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**WELCOME TO DEPARTMENT OF MATHEMATICS**

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**DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE**

A PROFILE UNIVERSITY OF JAMMU JAMMU Tel , Ext. 2545(HOD), Ext. 2544(OFFICE)

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**DEPARTMENT OF MATHEMATICS UNIVERSITY OF JAMMU**

INTRODUCTION

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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.

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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..

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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.

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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.

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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.

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The departmental profile is prepared to present the salient facts and achievements of the department to develop an intimate familiarity with the department.

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**OBJECTIVES, AIMS AND FUTURE PLANNING OF THE DEPARTMENT**

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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.

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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.

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**Prof. S.D. Sharma Head of the Department**

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

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**DEPARTMENT OF MATHEMATICS UNIVERSITY OF JAMMU A PROFILE**

Year of Establishment: Programmes of Study: M.A./M.Sc. with intake M.Phil., with intake Ph.D.

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**Faculty Positions: 12 Professor 5 Associate Professor 2**

Assistant Professor

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**Present Faculty with Specializations:**

Professors: Dr. S.D.Sharma Analytic Function Theory / Operator Theory. Dr. A.P. Singh Complex Analysis / Complex Dynamics.

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**Dr. B.S. Komal --------- Functional Analysis/ Operator Theory.**

Dr. C.L. Wangneo Algebra / Ring Theory. Dr. D.S. Jamwal Algebraic Topology/ Fuzzy Topology.

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**B. Associate Professors**

Dr. Romesh Kumar Complex Analysis / Operator Theory. Dr. Abdul Khaliq Applied Maths / Variational Inequalities.

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C. Asstt. Professors Dr. K.S. Charak Complex Analysis / Bicomplex Dynamics. Dr. Chanchal Kumar Algebraic Geometry. Dr. Shallu Sharma Functional Analysis / Operator Theory.

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M.Phil. / Ph.D. Awarded M.Phil Ph.D (Details at page …)

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**RESEARCH PUBLICATIONS**

Research Papers( ) = 51, Total = 309 All in Indexed / Impact Factor Journals (Details at page … ) Research Monograph = 1 (North Holland Publ. Co. Netherlands)

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**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

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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)

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**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

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**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.

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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.

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3. Abdul Khaliq On Variational and generalized variational Inequalities S .Y. Wu, National Ching Kung University, Taiwan A.H. Siddiqi, KFUPM, Saudi Arabia.

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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.

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**RESEARCH PROJECTS — FUNDED BY UGC AND NBHM**

Completed: Major= 5, Minor=10 On Going: Major=1

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**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.

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**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

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D.S. Jamwal: Greece Romesh Kumar: Poland, Spain, UK, Thailand. Abdul Khaliq: Iran, Italy, Taiwan K.S.Charak: Canada, Finland Chanchal Kumar: Italy.

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B. Past Faculty Members M.R. Puri: England, USA J.S. Gupta: Italy R.K Singh: USA Satya Deo: Canada, Germany, USA.

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**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

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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

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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

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**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

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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.

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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

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**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

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**PUBLICATIONS OF THE FACULTY MEMBERS**

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Prof. S.D. Sharma On composition operators acting between Besov spaces, International J. Math. Anal. 3(2009), Compact composition operators on Hardy Orlicz spaces, Math. Vesnik, 60(2008), Composition operators between Hardy and Bloch-type spaces of the upper half plane, Bull. Korean Math. Soc. 43(2007), Composition operators on weighted Bergman Orlicz spaces, Bull. Australian Math. Soc. 75(2007), Concrete operators on abstract functional Hilbert spaces, International J. Math. Anal. 1(2007),

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Weighted composition followed by differentiation between Bergman spaces, International Math. Forum, 2(2007), Riemann-Stieltjes operators between weighted Bloch and weighted Bergman spaces, International J. Contemp. Math. Sci. 2(2007), Weighted composition operators between Bergman-type spaces, Communications Korean Math. Soc. 21(2006), Carleson measures in a vector-valued Bergman space, J. Anal. Appl. 4(2006), Semigroups of composition operators on H(w), Math. Today, XXI(2005), 3-16.

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**Composition operators on the weighted Bergman-Nevanlinna space, Proc**

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), Invertible and isometric composition operators in vector-valued Hardy spaces, Bull. Korean Math. Soc., 41(2004), Conjugation Theorem in operator-valued functional Hilbert spaces, Indian J. Math., 45(2003), Composition operators on vector-valued Hardy spaces of the upper half-plane, J. Anal. Appl., 1(2)(2003), A space of analytic functions with Montel property, Indian J. Pure Appl. Math., 33(2002),

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On characterization of weighted composition operators on non-locally convex weighted spaces of continuous functions, Tamkang J. Math., 31(2)(2000), 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), Substitution operators with closed ranges and invariant subspaces, Ganita 50(1999), Composition operators on vector-vslued Hardy spaces, Extracta Math. 14(1999),

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**Composition operators on Hardy spaces of the upper half-plane, Bull**

Composition operators on Hardy spaces of the upper half-plane, Bull. Allahabad Math. Soc., 14(1999), A semi-dynamical system induced by composition operators, Indian J. Pure Appl. Math., 30(7)(1999), Composition operators on Bergman-Orlicz type spaces, Indian J. Math., 40(1998), Compact and Fredholm multiplication operators on a sequence space, Far East J. Math. Sci. 4(3)(1997), Dijointness preserving operators on C(X), Math. Today, VI(1997),

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**Substitution operators on some sequence spaces, Math**

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), On periodic functions in H2(π+), Univ. Timisosra Ser. Stiint. Mat., 32(1994) Inner functions and substitution operators, Acta Sci. Math. 58(1993),

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**Substitution operators on generalized spaces of entire functions, Math**

Substitution operators on generalized spaces of entire functions, Math. Today, XI(1993), Compact composition operators on H2(Dn), Indian J. Math. 34(1992), 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), A motion in H2(π+), J. B. Math. Soc.13(1990), 1-4.

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**Idempotent composition operators and several complex variables, Bull**

Idempotent composition operators and several complex variables, Bull. Cal. Math. Soc. 82(1990), 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), Composition operators and several complex variables, Bull. Austral. Math. Soc. 23(1981), Non-compact composition operators, Bull. Austral. Math. Soc. 21(1980),

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**Composition operators on a functional Hilbert space, Bull. Austral**

Composition operators on a functional Hilbert space, Bull. Austral. Math. Soc. 20(1979),

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Prof. A.P.Singh On semi-conjugation of entire functions, Bull. Pure Appl. Math. 2(1)(2008), An introduction to Complex Dynamics, Mathematics News Letter, Ramanujan Math. Soc. (1)18(2008)15-26. Composite entire functions with no unbounded Fatou component, J. Math. Anal.Appl.335(2007), On escaping sets of entire functions, Complex Dynamics and its related fields, Ed. M. Shishikura, M. Kisaka, Surikaisekikenyusho Kokyuroku, RIMS Proceeding No (2006),24-33. Julia sets of permutable holomorphic maps, Science in China Ser. A: Mathematics, (11)49(2006),

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Escaping sets and wandering domains of composition of entire functions, The Proceedings of the Ninth Conference on real and Complex Analysis in Hiroshima(2005), Transcendental entire functions whose Julia set is the Complex Plane, Complex Variables and Elliptic Equations, (9), 52(2007), Wandering domains of meromorphic functions, The Nepali Math. Sc. Report (1) 24(2005)59-70. On the singularities of composition of entire functions, Analysis in Theory and Applications, (4) 21(2005),

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**Fatou components in angular region, Proc**

Fatou components in angular region, Proc. 12th International Conference of Finite or Iinfinite Dimensional Complex Analysis and Applications, Kyushu Univ. Press (2005), Sharing values and normality of meromorphic functions, Complex variables, (6) 49(2004), 417-?. Advances in the dynamics of entire and meromorphic functions, Math. Student, (1-4) 73(2006), Some directions in Complex Dynamics, Math. Student, (1-4) 72(2005), On the dynamics of composition of entire functions, Math. Proc. Camb. Phil. Soc. 134(2003),

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Dnamics of transcendental meromorphic functions, Finite or Infinite Dimensional Complex Analysis: 7th International Colloquium, Ed. E. Taft and Z. Nashed, Marcel Dekker (2000), Unbounded components of the Fatou set, Complex Variables, 41(2000), On factorization of meromorphic functions, Bull. Allahabad math. Soc. 15(200), 9-15. Complex Analytic Dynamics, Lecture Notes in Mathematical Sciences, 6(1999), Some criteria for determining pseudo-primeness in divisor sense, Proc. Nat. Acad. Sci. India 68(A)IV (1998),

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Iterates of meromorphic functions: An Introduction, Functional Analysis with current applications in Sci. Tech. Industry, Ed. Martin Brokate, A.H. Siddiqi, Pitman Research Notes, No. 377(1998), Some results on pseudo-primeness of meromorphic functions, Bull. Cal. Math. Soc. 90(4) (1998), On factorization of meromorphic functions with finitely many zeros, Tamkang J. Math. 29(2) (1998), Factorization of certain classes of entire and meromorphic functions, Indian J. Pure Appl. Math. 28(1) (1997), Meromorphic functions that share small functions, J. Ramanujan Math. Soc. 11(1996), Meromorphic functions that share values by simple and

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**double zeros, Indian J. Pure Appl. Math. 26(7) (1995), 697-703.**

Wandering domains in the iterations of composition of entire functions, Ann. Acad. Sci. Fenn. 20(1995), A note on differential polynomials, Bull. Cal. Math. Soc. 87(1995), On order of differential polynomials, Proc. Nat. Acad. Sci. India 64(A)III (1994), Comparative growth of composition of entire functions, Indian J. Pure Appl. Math. 24(3) (1993), On meromorphic functions satisfying certain functional equations, Univ. Review(Fac. Sci.), Univ. Jammu (1993),27-32.

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**Maximum term of composition of entire functions, Proc. Nat. Acad. Sci**

Maximum term of composition of entire functions, Proc. Nat. Acad. Sci. India 63(A)II (1993), On Differential polynomials, Bull. Cal. Math. Soc. 85(1993), On deficiencies of differential polynomials, Proc. Indian Acad. Sci.(Math. Sci.) 102(2) (1992), A note on Nevalinna characteristic function, Math. Student, 57(1-4) (1991), On maximum modulus and maximum term of composition of entire functions, Indian J. Pure Appl. Math. 22(12) (1991),

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**Relative defects of monomials, J. Indian Acad. Math**

On exceptional values of entire functions and their derivatives, Bull. Cal. Math. Soc. 82 (1990), Relative defects of meromorphic functions, Proc. Nat. Acad. Sci. India 60(A)II (1990), A glimpse into Nevanlinna theory of meromorphic functions, Math. Student 57 (1989), On equality of orders of two meromorphic functions, Ramanujan International Symposium on Analysis, MacMillan India, (1989),

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**Some notes on differential polynomials, Proc. Nat. Acad**

Some notes on differential polynomials, Proc. Nat. Acad. India, 59(A)II (1989), On maximum term of composition of entire functions, Proc. Nat. Acad. India, 59(A)I (1989), Relative defects of homogeneous differential polynomials, Proc. Nat. Acad. India, 58(A)II (1988), On a class of slowly changing functions, Proc. Indian Acad. Sci. (Math. Sci.), 98(1) (1988), Deficient values of differential polynomials, Math. Chronicle, 15 (1987),

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**Deficient values of meromorphic functions, J. Indian Acad. Math**

Entire functions through Nevanlinna theory, Proc. VIII Annual Conference of ISPS, (1986), On Borel exceptional values, Bull. Bombay Math. Colloquium, 3(2) (1986), On order of homogeneous differential polynomials, Indian J. Pure Appl. Math. 16(7) (1985), Growth of composite entire functions, Kodai Math. J. 8(1) (1985),

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On Nevanlinna characteristic of homogeneous differential polynomials and deficient values, J. Shivaji Univ. (Sci.) 22( ), Analytic functions with continuous variables, J. Shivaji Univ. (Sci.) 22( ), On relative defects of meromorphic functions, Ranchi Univ. Math. J. 15(1984), Applications of Nevanlinna theory to differential equations, Indian J. Pure Appl. Math. 14(10) (1983), Relative defects corresponding to the common roots to two meromorphic functions, Kodai Math. J. 6(1983),

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**A note on Painleve differential equation, Math**

A note on Painleve differential equation, Math. Student ), On Nevanlinna characteristic function, Proc. Nat. Acad. Sci. India 52(A)II (1982), A note on right factor of an entire function, Math. Student 50(1982), A note on exceptional Picard for simple and double zeros, Math. Student 50(1982), A note on exceptional value Picard for simple zeros, Progr. Math. (Allahabad) (1-2) 15(1981), 9-11.

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**Relative defects of meromorphic functions, J. Indian Math. Soc**

On differential polynomials, Commentarii Mathematici Universitatis Sancti Pauli 29(2) (1980),

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Prof. B.S. Komal Multiplication operators induced by operator valued maps, Int. J. Contemp. Math. Sci. 3(2008), Operators of composition between Orlicz spaces, Aligarh Bull. Math. 25(2006), Numerical ranges of composition operators, Hokkaido Math. J. 35(2006), 1-12. Multiplication operators between Orlicz spaces, Integral Equations and Operator Theory 41(2001), Invertible and compact weighted composition operators on the space of continuousy differentiable functions, Indian J. Math. 43(2001),

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**Composition operators on Orlicz spaces, Indian J. Pure Appl. Math**

Compact composition operators, Math. Appl. Industry and Business, Narosa Pub. House New Delhi, (2000), Composition operators on Hilbert space of entire functions, Bull. Cal. Math. Soc. (2000) Multiplication operators on weighted spaces of continuous functions, Ganita, 50(1999), Weighted composition operators on space of entire functions, Functional Analysis, Selected Topics Narosa Pub. House, New Delhi (1998), ,

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**Composite integral operators, Pitman Research Notes 377(1998).**

Invertible composition operators on locally convex spaces of entire functions, Functional Analysis Topics, Narosa Pub. House New Delhi (1998), On operators of weighted substitution on generalized spaces of entire functions II, Far East J. Math. Sci. (1998), Isometric and Fredholm weighted substitution operators on the generalized spaces of entire functions, Far East J. Math. (1998), Non-archemedian multiplication operators, Bull. Cal. Math. Soc. 89(1997),

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On operators of weighted substitution on generalized space of entire functions, Math. Today, XV(1997), 3-10. A characterization of composition operators induced by matrices, Far East J. Math. Sci. 5(1997), Weighted substitution operators, Indian J. Math. 38(1996), Compact multiplication operators on spaces of operators, Allahabad Math. 10(1996), Composite multiplication operators on spaces of continuous functions, Far East J. Math. 4(1) (1996), 9-13.

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Weighted composition operators on a Hilbert spaces of vector-valued sequences, Bull. Cal. Math. Soc. 88(1996), On operators of composition of generalized spaces of entire functions, Math. Today, XIV(1996), 3-8. Some characterizations of invertible Hilbert-Schmidt weighted copmposition operators, Bull. Cal. Math. Soc. 87(1995), Invertible and compact operators on weighted spaces of differentiable functions, Far East J. Math. 3(1995), Composition operators on the space of entire sequences over non-Archemedian valued field, Bull. Cal. Math Soc. 87(1995),

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Invertible weighted substitution operators on the space of entire sequences over non-Archemedian valued fields, Banyan J. Math. 1(1994), Compact and invertible composition operators on l^p, 0<p<∞, Banyan J. Math. 1(1994), Composition operators on the spaces of entire sequences, Bull. Cal. Math. Soc. 87(1994), 5-10. Composition operators on l^p, 0<p<∞, University Review (1994), 41-48 Non-Archemedian multiplication operators and dynamical systems on the spaces of entire sequences, Far East J. Math. Sci. 2(1994), 1-8.

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Operators on weighted spaces of infinitely differentiable functions, Far East J. Math. Sci. 1(1993), Characterization of composition operators on function spaces, J. Scientific Research 41(1991), Some results on multiplication operators induced by operator valued maps, Bull. Cal. Math. Soc. 83(1991), Composition operators on space of operators, Indian J. Math. 33(1991), 1-17. On eigen values of composition operators, Indian J. Pure Appl. Math. 22(1991),

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**Composition operators on the space of entire functions, Kodai Math. J**

Invariant subspaces of composition operators on weighted sequence spaces, Proc. Invariant Subspaces and allied Topics, Narosa Publ. House, New Delhi, 1990. A characterization of composition operators on the space of entire sequences, Bull. Cal. Math. Soc. 82(1990), The spectra of quasinormal composition operators, Math. Today 8(1990), Idempotent composition operators, The University Review Special Volume (1989),

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**Translation invariant function spaces, Bull. Allahabad Math. Soc**

Normal composition operators, Acta Scientarum Math. 45(1984), Centered and hyponormal composition operators, J. Indian Math. Soc. 47(1983), Fredholm composition operators on weighted sequence spaces, Indian J. Pure Appl. Math. 14(1983), Characterizations and invariant subspaces of composition operators, Acta Scientarum Math. 46(1983),

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**Quasinormal composition operators, Indian J. Pure Appl. Math**

A counterexample to a problem of Morrel, Math. Student 48(1980), Some results on composition operators on l^2, Int. J. Math. Math. Sci. 2(1979), Composition operators, Bull. Austral. Math. Soc. 18(1978), Composition operators on l^p and its adjoint, Proc. Amer. Math. Soc. 70(1978),

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Prof. C.L.Wanganeo A note on certain ore extensions, Bull. Cal. Math. Soc.91(1999), The structure of some right Noetherian rings with Krull dimension one, Proc. Amer. Math. Soc. 118(1993), 677 – 680. Polynomial rings over rings integral over their centres, Bull. Austral. Math. Soc. 34(1986), Polynomial rings over FBN rings, Algebra and its applications (1981), 53-55, Lecture Notes in Pure and Appl. Math. 91, Dekker, New York, 1984. Right Noetherian rings integral over their centers, Comm. Algebra 7(1989), 1573 – 1598.

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Prof. D.S.Jamwal Finitisticness of L-topological spaces under sum and Lowen functor omega, Fuzzy logic and its applications in Topology and management, Narosa Publishing House, (2007), 32-37, Edited Volume containing the selected papers from the conference FIATEM held at IIT Kharagpur. Paracompact and metacompact spaces in L-topology, Bull. Pure Appld. Sciences, 26(2) (2007), ? On covering dimension of finitistic spaces in L-topology, J. Fuzzy Math. 14(1) (2006), On group topology and finitistic spaces, Bull. Pure Appld. Sciences 24E(1) (2005),

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**Fuzzy Ө-T2 spaces, Bull. Pure Appld**

Fuzzy Ө-T2 spaces, Bull. Pure Appld. Sciences, 23E(1) (2004), On covering dimensions of L-fuzzy subsets and L-topological spaces, J. Fuzzy Math. 12(2) (2004), Countably finitistic spaces are finitistic, Ganita 53(2) (2002), Covering dimension and finitistic spaces in L-topology, Proc. Of the conference on Fuzzy Set Theory and its Mathematical Aspects and Applications, BHU, Varanasi, (2002), ? Cohomology with exotic supports and the generalized-excision, , J. Austral. Math. Soc. Ser. A, 45(1988),

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**Finitistic and locally finitistic spaces, Indian J. Math**

Countable Sum Theorem for locally closed sets, Bull. Austral. Math. Soc. 29(1984),

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Dr. Romesh Kumar Composition operators on Orlicz-Lorentz spaces spaces, Integral Equations and Operator Theory, 60 (2008), 79 – 88. Essential norm of weighted composition operator on the Dirichlet space, Extracta Math. 21(3) (2006), Weighted composition operators via Berezin transform and Carleson measure, Commentationes Mathematicae, XLVI (1) (2006) , Matrix Multiplication operators on Banach Function spaces, Proc. Indian Acad. Sci. (Math. Sci.) 116(1)(2006), Composition operators on Banach function spaces, Proc. Amer. Math. Soc.133 (2005), 2109 – 2118.

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On finite dimensional algebras generated by composition operators on Orlicz sequence space with weight , Houston J. Math., 31(4)(2005), 1135 – 1152. Compact composition operators on Lorentz spaces, Matematicki Vesnik , 57(2005), 109 –112. Weighted composition operators on Hardy and Bergmann spaces, Recent Advances in Operator Theory, Operator Algebras, and their applications, Proc. XIXth International Conference on Operator Theory (Timisoara), 2002, Operator Theory: Advances and Applications, Vol. 153, Birkhäuser (2004), Composition operators on Orlicz spaces, J. Austral. Math. Soc., 76 (2004).

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**Substitution operators on some sequence spaces, Forum Math**

Substitution operators on some sequence spaces, Forum Math. X (1996), 9- Compostion operators on L-1 spaces, Proceedings of the Sixth Conference on Function Spaces, World Scientific Publishers, 2003. Carleson measure and compact composition operators on Hardy spaces of upper-half plane, Extracta Math. Vol 15, No. 1 (2000), Composition operators on Orlicz spaces, Integral Equations and Operator Theory, 29 (1997), Weighted substitution operators on weighted spaces of infinitely differentiable functions, Indian J. Math. Vol 38, No. 1 (1996),

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**Convergence of sequences of substitution operators on H(w), J**

Convergence of sequences of substitution operators on H(w), J. Indian Math. Soc., 62(1-4) (1996) Substitution operators on a space of infinitely differentiable functions, Indian J. Pure App. Math., 26(5)(1995) Substitution operators on weighted spaces of infinitely differentiable functions, Far East J. Math Sci, 1 (2) (1993) Substitution operators on generalised spaces of entire functions, Mathematics, Today XI (1993) Inner functions and subtitution operators, Acta Sci. Math (Szeged) 58 (1993)

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**Substitution operators on Hardy-Orlicz spaces, Proc. Nat. Acad. Sci**

Substitution operators on Hardy-Orlicz spaces, Proc. Nat. Acad. Sci. (India), 71(A) IV (1991) 535-4

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Dr. Abdul Khaliq Implicit vector quasi-equilibrium problems with applications to variational inequalities, Proc. 4th World Congress of Non-linear Analysts, Orlendo, USA, WENA 2004. Generalized implicit vector variational inequalities, SEA J. Math. Math. Sci., 2(4) (2004), On generalized vector quasi-equilibrium problems, Advances Non-linear Variational Inequalities, 7(1) (2004), Existence of solutions for generalized vector variational like inequalities, SEA J. Math. Math. Sci., 2(1) (2003), 1-4. Generalized non-linear vector quasi-variational like inequalities, Non-linear Analysis Forum, 8(1) (2003),

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**Vector quasi-equilibrium problems, Bull. Austral. Math. Soc**

Generalized vector quasi-variational like inequalities, Ganita, 22(2002), On generalized vector quasi-variational inequalities in Hausdorff topological vector spaces, Far East J. Math. Sci. 6(2) (2002), Completely generalized non-linear variational like inclusion with non-compact valued mappings, Non-linear Analysis Forum, 7(2) (2002), On generalized vector equilibrium, Ganita, 19(1999),

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**On generalized vector variational inequalities, J**

On generalized vector variational inequalities, J. Optimization Theory and Applications, 84(1995),

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Dr. K.S.Charak Two normality criteria and the converse of the Bloch Principle, J. Math. Anal. Appl. 353(2008), Normal families of bicomplex holomorphic functions, Fractals 2008(to appear). On factorization of bicomplex meromorphic functions, Quaterionic and Clifford Analysis-Trends in Mathematics, Birkhauser(Switzerland) (2008), On a class of prime entire functions, Acta Math. Sinica 2008 (to appear). Value distribution of meromorphic functions, Math. News Letter, Ramanujan Math. Soc (to appear).

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Some remarks on factorization of entire algebroidal functions, Southeast Asian Bull. Math. 32(2008), Factorization of some entire functions, Complex Variables, Theory and Applications 43(2001), Some results on pseudo-primeness of meromorphic functions, Bull. Cal. Math. Soc. 90(4) (1998), On factorization of meromorphic functions with finitely many zeros, Tamkang J. Math. 29(2) (1998), Factorization of certain classes of entire and meromorphic functions, Indian J. Pure Appl. Math. 28(1) (1997),

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**Meromorphic functions that share small functions, J. Ramanujan Math**

Meromorphic functions that share small functions, J. Ramanujan Math. Soc. 11(1996),

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Dr. Chanchal Kumar Linear systems and quotients of projective spaces, Bull. London Math. Soc. 35(2003), Invariant vector bundles of rank 2 on hyperelliptic curves, Michigan Math. J. 47(2000),

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Dr. Shallu Sharma Numerical ranges of composition operators, Hokkaido Math. J. 35(2006), 1-12.

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**DETAILS OF THE Ph.D’S. AWARDED**

Manjeet Singh J.S. Gupta Shakhti Bala D.K. Bhola Ashok Kumar R.K. Singh B.S. Komal S.D. Sharma Velluchamy R. David Kumar

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**9. D.K. Gupta ---------------**

Dharam Adhikari Deomurari Jasbir Singh Bhopinder Singh Romesh Kumar R.K.Singh & S.D.Sharma Rajeshwer Singh R.K.Singh & B.S.Komal Chander Shekher

93
S. Muttepowar Satya Deo Mohan Singh Ram Krishan Satya Deo Dalip Singh Janak Singh Chander Shekher Vaid Surinder Singh R. Tiwari Basant Ram Durai Raju M.S. Billoria A.P. Singh

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**27. Raj Shree Dhar --------------**

K.S. Charak Jagdish Lal Sharma Rajesh Sharma Ajay Singh Tirath Kumar B.S. Komal Sunil Gupta Nagesh Singh Nishchintak Sharma Shally Gupta

95
**37. Anupama Gupta --------------**

Kuldeep Raj Vinay Khosla Sadna Tiwari Shallu Sharma Udhay Bhanu S.D. Sharma Jagdish Raj Rekha Singh Ajay Kumar Shabir Ahmed

96
**47. Rekha Kumari ---------------**

Vijay Kumar Bhat C.L. Wangneo Shakeel Ahmed D.S. Jamwal Ashwani Kumar Sudershan Khajuria J.P. Srivastava Prabha Sharma Rakesh Gupta Rajiv Kumar Romesh Sharma Kr. Jatinder Singh Sonam Krishan Ab. Khaliq

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**57. Mohd Rashid ---------------**

Mohd Rouf

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**Ph. D. THESIS SUBMITTED 1. Kulwant Singh A.P.Singh**

2. Tejinder Kour B.S.Komal 3. Sandeep Sharma D.S.Jamwal 4. Sanjay Kumar S.D.Sharma 5. Zaheer Abbas S.D. Sharma

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UPDATING OF SYLLABI After every three years, the courses at M.A./M.Sc. and at M.Phil. levels are revised and updated. Revision of the syllabi in 2005 was significant in the sense that instead of four papers in each semester, five papers were introduced and thus the students pursuing Master’s Degree Programme in mathematics have to qulify twenty papers of four credits each instead of sixteen papers of four credits each. Presently it is at par with any standard university of the country and meets the requirements of the students at international level.

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LIBRARY FACILITIES A reasonably good library having about 6 thousand books and 29 research journals besides regular mathematical news letters and updates.

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**SCIENTIFIC EQUIPMENTS**

Total PCs in the department: PCs with internet: Overhead Projector: LCD: Xerox Machines: Printers:

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**NET QUALIFIED STUDENTS: 16**

Bhopinder Singh Atul Kumar Alka Gupta Chanchal Kumar Dinesh Khurana Rajeev Kumar Ajay Kumar Zaher Abbas

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Pavinder Singh Ashok Kumar Ajay Sharma Narinder Sharma Rohini Sharma Ravinder Kumar Rajat Sharma Anshu Sharma

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12 October, 2014 St Joseph's College ADVANCED HIGHER REVISION 1 ADVANCED HIGHER MATHS REVISION AND FORMULAE UNIT 2.

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