal of Math., Vol. 15, No.4, pp. 1629-1636, August 2011--Pdf.file
38. Asian Options with Stochastic Strike
Price, (with D.C. Chen and B. Alshamary), Applicable Analysis,Vol.
91, Issue 1, 2012, pp.91-104.--Pdf.
39. Geometric Optimization in Prey-Predator
Problems (with B. Alshamary), Journal of Mathematical Biology,
Vol: 63, issue 5, pp.881-900, 2011 -Pdf
40. Heat kernels for a class of degenerate
operators using the stochastic method (with D.C. Chang,
Y. L and J. Hui) Complex Variables and Elliptic Equations, 57,
no.2-4, pp.155-168, 2012--Pdf.
41.On Heat Kernels of a Class of Degenerate
Elliptic Operators (with D.C. Chang, Y. L and J. Hui),
Journal of Nonlinear and Convex Analysis, 12, no.2, pp.309-340,
42.On the Heat Kernel of a Left Invariant
Elliptic Operator, (with D.C. Chang, Y. Li), Excursions
in Harmonic Analysis, vol.2, pp.197-209, Appl. Numer. Harmon.
Anal., Birkhauser/Springer, New York, 2013--Pdf.file
43. Stochastic optimization approach of
car value depreciation, (with B. Alshamary), Applied Stochastic
Models in Business and Industry, Vol. 29, Issue 3, May/June
208–223, 2013.- Pdf.file
44.Global connectivity and optimization
on an infinite step distribution (with B. AlShamary and
D.C. Chen), Adv. Appl. Math. 50, no. 4, pp.634-644, 2013- PDF.file.
45. Integrability conditions for the Grushin
and Martinet distribution (with D.C. Chang and M. Eastwood),
Bulletin of the Institute of Mathematics, Academia Sinica (New
series), Vol. 8, No.2, June 2013
a stochastic car value depreciation deal, (with B.Alshamary),
Applied Stochastic Models in Business and Industry, 30, no.4,
pp. 509-516, 2014 -Pdf.file
Transience of diffusions on Heisenberg group, Journal of
Geometry and Physics, vol. 77, March 2014, pp. 131-142.-Pdf.
48. Integrability conditions for Heisenberg
and Grushin-type distributions (with D.C. Chang and M.
Eastwood), Analysis and Mathematical Physics, pp. 99-114, vol.
4, issue 1-2, 2014.- Pdf.
49. A stochastic variant of Chow-Rashewski
Theorem on the Grushin Distribution, (with C. Udriste and
I. Tevy) Balkan Journal of Geometry and Applications, 19, no.1,
50. Stochastic sub-Riemannian geodesics
on the Grushin distribution, Balkan Journal of Geometry
and Applications (with C. Udriste and I. Tevy), 19, no.2, pp.37-49,
51. Isometric elastic deformations (with F.
AlAzemi), pp. 1-8, BGS Proceedings, 2014.-Pdf.
Poincare’s lemma on the Heisenberg group (with J.
Hu and D.C. Chen), Adv. in Appl. Math. 60, pp. 90-102, 2014.-Pdf.file
53. Integrability conditions on Engel-type
manifolds, Anal. Math. Physics, vol.5, issue 3, pp. 217-231,
54. Asian Options with Harmonic Average
(with F. AlAzemi), Applied Mathematics and Information Sciences,
vol.9, no. 6, 2015-Pdf.file
55. An Optimality Model for Rust Formation
and Evolution (with B. AlShamary), accepted to Applied
Stochastic Models in Business and Industry, 2015
56. Integrability Conditions on a Sub-Riemannian
structure on S^3, submitted.
Integrability Conditions on a Sub-Riemannian structure on H^3,
Bond Valuation for term structure of interest with jumps,
1. Geometric Mechanics on Riemannian Manifolds,
with Applications to Partial Differential Equations, published
by Birkhauser (Boston Basel Berlin), Fall 2004 (with Chang,
2. Euclidean and Non-Euclidean Geometry:
A metric approach, Wiley (Custom Services), 2004.
3. An Introduction to Vectorial Geometry,
McGraw Hills Custom Publishing, 2005.
4. Wp-Calculus, An Introduction to Formal
Languages, Wiley Custom Services, 1st ed. 2006, 2nd ed.
2013 (with Zeiger, M.).
5. Geometric Analysis on Heisenberg Manifolds
and Generalizations (with Chang, D-C, and Greiner, P.)
Studies in Adv. Math. No. 40, AMS/IP, 2007.
6. SubRiemannian Geometry -- Theory and
examples (with Chang, D-C), Encyclopedia of Math and Its
Appl., 126 Cambridge University Press, 2009.
7. Heat Kernels-- Methods and Techniques,
Applied and Numerical Harmonic Analysis, Birkhauser (Boston
Basel Berlin), Fall 2010 (with Chang, D.C., Furutani, K. and
Geometric Modeling in Probability and Statistics (with
C. Udriste), Springer, 2014.
An Informal Introduction to Stochastic Calculus with Applications,
World Scientific, 2015.