024596   Bagheri S M;Mojtaba Moniri (Inst, for Stud in Theoretical Phys and Math (IPM), Tehran, Iran, Email: bagheri@ipm.ir) : Joint embedding and amalgamation for certain classes of ordered fields. J appl Algebra Discrete Structs 2005, 3(3), 159-67.

The class of real closed fields having JEP and AP implies the same for the class OF of ordered fields. For any regular cardinal λ, the family of real closed, Archimedean complete ordered fields of confinality λ is cofinal in OF. Therefore any subclass of OF containing that family has JEP and AP. E.g. either of the classes of Scott complete, Archimedean complete, non-rigid, p-real closed (p a positive integer) ordered fields or, those of cofinality λ or < ≤ has JEP and AP. Observing AP for Archimedean ordered fields, the question is raised whether the class λArchimedean ones has JEP or AP. Variants of JEP and AP by restricting the embeddings to be dense or cofinal are also mentioned.

7 ref

024595   Baburaj C;Surendranath M (Dep of Statist, Govt Coll Kasarasod, Kerala-671 123) : An M/M/1 bulk service queue under the policy (a,c,d). Int J agric statist Sci 2005, 1(1-2), 27-33.

In the general bulk service rule (GBSR) the service starts only when a specified number of units are present in the queue and if after completion of a service, the server finds less than the specified number in the queue, he stops service. Here we consider a Markovian bulk service queue with one more control limit. Specifically, the server starts service only when there are 'c' units in the queue and continues to serve even when the queue size is less than 'c' but not less than a secondary limit 'a', after a service completion epoch. The maximum service capacity is assumed to be 'd' (a<60>c<60>d). The Laplace transform of the transient probabilities, explicit expressions for the steady state probabilities and the expected queue length, are obtained. The busy period distribution is considered and expression for the expected busy is also obtained.

1 table, 6 ref

024594   Baburaj C;Jayakumar P (Dep of Statist, Govt Coll Kasaragod, Kerala-671 123) : AN (a, c, d) policy M/M/1 queue with single and batch service. Int J agric statist Sci 2005, 1(1-2), 51-63.

Single server queue rendering two types of service depending on the number of units in the system is considered here. The server serves the customers either one at a time or in batches according to the control limit policy (a, c, d). Specifically, if the number of units in the queue is less than a specified limit c then the server serves a single customer at a time and if the number of units in the queue exceeds the specified limit c, the server adopts batch service and serves a maximum of d units in a batch. When a batch service is started, the server may continue to serve in batches even when the queue size is less than c but not less than a secondary limit a (≥ c), after a service completion epoch. The server begins manual service, if the queue size is less than a. The transient and steady state behaviour of the model is studied and explict expressions for the steady state probabilities of the system states, the expected queue length and the expected busy period are obtained. The optimality problem is also discussed.

1 illus, 5 tables, 8 ref

024593   Babujee J B;Prabhakar Rao N (NO, Easwari Engng Coll, Ramapuram, Chennai-600 089, Email: baskarjee@yahoo.com) : Labellings in diagraph. Math Educ 2005, 39(2), 73-8.

It has been exhibited that all the pendent vertices of the tree are (1, 1) vertex magic. The concept of (1, 1) in degree vertex magic and (1, 1) out degree vertex magic labelling is introduced and studied in different types of directed graphs.

4 illus, 4 ref

024592   Babujee J B (Dep of Math, Rajiv Gandhi Coll of Engng and Technol, Kirumampakkam, Pondicherry-607 402, Email: baskarjee@yahoo.com) : On graph coding. Math Educ 2005, 39(3), 138-41.

A new type of coding system using labelled graphs has been introduced. The notion of fundamental theorem of arthmetic serves as an important tool to develop the concept of graph coding in a new direction.

2 illus, 3 ref

024591   Ares-Gastesi P;Biswas I (Sch of Math, Tata Inst of Fundamental Res, Mumbai-400 005, Email: Pablo@math.tifr.res.in) : The jacobian of a nonorientable klein surface, II. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 51-8.

Investigation of Jacobians of a Klein surface has been continued and an error has been corrected.

5 ref

024590   Ali M;Pal M;WOO J (NO, Ball St Univ, Muncie, Indiana, U.S.A.) : Inference on P (Y <60> X) in generalized uniform distributions. Calcutta Statist Ass Bull 2005, 57(225-226), 35-48.

Estimation and testing of P(Y<60>X), when X and Y follow independent generalized uniform distributions with known shape parameters have been considered.

5 ref

024589   Al Shaqsi K;Darus M (Sch of Math Sci Fac of Sci and Technol, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor D. Ehsan, Malaysia, Email: ommath@hotmail.com) : On a subclass of certain harmonic meromorphic functions. Far East J mathl Sci 2006, 20(2), 207-18.

A new subclass of harmonic meromorphic functions has been introduced. Coefficient bounds, distortion bounds, extreme points, convolution conditions and convex linear combinations for the functions belonging to this class are obtained.

5 ref

024588   Ahmmed S F;Biswas M H A;Uddin M S (Math Disciplne, Khulna Univ, Khulna, 9208, Bangladesh, Email: sfahmmed@yahoo.com) : The effect of applied magnetic field and viscosity of free convection flow from a vertical surface. Bull Calcutta Mathl Soc 2005, 97(5), 381-92.

A two-dimensional natural convection flow of a viscous incompressible and electrically conducting fluid with temperature dependent viscosity past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to nonsimilar boundary layer equation by introducing appropriate transformations and are integrated using the implicit finite difference method. From the simulated results, effect of the viscosity variation parameter, ε, on the surface shear-stress and the surface heat-flux for the fluid appropriate for low Prandtl number are shown and are depicted graphically. Effect of <101 on the viscosity distributions in the boundary layer region is also shown graphically. It is found that increase in the viscosity-variation parameter leads to increases in both the skin-friction and heat transfer.

5 illus, 1 table, 22 ref

024587   Afrouzi G A;Rasouli S H;Sedaghat R (Math Dep Fac of Basic Sci, Manzandaran Univ, Babolsar, Iran, Email: Afrouzi@umz.ac.ir) : Population models with indefinite weight and constant yield harvesting. Far East J mathl Sci 2006, 20(2), 135-41.

The existence of positive solution for the following reaction-diffusion equation {Δu = am(x)u - u² - ch(x), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where a and c are positive constants, Ω is a smooth bounded domain in R^N (N ≥3) with ∂Ω of class C² and connected are studied. The weight m satisfies m ∈ C(Ω) and m(x) ≥ m₀ <62> 0 for x ∈ Ω, also <157><157> m <157><157>_∞ = l <60> ∞ and h : Ω^- → R is a C^α (Ω^-) function satisfying h(x) ≥ 0 for x ∈ Ω, h(x) ≠ 0, max h(x) = 1 for x ∈ Ω and h(x) = 0 for x ∈ δΩ. The existence of the positive solution under certain conditions have been proved.

8 ref

023648   Zhao F Z;Wang T (Dep of Appl Math, Dalian Univ of Technol, Dalian-116 024) : Notes on some Rogers-Ramanujan type identities. J Indian Mathl Soc 2003, 70(1-4), 33-9.

Using a formula given by G.E. Andrews and other knowledge, the authors generalize an identity obtained by I. Gessel and D. Stanton. Further, some new Rogers-Ramanujan type identities are established has been generalized.

6 ref

023647   Zegeye T;Arora S C (NO, , ) : Spectrum of the compression of a slant Toeplitz operator. J Indian Mathl Soc 2003, 70(1-4), 221-8.

A slant Toeplitz operator A_φ with symbol φ in L(T), where T is the unit circle on the complex plane, is an operator where the representing matrix M = (a_ij) is given by a_ij = <193>(φ, z^2i-j<209>, where <193>., .<209> is the usual inner product in L²(T). The operator B_φ denotes the compression of A_φ to H²(T) (Hardy space). It has been proved that the spectrum of B_φ contains a closed disc and the interior of this disc consists of eigenvalues with infinite multiplicity, if T_φ is invertible, where T_φ is the Toeplitz operator on H²(T).

6 ref

023646   Vasuki K R;Shivashankara K (Dep of Math, Acharya Inst of Technol, Soldevanahalli, Chikkabanavara (Post) Hesaragatta Road, Bangalore-560 090) : Some new values for the Rogers-Ramanujan continued fraction. J Indian Mathl Soc 2003, 70(1-4), 87-95.

In his first and lost notebooks, Ramanujan has recorded several values for the Rogers-Ramanujan continued fraction. B.C. Berndt, H.H. Chan and L.-C. Zhang have established all these values on employing some of Ramanujan's eta-function identities. Some new values for the Rogers-Ramanujan continued fraction have been obtained.

18 ref

023645   Thakare K;Maeda S;Waphare B N (NO, , ) : Modular pairs, covering property and related results in posets. J Indian Mathl Soc 2003, 70(1-4), 229-53.

How should one define a modular pair in a general poset? queried Birkhoff, sixty years ago.This open problem satisfac-torily The interesting properties have been obtained concerning covering property, exchange property in a poset with zero. In this context a few counter examples are also supplied. This general study has led to thirteen characterizations of covering property in a lattice with zero. Del-relation and perspectiyity are characterized in posets. The study of atom spaces is extended to posets. Statischness in atomistic posets is characterized. Further, ortho-modular posets are also characterized and an interesting open problem in this context is raised.

4 ref

023644   Stevic S (Matematicki Fakultet, Studentski Trg 16 11000 Beograd, Serbia, Yugoslavia, Email: sstevo@matf.bg.ac.yu) : Composition operators on the generalized Bergman space. J Indian Mathl Soc 2003, 70(1-4), 215-9.

Let φ: U → U be analytic and nonconstant and w be convex modulus function. Then the composition operator T_φ(f) = f°φ on the generalized weighted Bergman space B_w, ω (U) satisfies the inequality: ||T_φ(f)||B_{w, ω} ≤ C||f||B_{w, ω} for some C independent of f, where ||f||B_{w, ω} = ƒ_U w(|f(z)|ω(z) dm(z).

11 ref

023643   Stevic S (Matematicki Fakultet, Studentski Trg 16, 11000 Beograd, Serbia, Yugoslavia, Email: sstevic@ptt.yu) : Note on isolation amongst the composition operators on the generalized weighted Bergman spaces. J Indian Mathl Soc 2003, 70(1-4), 67-71.

It has been proved that every composition operator is non-isolated in Comp (B_w ω) endowed with strong operator topology, where B_w, ω(U)={f ∈ H(U) <157> ƒ_u w(<157>f(z)<157>)ω (z) dm(z) <60> + ∞D}.

18 ref

023642   Soner N D;Chaluvaraju B;Janakiram B (Dep of Math, Univ of Mysore, Manasagangothri, Mysore-570 006) : The double global domination number of a graph. J Indian Mathl Soc 2003, 70(1-4), 191-5.

Let G = (V, E) be a graph. A double dominating set D of G is a double global dominating set, if D is also a double dominating set of G. The double global domination number γdg(G) of G is the minimum cardinality of a double global dominating set of G. A study on this new parameter is initiated.

7 ref

023641   Sahai V;Srivastava S (Dep of Math & Astr, Lucknow Univ, Lucknow-226 007, Email: vsahai@hotmail.com) : On models of q-representations of sl (2, C) and q-Euler integral transformation. J Indian Mathl Soc 2003, 70(1-4), 73-85.

Two variable models of irreducible q-representations of the Lie algebra sl (2, C) have been constructed. The q-Euler integral transformation is used to transform the models in the form of q-difference dilation operators. These models are further used to obtain some interesting identities.

14 ref

023640   Rana S S;Dubey Y P;Gupta P (Dep of Math and Computer Sci, R.D. Univ, Jabalpur-482 001) : Convergence of deficient quintic spline interpolation. J Indian Mathl Soc 2003, 70(1-4), 41-8.

A precise estimate of error bounds has been obtained for deficient quintic spline interpolant matching the given function values at the mesh points and at intermediate points between the successive mesh points.

11 ref

023639   Pujar S S (NO, Coll of Engng, Kopargaon-423 603) : Lorenzian para sasakian manifolds with an LP contact non-metric quarter symmetric phi-connection. J Indian Mathl Soc 2003, 70(1-4), 203-7.

In a LP-Sasakian manifold M of dimension n (n = 2m+ 1, m ≥ 1), an affine connection, called an LP-contact non-metric quarter symmetric φ-connection has been introduced. It is shown that if the LP-Sasakian manifold of dimension n ≥ 3 is Einstein and the curvature tensor of this new affine connection vanishes, then M is conformally flat if and onlyif it is flat, further some conditions are also obtained for M to be conformally flat. Finally a necessary condition is obtained for LP-contact mantold which admits LP-contact non-metric quarter symmetric φ-connection to be Sasakian.

6 ref

023638   Pathak R S;Tripathi S M (Dep of Math, Banaras Hindu Univ, Varanasi-221 005) : A class of Pseudo-differential operators involving Hankel convolutions. J Indian Mathl Soc 2003, 70(1-4), 145-56.

A pseudo-differential operator h^v_μ,a involving Hankel transforms, which maps the Zemanian space H_μ into H_v, is defined. An integral representation for h^v_μ,a is given an L¹-boundedness result is obtained.

9 ref

023637   Pant R P;Pant V;Lohani A B (Math Dep, Kumaon Univ, D.S.B. Campus, Nainital-263 002, Email: vyomeshpant@yahoo.co.in) : Reciprocal continuity and common fixed points. J Indian Mathl Soc 2003, 70(1-4), 157-67.

While studying the fixed point theorems for four mappings A, B, S and T(say) a Meir-Keeler type (ε, δ) contractive condition alone is not sufficient unless some additional condition is imposed on δ or a φ-contractive condition is also used together with it. Two common fixed theorems have been proved assuming a Meir-Keeler type (ε, δ) contractive condition together with a plane contractive condition or Lipschitz type analogue of a plane contractive condition. however, without imposing any additional restriction on δ or having a φ-contractive condition used together with it. Simultaneously, also shows that none of the mappings involved in the following theorems is continuous at their common fixed point. Thus not only the Meir-Keeler type and Boyd-Wong type fixed point theorems, but also provide one more answer to the problem on the existence of a contractive definition, which is strong enough to generate a fixed point but does not force the map to be continuous at the fixed point. The result extends the result of Pant.

24 ref

023636   Pant R P;Jha K;Lohani A B (Dep of Math, Kumaon Univ, D.S.B. Campus, Nainital-263 002) : Generalization of a Meir-Keeler type fixed point theorem. J Indian Mathl Soc 2003, 70(1-4), 57-65.

A fixed point theorem has been obtained for a sequence of mappings satisfying a weak form of Meir-Keeler type (ε, δ)-contractive condition together with a φ-contractive condition without assuming any additional conditions on δ and φ. The theorem extends and unifies the Meir-Keeler type and a φ-contractive type fixed point theorems.

17 ref

023635   Pant R P (NO, , ) : Fixed point theorems and dynamics of functions. J Indian Mathl Soc 2003, 70(1-4), 135-43.

A common fixed point theorem under a new contractive condition which is independent of the known contractive. Definitions has been obtained. In the second fixed point theorem the dynamics of a class of functions induced by real numbers has been studied and then applied. The result is then applied to obtain general tests for divisibility of numbers.

9 ref

023634   Pai D V (Math Dep, Indian Inst of Technol, Powai, Mumbai-400 076) : On well-posedness of some problems in approximation. J Indian Mathl Soc 2003, 70(1-4), 1-4.

Aimes at synthesizing some results on best approximants and restricted Chebyshev centres from the perspective of well-posedness of these problems. The related well-posedness notions for minimization problems are surveyed. This leads one, in particular, to a reinterpretation of generic uniqueness results for some problems in approximation from the angle of generic well-posedness.

38 ref

023633   Mahadeva Naika M S (Dep of Stud in Math, Univ of Mysore, Manasagangotri, Mysore-570 006, Email: msmnaika@rediffmail.com) : P-Q Eta-function identities and computation of Ramanujan-Weber class invariants. J Indian Mathl Soc 2003, 70(1-4), 121-34.

In his 'lost' notebook, Ramanujan recorded several P-Q identities. Obtains some new P-Q eta-function identities akin to Ramanujan's and, employ them to compute some new values for Ramanujan-Weber class invariant.

12 ref

023632   Kara H;Karakaya V (Art and Sci Fac Dep of Math, Yuzuncu Yil Univ, Zeve Campus-65080 Van/Turkey) : On some new sequence spaces involving invariant means. J Indian Mathl Soc 2003, 70(1-4), 49-55.

Related inclusions of the sequence spaces defined by invariant convergence sequences and some topological properties have been investigated.

6 ref

023631   Jain V K (Dep of Math, I.I.T. Kharagpur, Kharagpur-721 302) : On the zeros of a polynomial. J Indian Mathl Soc 2003, 70(1-4), 209-13.

For a polynomial P(z) = ∑^n-1_j=0 a_jzⁿ, of degree n (≥ 3), with complex coefficients, where not all of the numbers a₀,a₁,...,a_n-s (S ≥ 3), are equal to zero, a closed circular disc <157>z + 1/2 a_n-1<157> ≤ 1/2<157>a_n-1<157> + (<157>a_n-2<157>^1/2 + <157>a_n-3<157>^1/3 + ... + <157>a_n-s+1|^1/(s-1) + (ⁿ_{j = s}<157>a_n-j<157>α^j-s )^1/2, where α = 1/max_{s<131>j≤n <157>an-j<157>^1/j) containing all its zeros has been obtained. The result is best possible and gives, in many cases, better upper bounds (for moduli of zeros of P(z)), than those obtainable by other results of similar type.}

3 ref

023630   Jain V K (NO, , ) : On maximum modulus of polynomials with zeros in the closed exterior of a circle. J Indian Mathl Soc 2003, 70(1-4), 179-83.

Let f(z) be an arbitrary entire function and M(f, r) = max |f(z)|. If p(z) is a polynomial of degree n, having no zeros in <157>z<157> <60> k ≤ 1, with M(p,1) = 1, then for k = 1, it is known that. M(p,R) ↑ Rⁿ + 1/2, R <62> 1. the case k <60> 1 has been considerd and have obtained M (p,R) ≤ (Rⁿ + 1/kⁿ)/1 + kⁿ , r ≥ 1/k². provided |p'(z)| and |p'(z/k²)| attain their maximum at the same point on the circle |z| = 1. The bound is better than the only known bound.

6 ref

023629   Imdad M;Santosh Kumar (Dep of Math, Aligarh Muslim Univ, Aligarh-202 002, Email: mid@bharatmail.com) : Common fixed point theorems for four nonself mappings. J Indian Mathl Soc 2003, 70(1-4), 97-109.

Using suitable conditions of weak commutativity fixed point theorems have been proved for two pairs of nonself-mappings which generalize earlier known results doe to Rhoades and Som et at. An illustrative example and application are also discussed.

12 ref

023628   Dheena P;Karthy K (Dep of Math, Annamalai Univ, Annamalai Nagar-608 002) : On regular laminated near-rings. J Indian Mathl Soc 2003, 70(1-4), 197-201.

5 ref

023627   Chugh R;Savita (Dep of Math, Maharshi Daynand Univ, Rohtak-124 001) : Common fixed points of four R-weakly commuting mappings. J Indian Mathl Soc 2003, 70(1-4), 185-9.

Proves a common fixed point theorem, from the class of compatible continuous mappings to a larger class of mappings having non-compatible and pointwise R-weakly commuting mappings which generalizes the results of Singh and Chauhan.

7 ref

023626   Chugh R;Sanjay Kumar (Dep of Math, Maharshi Dayanand Univ, Rohtak-124 001) : Minimal commutativity and common fixed points. J Indian Mathl Soc 2003, 70(1-4), 169-77.

Common fixed point theorem, from the class of compatible continuous mappings to a larger class of mappings having non-compatible and discontinuous mappings, which generalizes the result of Jungck, Fisher, Kang and Kim, Jachymski, Rhoades and Pant has been proved.

15 ref

023625   Chakraborty N D;Sahu M;Sen B (Dep of Math, The Univ of Burdwan, Burdwan-713 104) : Pettis-type spaces for a bounded family of measures. J Indian Mathl Soc 2003, 70(1-4), 111-9.

Let (Ω, Σ, μ) be a probability space and let N C ca (Σ) be a bounded family of positive measures and X be a Banach space. Let P₁(N, X) be the Pettis-type spaces with respect to N. Assuming that X is weakly sequentially complete, we prove the completeness of P₁(N, X) with respect to the Pettis semi-norm. Also the "Vitali's convergence theorem, Lebesgue dominated theorem and a necessary and sufficient condition for a function to belong to P₁(N, X) have been proved.

11 ref

023624   Banerji P K;Shenan G M (Math Dep, JNU Univ, Jodhpur-342 005, Email: banerjipk@yahoo.com) : Applications of fractional derivative to study the mapping properties of starlike functions and the convexity of analytic functions-II. J Indian Mathl Soc 2003, 70(1-4), 25-32.

A Function is introduced using certain modified fractional derivative operator and the convolutions of three functions, an-alytic in the unit disc, are mentioned. Also investigated are the characterization properties of the said function in the open unit disc, in order to establish its belongingness to some subclasses of analytic functions and finally, some associations of the said properties with the convolution are mentioned.

9 ref

023623   Agarwal A K (Cent for Advd Study in Math, Panjab Univ, Chandigarh-160 014, Email: aka@pu.ac.in) : Extension of Euler's theorem. J Indian Mathl Soc 2003, 70(1-4), 17-24.

Euler's classical partition identity "The number of partitions of an integer v into distinct parts is equal to the number of its partitions into odd parts" is extended to eight more combinatorial functions. This results in a 10-way combinatorial identity which implies 45 combinatorial identities in the usual sense. Euler's identity is just one of them.

12 ref

022521   Swain P;Sherin Raj T P (Dep of Statist and Demography, Natn Inst of Hlth and Family Welfare, New Dehli) : Demography of ageing in India: state and district level analysis. Indian J Gerontol 2005, 19(3), 327-42.

Population of India is currently moving toward an old age structure and it is certain that there will be rapid growth in the elderly population in the near future. Inter-states and inter-districts differentials of elderly/aged population of India (defined in terms of those 60 and above) based on Census 2001 published by Registrar General of India. Urban-rural differentials, sex differentials, and old-age dependency ratio among the elderly population. According to census 2001, India accounts for 7.4% elderly population i.e., 76.6 million. The highest proportion of elderly among stales and union territories are located in Kerala (10.5%) and lowest proportion was found in Dadra & Nagar Haveli (4.0%). The percentage is higher in the southern slates (Kerala, Tamil Nadu, Karnataka and Andhra Pradesh), Himachal Pradesh, Goa, Maharasthra, Haryana, Punjab, Uttaranchal and Pondicherry than the Indian average. The evolution of old age structure changes the balance of men and women in the whole population. Sex ratios of older age group are higher in those states. There are 168 districts where elderly population is more than 8%. However, district level analysis show that there are 37 districts in India where more than 10 percent elderly are living there. The quantum of population ageing has important implications for government policies such as pension schemes old age homes, health care, and economic growth.

5 illus, 6 tables, 8 ref

022520   Prajapati D R;Mahapatra P B (Dep of Mechanical Engng, Punjab Engng Coll, Chandigarh-160 012, Email: praja_3000@yahoo.com) : History of observed samples: how much affects the ARL of X control charts. J scient ind Res 2006, 65(4), 335-43.

History of observed samples upon average run length (ARL) of X chart, when process shift takes place, because the performance characteristic of a control chart is measured in terms of ARL. The concept of proposed x chart is based upon the Chi square distribution; in which a Statistic, 'U' has been defined and calculated for the product of sample size (n) and history (H). ARL values of proposed chart are compared to the standard Shewhart chart, considering the control limits as ± 2σ and confidence level (CL) as 95%. The history of previous samples is considered to evaluate U and comparing it with the maximum permissible value of standard Chi Square Table to evaluate the status of running process. Sample sizes are taken as 4, 5, 6, 8 and 10, while previous history is considered from 4 to 10. For smaller shift (0.1-0.5σ), the length of history was found to affect ARL of Y chart to some extent, but for moderate and large shifts (<62>0.5σ), the effect of length of history is negligible.

8 illus, 7 tables, 15 ref

022519   Kamath S G (Dep of Math, Indian Inst of Technol Madras, Chennai-600 036, Email: kamath@iitm.ac.in) : Energy-momentum tensor, the trace identity and the Casimir effect. Pramana J Phys 2006, 66(2), 345-60.

The trace identity associated with the scale transformation x^μ → x'^μ = e^-ρx^μ on the Lagrangian density for the noninteracting electromagnetic field in the co-variant gauge is shown to be violated on a single plate on which the Dirichlet boundary condition A^μ(t,x¹, x², x³ = -a) = 0 is imposed. It is however respected in free space, i.e. in the absence of the plate. These results reinforce assertions in an earlier paper where the same exercise was carried out using the Lagrangian density for the free, massive, real scalar field in 2 + 1 dimensions.

11 ref

022518   Chanda N K;Chao D;Mir U A;Bhatia H (Dep of Psychology, Univ of Delhi, Delhi-110 007) : Structure of social network of the elderly in Delhi. Indian J Gerontol 2005, 19(3), 307-26.

Nature and importance of social network among the old people. Social network especially for the old has tremendous meanings for their existence. The basic substance of all social networks is persons and their social relations. Understanding the nature and size of social network from where one expects supports to maintain relationships which changed through aging process is becoming prominently important for any gerontologists. Meaningful, genuine and quality of relationships within the domain of social networks considered important for the elderly. To study the welfare of this disadvantaged group of our society, understanding their social world and their networks is imperative. How many people share their concerns with ? What types of people and their importance, content of interaction, frequency of interaction, accessibility and approachability are some of the important issues. Factors influencing the size of social network are gender, marital status, age level, family type, etc. Findings of this study may help social scientists, and care-givers to identify the determinants of the elderly perception of support system which is dependent on social network, demographic variables, social involvement and personality type. This study conceptualizes those three dimensions which determine elderly, perception of social support : (I) willingness of others (members of the society) to listen when they want to talk, (2) level of caring by the fellow members provided to them, and (3) concerns of others to provide support in times of sickness or problematic situations.

3 illus, 4 tables, 25 ref

021585   Zhang P;Zhao K (NO, Inst of Math Zhejiang Sci-Tech Univ, Hangzhou 310018, People's Republic of China) : Commutators of integral operators with variable kernels on hardy spaces. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 399-410.

Let T Ω,α 0 ≤ α N) be the singular and fractional integrals with variable kernel Ω (x, z), and [b, T_Ω,α] be the commutator generated by TΩ, α and a Lipschitz function b. Study the boundedness of [b,TΩ,α] on the Hardy spaces, under some assumptions such as the L^r-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators TΩ, α (0 ≤ α <60>). The smoothness conditions imposed on Ω are weaker than the corresponding known results.

30 ref

021584   Xue L (Math Dep, Bradley Univ, Peoria, Illinois 61625, USA, Email: lxue@bradley.edu) : On azumaya invariant subrings of a Galois extension. Int J mathl Sci 2005, 4(2), 217-24.

Let B be a ring with 1, C the center of B, G a finite automorphism group of B, and B^G the set of elements in B fixed under each element in G. Then it is shown that if B is a commutator Galois extension with Galois group G, then B is an Azumaya C-algebra if and only if B^G is an Azumaya C^G-algebra. This generalizes F. DeMeyer's result for center Galois extensions. A Galois H-separable extension of an Azumaya algebra is also characterized.

10 ref

021583   Xu L;Mazumdar S;Greer P J;Price J (NO, Merck & Co. Inc., USA) : Stimulant-induced spatial temporal patterns in pet data : illustrations using SPM, MANACOVA-CVA and PLS. Calcutta Statist Ass Bull 2005, 56(Spl), 209-30.

Functional brain images are extraordinarily rich data sets that reflect brain function such as cerebral blood flow. These images are widely applied to study brain activity after drug administration or in response to perceptual and cognitive stimuli. Positron Emission Tomography (PET) constitutes one important modality that provides functional brain images. Spatial and temporal patterns in brain activities captured from these images have helped to better understand brain dysfunction in disease and aid in diagnosis and treatment of diseases including neurogenerative disorders. As PET provides maps consisting of average levels of activity for cuboidal voxels of tissue, it is a substantial analytic challenge to integrate the temporal, spatial and statistical signals making up these data. The paper presents a comparative analysis of three voxel-based methods for characterization of spatial-temporal patterns provided by PET images of cerebral blood flow. The methods are statistical parametric mapping (SPM) providing a voxel-wise brain map of a seleted statistic, multivariate analysis of covariance jointly with canonical variate analysis (MANCOVA-CVA) identifying regions of the brain that are most responsible for global statistical significance and partial least squares (PLS) that uses a path modeling technique with latent variables for dimension redunction.

7 illus, 17 ref

021582   Tu D;Chen J;Shi P;Wu Y (NO, Natn Cancer Inst of Canada Clin Trials Grp Queen's Univ, Kingston, ON K7L 3N6, Canada, Email: dtu@ctg.queensu.ca) : Bartlet type correction for Rao's score test in Cox regression model. Sankhya 2005, 67(4), 722-35.

Gu and Zheng (1993) established a Bartlett adjustment for the partial likelihood ratio test in the Cox proportional hazards regression model. It is known that the same method of adjustment cannot be used to improve the accuracy of the test statistic derived by Rao's score method. The method of Cordeiro and Ferrari (1991) is used to derive a Bartlett type correction for the score test in the Cox proportional hazards regression model. As a special case, a test which is more accurate than the popular log-rank test is obtained.

1 table, 17 ref

021581   Tripathy B C;Mahanta S;Et M (Math Sci Div, Inst of Advd Study in Sci and Technol, Paschim Boragaon; Garchuk, Guwahati-781 035, Email: tripathybc@yahoo.com) : On generalized lacunary difference vector valued paranormed sequences defined by orlicz functions. Int J mathl Sci 2005, 4(2), 341-55.

Lacunary paranormed difference sequence spaces [N_θ, M, Δ^m, p, q]₀, [N_θ, M, Δ^m, p, q]₁ and [N_θ, M, Δ^m, p, q]_∞, on generalizing the sequence space [N_θ, M, p], using m^th-difference and seminorm have been introduced. Different properties have been studied and some inclusion relations involving the spaces [N_θ, M, Δ^m, p, q]₀, [N_θ, M, Δ^m, p, q]₁ and [N_θ, M, Δ^m, p, q]_∞, the Cesaro summable and the strongly Cesaro summable methods have been obtained.

17 ref

021580   Sudo T (Math Sci Dep Fac of Sci, Univ of the Ryukyus, Nishihara, Okinawa-903 0213, Japan, Email: sudo@math.u-ryukyu.ac.jp) : K-theory of continuous fields of the generalized furstenberg transformation group C<. Int J mathl Sci 2005, 4(2), 193-9.

K-theory of continuous fields of the generalized Anzai and Furstenberg transformation group C^*-algebras has been studied. Moreover, the case of the generalized quantum Anzai and Furstenberg transformation group C^*-algebras has been considered.

7 ref

021579   Som T (Math Dep, Assam Univ, Silchar-788 011, Email: som_tanmoy@yahoo.co.in) : Some fixed point results in 2-Banach space. Int J mathl Sci 2005, 4(2), 323-8.

Generalizations of fixed point theorems of Cho et.al. have been dealt with for a single mapping to the common fixed point and coincidence point results for a pair of non-linear mappings in 2-Banach space, which in turn also extend the results of Chang, Xiong et.al. and Zhao.

12 ref

021578   Sharma k k;Singh B;Rathi S (NO, C.C.S. Univ, Meerut) : On the robustness of the reliability characteristics of a discrete lifetime model in view of prior variations. IAPQR Trans 2005, 30(1), 1-15.

Prior distributions represent random variations in the parameters of lifetime distributions. this prior knowledge is updated by using experimental data in the bayesian framework. However, updating the basic lifetime distribution is respect of these parametric variations is another important aspect to be considered in reliability analysis. Uning this concept, the study considers the analysis of the reliability characteristics of a discrete lifetime distribution when prior variations in its parameter are suspected.

7 ref

021577   Sans W;Stubner D;Sen S;Zhai X (NO, Inst of Appl Math and Statist, Wurzburg, Germany) : Improving the variability function in case of a uniform distribution. IAPQR Trans 2005, 30(1), 1-15.

The set of all probability measures suitable for describing real worked random structures is divided into disjoint families according to the complexity of the random structure. A more complex structure needs more information to select an appropriate probability distribution. Once the family has been identified by easy-to-check qualitative properties, the family member has to be determined using quantitative information. A general method is developed for shortening the selected range of variability of a random variable X and applied to the family of uniform probability measures.

3 tables, 12 ref

021576   Sabnis S V;Nair H (NO, IIT, Bombay) : Reliability test plan for parallel systems having stochastic failure rates. IAPQR Trans 2005, 30(1), 33-42.

Consider a parallel system consisting of k components with lifetimes assumed to be independent random variables having exponential distribution with parameters λ₁,J= 1,2....k. This paper generalizes the construction of component level reliability test plans for parallel systems in the sense that λ'₁s are assumed to be random variables having a specific distribution.

2 tables, 10 ref