T. M. G. Ahsanullah (Partly updated CV is attached below)
Name: T. M. G. AHSANULLAH (AHSANULLAH, TMG)
Address: (Official) Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
Address in home country: House # 02, Flat # D-3, Road # 15, Sector # 07, Uttara Model Town, Dhaka – 1200, Bangladesh
Telephone: +966-1-4675177
Fax : +966-1-4676512
E-Mail Address: tmga1@ksu.edu.sa; tmglily5@gmail.com
Website: http://fac.ksu.edu.sa/tmga1
Present Position: Professor of Mathematics
Marital Status: Married to Kishwar Sultana (Lily) with 3 children: Safwan Ahsan, Sumaiya Ahsan (Bushra), Arsh Ahsan.
Education
1. From October 1979 to April 1984 worked as a doctoral reserach fellow at the Free University of Brussels, Belgium (Vrije Universiteit Brussel) under the Fellowship from the Ministry of Higher Education and Dutch Culture, Government of Belgium, specializing Fuzzy Topological Structures on Groups and Semigroups, generalizing Topological Structures on Groups and Semigroups leading to Ph. D degree.
Obtained Doctor of Science (Ph. D) degree in Mathematical Sciences (Pure Mathematics), Free University of Brussels, 27th June 1984.
Title of the Ph. D thesis: On Fuzzy Topological Groups and Semigroups.
Title of the Annex thesis: Generalization of classical Urysohn lemma for normal topological spaces.
Supervisors: Professor Dr. Piet Wuyts and Professor Dr. Robert Lowen.
2. Obtained a scholarship (NST Fellowship) from the Ministry of Science and Technology, Government of People's Republic of Bangladesh in mid 1979 for doing reserach leading to M. Phil degree attached to the Department of Mathematics, University of Dhaka but a few months later obtained a scholarship from Belgium Government for higher studies.
3. Master of Science degree in Pure Mathematics, University of Dhaka, 1976 (Examination held in early 1979) (Subject taken: Topology, Real Function Theory, Theory of Numbers, and Theory of Groups).
4. Bachelor of Science (Honors) degree in Mathematics, University of Dhaka, 1975 (Examination held in 1977).
5. Higher Secondary School Certificate Examination, Dhaka, 1972 (Examination held in 1973).
6. Secondary School Certificate Examination, Board of Intermediate and Secondary Education, Rajshahi (Bangladesh), 1970.
Teaching Experience
1. Joined the Department of Mathematics, University of Dhaka on February 2, 1985 as a Lecturer.
2. Appointed as Assistant Professor at the Department of Mathematics, University of Dhaka, December 1985.
3. Appointed as Associate Professor at the Department of Mathematics, University of Dhaka in June 1991 (in absentia).
4. Joined the Department of Mathematics, King Saud University, Riyadh, Saudi Arabia (with extraordinary leave from Dhaka University, Bangladesh) as an Assistant Professor on 26th October 1990 and served this department till June 26, 1994.
5. Rejoined at the Department of Mathematics, University of Dhaka (at the end of extraordinary leave taken from the University of Dhaka in 1990) as an Associate Professor on 16th July 1994.
6. Promoted to the position of Professor of Mathematics on 27th March, 2001 at the Department of Mathematics, University of Dhaka.
7. Joined at the Department of Mathematics, King Saud University, Riyadh, Saudi Arabia as a Professor of Mathematical Sciences on 29th January 2002.
8. Served as part time Professor of Mathematics at the North South University, Dhaka, Bangladesh to teach Mathematics for the students of Computer Sciences, Business Admistration and Environmental Sciences.
9. Served as part time Professor of Mathematics at the Department of Statistics, University of Dhaka, Bangladesh to teach Mathematical Analysis to the students of Statistics.
Teaching the following courses
King Saud University
Math #700, Math #600 level courses for Ph D students, various courses, Math #500 level for Master students mainly Topology, Measure Theory, and Many-valued topology and its Applications; Math #548 (Mathematics of Fuzzy Sets and Applications); Math #373 (Elementary Topology), Math #348 (Real Analysis II); various courses for Engineering students: Math #140 (Foundation course of beginers), Math # 105 (Differential calculus) Math #106 (Differential and Integral Calculus), Math #107 (Linear algebra, Vectors and Calculus), Math #109 for Pharmacy students, Math #203(Multivariable Calculus), Math #204 (Differential Equation and its Applications).
Dhaka University
Topology at the postgraduate and undergraduate levels; Fuzzy Topology at M Phil level; Fuzzy Mathematical techniques at the Master degree level; Real Analysis; Advanced calculus at Master (Part I) level; Mathematical Methods; Differential Equations and Boundary Value Problems; Mathematical Analysis at Honors level; also taught various courses for subsidiary and minor students of Computer Sciences; Physics; Applied Physics and Electronics; Chemistry; Biochemistry; Soil Science; Statistics; Geography; Intusdrial Arts; Psychology; Geology students.
North South University
Math #112 (Foundation course in Mathematics); Math #125 (Elementary Linear Algebra and its Applications); Math #120 (Calculus I); Math #130 (Calculus II); Math #240 (Calculus III); Math # 250 (Calculus IV).
Present Reserach Interest
Primary Interest: General Topology. Secondary Interest: Lattice-Valued Topology.
AMS Sub Class: 54H11, 54E15, 54 A 20, 18 B 30; 54A40
Probabilistic Metric Spaces, Probabilistic Convergence Group Theory, Uniformization, Metrization, Approach Group Theory, Approach Convergence Group Theory.
Topological groups, Convergence Groups, Application of Convergence Structures to Functional Analysis, Convenient Topology, Category.
Editorial Activities
- Member of the Editorial Board (Mathematics of Uncertainty): New Mathematics and Natural Computation, World Scientific Publishing
http://www.worldscientific.com/page/nmnc/editorial-board
- Member of the Editorial Board (Fundamental Journal of Mathematics and Mathematical Sciences)
http://www.frdint.com
Ph. D Thesis Supervision
1. Jawaher Al-Mufarrij (degree obtained, 2009)
2. Jomana Binte Hussein Ali Al-Safar (degree obtained, 2013)
Personal Interest
Travelling, listening to music, cooking
Countries visited
Belgium, The Netherlands, Luxemberg, Germany, France, U. K., Saudi Arabia, U.S.A., United Arab Emirates, Turkey, China, Malaysia, India, Qatar, Bahrain, New Zealand, Canada, Greece, Spain, Serbia.
Research Activities/Publications
1. T. M. G. Ahsanullah, Some results on fuzzy neighborhood spaces, J. Pure Manuscript 4(1985), 97-106.
2. T. M. G. Ahsanullah, Separation axioms in fuzzy neighborhood spaces, Bull. Malaysian Math. Soc. 9(10)(1986), 27-31.
3. T. M. G. Ahsanullah, On fuzzy neighborhood groups, J. Math. Anal. Appl. 130(1988), 237-251.
4. Abu Osman M. T. and T. M. G. Ahsanullah, On fuzzy subsemigroups via triangular norms 18(4)(1989), 29-35.
5. T. M. G. Ahsanullah and S. Ganguly, On fuzzy neighborhood rings, International J. Fuzzy Sets and Systems 34(1990), 255-260.
6. T. M. G. Ahsanullah, On fuzzy neighborhood modules and algebras, International J. Fuzzy Sets and Systems 35(1990), 219-229.
7. T. M. G. Ahsanullah, On the small invariant fuzzy neighborhood groups, Calcultta Math. Soc. 84(1992), 457-464.
8. M. K. Chakraborty and T. M. G. Ahsanullah, Fuzzy topologies on fuzzy sets and tolerance topologies, International J. Fuzzy Sets and Systems 45(1992), 103-108.
9. T. M. G. Ahsanullah and N. N. Morsi, Invariant probabilistic metrizability of fuzzy neighborhood groups, International J. Fuzzy Sets and Systems 47(1992), 233-245.
10. A. F. M. Khodadad Khan and T. M. G. Ahsanullah, Sequential convergence in fuzzy neighborhood spaces, International J. Fuzzy Sets and Systems 46(1992), 115-120.
11. A. F. M. Khodadad Khan and T. M. G. Ahsanullah, Some properties of fuzzy neighborhood normed linear spaces, International J. Fuzzy Sets and Systems 54(1993), 333-339.
12. T. M. G. Ahsanullah and Fawzi Al-Thukair, Conditions on a semigroup to be a fuzzy neighborhood group, International J. Fuzzy sets and Systems 55(1993), 330-340.
13. T. M. G. Ahsanullah and Fawzi Al-Thukair, A characterization of fuzzy neighborhood commutative division rings, International J. Math. Math. Sci. 16(4)(1993), 709-716.
14. Marouf Samhan and T. M. G. Ahsanullah, Fuzzy congruences on groups and rings, International J. Math. Math. Sci. 17(3)(1994), 469-474.
15. T. M. G. Ahsanullah and Fawzi Al-Thukair, Characterization of fuzzy neighborhood commutative division rings II, International J. Math. Math. Sci. 18(2)(1995), 323-330.
16. T. M. G. Ahsanullah and Marouf Samhan, On the N-topological right quasi-regularity in N-rings, J. Fuzzy Math.(International Fuzzy Mathematics Institute, Los Angeles) 3(2)(1995), 273-283.
17. T. M. G. Ahsanullah, Stictly minimal fuzzy neighborhood division rings, International J. Fuzzy Sets and Systems 78(1996), 371-380.
18. M. A. Qureshi and T. M. G. Ahsanullah, Compactness and some characterizations of fuzzy neighborhood algebraic structures, J. Fuzzy Math. (International Fuzzy Mathematics Institute, Los Angeles, USA) 4(4)(1996), 815-828.
19. T. M. G. Ahsanullah, Minimal locally bounded fuzzy neighborhood commutative division rings, International J. Fuzzy Sets and Systems 87(1997), 87-97.
20. A. F. M. Khodadad Khan and T. M. G. Ahsanullah, Net-convergence in fuzzy neighborhood spaces, International J. Fuzzy Sets and Systems 101(2000), 197-203.
21. T. M. G. Ahsanullah, Cauchy-nets in fuzzy neighborhood Abelian groups, rings and modules, J. Bang. Acad. Sci. 24(2000), 212-134.
22. T. M. G. Ahsanullah, Applications of net and sequential convergence in various fuzzy neighborhood structures, J. Fuzzy Math. (International Fuzzy Mathematics Institute, los Angeles, USA) 9(2)(2001), 325-351.
23. T. M. G. Ahsanullah, On quotient fuzzy topological groups, Ganit (J. Bangladesh Math. Soc.) 5(1985), 37-42.
24. T. M. G. Ahsanullah and M. S. Rahman, Some remarks on fuzzy topological semigroups, J. Bang. Acad. Sci. 9(20)(1985), 131-135.
25. T. M. G. Ahsanullah, Inverse limits of fuzzy neighborhood spaces and fuzzy neighborhood groups, J. Bang. Sci. Res. 4(1)(1986), 1-6.
26. T. M. G. Ahsanullah, On fuzzy neighborhood semigroups, Dhaka University Studies 33(2)(1985), 295-303.
27. T. M. G. Ahsanullah, Initial and final fuzzy neighborhood groups, Dhaka University Studies 34(1)(1986), 99-109.
28. A. F. M. Khodadad Khan and T. M. G. Ahsanullah, on fuzzy topological groups, Dhaka University Studies 34(2)(1986), 223-230.
29. T. M. G. Ahsanullah and A. F. M. Khodadad Khan, Fuzzy uniformities on initial fuzzy neighborhood groups, J. Bangladesh Acad. Sci. 35(1)(1987), 85-90.
30. T. M. G. Ahsanullah, Some properties of the level spaces of fuzzy neighborhood spaces and fuzzy neighborhood groups, J. Bangladesh Acad. Sci. 13(1)(1989), 91-96.
31. T. M. G. Ahsanullah and A. F. M. Khodadad Khan, Inverse limits of topological spaces and fuzzy neighborhood groups with operators, J. Math. Math. Sci. 2(1989), 55-61.
32. A. F. M. Khodadad Khan and T. M. G. Ahsanullah, Fuzzy differentiation in fuzzy neighborhood linear spaces, Ganit (J. Bangladesh Math. soc.) 8(10)(1988), 69-76.
33. M. Ataharul Islam, T. M. G. Ahsanullah and A. F. M. Khodadad Khan, A note on linear regression modeling of fuzzy membership functions, J. Bangladesh Sci. Res. 8(1990), 13-37.
34. T. M. G. Ahsanullah, Precompactness in fuzzy neighborhood groups, J. Bangladesh Acad. Sci. 14(1)(1990), 99-105.
35. Shapla Shirin, A. F. M. Khodadad Khan and T. M. G. , Ahsanullah, Fuzzy neighborhood Schwartz spaces, Dhaka University Sci. Journal 44(1)(1996), 79-86.
36. Shapla Shirin and T. M. G. Ahsanullah, On coupling and consistency of fuzzy neighborhood topologies, J. Bangladesh Acad. Sci. 22(2)(1988),119-126.
37. T. M. G. Ahsanullah, Cauchy-net in fuzzy uniform spaces, J. Fuzzy Math. (International Fuzzy Mathematics Institute, Los Angeles, USA) 10(2002), 169-187.
38. T. M. G. Ahsanullah and M. A. Bashar, A non-trivial example of fuzzy neighborhood Abelian groups, J. Bangladesh Acad. Sci. 25(2)(2001), 177-185.
39. T. M. G. Ahsanullah, M. A. Bashar and A. F. M. Khodadad Khan, Fuzzy bornological vector spaces, Dhaka University J. Sci. 50(1)(2002), 73-82.
40. T. M. G. Ahsanullah and Fawzi Al-Thukair, T-neighborhood groups, International J. Math. Math. Sci. 14(2004), 703-719.
41. T. M. G. Ahsanullah, Fawzi Al-Thukair and M. A. Bashar, On the weakability of fuzzy neighborhood systems on various algebraic structures, J. Fuzzzy Math. (International Fuzzy Mathematics Institute, Los Angeles, USA) 12(2)(2004), 261-284.
42. T. M. G. Ahsanullah and Fawzi Al-Thukair, N-topo nilpotency in fuzzy neighborhoodd rings, International J. Math. Math. Sci. 13(2004), 679-696.
43. T. M. G. Ahsanullah, M. A. Bashar and S. Shirin, Fuzzy topological divisor of zero in a fuzzy neighborhood rings, J. Algebras, Groups and Geomtries (Hadronic Press, Palm Harbor, Florida, USA) 22(2005), 457-472.
44. Jawaher Al-Mufarrij and T. M. G. Ahsanullah, On the category of fixed basis frame-valued topological groups, International J. Fuzzy Sets and Systems 159(2008), 2529-2551.
45. T. M. G. Ahsanullah and Jawaher Al-Mufarrij, Frame-valued stratified generalized convergence groups, Quaestiones Mathematicae 31(2008), 279-302.
46. T. M. G. Ahsanullah and Fawzi Al-Thukair, On the relationship between topological rings and $L$-neighborhood rings, Procd. Sharjah Math. Conference, 2007.
47. T. M. G. Ahsanullah lattice-valued convergence ring and its uniform convergence structure, Quaestiones Mathematicae 33(2010), 21-51.
Abstract: Considering $L$ a frame, we introduce the notion of stratified $L$-neighborhood topological ring, produce some characterization theorems including its $L$-uniformizability. With the help of the notions of stratified convergence structure attributted to Gunther Jager [A category of $L$-fuzzy convergence spaces, Quaestiones Mathematicae 24(2001), 501-517], we introduce and study various subcategories of stratified $L$-convergence rings. In so doing, we bring into light, among others, the notion of stratified $L$-uniform group and stratified $L$-uniform convergence group in an attempt to show that every stratified $L$-uniform convergence structure of Jager and Burton [Stratified $L$-uniform convergence space, Quaestiones Mathematics 28(2005), 11-36], and the category of stratified $L$-uniform groups and uniformly continuous group homomorphisms, S$L$-UnifGrp is isomorphic to the category of principal stratified $L$-uniform convergence groups and uniformly continuous group homomorphisms, S$L$-PUConvGrp. Introducing the notion of stratified $L$-Cauchy rings, we show that the category of stratified $L$-Cauchy rings and Cauchy-continuous ring homomorphisms, S$L$-ChyRng is topological over the category of rings, Rng with respect to the forgetful functor, and that every stratified $L$-Cauchy ring is a stratified $L$-convergence ring. We observe that if $L$ is a Boolean algebra, then each stratified $L$-uniform convergence ring serves as a natural example of a stratified $L$-Cauchy ring. We give necessary and sufficient conditions for a stratified $L$-convergence structure and a ring structure to be a stratified $L$-convergence ring.
48. Jawaher Al-Mufarrij and T. M. G. Ahsanullah, On the relationship between various lattice-valued topological groups and their uniformities, Presented at the International Conference on Topology and its Applications at Hacettepe University, Ankara, Turkey held on July 6-11, 2009; the session chaired by Professor Alexandar P. Sostak.
Abstract : Following the Hohle-Sostak notion of lattice-valued neighborhood topological structures [Axiomatic foundations of fixed basis fuzzy topology, in: Mathematics of Fuzzy Sets: Topology, Logic and Measure Theory, Edited by U. Hohle and S. E. Rodabaugh, Kluwer Academic Publisher, Dordrecht, 1999], we introduced as a general frame work a notion of fixed basis frame valued neighborhood topological groups [Jawaher Al-Mufarrij and T. M. G. Ahsanullah, On the caategory of fixed basis frame valued topological groups, International J. Fuzzy Sets and Systems 159(2008), 2529-2551]; and following the remarkable filter-based unification [J. Gutierrez Garcia, M. A. de Prada Vicente and A. P. Sostak, A unified approach to the concept of fuzzy $L$-uniform space, in S.E. Rodabaugh and E. P. Klement, editedTopological and Algebraic Structures in Fuzzy Sets, Kluwer Academic Publishers, Dordrecht, 2003] of known notions of fuzzy uniformity of various kinds, we studied stratified frame valued uniform structures, such as left, right, their infimum and supremum uniformities on fixed basis stratified frame valued neighborhood topological groups. Since the inception of the notion of fuzzy topological groups attibuted to D. H. Foster [J. Math. Anal. Appl. 67(1979), 549-564], various authors, notably, U. Hohle, A. K. Katsaras, T. M. G. Ahsanullah, Jin-Xuan Fang and Huan Huang introduced and studied this notion from different view point.
The purpose of this article is to make an investigation on the relationship of all of these notions of lattice-valued topological groups, and the uniformities they inherit. In doing so, again we take advantage of the excellent papr of Gutierrez Garcia-Vicente-Sostak on unification to look at the relaationship between:
a) Crisp sets of lattice-valued neighborhood groups and probabilistic lattice-valued neighborhood topological groups, and their uniformities (Hohle's probabilistic uniformity and Gutierrez Garcia et al type uniformity);
(b) Lattice-valued topological groups of ordinary subsets and fuzzy neighborhood groups, and their uniformities (Gutierrez Garcia et al type uniformity and Lowen fuzzy uniformity);
c) Lattice-valued neighborhood topological groups and their level spaces.
49. T. M. G. Ahsanullah and Fawzi Al-Thukair, Change of basis for lattice-valued convergence groups, New Math. and Natural Computation 7(3) (2011), 453-469, World Scientific Publishing.
Abstract: Using the idea of changing the basis-lattice, we investigate in this article the impact of change-of-basis to the notion of stratified lattice-valued generalized convergence group by employing so-called functorial mechanism. We discuss here some of the subcategories of the category of stratified lattice-valued generalized convergence groups, such as, stratified lattice-valued Kent convergence groups, stratified lattice-valued limit groups, and look into the possible link between these objects with stratified lattice-valued neighborhood groups and stratified lattice-valued neighborhood topological groups, when bases are changed. Moreover, with the help of the notion of stratified lattice-valued filter attributed to U. Hohle and A. P. Sostak, we introduce a category HS-S$L$-FilGrp, of stratified lattice-valued filter groups, and study its relationship with other categories so far achieved in this paper.
50. T. M. G. Ahsanullah and Fawzi Al-Thukair, On some subcategories of stratified lattice-valued generalized convergence groups and lattice-valued categories (submitted for publication).
51. T. M. G. Ahsanullah, category of lattice-valued Preuss filter groups and its related categories (25th Topology conference, July 25-30, 2010, Kielce, Poland; Abstract Accepted.)
52. Jawaher Al-Mufarrij and T. M. G. Ahsanullah, On the category of $L$-fuzzy neighborhood groups and its connections with various categories of $L$-convergence groups (International Conference on Topology and its Application, Nafpaktos, Greece, June 26-30, 2010; Abstract Accepted.)
Abstract: Motivated by the notion of $L$-fuzzy neighborhood system attributed to U. Hohle and A. P. Sostak [Axiomatic foundations of fixed basis fuzzy topology, in: Mathematics of Fuzzy Sets: Topology, Logic and Measure Theory, Edited by U. Hohle and S. E. Rodabaugh, Kluwer Academic Publishers, Dordrecht, 1999], we introduce for a frame $L$, categories S$L$-FNeighGrp, of stratified $L$-fuzzy neighborhood groups, and S$L$-FIntGrp, of stratified $L$-fuzzy interior groups. We show that these two categories are isomorphic; some basic facts along with some characterization theorems are presented. Considering the notion of stratified $L$-pre-topological convergence space due to H. Boustique, R. N. Mohapatra and G. Richardson [Lattice-valued fuzzy interior opeators, International J. Fuzzy Sets and Systems 160(2009), 2947-2955], we show that the category S$L$-P-TopConvGrp, of stratified $L$-pre-topological convergence groups, is isomorphic to the category S$L$-FNeighGrp. Also, considering a full subcategory S$L$-FNeighGrp', we show that this category is isomorphic to a subcategory of the category S$L$-GConvGrp, of stratified $L$-generalized convergence groups [T. M. G. Ahsanullah and Jawaher Al-Mufarrij, Frame-valued stratified generalized convergence groups, Quaest. Math. 31(2008), 279-302]; the key item of this category is the notion of stratified $L$-generalized convergence structure initiated by G. Jager [A category of $L$-fuzzy convergence spaces, Quaest. Math. 24(2001), 501-517]. Finally, we propose two more categories HS-S$L$-FFil, of Hohle-Sostak straified $L$-fuzzy filter spaces, and HS-S$L$-FFilGrp, of stratified $L$-fuzzy filter gropus, and discuss some of their features.
53. T. M. G. Ahsanullah, Continuous action of stratified lattice-valued convergence groups (2nd International Conference on Mathematical Analysis, Putra World Trade Center, Kuala Lumpur, Malaysia, 30 November - 3 December, 2010; Abstract Accepted.)
Abstract: Using the ideas of stratified lattice-valued convergence structure attributed to G. Jager [A category of $L$-fuzzy convergence spaces, Quaest. Math. 24(2001), 501-517], and stratified frame-valued generalized convergence group introduced in [T. M. G. Ahsanullah and Jawaher Al-Mufarrij, Frame-valued stratified generalized convergence groups, Quaest. Math. 31(2008), 279-302], we present here a notion of continuous action of stratified lattice-valued convergence group on stratified lattice-valued convergnce space. We discuss how stratified lattice-valued convergence group act continuously on a set of contnuous functions bestowed with stratified lattice-valued convergence structure of contnuous convergence of Jager. Finally, we show that there exists a one-to-one correspondence between the homeoporphic representation of stratified lattice-valued convergence group and its continuous actions on a stratified lattice-valued limit space [G. Jager, Subcategories of lattice-valued convergence spaces, International J. Fuzzy Sets and Systems 156(2005), 1-24.]
Reviewer
1. Mathematical Reviews (American Mathematical Society) (reviewer)
2. Zentralblatt fur Mathematik (Mathematics Abstract) (Springer Verlag, Berlin)
3. International Journal for Fuzzy Sets and Systems (Elsevier Publishers)
4. Information Sciences: An International Journal (Elsevier Publishers)
5. Kluwer Academic Publishers (Book Reviewed)
6. Collectanea Mathematica, Universite de Bercelona, Spain
7. Journal of Fuzzy Mathematics, International Fuzzy Mathematice Institute, Los Angeles, USA
8. Arab Journal of Mathematical Sciences (Saudi Mathematical Society)
9. Bulletin Calcutta Mathematical Society, India
10. Indian Journal of Pure and Applied Mathematics
11. International Journal of Uncertainity, Fuzziness and Knowledge-Based Systems, World Scientific Publishing
12. Journal of New Mathematics and Natural Computations, World Scientific Publishing
13. Journal of Computers and Mathematics with Applications, Elsevier Publishing company
14. De Gruyter Journal of Group Theory, Germany
15. Bulletin Malaysian Mathematical Society, Kuala Lumpur, Malaysia
16. Journal of Bangladesh Mathematical Society: GANIT
17. Dhaka University Science Journal, Bangladesh
18. Journal of Shah Jalal University of Science and Technology (Bangladesh)
19. Bangladesh Journal of Science and Technology
20. Rajshahi University Studies (Bangladesh)
21. Journal of Neural Computation and Application, (Elsevier Publishers)
22. Journal of Mathematics and Statistics, Hecettepe University, Ankara, Turkey
23. Tripura University Mathematics Journal, Tripura, India
24. Annals of Fuzzy Mathematics and Informatics, South Korea
25. Journal of Mathematical and Computer Modelling (Elsevier Publishers)
26. Journal of Mathematics and Computer Sciences
27. Filomat (Serbian Journal on Mathematics)
28. Soft Computting (Springer Varlag)
29. Songklanakarin Journal of Science and Technology
Supervisor/ Examinier/ Academic Responsibilities
A. Supervised Ph D student: Dr. Jawaher Al-Mufarrij , Department of Mathematics, Women Section at the King Saud University, obtained degree on19th April, 2009.
Title of the Ph D thesis: On the Subcategories of Frame Valued Topological Groups and Generalized Convergence Groups
Abstract: Considering $L$ a frame, first we introduced within the framework of Hohle-Sostak lattice-valued topologicl structures, the notion of $L$-neighborhood topological groups, and stratified $L$-neighborhood topological groups which are objects from the subcategories of the category of $L$-topological groups. We studied their fundamental properties and provided with characterization theorems. In doing so, we looked into some related structures, such as, initial, final and quotient stratified $L$-neighborhood topological groups. We showed that the category of $L$-neighborhood topological groups and $L$-continuous group homoorphisms, $L$-NTopGrp is topological over the category of groups, Grp with respect to forgetful functor. We settled down one of the crucial issues that every stratified $L$-neighborhood topological group is $L$-uniformizable. This is done for the first time within the unified approach of $L$-uniform spaces attributed to Gutierrez Garcia, De Prada Vicente, and Sostak. In this respect, we obtained various $L$-uniformities of stratified $L$-neighborhood topological groups, such as, left, right, infimum and supremum. Considering quotient $L$-uniformity due to Garcia, we looked into its impact with quotient stratified $L$-neighborhood topological groups.
Introducing the notions of $L$-equicontinuity, $L$-uniform equicontinuity and balanced stratified $L$-neighborhood topological groups in appropriate spaces, we provided with various results along with some cannonical examples. Here, we gave characterization theorems on balanced stratified $L$-neighborhood topological groups and obtained a full subcategory BS$L$-NTopGrp of balanced stratified $L$-neighborhood topological groups and $L$-continuous group homomorphisms, of the category S$L$-TopGrp of stratified $L$-topological groups. We derived the relationship between $L$-neighborhood topological groups with various $L$-topological groups, and set relationship between uniformities they inherit.
Finally, following the notion of stratified $L$-fuzzy convergence space of Gunther Jager, we introduced which we believe to be a new notion, the notion of stratified $L$-generalized convergence group. By dropping the topological condition from the notion of $L$-neighborhood topological system, we introduced the notion of stratified $L$-neighborhood groups, and studied some other intimately related objects, manely, stratified $L$-Kent convergence groups, and stratified $L$-principal convergence groups. We showed that the category of stratified $L$-principal convergence groups, S$L$-GCGrp is topological over the category of groups, Grp with respect to the forgetful functor, and we observed that the category S$L$-NeighGrp, of stratified $L$-neighborhood groups is isomorphic to a subcategory of S$L$-GCGrp. We give necessary and sufficient conditions for a group structure and a stratfied $L$-generalized convergence structure to be stratified $L$-generalized convergence groups. We showed that every stratified $L$-generalized convergence group possessing a stratified $L$-principal convergence structure gives rise to a stratified $L$-neighborhood topological group. We ended up by stating a nice relationship that exist among the subcategories of stratified $L$-neighborhood topological groups and newly founded objects in the domin of stratified $L$-generalized convergence groups.
Keywords: Frame, lattice-valued topology, topological group, uniform space, generalized convergence group, category.
AMS Subject Classification (2000): 54A40, 54E15, 54H11, 54A20, 18B30.
B. Supervised Ph D student: Ms Jomana Hussein Ali Al-Safar
Title of the Ph D thesis: Subcategories of Stratified Lattice-Valued Semiuniform Convergence Groups and Change of Basis Lattice, 2012.
C. Supervised M. Sc thesis: Dhaka University, Bnagladesh
1. Shapla Shrin (A Study on Fuzzy Neighborhood Linear Spaces)
2. Mohammad Parvez (Fuzzy Measure Theory)
3. Shirajul Islam (Equivalent Uniformities in Topological Groups)
4. Rafiq Amer (On the category of Topological Transformation Groups)
5. Gautom Pal (Equivalent Uniformities and Measurability in Topological Groups)
6. M. A. Bashar (On Fuzzy Neighborhood Order Spaces)
7. Morari Mohan Das (Some Results on Fuzzy Groups)
8. M Farid Uddin (A Study of Ultracompletion of Fuzzy Neighborhood Linear Spaces)
9. Mostaq Ahmad (On Some Fuzzy Algebraic Structures)
10. Jbaida Begum (On Different Types of Fuzzy Operators)
11. Mahbul Khan (A Study on Various t-norms)
12. Sharifullah Majumdar (On the Subcategories of Topological Groups and Many Valued Topological Spaces)
D. Examined M Phil Thesis for a student of Dhaka University
E. Examined Ph D Thesis from Various Universities from India
F. Performed responsibilities as chairman and member of different examination committee at Dhaka University
G. Served as coordinator of Math # 107 at the Department of Mathematics, King Saud University
H. External member of selection committee for Associate Professor and Professor, various universities from different countries
Member of Different Learned Societies
1. American Mathematical Society (Reciprocity Membership)
2. Bangladesh Mathematical Society (Life Member)
3. Calcutta Mathematical Society (Life Member)
4. London Mathematical Society (Reciprocity Member)
5. Saudi Mathematical Society (Ordinary Membership)
6. SMU - Society for the Mathematics of Uncertainty, Department of Electrical and Computer Engineering, Duke University, North Carolina, USA
7. IEEE (Institute of Electrical and Electronics Engineers -The World's Largest Professional Association for the Advancement of Technology)
8. Canadian Mathematical Society
Invited Speaker/Speaker
1. Delivered lecture on Fuzzy Mathematics at the National Center of Knowledge-Based Computing at the Statistical Institute of India, Calcutta, West Bengal, India, 1987.
2. Delivered lecture at the Department of Pure Mathematics, Balygang Circular Road, Calcultta University, West Bengal, India, jointly sponsored by the University Grant Commission, Bngladesh and Indian Society for Fuzzy Mathematics and Information Processing, 1987 .
3. Delivered lecture at the Department of Applied Mathematics, Calcutta University, West Bengal, India, 1987.
4. Given two seminars on Fuzzy Topologies and Topological Algebraic Structures at the Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia, November-December, 1990.
5. Given a talk on Fuzzy Topologies on Algebraic Structures at the King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, NOvember, 1992.
6. Paper presented at the International Conference organized by the Saudi Association of Mathematical Sciences, Riyadh, April 5-7, 1994.
7. Delivered lectures on Fuzzy Mathematics and its Applicatioons at Summer Seminar at the Department of Mathematics, University of Dhaka, Bangladesh.
8. Delivered lectures at the International Seminar at the Department of Mathematics on Fuzzy Mathematics sponsored by the Bangladesh Mathematical Society and University of Dhaka.
9. Delivered lectures at the symposium and annual conferences held at different Universities in Bangladesh.
10. Presented paper at the International Conference held at Prince Sultan University of Science and Technology, Riyadh, Saudi Arabia, 2003.
11. Presented paper at the International Conference on Mathematics and its Application at Sharjah University, United Arab Emirates, 2004.
12. Presented paper at the Saudi International Conference of Science and Technology, Riyadh, Saudi Arabia, 2006.
13. Presented paper at the International Conference on Mathematics and its Applications at Sharjah, United Arab Emirates, 2007.
14. Chaired a scientific session at the International Conference on Mathematics and its Application at Sharjah, United Arab Emirates, 2007.
15. Presented paper at the International Conference on Topology and its Applications held at Hacettepe University, Ankara, Turkey, July 6-11, 2009.
16. Given a talk on fixed basis frame valued convergence group and its uniform convergence structure at Maltepe University, Istanbul, Turkey, 9th July, 2009.
17. Delivered a talk on Change of basis structure of convergence groups, First Annual Math Day Conference at King Saud University, December 16-17, 2009.
18. Chaired a session at the First Annual Math Day Conference, KSU, December 16-17, 2009.
19. Chaired a scientific session of the International Conference on Topology and its Applications, Ankara, Turkey on July 6-11, 2009.
20. Given a talk on Lattice-valued semitopological convergence groups at the 45th Annual Spring Topology and Dynamics Conference held at the University of Texas, Tyler, USA, March 17-19, 2011.
Abstract of the talk: In this talk we focus the following:
(a) to introduce the notion of lattice-valued semitopological group, generalizing classical notion of semitopological group [W. Ruppert, Compact semitopological semigroups: An Instrinsic Theory, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1984; A. Arhangelskii and M. Tkachenco, Topological Groups and Related Structures, Atlantis Press/World Scientific, Amstardam, 2008], and lay down some of their basic features;
(b) to introduce the notion of lattice-valued semitopological convergence group and discuss the interrelationship with some of the existing notions of lattice-valued convergence groups [T. M. G. Ahsanullah and Jawaher Al-Mufarrij, Frame valued stratified generalized convergence groups, Quaestiones Mathematicae 31(2008), 279-303; T. M. G. Ahsanullah, Lattice-valued convergence ring and its uniform convergence structure, Quaestiones Mathematicae 33(2010), 25-51; Jawaher Al-Mufarrij and T. M. G. Ahsanullah, On the category of fixed basis frame valued topological groups, International Journal of Fuzzy Sets and Systems 159(2008), 2529-2551].
In doing so, we provide some examples based on lattice-valued convergence structure of continuous convergence due to G. Jager [A category of $L$-fuzzy convergence spaces, Quaestiones Mathematicae 24(2001), 501-517];
(c) considering the notion of probabilistic convergence structure attributed to G. Richardson and D. C. Kent [Probabilistic convergence spaces, J. Australian Math. Soc. Series A 61(1996), 1-21], we present the notion of probabilistic convergence group and examine its relationship with some known lattice-valued convergence groups.
Keywords: Lattice-valued topology, lattice-valued semitopological groups; lattice-valued topological groups; lattice-valued semitopological convergence groups; probabilistic convergence groups; lattice-valued Choquet convergence groups; lattice-valued convergence structure of continuous convergence.
AMS Subject Classification (2010): 54A20, 54A40, 54H11.
21. Visited Sichuan University, Chengdu, China from 3rd September to 8th September, 2011.
Host: Professor Dr. Dexue Zhang, Department of Mathematics, Sichuan University, Chengdu, PRC.
Given a talk on the subcategories of stratified frame-valued ordered convergence groups at the Sichuan University, Chengdu, People's Republic of China on 6th of September, 2011.
22. Visited Auckland University, New Zealand from 3rd November, 2011 to 9th November, 2011.
Host: Professor Dr. David Gauld, Department of Mathematics, Auckland University, New Zealand.
Given a seminar on Enriched lattice-valued topological groups and convergence groups at the Department of Mathematics, Auckland University, New Zealand on 7th November, 2011.
Article recently accepted:
1. Jawaher Al-Mufarrij and T. M. G. Ahsanullah, On the relationships between various lattice-valued topological groups and their uniformities, Accepted to the Journal of New Mathematics and Natural Computation, World Scientific Publishing (in press, to appear in November, 2012)
Article recently published
1. T. M. G. Ahsanullah and Fawzi Al-Thukair, Change of basis for lattice-valued convergence groups, New Math. & Natural Computation, World Scientific Publishing 7(3)(2011), 453-469.
Article recently submitted
T. M. G. Ahsanullah, David Gauld, Jawaher Al-Mufarrij and Fawzi Al-Thukair, Enriched lattice-valued topological groups and convergence groups(under review).
Paper accepted to present at the last conference
T. M. G. Ahsanullah, Jomana Al-Safar, On the categories of lattice-valued convergence groups,
46th Annual Spring Topology and Dynamics Conference, March 22-24, 2012, Universidad Nacional Autonoma de Mexico(UNAM), Mexico City, Mexico.
23. Visited the Department of Mathematics and Statistics, Concordia University, Montreal, Canada from 23rd March to 28th March, 2012.
Host: Professor Dr. S. T. Ali, Department of Mathematics and Statistics, Concordia University, Montreal, Canada.
Given a seminar on a topic entitled: On the subcategories of enriched cl-premonoid valued generalized convergence groups and change of basis lattice.
Recently published article:
J. Al-Mufarrij and T. M. G. Ahsanullah, On the relationships between various lattice-valued topological groups and their uniformities, New Math. & Natural Computation, 8(3)(2012), 361-383.
Articles in preparation:
1. Various categories of stratified lattice-valued convergence spaces (jointly with Jomanna Al-Safar)
2. Categories of stratified lattice-valued semiuniform convergence groups(jointly with Jomana Al-Safar)
3. Stratified lattice-valued ordered convergence groups(jointly with Jomana Al-Safar).
Recently Published and accepted articles:
1. Enriched lattice-valued convergence groups (jointly with David Gauld, Auckland University, New Zealand, Jawaher Al Mufarrij and Fawzi Al Thukair, KSU), Fuzzy Sets and Systems 238(1)(2014), 71-88.
http://www.sciencedirect.com/science/journal/01650114/238
2. Enriched lattice-valued topological groups (jointly with David Gauld, Auckland University, New Zealand, Jawaher Al MUfarrij and Fawzi Al Thukair, KSU).
Publication data: New Math. & Natural Computation 10(1)(2014), 27-53, World Scientific Publishing.
http://www.worldscientific.com/toc/nmnc/10/01
3. Probabilistic limit groups under t-norm (jointly with Gunther Jaeger, University of Applied Sciences, Stralsund, Germany), Topology Proceedings, published by Auburn University, Auburn, Alabama, USA and Nipissing University, North Bay, Ontario, Canada.
Publication Data: Top. Proc. 44(2014), 59-74.
(E-published on June 3, 2013)
http://topology.auburn.edu/tp/reprints/v44/
Accepted Article
On approach limit groups and their uniformization (jointly withGunther Jaeger, University of Applied Sciences Stralsund, Germany), (Appeared Electronically on 30th March, 2014.)
Publication Data: Int. Journal of Contemp. Math. Sciences 9(5)(2014), 195-213.
http://www.m-hikari.com/ijcms/ijcms-2014/5-8-2014/ahsanullahIJCMS5-8-2014.pdf
Attended Conference in 2014
Attended Joint Mathematics Meeting (American Mathematical Society) on Categorical Topology on 19th January, 2014 held at Baltimore, Maryland, USA.
Topology Conference
2014 International Conference on Topology and its Applications, July 3-July 7, 2014 at Nefpaktos, Greece
http://www.lepantotopology.gr/
Attended the conference and given a talk on probabilistic convergence groups under triangular norms and uniformization.
Recently submitted/Published/Under consideration Articles
1. Links between probabilistic convergence groups under triangular norms and enriched lattice-valued convergence groups (Jointly with Dr Fawzi Al-Thukair at KSU), International Journal of New Mathematics and Natural Computation, 12(2)(2016), 53--76.
2. Probabilistic uniform convergence spaces redefined (Jointly with Professor Gunther Jaeger, University of Applied Sciences Stralsund, Germany), Appeared in Acta Math. Hungar. 146(2) (2015), 376-390. DOI: 10.1007/s10474-015-0525-6
3. Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups (jointly with Professor Gunther Jaeger) , Accepted.
4. Lattice-valued quasi-bi-uniformizability of lattice-valued quasi-bi-topological nighborhood groups (jointly with Dr. Fawzi Al-Thukair and Dr. Jawaher Al-Mufarrij, KSU), International Journal of Contemporary Mathematical Sciences 10(6) (2015), 253-268.
Attending Conference:2015-2016
1. Attended and presented a paper entitled: On the category of approach convergence rings at the 49th Topology and Dynamics Conference held at the Bowling Greeen State University, Bowling Green, USA from 14-16 May, 2015.
2. Attended and presented a paper entitled: Probabilistic topological convergence groups at the General Topology and Applications Congress ITES205, Pamplona, Spain, July 15-July 18, 2015.
3. Attended and presented a paper entitled: Probabilistic convergence transformation groups at the 50th Spring Topology and Dynamical Systems Conference held at Baylor University, Waco, Texas, USA, 10-13 March, 2016.
Abstract accepted for the upcoming conference
31st Summer Conference on Topology and its Applications, August 2-5, 2016, University of Leicester, Leicester, United Kingdom.
Title: $S$-Stratified $LMN$-Topological Convergence Groups and their uniformizations
Abstract: The idea of stratification mapping between frames $L(=\left(L,\leq,\wedge\right))$ and $M(=\left(M,\leq,\wedge\right))$ introduced and intensively studied by J\"{a}ger in [1] for LMN-convergence tower spaces. With this stratification mapping, we introduce a notion of $s$-stratified $LMN$-topological convergence group, $N(=\left(N,\leq,\ast\right))$ being a quantale [2]. While achieving various results, we provide with a variety of motivating examples, some of which are attached to Lowen-Lowen approach convergence spaces [3], Herrlich-Zhang probabilistic convergence spaces [4], Preuss's convergence spaces [5], and probabilistic convergence spaces under so-called triangle function $\tau$ on the set of all distance distribution functions $\Delta^+$ studied in [6].
References
[1] G. Jeger, Stratified LMN-convergence tower spaces, Fuzzy Sets and systems 282(2016), 62-73.
[2] P. T. Johnstone, Stone Spaces, Cambridge University Press, 1982.
[3] E. Lowen and R. Lowen, A quasitopos containing CONV and MET as full
subcategories, Internat. J. Math. Math. Sci. 11(1988), 417 438.
[4] H. Herrlich and D. Zhang, Categorical properties of probabilistic convergence spaces, Appl. Categ. Struct. 6(1998), 495--513.
[5] G. Preuss, Foundations of Topology, Kluwer Academic Publishers, 2002.
[6] T. M. G. Ahsanullah and G. Jaeger, Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups, to appear in Math. Slovaca.
Abstract Accepted for presentation at the upcoming Algebra, Topology and Analysis Conference to be held in Serbia July 5-9, 2016.
Abstract: Considering a complete Heyting algebra H, we introduce a notion of stratified H-generalized convergence semigroup, generalizing a notion on stratified enriched lattice-valued convergence groups [1]. We develop basic theory on the subject, besides obtaining conditions under which a stratified H-generalized convergence semigroup is a stratified H-generalized convergence group.
We supply a good number of natural examples which incude among others, ultra approach convergence semigroups [3], Herrlich-Zhang probabilistic convergence semigroups [4], and stratified H-generalized convergence semigroups arising from H-convergence structures, such as structures of pointwise convergence, and continuous convergence on function spaces [5,6].
References
[1] T. M. G. Ahsanullah, David Gauld, Jawaher Al-Mufarrij and Fawzi Al-Thukair, Enriched lattice-valued convergence groups, Fuzzy Sets and Systems 238(2014), 71--88.
[2] G. Jaeger, Subcategories of lattice-valued convergence spaces, Fuzzy Sets and Systems 156(2005), 1--24.
[3] R. Lowen and B. Windels, Approach groups, Rocky Mountain, J. Math. 30 (2000), 1057--1073.
[4] H. Herrlich and D. Zhang, Categorical properties of probabilistic convergence spaces, Appl. Categ. Struct. 6(1998), 495--513.
[5] G. Jaeger, Compactness in lattice-valued function spaces, Fuzzy Sets and Systems 161(2010), 2962--2974.
[6] G. Jaeger, Connectedness and local connectedness for lattice-valued convergence spaces, Fuzzy Sets and Systems(2016), http://dx.doi.org/10.1016/j.fss.2015.11.013.
Note: Please see the publication section for papers published in the last years
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