ISA

Bounded weighted composition operators on the bloch space in the unti ball
Zhang T

008046   Zhang T (Mathematics Dep, Nanjing Univ of Information Science and Technology, Nanjing, Jiangsu-210 044, Peoples' Republic of China, Email: ztz@nuist.edu.cn) : Bounded weighted composition operators on the bloch space in the unti ball. Indian J pure appl Math 2007, 38(4), 253-8.

Proves a sufficient and necessary condition for a weighted composition operator of the Bloch space on the unit ball of high dimension to be bounded.

6 ref

Lemma of musielak-orlicz sequence space l Φ
Zhang T

008045   Zhang T (Mathematics Dep, TongJi Univ, ShangHai-200 092, P. R. China, Email: shuxuezhang@gmail.com) : Lemma of musielak-orlicz sequence space l Φ. Far East J mathl Sci 2007, 24(3), 313-19.

Lemma of Musielak-Orlicz sequence space lπ has been proved.

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On-non developable ruled surfaces in Euclidean 3-spaces
Yoon D W

008044   Yoon D W (Mathematics Dep, Education and RINS, Gyeongsang National Univ, Chinju 660-701, Korea, Email: dwyoon@gsnu.ac.kr) : On-non developable ruled surfaces in Euclidean 3-spaces. Indian J pure appl Math 2007, 38(4), 281-90.

Authors classify ruled surfaces in a 3-dimensional Euclidean space satisfying some algebraic equations in terms of the second Gaussian curvature, the mean curvature and the Gaussian curvature.

1 illus, 15 ref

Local spectral properties of point spectrum preserving linear maps
Yoo J K

008043   Yoo J K (Liberal Arts and Science Dep, Chodang Univ, 419 Sungnamri Muangun 534-701 Chonnam, Korea, Email: jkyoo@chodang.ac.kr) : Local spectral properties of point spectrum preserving linear maps. Far East J mathl Sci 2007, 24(3), 447-52.

Proved that if π : τ(X) → τ(X) is a point spectrum surjective linear mapping, then the following are preserved under π: spectrum, single valued extension property, analytic residuum, injective operators in both directions and finite ascent. Moreover, ππ(T)(Ax) ⊆ σ(X) for every x and AET(F) π Eπ(T) (F) for all closed F ⊆ C and for some invertible A ∈ τ(X).

9 ref

On a very particular class of Ramanujan Nagell type equations
Walsh P G

008042   Walsh P G (Mathematics Dep, Ottawa Univ, 585 King Edward St. Ottawa, Ontario, Canada K1N 6N5, Email: gwalsh@mathstat.uottawa.ca) : On a very particular class of Ramanujan Nagell type equations. Far East J mathl Sci 2007, 24(1), 55-8.

Simple algorithm that will efficiently compute all integer solutions to Ramanujan-Nagell type equations x<^>2 + D = y<^>2n, for D <62> 0 in any reasonable range of interest has been described. For example, we perform 12 a small computation to solve the equation for all D <60> 10<^>12. The elementary method we provide avoids the technical machinery (the structure of class groups of certain associated rings of integers of quadratic fields) used in some recent work on this equation in [5].

6 ref

Uniform convergence with certain linear operators
Walczak Z;Gupta V

008041   Walczak Z;Gupta V (Institute of Mathematics, Poznan Univ of Technology Piotrowo 3A, 60-965 Poznan, Poland, Email: zwalczak@math.put.poznan.pl) : Uniform convergence with certain linear operators. Indian J pure appl Math 2007, 38(4), 259-69.

Considers some linear operators in weighted spaces of functions of one variable and study approximation properties of these operators, including theorems on the degree of approximation.

20 ref

Categorical abstract algebraic logic: structure systems and Llos'theorem
Voutsadakis G

008040   Voutsadakis G (School of Mathematics and Computer Science, Lake Superior State Univ, Sault Sainte Marie MI 49783, U.S.A., Email: gvoutsad@lssu.edu) : Categorical abstract algebraic logic: structure systems and Llos'theorem. Far East J mathl Sci 2007, 24(1), 73-98.

Following work on abstracting the concept of an algebra to that of an algebraic system and of an ordered algebra to that of an ordered algebraic system, the notion of a first-order structure is abstracted to obtain structure systems. The algebraic part of a structure system is an algebraic system rather than an algebra as is the case in the ordinary first-order structures. This abstraction is accompanied by the introduction of a suitably modified notion of a countable first-order language with the aim of developing a first-order model theory of structure systems and, therefore, axiomatizing classes of structure systems. After introducing some basic constructions on structure systems, including the ultraproduct construction, an analog of Los' Ultraproduct Theorem is provided for structure systems.

33 ref

The quantum zeno effect - watched pots in the quantum world
Venugopalan A

008039   Venugopalan A (NO, Centre for Philosophy and Foundations of Science Darshan Sadan, E-36 Panchshila Park, New Delhi-110 017, Email: venugopalan@gmail.com ) : The quantum zeno effect - watched pots in the quantum world. Resonance 2007, 12(4), 52-68.

In the 5th century BC, the philosopher and logician Zeno of Elea posed several paradoxes which remained unresolved for over two thousand five hundred years. In recent times, the Zeno effect made an intriguing appearance in a rather unlikely place - a situation involving the time evolution of a quantum system which is subject to 'observations' over a period of time. In 1977, B Misra and EGG Sudarshan published a paper on the quantum Zeno effect, called "The Zeno's paradox in quantum theory". Their fascinating result revealed the bizarre workings of the quantum world. The quantum Zeno effect is described and a brief outline of some of the work following Misra and Sudar-shan's paper is given.

4 illus, 6 ref

Peristaltic transport and heat transfer in a vertical porous tube
Vajravelu K;Radhakrishnamacharya G; Radhakrishnamurthy V

008038   Vajravelu K;Radhakrishnamacharya G; Radhakrishnamurthy V (Mathematics Dep, Central Florida Univ, Orlando, F L 32816, U S A, Email: vajravel@pegasus.cc.ucf.edu) : Peristaltic transport and heat transfer in a vertical porous tube. Indian J Math mathl Sci 2007, 3(1), 17-28.

Peristaltic transport of a Newtonian fluid, with heat transfer, in a vertical porous axisymmetric tube under long wave length approximation is considered. A closed form solution is obtained as an asymptotic expansion in terms of free convection and porosity parameters. Expressions for temperature, the pressure flow relationship, and the heat transfer coefficient at the tube wall are derived. It is observed that pressure drop increases as the amplitude ratio increases. Further, it is noticed that the, mean flux increases by about 8 to 10 percent as the free convection parameter increases from 1 to 2 for given values of other parameters.

8 illus, 4 tables, 14 ref

Strongly feebly compact spaces
Thakkar D K;Viradia R

008037   Thakkar D K;Viradia R (Mathematics Dep, Saurashtra Univ, Campus University Road, Rajkot-360 005) : Strongly feebly compact spaces. Indian J Math 2007, 49(2), 253-62.

Strongly feebly compact spaces have been defined in this paper. Their characterizations using functions having strongly closed graphs, strongly subclosed graphs have been obtained. It is proved that a Hausdorff space Y is strongly feebly compact if and only if for each first countable space X and for each bijection g : X → Y with strongly closed graph is weakly continuous. Further it is proved that a space X is strongly feebly compact if and only if each countable filter base on X is θ-adherent convergent. An example of a feebly compact space which is not strongly feebly compact space is given. Some other characterizations of strongly feebly compact spaces have also been obtained.

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Complex symplectic geometry characterization for self-adjoint extensions of hamiltonian differential operator
Sun S;Han Z;Chen S

008036   Sun S;Han Z;Chen S (School of science, Jinan Univ, 250022, Peoples' Republic of China, Email: sshrong@163.com) : Complex symplectic geometry characterization for self-adjoint extensions of hamiltonian differential operator. Indian J pure appl Math 2007, 38(4), 331-40.

Gives complex symplectic geometry characterization for symmetric extensions and self-adjoint extensions of Hamiltonian differential operator.

8 ref

Stable rank of the reduced c*-algebras of multi-amalgams of discrete groups
Sudo T

008035   Sudo T (Mathematical Sciences Dep, Faculty of Science, Ryukyus Univ, Nishihara, Okinawa 903-0213, Japan, Email: sudo@math.u-ryukyu.ac.jp) : Stable rank of the reduced c*-algebras of multi-amalgams of discrete groups. Far East J mathl Sci 2007, 24(3), 377-83.

Stable rank of the reduced group C* algebras of multi-amalgams of discrete groups have been shown over their intersections that are finite groups like SLn (Z) (n <62> 2) is l.

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Some novel class of analytic functions involving generalized fractional calculus operators
Srutha Keerthi B;Adolf Stephen B;Gangadharan A;Sivasubramanian S

008034   Srutha Keerthi B;Adolf Stephen B;Gangadharan A;Sivasubramanian S (Applied Mathematics Dep, Shri Venkateswara College of Engineering Pennalur, Chennai-602 105) : Some novel class of analytic functions involving generalized fractional calculus operators. Indian J Math 2007, 49(2), 129-38.

8 ref

Godel's proof II. Semantics of first order theory and Hilbert's program
Srivastava S M

008033   Srivastava S M (Stat-Math Unit, Indian Statistical Institute 203, BT Road, Kolkata-700 108, Email: smohan@isical.ac.in) : Godel's proof II. Semantics of first order theory and Hilbert's program. Resonance 2007, 12(3), 35-46.

Basic aspects of model of a theory are reviewed. The well known Hilbert's program, that sought to set the agenda for 20th century mathematics, 4 is presented.

4 ref

Godel's proof III. Incompleteness theorems
Srivastava S M

008032   Srivastava S M (NO, Stat-Math Unit Indian Statistical Institute 203, BT Road, Kolkata-700 108, Email: smohan@isical.ac.in) : Godel's proof III. Incompleteness theorems. Resonance 2007, 12(5), 71-84.

After presenting the technique developed by Godel to examine questions about a theory such as Number Theory, Set Theory by the theory itself, presents the surprising Incompleteness Theorems of Godel.

4 ref

Finite capacity multiserver Poisson input queue with interdependent interarrival and service times and controllable arrival rates
Srinivasan A;Thiagarajan M

008031   Srinivasan A;Thiagarajan M (Mathematics P.G. & Research Dep, Bishop Heber College (Autonomous) Tiruchirappalli, Tamilnadu-620 017, Email: mathsrinivas@yahoo.com) : Finite capacity multiserver Poisson input queue with interdependent interarrival and service times and controllable arrival rates. Bull Calcutta Mathl Soc 2007, 99(2), 153-62.

Finite capacity multiserver Poisson input queue with interdependent interarrival and service times and controllable arrival rates is considered. The steady state solutions and the system characteristics are derived and analyzed for this model.

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Characterization of distributive lattice in a space 'x'
Srinivas K V R

008030   Srinivas K V R (NO, G. V. P. Engineering college, Visakhapatnam-41) : Characterization of distributive lattice in a space 'x'. Indian J Math mathl Sci 2007, 3(1), .

Concept of codistributive pair was introduced by Repritskii (2) in a general lattice. He also introduces the concept of d-prime ideal. K.V.R. Srinivas (5) obtained a characterization for a lattice to be distributive interms of d-prime ideals. A characterization for a lattice to be distributive ina space 'X' of d-prime ideals together with the well known topology {Xa : a∈L}. where Xa = {P ∈ X: a∈P} as an open sub-base is obained.

6 ref

On integers with prime factors restricted to certain congruence classes
Spearman B K;Williams K S

008029   Spearman B K;Williams K S (NO, , ) : On integers with prime factors restricted to certain congruence classes. Far East J mathl Sci 2007, 24(2), 153-61.

A asymptotic formula is given for the sum ∑*En≤x n<^>a, where a ≥-1, and the asterisk indicates that the summation is restricted to those positive integers n whose prime factors belong to certain congruence classes.

5 ref

Conductor of Lecacheux's parametric family of cyclic quintic fields
Silvester A K;Spearman B K;Williams K S

008028   Silvester A K;Spearman B K;Williams K S (Mathematics and Statistics Dep, Okanagan Univ of British Columbia, Kelowna, B.C. Canada V1V 1V7, Email: mascdman@canada.com) : Conductor of Lecacheux's parametric family of cyclic quintic fields. Indian J pure appl Math 2007, 38(4), 231-41.

Formula for the conductor of Lecacheux's parametric family of cylic quintic fields is given.

7 ref

Communication network with random phases of transmission
Shvarma P S;Srinivasa Rao K;Prasad Reddy P V G D

008027   Shvarma P S;Srinivasa Rao K;Prasad Reddy P V G D (Computer Science Dep, Engineering College GITAM, Visakahapatnam, Email: vermaps@yahoo.com) : Communication network with random phases of transmission. Indian J Math mathl Sci 2007, 3(1), .

Communication network have been developed analysed with the assumption that the arrival of request in a communication network follows a poisson process and the transmission through the transmitter is in phases. Each phase is having exponentially distributed processing times. The number of phases required by a packet is random and follows a Binomial distribution with parameters n and p. where n is the maximum number of phases in the transmitter, and p is the Probability that the transmission of the packet terminates at a particular phase. Then the inter transmission times required by the packets in the transmitter follows a compound Erlangian ∧ Binomial distribution. Assuming that the network is in steady state, the probability generating function of the buffer size distribution, the average number of packets in the buffer, the throughput of the communication network, the average delay time distribution and average delays etc., are derived and analyzed with respect to the parameters. This communication network gives closure approximation than the communication network with Erlangian transmission times having fixed number of phases. Sensitivity of the network with respect to the parameters is also discussed. This network is useful for performance evaluation of ATMs, Communication networks, CPU scheduling etc,.

2 tables, 18 ref

Multiple objective model for nurse scheduling
Sharma P K;Jain M

008026   Sharma P K;Jain M (Mathematics Dep, D. A. V. College, Dehradun, Uttaranchal) : Multiple objective model for nurse scheduling. Indian J Math mathl Sci 2007, 3(1), 7-15.

Computerized nurse-scheduling model is developed. The model is an alternative to the current manual-made schedules which is an intricate and time-consuming phenomena. Even then it leaves the users (nurses) in a dissatisfying state. The developed model accounts both for hospital-objectives and nurses' preferences. Hospital objectives includes ensuring a continuous service with appropriate skills and the staff-requirement avoiding additional costs for unnecessary overtime. Nurses-preferences include unbiased consideration, avoiding consecutive shifts, one shift in a day and more day-shifts than night-shifts. The paper presents an application of 0-1 goal programming for nurse-scheduling with multiple conflicting objectives of a study for one week distribution. The results of the study indicate that this model can be used in hospitals in today's competing decision-environment.

3 tables, 12 ref

Decoding Reed-Solomon codes using Euclid's algorithm
Shankar P

008025   Shankar P (Computer Dep, Science and Automation Indian Institute of Science, Bangalore-560 012, Email: priti@csa.iisc.ernet.in) : Decoding Reed-Solomon codes using Euclid's algorithm. Resonance 2007, 12(4), 37-51.

Reed-Solomon codes are indeed an elegant illustration of a very practical application of abstract algebra. An interesting discovery was the fact that Euclid's algorithm for finding greatest common divisors of polynomials, could be used for decoding these codes. Explains this connection.

2 illus, 4 ref

Berinde's criterion for the convergence of the newton-like method
Sen R;Biswas A;Patra R;Mukherjee S

008024   Sen R;Biswas A;Patra R;Mukherjee S (Applied Mathematics Dep, Calcutta Univ, 92, Acharya Prafulla Chandra Road, Kolkata-700 009, Email: sulekha@klyuniv.ernet.in) : Berinde's criterion for the convergence of the newton-like method. Bull Calcutta Mathl Soc 2007, 99(2), 101-6.

Berinde has shown that Newton's method for a scalar equation f(x) = 0 converges under some conditions involving only f and f' and not F", when a generalized stopping inequality is valid. Extends Berinde's theorem to the case where f' (x) ≠= 0 need not necessarily be true.

3 ref

Lot sizing decisions under trade credit with variable demand rate under inflation
Sarbjit Singh;Shivraj Singh;Hari Kishan

008023   Sarbjit Singh;Shivraj Singh;Hari Kishan (NO, D. N. College, Meerut, Email: sarbjit200478@yahoo.co.uk.) : Lot sizing decisions under trade credit with variable demand rate under inflation. Indian J Math mathl Sci 2007, 3(1), .

Model having variable demand rate for deteriorating items is considered. The factor of inflation is also considered. The concept of permissible delay has also been used. The expression for total cost of inventory is obtained first, then an optimal order quantity and maximum allowable shortages are obtained. The research will aid the retailers in economically stocking the inventory under the influence of different decision criteria such as time value of money, inflation, variable demand rate and constant deterioration rate.

2 ref

Integer equation controlled descending path to a protean pure integer program
Santosh Kumar;Munapo E;Jones B C

008022   Santosh Kumar;Munapo E;Jones B C (Mathematics and Statistics Dep, Melbourne Univ, P. O. Box 14428, Melbourne City MC 8001, Australia, Email: skumar@csm.vu.edu.au) : Integer equation controlled descending path to a protean pure integer program. Indian J Math 2007, 49(2), 211-37.

Method is devel-oped to find the descending path to reach the required integer solution for the pure integer-programming (PIP) problem. The path is controlled by an integer equation, derived from the LP relaxation of the given PIP. The computational effort required is compared with some of the existing methods. It is claimed that the method presented in this paper seems to be computationally superior. In addition, the proposed method has many special features unique to it. The method has been extended to find the kth best PIP solution and also to solve a protean PIP problem. The method is still in the developing stages, and much more work has to be done to establish its computational superiority, if any, and various other characteristics of this approach.

4 tables, 3 illus, 27 ref

Bayesian estimation of heritability in different situations
Sandhya Kiran;Bhatia V K;Paul A K

008021   Sandhya Kiran;Bhatia V K;Paul A K (NO, , 12-5-101/1, Veeramchaneni Laxi Nivasam, Vijayapuri Colony, South Lallagude, Secunderabad, Andhra Pradesh-500 017) : Bayesian estimation of heritability in different situations. Indian J Anim Sci 2007, 77(11), 1188-91.

Application of Bayesian statistical techniques has been illustrated by subjecting the simulated data sets to Bayesian procedure of estimating variance components. This technique is based on the posterior distribution of the unknown parameters by utilizing data and some prior distribution of the parameters. This method ensures non-negative estimates of variance components and heritability for all the practical situations.

1 illus, 3 tables, 7 ref

Regularization of an abstract ILL-posed second order Cauchy problem
Saidouni C

008020   Saidouni C (Laboratoire Equations Differentielles. Departement de Mathematiques, Faculte des Sciences Universite Mentouri, Constantine 25000 Constantine, Algeria, Email: cherifsaidouni@yahoo.fr) : Regularization of an abstract ILL-posed second order Cauchy problem. Far East J mathl Sci 2007, 24(2), 271-80.

Initial value problem for an abstract elliptic second order differential equation has been studied. This problem is ill-posed. Perturbing initial conditions we obtain an approximate nonlocal problem depending on small parameters. Approximate problems are well-posed. Etimates of solutions of the approximate problems and a convergence result has been obtained.

14 ref

Common fixed point theorem for gregus type mappings in a metric space without convexity
Sahu D R;Diwan S D

008019   Sahu D R;Diwan S D (Applied Mathematics Dep, Shri Shankaracharya College of Engineering and Technology Junwani, Bhilai-490 020, Email: sahudr@rediff.com) : Common fixed point theorem for gregus type mappings in a metric space without convexity. Indian J Math 2007, 49(2), 165-74.

Common fixed point theorem for Gregus type mappings in a metric space without using the convexity property has been proved. Result extends the result of Huan'g and Cho [5].

14 ref

Measure in generalized fuzzy sets
Sahin M;Yapar Z

008018   Sahin M;Yapar Z (Mathematics Dep, Faculty of Arts and Sciences, Gaziantep Univ, Gaziantep, Turkey, Email: mesahin@gantep.edu.tr) : Measure in generalized fuzzy sets. Far East J mathl Sci 2007, 24(2), 217-26.

Construction of fuzzy sets without depending on membership function, algebric properties of a family of fuzzy sets, three notions including a ring of generalized fuzzy sets GF(X) of X, a complete Heyting algebra (cHa) which contains the power set P(X) of X, an extension lattice B(L), where B = P(X). and the set of L-fuzzy sets, where L = (Lx <157>x ∈ X}, definitions of fuzzy σ-algebra and fuzzy measure are generalized. Some results using these definitions which include a generalization of Proposition 2 in [4] has been obatained.

12 ref

Euclid's fifth postulate
Ravindran R

008017   Ravindran R (NO, , ) : Euclid's fifth postulate. Resonance 2007, 12(4), 26-36.

Reviews the fifth postulate of Euclid and trace its long and glorious history, That after two thousand years, it led to so much discussion and new ideas speaks for itself.

12 illus, 5 ref