** THE MATHEMATICS STUDENT
**

The Society publishes two periodicals – The Journal of the Indian Mathematical Society (** JIMS ; the Journal ; ISSN 0019-5839 **) and The Mathematics Student (** MS ; the Student ; ISSN 0025-5742 **) , both of which are quarterly. Contributions are welcome.

** Only the research papers of high quality are published in the Journal.**

The Mathematics Student seeks to publish material of interest not just to mathematicians with specialized interests but to undergraduate and postgraduate students and teachers of Mathematics in India. With this in view, it will publish material of the following type:

** 1. Expository articles.**

** 2. Popular articles.**

** 3. Classroom notes **(this can include hints on teaching certain topics or filling vital gaps in the usual t6reatment of topics to be found in in text-books or how some exercises can and should be made an integral part of teaching, etc.)

** 4. Problems and solutions.**

** 5. Information on articles of common interest published in other periodicals.**

** 6. Proceedings of IMS Conferences.**

** 7. News and Views.**

Contributions of these type and research papers are welcome for publication in THE MATHEMATICS STUDENT.

**
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Manuscripts intended for publication in both the periodicals should preferably be submitted

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For the Journal, manuscripts should be submitted to

Professor N. K. Thakare, Editor, JIMS.

C/o. Department of Mathematics, University of Pune,

Pune – 411 007 (MS), India.

E-mail : jims@math.unipune.ernet.in .

For the Student, manuscripts should be submitted to

Professor J. R. Patadia, Editor, MS.

Department of Mathematics, Faculty of Science,

The Maharaja Sayajirao University of Baroda,

Vadodara – 390 002 (Gujarat), India.

E-mail : jamanadasp@yahoo.com

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*Title Page:***The following page should include an abstract of not more than 100 words, a list of two to six key words and AMS subject classification (2000).**

*Abstract:***The text of the manuscript should begin on a new page. The introduction should have heading number 1. Subsequent section headings (including appendices) should be designated by Hindu-Arabic numerals (2,3,…etc.) and subsection headings should be numbered 2.1, 2.2, etc. Figures, tables and displayed equations should be numbered consecutively throughout the text (1, 2,… etc.). Equation numbers should appear flush left in parentheses and running variables for equation (e.g., i =1,2,…, n) flush right in parentheses.**

*Text:***Responsibility for the accuracy of bibliographic citations lies entirely with the Authors. References in the text be indicated by number(s) in square brackets in line with the text. Example: “… as mentioned in [2, 8]. Ramanujan [9] obtained the following result …”. In the list, the references should be numbered in the order in which they appear in the text.**

*References:*Examples:

Reference to a journal publication:

1. G. Birkhoff, Neutral elements in general lattices,

Bull. Amer. Math. Soc. 46 (1940), 702 – 705.

Reference to a book:

1. J. Munkres, Elements of Algebraic Topology,

Addison–Wesley, 1984.

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Business correspondence relating to the STUDENT should be addressed to

**
Dr. (Miss) S. P. Arya,
Treasurer,
Indian Mathematical Society,
Maitreyi College, Bapu Dham Complex,
Chanakyapuri, New Delhi-110 021, India.
e mail : shsh_ry@yahoo.co.in
**

The following volumes of The Mathematics Student are recently published :

** Vol. 75, Nos. 1-4, (2006) **

** Vol. 74, Nos. 1-4, (2005) **

** Vol. 73, Nos. 1-4, (2004) **

** Vol. 72, Nos. 1-4, (2003) **

** Vol. 71, Nos. 1-4, (2002) **

The following volumes of The Mathematics Student are under print and will soon be published :

** Special Centenary Volume (2007) **

and

** Vol. 76, Nos. 1-4, (2007) **

** The CONTENT of these volumes are displayed in the following:**

**
CONTENT of The Special Centenary Volume (2007) of The Mathematics Student. : **

** Sr. No.**
** Author **
** Title of the article / Paper**
** Pages **
** 1. **
** Nayandeep Deka Baruah,
Brice Berndt and Heng Huat Chan **

**Ramanujan's series for 1/pi : a survey****01-24****2.****George E. Andrews****The theory of compositions IV :**

MulticompositionsMulticompositions

**25-32****3.****V. S. Varadarajan****Unitary representations of super Lie groups**

and some applicationsand some applications

**33 - 62****4.****M. S. Raghunathan****Discrete subgroups of Lie groups****63-79****5.****S. P. Dutta****A connection between two sets of conjectures****81-92****6.****K. Varadarajan****Formal trianglular matrix rings and**

modules over them - a surveymodules over them - a survey

**93-112****7.****Indranil Biswas****Notes on holomorphic principal bundles**

over a compact Kahler manifoldover a compact Kahler manifold

**113-125****8.****Sudhir Ghorpade and**

Balnohan V. LimayeBalnohan V. Limaye

**Sylvester's minorant criterion, Lagrange-Beltrami identity**

and nonnegative definitenessand nonnegative definiteness

**127-134****9.****Satya Deo****Cohomology theories best suited for**

algebraic dimension theories Applicationsalgebraic dimension theories Applications

**135-151****10.****T. N. Shorey****Theorems of Sylvester and Schur****153-165****11.****Rahul Roy****Covering of space by random sets****167-176****12.****Ramaiyengar Sridharan**

and Raja Sridharanand Raja Sridharan

**A remarkable proof of Gordon on the reduction of**

the general quintic to Brioschi normal formthe general quintic to Brioschi normal form

**177-193****13.****A. S. Gupta****Deterministic chaos****195-204****14.****Murali K. Srinivasan****Some problems motivated by the**

notion of threshold graphsnotion of threshold graphs

**205 -218****15.****S. Thangavelu****Invariant Hilbert spaces of holomorphic functions****219-235****16.****J. K. Verma****Hilbert coefficients and depth of the**

associated graded ring of an idealassociated graded ring of an ideal

**237-264****17.****R. Sujatha****Euler : A life of mathematics.****265-273****18.****Raja Sridharan****On a certain lemma en-route to the proofs**

of the nullstellensatz, the quillen-suslin theorem

and Forster's conjectureof the nullstellensatz, the quillen-suslin theorem

and Forster's conjecture

**275-279****19.****S. K. Tomar****Elastic wave propagation in materials with voids - a review****281-300****20.****N. M. Bujurke,**

Ramesh B. Kudenatti

and V. B. AwatiRamesh B. Kudenatti

and V. B. Awati

**Analysis of boundary layer equations by**

the method of Asymptotic functionthe method of Asymptotic function

**301-314**
**
CONTENT of The Mathematics Student, Vol. 75, Nos. 1 - 4 (2006): **

** Sr. No.**
** Author **
** Title of the article / Paper**
** Pages **
** 1. **
** N. K. Thakare **
** Prof. H. C. Khare : A Tribute **
** 01-02 **
** 2. **
** Satya Deo **
** Rough and Soft : Prof. H. C. Khare **
** 03-05 **
** 3. **
** R K Srivastava **
** Prof. H. C. Khare : Selfless Wisdom and
Academic Vision Anthromorphized **

**07 - 08****4.****A. K. Das and**

S. S. KhareS. S. Khare

**On Conjectures of H. Singh****09-16****5.****Prem Narain****Statistical tools in Bioinformatics****17-27****6.****I B S Passi****Presidential Address (General)****29-35****7.****I B S Passi****Homological and Combinatorial Methods in Group Rings****37-63****8.****-****Abstracts of Papers-72nd Annual Conference**

of the IMS held at Rani Durgavati University

Jabalpur during December 27-30, 2006of the IMS held at Rani Durgavati University

Jabalpur during December 27-30, 2006

**65-85****9.****P. K. Banerji****Unfolding the Concepts of Boehmians and their Applications****87-121****10.****Phoolan Prasad****P. L. Bhatnagar and the BGK Model****123-136****11.****Subhash S. Bhoosnurmath****Birth and Development of Hyperbolic Metric and**

its impact on the 21st Century Mathematicsits impact on the 21st Century Mathematics

**137-157****12.****R. J. Hans-Gill****On a Conjecture of Minkowski****159-166****13.****R K Singh****Invariant Subspace Problem and**

Development of Mathematics around itDevelopment of Mathematics around it

**167-172****14.****Surindar Mohan Uppal****Can Mathematics Bring Peace ?****173-178****15.****Sanjay Jain and**

Mukesh KumarMukesh Kumar

**EOQ for Varying Marketing Policies Under**

a Replacement Policy for Damaged Itemsa Replacement Policy for Damaged Items

**179-186****16.****Sanjay Jain,**

Adarsh Mangal

and P. R. PariharAdarsh Mangal

and P. R. Parihar

**On the Posynomial Linear Plus Fractional Programming Problem****187-196****17.****Ajai Choudhary****The Algebraic Structure of the set of Integer Solutions**

of a quadratic Diophantine Equationof a quadratic Diophantine Equation

**197-201****18.****T. Phaneendra****Orbits relative to Two Self-maps and Common Fixed Point****203-207****19.****Hemant Kumar Nashine**

and C. L. Dewanganand C. L. Dewangan

**An Existence Result on KY Fan Best Approximant****209-214****20.****Ajai Choudhary****Matrix Analogues of the Terry-Escott Problem,**

Multigrade Chains and the Equation of FermatMultigrade Chains and the Equation of Fermat

**215-224****21.****Jyoti Kaushik and**

Neeru KashyapNeeru Kashyap

**Weighted Weyl's Spectrum****225-230****22.****G S Saluja****Fixed Points for an Admissible Class of**

Asymptotically Regular semigroup in Banach Spaces

with Weak Uniformly Normal StructureAsymptotically Regular semigroup in Banach Spaces

with Weak Uniformly Normal Structure

**231-238****23.****Ajai Choudhary****A Diophantine System****239-241****24.****Yaakov S. Kupitz and**

Horst MartiniHorst Martini

**Equilibrium under Atmospheric Pressure****243-252****25.****T N Venkataramana****Book Review****253-256**
**
CONTENT of The Mathematics Student, Vol. 74, Nos. 1 - 4 (2005): **

** Sr. No.**
** Author **
** Title of the article / Paper**
** Pages **
** 1. **
** P. C. vaidya **
** Professor J. N. Kapur - A Rare Leader **
** 01-02 **
** 2. **
** A. M. Vaidya **
** Integer Sided Triangles With One Agle 60 Degree **
** 03-05 **
** 3. **
** Prem Narain **
** Mapping of Quantitative Trait Loci (QTL)**
** 07 - 18 **
** 4. **
** D. K. Sinha **
** Some Snapshots of Reminiscing Professor J. N. Kapur : A Tribute **
** 19-23 **
** 5. **
** Sunder Lal **
** Professor J. N. Kapur : A Multidimensional Mathematician **
** 25-27**
** 6. **
** P. N. Tiwari and A. R. verma **

**Professor J. N. Kapur : Promoter of Ethics and Norms of Science****29-35****7.****B. K. Sachdeva****Professor J. N. Kapur**

(Some Personal Reminiscences)(Some Personal Reminiscences)

**37-38****8.****L. S. Kothari****Professor J. N. Kapur : A Great Teacher and Promoter of Mathematics****39****9.****Prem Narain****Tribute to Professor J. N. Kapur****41-42****10.****Sarva Jit Singh****Presidential Address (General)****43-47****11.****Sarva Jit Singh****Recent Developments in Poroelasticity****49-67****12.****-****Abstracts of Papers-71st Annual Conference**

of the IMS held at I. I. T. Roorkee,

Roorkee during December 26-29, 2005of the IMS held at I. I. T. Roorkee,

Roorkee during December 26-29, 2005

**69-121****13.****S. Parvathi****"Schur Weyl Duality" for a Larger**

Class of AlgebrasClass of Algebras

**123-142****14.****Aloke Dey****Orthogonal Arrays****145-152****15.****Aalok Misra****(String Theory Inspired) Excursions into**

(Complex)Differential Geometry of some

non-Kahler six-folds and their

exceptional uplifts(Complex)Differential Geometry of some

non-Kahler six-folds and their

exceptional uplifts

**153-170****16.****T K Das****On Posets of Certain Classes of Maps****171-181****17.****V. Balaji****C. S. Seshadri : A Distinguished Mathematician****183-187****18.****Ramadas**

Ramakrishnan

TrivandrumRamakrishnan

Trivandrum

**M. S. Narasimhan : A Distinguished Mathematician****189-191****19.****R. Sujatha****Parimala Raman : A Distinguished Mathematician****193-197****20.****Tikam Singh and**

Bhavana soniBhavana soni

**Approximation by Generalized**

de la Vallee Poussin Operatorsde la Vallee Poussin Operators

**199-206****21.****R. K. Yadav and**

S. D. PurohitS. D. Purohit

**On q-Laplace Transforms of Certain**

Multiple Basic Hypergeometric FunctionsMultiple Basic Hypergeometric Functions

**207-215****22.****S. Arumugam****Difference Labelling and Common**

Weight Decompositions of GraphsWeight Decompositions of Graphs

**217-223****23.****S. Bhargava,**

D. D. Somashekara and

Syeda Noor FathimaD. D. Somashekara and

Syeda Noor Fathima

**A new Transformation for Basic**

Bilateral Hyper Geometric SeriesBilateral Hyper Geometric Series

**225-230****24.****Ajai Choudhary****Some Diophantine Equations**

Involving Sixth PowersInvolving Sixth Powers

**231-236****25.****Sunder Lal and**

Vandani VermaVandani Verma

**Identity based Strong Designated**

Verifier Proxy Signature SchemeVerifier Proxy Signature Scheme

**237-244****26.****Eknath Ghate,**

Dipendra Prasad and

Riddhi ShahDipendra Prasad and

Riddhi Shah

**Book Reviews****245-249****27.****G. S. Srivastava****71st IMS Conference : A Brief Report****251-254****28.****-****Report on IMS Sponsored Lectures****255-256**
**
CONTENT of The Mathematics Student, Vol. 73, Nos. 1 - 4 (2004): **

** Sr. No.**
** Author **
** Title of the Paper**
** Pages **
** 1. **
** T. Thrivikraman**
** Traditional Mathematics in India after Bhaskara - New Approach Needed **

**01-02****2.****T. Thrivikraman****Topological Systems - A Potentially Productive Approach****03-12****3.****-****Abstracts of Papers - 70th Annual Conference of IMS**

held at J.N.V. University at Jodhpur.held at J.N.V. University at Jodhpur.

**13 - 42****4.****S. K. Nimbhorkar****Bear*-Rings, Lattice Theory , Graph Theory and Their Interrelationship****43-59****5.****Anand P. Singh****Advances in the Dynamics of Entire and**

Meromorphic FunctionsMeromorphic Functions

**61-72****6.****V. K. Balchandran****Agebraic Topology : Some Historic Perspectives****73-86****7.****Chandrasekhar Adiga****Sums of Squares and Sums of Triangular Numbers**

and their relationshipand their relationship

**87-94****8.****M. A. Sofi****Banach Spaces arising as Solutions of Equations**

involving Nuclear Operatorsinvolving Nuclear Operators

**95-108****9.****S. L. Kalla****Mathematical Models for Temperature Fields in Oil Strata****109-117****10.****G. S. Srivastava****Spaces of Entire Functions****119-128****11.****M. P. Wasadikar****Generalizations of Normal Lattices****129-133****12.****dr. S. S. Bhusnurmath****Differential Geometric Techniques in Complex Analysis****135-144****13.****A. Rao****Cocyclic Binary and Non-Binary Codes****145-156****14.****M. S. Choudhary****Generalized Functions : Different Approaches****157-165****15.****P. K. Banerjee**

and S. K. Al-Omariand S. K. Al-Omari

**Distributional Struve and Hankel Transformations of Compact Support****167-173****16.****B. Basavangoud and**

V. R. KulliV. R. Kulli

**Hamiltonian and Eulerian properties of Plick Graphs****175-181****17.****R. K. Yadav and**

Balraj SinghBalraj Singh

**On a set of Basic Polynomials Zn,alpha(x;k,q)**

suggested by Basic Laguerre polynomials Ln,alpha(x;q)suggested by Basic Laguerre polynomials Ln,alpha(x;q)

**183-189****18.****B.P.Verma****Solution of a Problem posed by Fisher and some generalization.****191-192****19.****Deshna Loonker and**

P.K.BanerjeeP.K.Banerjee

**Distributional Laplace - Hankel Transform by Fractional Integral Operators****193-197****20.****S. Bhargava and**

N. AnithaN. Anitha

**A Continued Fraction for certain q-Series of Ramanujan****199-404****21.****R. D. Giri and**

P. B. BahatkarP. B. Bahatkar

**On Triangular, Mersener's and Fermat's numbers****205-207****22.****S. B. Gaikwad and**

M. S. Choudhary

and K. ShivashankaraM. S. Choudhary

and K. Shivashankara

**Abelian Theorem for the Distributional Modified Stieltjes Transform****209-218****23.****M. G. Nadkarni****Did Cantor sow the seed of Measure and Integral?****219-230****24.****Asha Rani Singal****Cryptology : A journey from waxed Tablets to Euler's Theorem - I.****231-246****25.****B. Choudhary****Matrix Transformations and isomorphic structure of Locally Convex FK-Spaces****247-252****26.****Saurabh Singal****Book Reviews****253-258****27.****-****News and Announcement****259-260**
**
CONTENT of The Mathematics Student, Vol. 72, Nos. 1 - 4 (2003): **

** Sr. No.**
** Author **
** Title of the Paper**
** Pages **
** 1. **
** T. Parthasarathy **
** Injectivity of Mappings in Rn **
** 01-04 **
** 2. **
** T. Parthasarathy **
** Five Decades of Stochastic Games **
** 05-10 **
** 3. **
** - **
** Abstracts of Papers - 69th Annual Conference of IMS held at University of Lucknow, Lucknow. **

**11 - 29****4.****M. A. Pathan****Some Formulas of Ramanujan on Hypergeometric series****31-44****5.****B. K. Lahiri****Uniformly Normal Structure****45-52****6.****S. Sri Bala****Jordan Algebras****53-67****7.****Rajiv K. Srivastava****Bicomplex Numbers : Analysis and Applications****69-87****8.****Anand P. Singh****Some directions in Complex Dynamics****89-100****9.****C. M. Joshi****Rogers-Ramanujan Identities : A Historical Overview**

and significance of Baily's Transformand significance of Baily's Transform

**101-112****10.****D. V. Pai****Strong Unicity of Order Two in simultaneous approximations****113-121****11.****S. P. Arya and**

Neeru JainNeeru Jain

**Some Weaker form of Fuzzy Weak Continuity****123-131****12.****T. N. Sinha****On the Diophantine Equation x4 + kx2y2 +y4 = z2****133-137****13.****Peter Lindqvist**

and Jaak Peetreand Jaak Peetre

**p-Arc length of q-Circle****139-145****14.****Takeshi Okano****A note on Irrationality of Some Numbers****147-148****15.****Yaakov S. Kupitz**

and Horst Martiniand Horst Martini

**On the Monotonicity of (sinx)/x from the Ancient**

to a Modern Point of Viewto a Modern Point of View

**149-161****16.****Rinu Srivastava and**

B.M.L. SrivastavaB.M.L. Srivastava

**Identities of I function of One Variable****163-164****17.****M. Imdad and**

Q.H.KhanQ.H.Khan

**Remarks on Fixed and Coincident points of**

Certain Composite Involutions in Banach SpacesCertain Composite Involutions in Banach Spaces

**165-169****18.****M.S.Younis****On the Mapping Properties of an Index of the Fourier Transforms**

of Lipschitz Functions on Certain Motion Groupsof Lipschitz Functions on Certain Motion Groups

**171-179****19.****P.K.Banerjee and**

Abha PurohitAbha Purohit

**Integral Transform on Lp-spaces****181-185****20.****D. J. Prabhakaran****On certain Integral Transforms of Meromorphic Starlike Functions****187-196****21.****Devbhadra V. Shah****On Triangular, Mersener's and Fermat's numbers****197-199****22.****M.S.Mahadev Naika**

and K. Shivashankaraand K. Shivashankara

**Some values for the Ratios of Theta-Functions****201-204****23.****D. V. Shah****Corrections in the Formula for P5(n)****205-211****24.****D. P. Shukla****On an orthonormal Set of Polynomials****213-219****25.****S.P.Singh and**

Lilawati PalLilawati Pal

**Certain Transformation Formulae for q-Hypergeometric Series****221-225****26.****Rakesh Goel****A Method to Calculate the Value of pi****227-232****27.****Asha Rani Singal,**

Saurabh Singal and

Arun M. VaidyaSaurabh Singal and

Arun M. Vaidya

**Book Reviews****233-249****28.****-****News and Announcements****250-252**
**
CONTENT of The Mathematics Student, Vol. 71, Nos. 1 - 4 (2002): **

** Sr. No.**
** Author **
** Title of the Paper**
** Pages **
** 1. **
** P. V. Arunachalam **
** Presidential Address - General **
** 01-03 **
** 2. **
** P. V. Arunachalam **
** Mathematics of the Twentieth Century - A Point of View **
** 05-20 **
** 3. **
** - **
** Abstracts of Papers - 67th Annual Conference of IMS held at Aligarh Muslim University, Aligarh, Jan 27-30, 2002 **

**21 - 48****4.****J. R. Patadia****Lacunary Fourier series and Sidon sets****49-71****5.****S. P. Singh and**

Mahi R. SinghMahi R. Singh

**Fixed Points Theorems and Applications****73-81****6.****M. K. Gupta****On some Weak Separation Axioms****83-89****7.****Neville Robbins****On Modified R-regular Partitions****91-96****8.****S. P. Arya****Teacher training in India****97-105****9.****M. A. Pathan****Presidential Address - General****107-110****10.****M. A. Pathan****Lie Algebraic Analysis of Differential Equations and Special Functions****111-124****11.****-****Abstracts of Papers - 68th Annual Conference of IMS**

held at Shivaji University, Kolhapur, December 20-23, 2002held at Shivaji University, Kolhapur, December 20-23, 2002

**125-148****12.****S. G. Deo****Trigonometric like Operators in Banach Spaces****149-160****13.****L. Radhakrishna****The Taxonomy of Mathematics and Einstein****161-169****14.****R. C. Srivastava****Converging Shock in the Welfare of Mankind****171-186****15.****Chandrasekhar Adiga****Ramanujan's Continued Fractions and Their Evaluations****187-199****16.****S. P. Arya and Neeru Jain(nee Singal)****Fuzzy Somewhat Continuous functions****201-207****17.****M. K. Singal****The Indian Mathematical Society : An Overview****209-246****18.****-****News and Announcements****247-250**