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## WELCOME TO DEPARTMENT OF MATHEMATICS

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**DEPARTMENT OF MATHEMATICSFACULTY OF SCIENCE**A PROFILE UNIVERSITY OF JAMMU JAMMU-180 006 Tel. 0191-2452888, 2435248 Ext. 2545(HOD), Ext. 2544(OFFICE)**DEPARTMENT OF MATHEMATICSUNIVERSITY OF JAMMU**INTRODUCTION**The Department of Mathematics was started in 1966 with a**Master’s Degree Programme in Mathematics. Initially, the faculty strength was 3 only but in 1968 another faculty member with Complex Analysis as specialization and doctorate from IIT, joined the department and initiated the research programme in Complex Analysis. Later, in seventies two more people with specializations in modern branches of Mathematics viz. Functional Analysis and Algebraic Topology, and with doctorates from US, joined the department and then the department pursued its research programme in three sub-areas of mathematics. Later in eighties people with specializations in Algebra, Geometry, Complex Analysis and Functional Analysis joined the department and thereby making the faculty strength 12.**Now the department has a strong faculty with their**doctorates from US, IIT, AMU, University of Jammu, and TIFR(Mumbai). The department carries research in the areas of Algebra, Algebraic Topology, Algebraic Geometry, Complex Analysis, and Functional Analysis. The faculty members of the department have reasonably good research exposure and have their publications in the indexed national and international Journals of good impact factor, and participate in mathematical activities at international level by participating in international conferences/ workshops/ seminars and by establishing international collaborations with mathematicians from Austria, Canada, Finland, France, Germany, Japan, Spain, US, and UK..**The department is quite active and is there on the**international map of mathematics The publication track of each faculty member (at page …) speaks about the quality work carried out by them. In the field of teaching, the department has too established itself at national level as the department has produced 16 NET/JRF students. To create mathematical awareness in this part of the country and to give a necessary exposure to our researchers, in 1990 the Jammu Mathematical Society was formed. It organizes national and international conferences/seminars/ workshops in collaboration with other national and international Mathematical Societies. We have been organizing annual conferences of the Jammu math. Soc. regularly since its inception.**For college and school students of this region, the society**organizes mathematical competitions and one day students conference annually.On the basis of academic excellence of the department, the National Board for Higher mathematics (Department of Atomic Energy, Govt. of India) gives Rs. 5 lac per anum as library grant particularly to purchase books and back volumes of research journals. This has led the department to have a very good departmental library.**Besides annual library grant, NBHM provides scholarships,**fellowships and travel grants to the students, scholars and faculty members of the department. A Computer Laboratory with internet facility has been established out of the funds given by UGC. Besides the academic achievements, the department has an honour to give educational administrators to the University system like Vice-Chancellor, Controller of Examinations, Dean of the faculty, members of the University Council and Syndicate, Presidents of Academic Societies and members of National Societies. Thus the department has been marching ahead in the direction of academic excellence and is committed to keep its march on as the excellence is a direction, not a destination.**The departmental profile is prepared to present the salient**facts and achievements of the department to develop an intimate familiarity with the department.**The main objective of the department is to provide the**quality education in mathematics in this part of the country so as to bring the department at the international map of mathematics. Though we have been successful to some extent in achieving the excellence both in teaching and research but still we need to cover a long distance as there is no end to excellence.**The department aims to convert it into a Centre of Advanced**Studies in Mathematics. A few steps have already been taken in this direction. For instance to cater to the needs of technology and hence industry the department has now floated a proposal to start a Master’s Degree Programme in Applied Mathematics. The department has also initiated a process of bringing out a high quality refereed Mathematics Journal with Editorial Board comprising eminent mathematicians both from India and abroad.**Preliminary deliberations in this direction have already**been made. The department has also intiated the process of forming a separate faculty viz. Faculty of Mathematical Sciences which will include Mathematics, Statistics and Computer sciences. After introducing the Master’s Degree Programme in Applied Mathematics, the department will move to get itself converted into ‘The School Mathematics’ with some other programmes in it. Prof. S.D. Sharma Head of the Department**DEPARTMENT OF MATHEMATICSUNIVERSITY OF JAMMUA PROFILE**Year of Establishment: 1966. Programmes of Study: • M.A./M.Sc. with intake 50 • M.Phil., with intake 10 • Ph.D.**Faculty Positions: 12**• Professor 5 • Associate Professor 2 • Assistant Professor 5**Present Faculty with Specializations:**• Professors: • Dr. S.D.Sharma-------- Analytic Function Theory / Operator Theory. • Dr. A.P. Singh ---------- Complex Analysis / Complex Dynamics.**Dr. B.S. Komal --------- Functional Analysis/**Operator Theory. • Dr. C.L. Wangneo --------- Algebra / Ring Theory. • Dr. D.S. Jamwal------------ Algebraic Topology/ Fuzzy Topology.**B. Associate Professors**• Dr. Romesh Kumar------- Complex Analysis / Operator Theory. • Dr. Abdul Khaliq--------- Applied Maths / Variational Inequalities.**C. Asstt. Professors**• Dr. K.S. Charak------------ Complex Analysis / Bicomplex Dynamics. • Dr. Chanchal Kumar------ Algebraic Geometry. • Dr. Shallu Sharma--------- Functional Analysis / Operator Theory.**M.Phil. / Ph.D. Awarded**• M.Phil. 203 • Ph.D. 58 (Details at page …)**RESEARCH PUBLICATIONS**• Research Papers(2004-2008) = 51, Total = 309 All in Indexed / Impact Factor Journals (Details at page … ) • Research Monograph = 1 (North Holland Publ. Co. Netherlands)**HONOURS AND AWARDS TO FACULTY MEMBERS**• Fullbright Faculty Fellowship: R.K.Singh • Indo-German Fellowship: Satya Deo • Commonwealth Fellowship: A.P.Singh, J.S.Manhas, Romesh Kumar • Royal Society Fellowship: Romesh Kumar • National Associateship: R.K.Singh, Satya Deo • Visiting Prefessorship Abroad: R.K.Singh**Member on Committees**of NBHM and UGC: R.K.Singh • Rashtriya Gaurav Award: A.P.Singh • Vijay Rattan Award: S.D.Sharma, B.S.Komal • Post Doctoral Fellowship: Abdul Khaliq (R.O.C. Taiwan) • Post Doctoral Fellowship: K.S.Charak (Univ. Joensuu, Finland)**Young Scientist Award: J.S.Manhas,**(DST, J&K) Romesh Kumar • Best Paper Presentation Awards: (i) Ramanujan Award(RMS): K.S.Charak. (ii) Bharat Ganita Parishad Award: K.S.Charak, Chanchal Kumar**INTERNATIONAL RESEARCH COLLABORATIONS**• A.P.Singh: • Complex Dynamics • I.N. Baker, Imperial College London. • F. Peterstorfer, Johannes Kepler Instt., Linz, Austria. • W. Bergweiler, University of Keil. Germany. • M. Taniguchi, Kyoto University, Japan. • Y. Wang, Chinese Acad. of sciences, China.**2. Romesh Kumar:**• Weighted composition operators on Hardy, Bergman and Orlicz spaces • J.R. Partington, Univ. of Leeds, U.K. • H. Hudzik, Adam Mickiewicz Univ. Poznan, Poland. • Y. Cui, Univ. of Harbin, China. • L. Maligranda, Univ. of Sci. & Tech. Luela, Sweden. • G.H. Erajee, Shiraz Univ. Iran.**3. Abdul Khaliq**• On Variational and generalized variational Inequalities • S .Y. Wu, National Ching Kung University, Taiwan • A.H. Siddiqi, KFUPM, Saudi Arabia.**4. K.S. Charak**• Factorization of meromorphic functions, Normal Families and Bicomplex Dynamics • Ilpo Laine, University of Joensuu, Finland. • Jarkko Rieppo, University of Joensuu, Finland. • Dominic Rochon, Universite du Quebec, Canada.**RESEARCH PROJECTS — FUNDED BY UGC AND NBHM**• Completed: Major= 5, Minor=10 • On Going: Major=1**NBHM/UGC GRANTS**• Annual Library Grant: Rs. 5 lacs • Annual Post Graduate Scholarships: Rs. 57,600. • UGC for establishment of Computer Lab: Rs. 15 Lacs.**FOREIGN VISITS BY FACULTY MEMBERS FOR ACADEMIC WORKS**A. Present Faculty Members • A.P. Singh: Armenia, Austria, China, UK, Germany, Japan, Russia, Turky, Taiwan, USA. • S.D. Sharma: USA, S. Korea • C.L. Wangneo: USA**D.S. Jamwal: Greece**• Romesh Kumar: Poland, Spain, UK, Thailand. • Abdul Khaliq: Iran, Italy, Taiwan • K.S.Charak: Canada, Finland • Chanchal Kumar: Italy.**B. Past Faculty Members**• M.R. Puri: England, USA • J.S. Gupta: Italy • R.K Singh: USA • Satya Deo: Canada, Germany,USA.**FOREIGN MATHEMATICIANS WHO VISITED THE DEPARTMENT**• Prof. S. Adian: Russia • Prof. R. Alfonso: Spain • Prof. S. Al-Homidan Saudi Arabia • Prof. Z. Aslan Turkey • Prof. M. Boulbrachene Oman • Prof. Peter Blanksby: Australia • Prof. Aldrik Brown: UK • Prof. F. Fridli Hungry • Prof. K. Furati Saudi Arabia • Prof. D. Ghosal: USA**Prof. N. Govil USA**• Prof. Narain Gupta: Canada • Dr. Hossein Iran • Prof. B. Jones: USA • Prof. R. Lozi France • Prof. S. Messaoudi Saudi Arabia • Prof. H. Mittleman USA • Prof. R. Mittleman USA • Prof. M. Rajagopalan: USA • Prof. S. Rehman Saudi Arabia • Prof. D. Rochon: Canada • Prof. Helga Schimer: Canada**Prof. F. Schipp Hungry**• Prof. A.H. Siddiqi Saudi Arabia • Prof. Robert Silverman: USA • Prof. K.R. Srinivasan Italy • Prof. W.H. Summers: USA • Prof. M.L. Tickoo: Canada • Prof. K. Vardrajan: Canada**EMINENT MATHEMATICIANS OF VARIOUS INDIAN UNIVERSITIES WHO**VISITED THE DEPARTMENT • Prof. P.K. Agarwal: Punjab Univ. Chandigarh • Prof. S.C. Arora: Univ. of Delhi • Prof. R. Bhatia: ISI Delhi • Prof. B. Choudhary: Jadavpur Univ. • Prof. G.S. Dani: TIFR Mumbai • Prof. H.P. Dikshit R.D. Univ. Jabalpur**Prof. N.K. Gupta IIT Delhi**• Prof. P.K. Jain: Univ. of Delhi • Prof. J.N. Kapoor: IIT Kanpur • Prof. G.P. Kapoor IIT Kanpur • Prof. Inderajit Lahiri: Univ. of Kalyani • Prof. V.V. Menon: BHU • Prof. R.S. Mishra: BHU • Prof. Gadadhar Mishra: Indian Institute of Sc. Bangalore • Prof. M.G. Nadkarni: Bombay Univ. • Prof. S. Narayanan: TIFR Mumbai • Prof. G.S. Pandey: Lucknow Univ.**Prof. R.S. Pathak: BHU**• Prof. V.D. Pathak: MS Univ. Baroda • Prof. T.C. Panda Behram Univ. Orissa • Prof. E. Sampathkumar: Univ. of Mysore • Prof. B.L. Sharma: Univ. of Allahabad • Prof. U.N. Singh: Univ. of Delhi • Prof. Ajit Iqbal Singh: Univ. of Delhi • Prof. Dinesh Singh: Univ. of Delhi**Prof. Sitaramaya: Univ. of Hyderabad**• Prof. R.S.L. Srivastava: IIT Kanpur • Prof. G.S. Srivastava: IIT Roorki • Prof. V.S. Sunder: MS Chennai • Prof. U.B. Tiwari: IIT Kanpur • Prof. H.L. Vasudeva: Punjab Univ. • Prof. B.S.Yadav: Univ. Delhi**Prof. S.D. Sharma**• On composition operators acting between Besov spaces, International J. Math. Anal. 3(2009), 133-143. • Compact composition operators on Hardy Orlicz spaces, Math. Vesnik, 60(2008), 215-225. • Composition operators between Hardy and Bloch-type spaces of the upper half plane, Bull. Korean Math. Soc. 43(2007), 475-482. • Composition operators on weighted Bergman Orlicz spaces, Bull. Australian Math. Soc. 75(2007), 273-287. • Concrete operators on abstract functional Hilbert spaces, International J. Math. Anal. 1(2007), 339-354.**Weighted composition followed by differentiation between**Bergman spaces, International Math. Forum, 2(2007), 1647-1656. • Riemann-Stieltjes operators between weighted Bloch and weighted Bergman spaces, International J. Contemp. Math. Sci. 2(2007), 759-772. • Weighted composition operators between Bergman-type spaces, Communications Korean Math. Soc. 21(2006), 465-474. • Carleson measures in a vector-valued Bergman space, J. Anal. Appl. 4(2006), 65-76. • Semigroups of composition operators on H(w), Math. Today, XXI(2005), 3-16.**Composition operators on the weighted Bergman-Nevanlinna**space, Proc. First Advanced Course in Complex Analysis and Operator Theory, held at Universidad de Sevilla(Spain)(2004), 123-132. • Invertible and isometric composition operators in vector-valued Hardy spaces, Bull. Korean Math. Soc., 41(2004),413-418. • Conjugation Theorem in operator-valued functional Hilbert spaces, Indian J. Math., 45(2003), 325-332. • Composition operators on vector-valued Hardy spaces of the upper half-plane, J. Anal. Appl., 1(2)(2003), 113-123. • A space of analytic functions with Montel property, Indian J. Pure Appl. Math., 33(2002), 1409-1416.**On characterization of weighted composition operators on**non-locally convex weighted spaces of continuous functions, Tamkang J. Math., 31(2)(2000), 1409-1416. • On sequences of composition operators, Scientia Iranica, 7(7)(2000), 5-8. • Compact composition operators and Carleson measure in the upper half-plane, Extracta Math. 15(2000), 175-180. • Substitution operators with closed ranges and invariant subspaces, Ganita 50(1999), 31-35. • Composition operators on vector-vslued Hardy spaces, Extracta Math. 14(1999), 31-39.**Composition operators on Hardy spaces of the upper**half-plane, Bull. Allahabad Math. Soc., 14(1999), 129-145. • A semi-dynamical system induced by composition operators, Indian J. Pure Appl. Math., 30(7)(1999), 715-720. • Composition operators on Bergman-Orlicz type spaces, Indian J. Math., 40(1998), 227-235. • Compact and Fredholm multiplication operators on a sequence space, Far East J. Math. Sci. 4(3)(1997), 443-451. • Dijointness preserving operators on C(X), Math. Today, VI(1997), 51-54.**Substitution operators on some sequence spaces, Math. Forum,**X(1996), 9-15. • Substitution operators on Orlicz sequence spaces, Banyan Math J., 3(1996), 7-16. • Convergence of sequencesof substitution operators on H(w), J. Indian Math. Soc., 62(1996), 196-204. • On periodic functions in H2(π+), Univ. Timisosra Ser. Stiint. Mat., 32(1994)111-113. • Inner functions and substitution operators, Acta Sci. Math. 58(1993), 505-512.**Substitution operators on generalized spaces of entire**functions, Math. Today, XI(1993), 21-26. • Compact composition operators on H2(Dn), Indian J. Math. 34(1992), 73-79. • Characterization of composition operators on function spaces, J. Scientific Research, 41C(1991), 1-8. • Substitution operators on Hardy-Orlicz spaces, Proc. Nat. Acad. Sci. India, 61(A), 535-541. • A motion in H2(π+), J. B. Math. Soc.13(1990), 1-4.**Idempotent composition operators and several complex**variables, Bull. Cal. Math. Soc. 82(1990), 13-15. • Translation invariant function spaces, Bull. Allahabad Math. Soc. 3(1988), 1-10. • Compact and Hilbert-Schmidt composition operators on Hardy spaces of the upper half-plane, Acta Sci. Math.(Hungary), 46(1983),197-202. • Composition operators and several complex variables, Bull. Austral. Math. Soc. 23(1981), 237-247. • Non-compact composition operators, Bull. Austral. Math. Soc. 21(1980), 125-130.**Composition operators on a functional Hilbert space, Bull.**Austral. Math. Soc. 20(1979), 277-284.