017912   Mathur Trilok (Mathematics Dep, University of Rajasthan, Jaipur-302 004, Email: trilokmathur@yahoo.com) : Coefficient inequalities for certain classes of meromorphically multivalent starlike and convex function. J Indian Acad Math 2006, 28(1), 147-56.

Class Σ_p* of meromorphic multivalent (p-valent) functions f(z) in a punctured disk D_r with a pole of order p at centre of disk is defined. Two subclasses S_{p*(α) and Kp*(α) are considered in Σ*p. These subclasses denote meromorphic p-valently starlike functions of order α and meromorphic p-valently convex functions of order (α) respetively. Established some coefficient properties of functions f(z) to be in the classes S*p(α) and K*p(α). Also the starlikeness and the convexity of functions of f(z) in Σ*p are discussed. Lastly, some (known and new) special cases of results are mentioned.}

18 ref

017911   Mandal P K;Gupta M (Mathematics Dep, Jadavpur University, Colcutta-700 032) : Non-linear parametric amplification of acoustic waves in a thermopiezo-semiconducting medium. J Indian Acad Math 2006, 28(1), 1-9.

Amplification of acoustic wave due to non-linear interaction in a n-typc degenerate thermopiezosemiconducting medium has been investigated. The non-linearity arises from the non-linear transport property of electrons in the medium. The relative change in energy of the signal wave is computed for different propagation distances by numerical calculations.

1 illus, 1 table, 7 ref

017910   Malgonde S P;Waphare B B (Mathematics Dep, Bract's Viswakarma Institute of Technology, Pune-411 037, Email: spmalgonde@rediffmail.com) : On a hankel type convolution of genealized functions. J Indian Acad Math 2006, 28(1), 85-104.

A classical Hankel type convolution are defined and extended to a class of generalized functions. Algebraic properties of the convolution are explained and the existence and significance of an identity element are discussed.

11 ref

017909   Kohli J K;Vashistha S (Mathematics Dep, Hindu College, University of Delhi, Delhi-110 007) : Common fixed point theorem in metric spaces. J Indian Mathl Soc 2005, 72(1-4), 107-14.

Aim of the present paper is to prove a common fixed point theorem for weakly compatible maps which are not necessarily continuous. This generalizes several known results in the literature including those of Chugh and Kumar, Kang and Kim, Jachymski, Rhoades, Fisher, and Jungck.

16 ref

017908   Khare S S (Mathematics Dep, North Eastern Hill University, Shillong-793 002) : On bounding and independence of wall manifolds. J Indian Mathl Soc 2005, 72(1-4), 195-201.

Object of this paper is to find the values of m and n for which the Wall manifold Q(m, n) bounds; and show that for a given d, the set of non-zero bordism classes of Wall manifolds Q(m, n) of dimension d is independent in the unoriented bordism group N_d over Z₂.

6 ref

017907   Jaisankar R;Sathiyamoorthi R (Statistics Dep, Annamalai Univ, Annamalai Nagar-608 002) : Stochastic model for expected time to cross the antigenic diversity threshold (CADT) in HIV infection. Ultra Scient phys Sci 2006, 18(2), 249-54.

Successive contacts with a HIV infected person tends to weaken the immune system which is due to genetic variability gained by HIV and this is called the antigenic diversity. As the antigenic diversity reaches the antigenic diversity threshold, the immune system is unable to sustain against the viral population and gets collapsed which leads to the state of onset of AIDS symptoms. Describes of simple mathematical model to estimate the time to cross the antigenic diversity threshold, which signifies onset of AIDS. The expected time to the collapse of the immune system and its variance are obtained assumming that the threshold follows Erlang 2 distribution.

2 illus, 2 tables, 2 ref

017906   Jain V K (Mathematics Dep, I.I.T., Kharagpur-721 302) : Certain sharp inequality for polynomial a₀ + a₁z + a₂z<. J Indian Mathl Soc 2005, 72(1-4), 141-5.

5 ref

017905   Jain S;Mangal A (Mathematics Dep, Govt. College, Ajmer-305 001, Email: drjainsanjayl@refiffmail.com) : Solution of a multiobjective frctional programming problem. J Indian Acad Math 2006, 28(1), 133-41.

In this paper, a multiobjective fractional programming problem with linear constraints and the objective function is the sum of the functions of the form f(x) + g(x)/h(x), i.e., sum of a linear and a quotient function, where f(x), g(x) and h(x) are linear functions has been discussed. Solution of the multiobjective fractional programming problem can be recovered by reducing it to a fractional programming problem.

8 ref

017904   Ikai H (Mathematical Institute, Tohoku Univ, Sendai-980-8578, Email: ikai@math.tohoku.ac.jp) : On Lipschitz'lifting of the cayley transform. J Indian Mathl Soc 2005, 72(1-4), 1-12.

Cayley's rational parameterization of orthogonal groups (Cayley transform) and its lifting to coverings discovered by Lipschitz are generalized. They acquire validity with functorial behaviour for all regular and semi-regular quadratic modules over any commutative base ring. Exterior algebras and their exponential maps play fundamental role.

13 ref

017903   Hazarika M (Mathematical Sciences Dep, Tezpur University, Napaam-784 028, Email: munmun@tezu.ernet.in) : Recursively generated subnormal shifts. J Indian Acad Math 2006, 28(1), 11-23.

For M ≥ 1, let A₀, A₁, ..., A_m0, A₁, ..., A_m.

5 ref

017902   Ghadle K P;Khobragade N W (Mathematics Dep, MJP Educational Campus, Nagpur University, Nagpur-440 010) : Inverse problem of thermoelastic deformation of a thin circular plate in Marchi-Fasulo transform domain. J Indian Acad Math 2006, 28(1), 45-55.

Two inverse problems of thermoelasticity has been solved. In the first problem, an attemt has been made to determine the unknown temperature, displcement and stress functions on the outer curved surface of a thin circular plate occupying the space D : 0 ≤ r ≤ a, -h ≤ z ≤ h by applying finite Marchi-Fasulo transform technique. The third kind of boundary condition [T (r, z,) + c ∂T/∂r (r, z)]_r = ε = f(z) for a fixed value of ε, 0 <60> ε <60> a is a known function of z and homogeneous boundary condition of the third kind is maintained on the plane surfaces of a thin circular plate. In the second problem, an attemt has been made to determine the unknown temperature, displacement and stress functions on the outer curved surface of a thin circular plate occupying the space D : 0 ≤r ≤ a, -h ≤ z ≤ h by applying finite Marchi-Fasulo transform technique. The third kind of boundary condition [T(r,z,t) + c∂T/∂r (r,z,t)]_r = ε = f (z, t ), t <62> 0 for a fixed value of ε, 0 <60> ε <60> a is a known function of z and t and homogeneous boundary condition of the third kind is maintained on the plane surfaces of a thin circular plate.

10 ref

017901   Garg M;Mishra R (Mathematics Dep, University of Rajasthan, Jaipur-302 004, Email: garghome@satyam.net.in) : On r-dimensional N-fractional differentegral of multivariable H-function. J Indian Acad Math 2006, 28(1), 189-98.

R-dimensional Nishimoto's N-fractional differintegral of multivariable H-function has been obtained whose arguments involve the product of two power functions. On account of the general nature of this result, N-fractional differintegral of a large variety of special functions of one and several variables having general arguments follow as special cases of findings. References of some known results which follow from the main findings of this paper hive also been given.

14 ref

017900   Fatokun J O (Mathematics Dep, Nasarawa State Univ, Keffi, Nigeria) : Parameter expansion with the standard finite difference method of order two for the two-point singularly perturbed boundary value problems. Ultra Scient phys Sci 2006, 18(2), 363-70.

A parameter expansion with the standard Finite Difference Method of order two is presented. An economized polynomial in powers of the small parameter ε appearing in the differential equation is obtained with the Finite Difference Method. The procedure can be applied conveniently to handle two-point Singularly Perturbed Boundary Value Problems. Two numerical examples are shown and the errors are compared with that of the parameter expansion in the Tau method. The new procedure competes favourably and can be applied to a wider range of problems with non-polynomial coefficients.

2 tables, 10 ref

017899   Eswara Prasad G;Nagarajan D (S.T. Hindu Coll, , Nagercoil) : Modelling of gene frequencies. Ultra Scient phys Sci 2006, 18(2), 371-5.

Every human being can be clasified into one of the four blood groups O,A,B and AB. The inheritance of these blood groups are controlled by three allelomorphic genes 0, A, B of which 0 is recessive to A and B. Analyses the homogeneity of rural, urban matured and prematured babies blood groups and examine whether the frequencies in each group are in accordance with Bernstein's hypothesis and test whether the gene frequencies are the same in all population.

8 tables, 3 ref

017898   Elangovan R;Nantharaj C;Sathiyamoorthi R (Statistics Dep, Annamalai Univ, Annamalai Nagar-608 002, Email: srelangovan@rediffmail.com) : Shock model approach to the determination of optimal time interval between recruitments. Ultra Scient phys Sci 2006, 18(2), 233-8.

In any organization the exit or wastage of personnel is very common. The exit of personnel in marketing organizations is very frequent, especially when policies regarding incentives, targets are revised. The optimal time. interval between recruitments is obtained using the shock model approach with associated costs. The probability of the breakdown of the organization for the first time due to the exists of personnel is also incorporated while considering the cost aspects. Special cases are discussed with numerical illustrations.

3 tables, 8 ref

017897   Dheena P;Sivakumar D (Mathematics Dep, Annamalai University, Annamalainagar-608 002) : N_c pure regular near-rings. J Indian Mathl Soc 2005, 72(1-4), 157-61.

In this paper author introduced the notion of N_c-pure and strict N_c-pure near-rings. It is shown that a reduced near-ring N with identity is N_c-pure if and only if whenever e ≤ a for some e ∉ N_c and a ∈ N implies e = ea = ae and a - e is an idempotent element. Also obtained an equivalent condition for a N_c-pure near-ring to be strict N_c-pure.

4 ref

017896   Dharmaiah V (Mathematics Dep, Osmania University, Hyderabad-500 007) : Proof of existence of a solution lying between any pair of lower and upper solutions of initial value problem. J Indian Acad Math 2006, 28(1), 143-5.

2 ref

017895   Deo S;Awasthi V V (Harish-Chandra Research Institute (HRI), Chhatnag Road, Jhunsi, Allahabad-211 019, Email: sdeo@mri.ernet.in) : Strongly contractible polyhedra which are not simply contractible at n points for any n≥2. J Indian Mathl Soc 2005, 72(1-4), 75-82.

Studied the concept of strict contractibility defined by E. Michael and construct an example stated in the title of the paper. Author gave examples of compact metric spaces in Euclidean 3-space which are simply contractible at n points, for any n ≤ 1, but are not strongly contractible at those points.

6 ref

017894   Deheri G M (Mathematics Dep, Sardar Patel University, Vallabh, Vidyanagar-388 120) : Lemda (P; IN)-nuclear spaces and A₁(α)-nuclear spaces with bases and their topological identification with kothe spaces. J Indian Mathl Soc 2005, 72(1-4), 227-39.

It is shown that the collection of all λ(P; IN)-nuclear spaces in which there is an equicontinuous basis coincides with the collection of all λ(P; IN)-nuclear Kothe spaces which generalizes the famous classical result of Pietsch. This in turn, has been used to establish that a locally convex space having a Q-fully-λ(P)-basis is topologically identified with a λ(P; IN)-nuclear Kothe space. With regard to A₁(α)-nuclearity, it is observed that the collection of all A₁(α)-nuclear spaces in which there is an equicontinuous basis is same as the collection of all A₁(α)-nuclear Kothe spaces. Using this it is deduced that a locally convex space having a Q-fully A₁(α)^x-basis is topologically isomorphic to a A₁(α)-nuclear Kothe space. It is seen that if the strong dual of a polar-reflexive space E having a basis, is λ(P; IN)-nuclear with a fundamental collection of bounded sets, then E can be ∞ topologically identified with a uniformly λ(P; IN)-nuclear Kothe space. It is noticed that a barrelled space with an absolute, ∞-absolute basis is isomorphic to a Kothe space whose bounded sets are simple. It is proved that a A₁(α)-nuclear Frechet space having a Schauder basis can be identified topologically with a uniformly A₁(β)-nuclear Kothe space for some β = β(α). For a λ(P, IN)-nuclear space A₁(α) it is concluded that a A₁(α)-nuclear Frechet space with a basis is isomorphic to a uniformly λ(P)-nuclear Kothe space. In addition, the discussion also says that there exist spaces whose A₁(α)-nuclearity is same as the A(α)-nuclearity.

36 ref

017893   Datta S K (Mathematics Dep, Krishnath College, Berhampore, Murshidabad-742 101) : Growth of composition of entire and meromorphic functions. J Indian Acad Math 2006, 28(1), 33-44.

Comparative growths of log ^[2]M(r, fog) and log T(r, fog) where f and g are any two entire functions were studied. Comparative growth of a composite entire or meromorphic function and a Wronskian generated by one of the factors were also studied. Order and lower order of composite entire functions was found under different conditions.

15 ref

017892   Das R (Mathematics Dep, Faculty of Science, The M.S. University of Baroda, Vadodara-390 002, Email: ruchid99@yahoo.com) : On G-expansive homeomorphisms and generators. J Indian Mathl Soc 2005, 72(1-4), 83-9.

Defines the notion of a G-generator for a homeomorphism on a compact G-space and characterize G-expansive homeomor-phism on a compact metric G-space in terms of G-generator. Obtained the relation between G-expansiveness of a pseudoequivariant homeomorphism on a metric G-space X and expansiveness of its induced homeomorphism on the orbit space XIG. This relation was used to prove the non-existence of pseudoequivariant G-expansive. homeomorphism on closed unit interval. Finally, author showed that a compact metric G-space admitting a pseudoequivariant G-expansive homeomorphism must be of finite dimension when G is finite.

017891   Das A (Salt Lake School (Eng. Medium), , CA-221, Salt Lake City, Kolkata-700 064) : On an extension of bilateral Generating function of gegenbauer polynomials by group theoretic method. Ultra Scient phys Sci 2006, 18(2), 385-7.

Obtains an extension of a bilateral generating relation of Gegenbauer polynomials by group theoretic method. An application of the theorem is also given here.

2 ref

017890   Dalela A K;Goyal A;Tiwari S K (NO, , Virkamal, Anand Colony, Baldebagh, Jabalpur-482 002) : Approximation of functions by (N, P_n<. Ultra Scient phys Sci 2006, 18(2), 376-80.

4 ref

017889   Chugh R;Rathi S (Mathematics Dep, Maharshi Dayanand Univ, Rohtak-124 001) : Fixed points of expansive mappings in probabilistic D-metric spaces. Ultra Scient phys Sci 2006, 18(2), 329-34.

Observes that under suitable conditions an expansive mapping can be viewed as a Banach contraction mapping in probabilistic D-metric space. Proves some common fixed point theorems for expansive mapping in probabilistic D-metric spaces, which are probabilistic analogue of the result of Ahmad, Ashraf and Rhoades in D-metric space. It is shown that the class of probabilistic D-metric spaces is metrizable. The metric D (as defined by Dhage in) is related to the distribution function F by D(x,y,z) <60> t if and only ifF(x,y,z;t) <60> I-t.

17 ref

017888   Chugh R;Rathi S (Maths Dep, Maharshi Dayanand Univ, Rohtak-124 001) : Weakly compatible maps in probabilistic metric spaces. J Indian Mathl Soc 2005, 72(1-4), 131-40.

Proved common fixed point theorems for six mappings from a class of compatible continuous mappings to a larger class of map-pings having weakly compatible maps, without appeal to continuity in probabilistic metric space, which generalize the result of Mishra and Xieping. Example in support of this theorem has been provided.

18 ref

017887   Chi-Ming C (Mathematics Education Dep, National Hsinchu Teacher's College, Hsinchu, Taiwan, R.O.C.) : G-KKM theorem on non-convex sets and its applications. J Indian Mathl Soc 2005, 72(1-4), 43-51.

In this paper, author invoked non-convexity of constraint regions in place of convexity and author obtained the new Fixed point theorem, "Let X be an almost G-convex subset (nearly G-convex set) of a locally G-convex space E. If T ∈ G-KKM(X, X) is compact and closed, then it has a fixed point."

7 ref

017886   Chaudhary R C;Jha A K;Sawai Singh (Mathematics Dep, Univ of Rajasthan, Jaipur-302 044) : Oscillatory free convection flow of an elastico-viscous fluid past an infinite vertical oscillating plate with constant heat flux. Ultra Scient phys Sci 2006, 18(2), 283-92.

Free convection flow of an elastico-viscous fluid past an infinite vertical oscillating plate with constant heat flux has been discussed. The flow is subjected to a constant suction. Analytica1 expressions are derived for mean and transient velocities and temperature field. The effects of k, the elastic parameter, ω, the frequency of oscillation, P, the Prandtl number have been discussed in detail with the help of graphs.

9 illus, 1 table, 23 ref

017885   Chattopadhyay A;Das S;Jain V K;Konwar H (Mathematics Dep, I.I.T., Kharagpur-721 302) : Certain generalizations of enestrom-kakeya theorem. J Indian Mathl Soc 2005, 72(1-4), 147-56.

16 ref

017884   Carbone A (Dip Di Matematica, University of Calabria, Italy) : Extensions of a few fixed point theorems. J Indian Acad Math 2006, 28(1), 125-131.

Gives a few results in general setting and then drive well known results as easy corollaries. Results dealing with best approximation are also discussed. The fixed point theory has applications in various fields including mathematical problems on nonlinear analysis, optimization theory, variational inequalities, approximation theory, game theory and mathematical physics. The theory is also useful in the study of mathematical economics and eigenvalue problems.

8 ref

017883   Bhattacharjee T (Mathematics Dep, University of Chittagong, Chittagong, Bangladesh) : Group-theoretic origins of some generating functions for LD_n<. J Indian Mathl Soc 2005, 72(1-4), 163-81.

Derived some generating relations by L. Weisner's group theoretic method in case of Laguerre Dirichlet polynomials LD_n^(α)(z).

6 ref

017882   Bhargava S;Vasuki K R;Srivatsa Kumar B R (Stud Maths Dep, Mysore Univ, Manasa Gangotri, Mysore-570 006, Email: srinivasamurthyb@yahoo.com) : Evaluation of Ramanujan-weber class invariant g_n. J Indian Mathl Soc 2005, 72(1-4), 115-27.

By employing P - Q eta function identities involving 4 arguments, authors established several values of the class invariant g_n.

15 ref

017881   Bhajantri M R;Eldho T I;Deolalikar P B (Department of Civil Engineering, IIT-Bombay, Mumbai 400 076) : Hydrodynamic modelling of flow over a spillway using a two-dimensional finite volume-based numerical model. Sadhana 2006, 31(6), 743-54.

Spillway flow, a classical problem of hydraulics, is generally a gravity-driven free surface flow. Spillway flows are essentially rapidly varying flows near the crest with pronounced curvature of the streamlines in the vertical direction. Two processes simultaneously occur in the flow over the crest, that is, formation and gradual thickening of the turbulent boundary layer along the profile, and gradual increase in the velocity and decrease in the depth of main flow. Spillway hydrodynamics can be obtained through physical modelling or numerical modelling. Physical modelling of spillways is expensive, cumbersome and time-consuming. The main difficulties in solving the spillway problem numerically are: rapidly varying flow, existence of both subcritical and supercritical flows, development of turbulent boundary layers, unknown free surface and air entrainment. Numerical simulation of such flows over spillways in all flow regimes is a challenging task. This paper describes a numerical model and its application to a case study to investigate the hydraulic characteristics of flow over spillway crest profiles by simulating the velocity distribution, pressure distribution and discharge characteristics. Results of the numerical modelling are compared with those from the physical modelling and found to be satisfactory.

6 illus, 20 ref

017880   Barik S P;Kanoria M;Chaudhuri P K (Mathematics Dep, University of Calcutta, 92, A.P.C. Road, Kolkata-700 009, Email: pkcha@vsnl.net) : Contact problem for an anisotropic elastic layer lying on an anisotropic elastic foundation under gravity. J Indian Acad Math 2006, 28(1), 205-23.

Contact problem for a transversely isotropic layer lying on another semi-infinite transversely isotropic foundation under the action of uniform body force due to gravity, a uniform clamping pressure and a concentrated lifting load, is studied. The contact between the layer and the foundation is frictionless and only compressive normal traction can be transmitted through the interface. The problem of continuous contact is considered and critical value of the load corresponding to interface separation is determined. The mixed boundary value problem for discontinuous contact is formulated in terms of singular integral equation and is solved with the help of Gauss-Chebyshev integration formula. Numerical results are depicted graphically. It is observed that for transversely isotropic layered media lying on a semi-infinite transversely isotropic foundation the critical value of the concentrated load is greater than that of the isotropic layered media lying on semi-infinite rigid foundation whereas it is less than that of transversely isotropic layered media lying on a semi-infinite rigid foundation.

7 illus, 13 ref

017879   Arumugam S;Suresh Suseela J (NO, Arulmigu Kalasalingam Engng Coll, Krishnakoil-626 190) : Geodesic graphical covering number of a graph. J Indian Mathl Soc 2005, 72(1-4), 99-106.

A geodesic graphoidal cover of a graph G is a collection Ψ of shortest paths in G such that every path in Ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in Ψ and every edge of G is in exactly one path in Ψ. The minimum cardinality of a geodesic graphoidal cover of G is called the geodesic graphoidal covering number of G and is denoted by η_g. In this paper author determine η_g for several classes of graphs. Also proved that η_g ≥ [q/d(G)] where d(G) is the diameter of G and characterize some classes of graphs which attain this bound.

6 ref

017878   Ahmed S (Mathematics Dep, Govt Degree Coll Thanna Mandi, Thanna Mandi-185 212) : On covering dimension of crisp subsets in L-topology. Ultra Scient phys Sci 2006, 18(2), 309-14.

Introduces the concept of covering dimension of crisp subsets in L-topological spaces and studied it's various properties.

20 ref

017877   Agarwal P;Koul C L (Mathematics Dep, Malaviya National Institute of Technology, Jaipur-302 017) : Relations involving Psi-functions and H-function of several variables. J Indian Acad Math 2006, 28(1), 63-72.

Four relations involving the Psi-function Ψ (z) and the H-functions of several variables H[x₁ .... x_n] are established here. Number of particular cases, both known and new ones have been mentioned.

4 ref

016930   Vasuki K R;Srivatsa Kumar B R (Mathematics Dep, Acharya Institute of Technology, Soldevanhalli, Chikkabanavara (Post), Hesaragatta Road, Bangalore-560 090, Email: vasuki_kr@hotmail.com) : Evaluations of the ramanujan-Gollnitz-gordon continued fraction H (q) by modular equations. Indian J Math 2006, 48(3), 275-300.

As a sequel to some works of Chan and Huang author evaluate H (e^{-π √N}) for certain values of n. The required modular identities are also obtained.

8 ref

016929   Thakare N K;Pawar M M;Waphare B N (NO, , 4B, Mitrakunj Society, Sakri Road, Dhule-424 001, Email: nimbkt@yahoo.com) : Modular pairs, standard elements, neutral elements and related results in partially ordered sets. J Indian Mathl Soc 2004, 71(1-4), 13-53.

Five distinct notions of modular pair in a general poset are discussed and studied. Interrelationships between these five concepts are looked into and several counter-examples are supplied. The covering properties and the exchange property in general posets are thoroughly studied and several characterizations of these properties are obtained. As an offshoot of study, twentythree characteizations of the covering property in atomistic lattices are accomplished. Investigations of del-relation, del-tilda relation, perspectivity, sub-perspectivity etc. in posets are carried out. In the context of another open problem posed by Birkhoff concerning how to define natural extensions of the concepts of neutral elements and standard elements, authors cover substantial ground and supply adequate solution to this query. Special posets such as SSC-posets, SSC*-posets, or thomodular and orthocomplemented posets are studied and several characterizations are obtained.

32 ref

016928   Tamizh Chelvam T;Meenakumari N (Mathematics Dep, Manonmaniam Sundarnar University, Tirunelveli-627 012) : B-regular Γnear-rings and bi-ideals. J Indian Mathl Soc 2004, 71(1-4), 119-24.

In generalization of regular Γ-near rings, authors introduces b-regular Γ-near-rings and obtain some characterization of b-regular Γ-near-rings via bi-ideals.

6 ref

016927   Srivastava J K (Mathematics and Statistics Dep, D.D.U Gorakhpur University, Gorakhpur-273 009) : Kothe-topeplitz and topological duals of spaces of strongly summable vector sequences. J Indian Mathl Soc 2004, 71(1-4), 141-52.

Characterizes generalized α-, β- and →-duals of the spaces of strongly summable vector sequences l(X, p), C₀(X,p), c(X,p) and l_∞ (X,p) where sequences are taken from a Hausdorff locally convex space X. Besides the investigations of some topological properties. Determines topological duals l(X, p), C₀ (X, p) and c(X, p) when considered with natural linear topologies on them generated by the family of paranorms.

18 ref

016926   Sharma S N;Saxena R;Saxena S C (NO, Smart Ashok Technological Institute, Vidisha-464 001) : Sharpening the response of an FIR filter using fractional Fourier transform. J Indian Inst Sci 2006, 86(2), 163-8.

Methodology to sharpen the transition band of a linear phase, finite impulse response (FIR), Kaiser window filter using fractional Fourier transform (FRFT) is proposed. Transition bandwidth of a window-based FIR filter is proportional to the main lobe width of the window function used and FRFT of Kaiser window exhibits shrinkage in the main lobe width as the FRFT angle is reduced. Thus, apart from the traditional usage of window shape parameter and window length, FRFT angle can be used as a third parameter to effect changes in the frequency response of a window-based FIR filter. The merit of using FRFT in FIR filter design is that the impulse response need not be recomputed to improve filter sharpening and thus online improvement in the frequency response can be obtained.

^ssc3 illus, 12 ref

016925   Sarma A K;Misra R;Chandramouli V (NO, Indian Institute of Technology, Guwahati, North Gauwahati, Guwahati-781 039, Email: aks@iitg@ernet.in) : Application of genetic algorithm to determine optimal cropping pattern. Opsearch 2006, 43(3), 320-9.

Optimal cropping pattern plays an important role in improving the agricultural economy. Explores the potential of applying the Genetic-Algorithms to the non-linear formulation of the optimal cropping pattern problem. A practical problem using the agricultural data of the Batadrava development block of Nagaon district of Assam, India, is solved to demonstrate the application of Genetic-Algorithms. GA, which is a population-based search technique, has been found to be quite efficient in deciding optimal cropping pattern considering the various constraints and complexities representing the real situation. An analysis is also made to suggest suitable GA parameters for the problem.

2 illus, 3 tables, 12 ref

016924   Sahai V;Srivastava S (Mathematics and Astronomy Dep, Lucknow University, Lucknow-226 007, Email: vsahai@hotmail.com) : On models of Lie algebra G(0, 1) and Euler integral transformation. J Indian Mathl Soc 2004, 71(1-4), 195-205.

An attempt is made to construct models of Lie algebra G(0, 1). A two fold integral transformation similar to Euler transformation is used to transform the models in the form of difference-differential operations. These models are further used to obtain recurrence relations and generating functions.

11 ref

016923   Rosas E;Carpintero C (Departamento De Matematcas, Universsidad De Orientero Nucleo De Sucre, Venezuela, Email: erosas@sucre.udo.edu.ve) : (α, β - γ - semi open sets and some new generalized separation axioms. Indian J Math 2006, 48(3), 301-16.

Let (X, T) be a topological space and α, β, γ : P(X) → P(X) be operators associated with t. Concept of (α,β)-φ-semi open sets have been introduced. Also analyzed the relationship with some well known separation notions.

12 ref

016922   Reddy D R K (Applied Mathematics Dep, Andhra University, Visakhapatnam-530 003) : On Einstein-Rosen vaccum in a scalar-tensor theory of gravitation. J Indian Mathl Soc 2004, 71(1-4), 189-93.

Vacuum field equations for the Einstein-Rosen cylindrically symmetric metric are obtained in a scalar-tensor theory of gravitation proposed by Ross [D.K. Ross, Phys. Rev. D.5 (1972), 284]. It is shown that in each of the static and non-static cases the solutions of the field equations simply yield the vacuum models of general relativity.

14 ref

016921   Parhi N;Rath R N (NO, , Plot No. 1365/3110, Shastri Nagar, Unit-4, Bhubaneshwar-751 001) : Oscillation of solutions of a class of first order neutral differential equations. J Indian Mathl Soc 2004, 71(1-4), 175-88.

Sufficient conditions are obtained for oscillation of all solutions (or all bounded solutions) of first order neutral differential equations of the form [y(t)-p(t)y(t-τ)]' + Q(t) G(y(t - σ)) = f(t) and [y(t)-p(t)y(t-τ)]' + Q(t) G(y(t-σ)) = 0 for different ranges of p(t). For (*) one of the conditions states that F(t) changes sign finitely, where F ∈ C¹ ([0, ∞), R) such that F'(t) = f(t). In results concerning (**), the superlinearity or sublinearity of G plays as an important role.

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016920   Pant V;Jha K (FF(HC), FF Division, MHA, 1st Floor, Lok Nayak Bhavan, Khan Market, New Delhi-110 003, Email: vyomeshpant@yahoo.co.in) : On discontinuity and fixed points. J Indian Mathl Soc 2004, 71(1-4), 103-7.

Aimes at proving a fixed point theorem under the (ε, δ) contractive conditon, however without either imposing any additional restriction on δ or on continuity of the map of assuming the Φ-contractive condition together with it. In the setting of the fixed point theorem it was shown that the map is discontinuous at the fixed point. This theorem extends the results of Pant [Theorem 1, [13]] and Pant [17].

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016919   Pant R P (Mathematics Dep, Kumaun University, D.S.B. Campus, Nainital-263 002) : Non-expansive mappings and meir-killer type conditions. J Indian Mathl Soc 2004, 71(1-4), 239-44.

Obtained fixed point theorems for generalized non-expansive mappings in metric spaces by employing Meir-Keeler type conditions. Results open up the unexplored area of fixed points on non-expansive self-mappings of metric spaces for investigation. The method developed by author also provides a new tool to deal with non-expansive mappings in Banach spaces.

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016918   Nandal;Pradeep Kumar (Mathematics Dep, Faculty of Scinece, Banaras Hindu University, Varanasi-221 005) : Spectrum of certain unbounded composition transformation in l<. J Indian Mathl Soc 2004, 71(1-4), 125-9.

Let l² be the Hilbert space of all summable sequences of complex number under the standard inner product on it. Let C_φ be an unbounded densely defined composition transformation in l² induced by a function φ on N into itself such that n ∈ φ^-1 (n) for each n in the range of φ. Authors proved that spectrum of C_φ is all of C.

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016917   Nanda S (Mathematics Dep, IIT Kharagpur, Kharagpur-721 302) : Almost continuity and almost compactness. J Indian Mathl Soc 2004, 71(1-4), 227-32.

Almost convergence for sequence of real or complex numbers was discussed by Lorentz, Acta Math. (1948) and almost convergence in Banach space was studied by Kurtz, Tohoku Math. J. (1972). Introduces and studies the concept of almost continuous mappings, almost compact sets and almost operators in Banach spaces.

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