005466   Wali K S;Talwar A (Dept of Statist, Gulbarga Univ, Gulbarga-585 106) : Statistical analysis of malaria incidences in Raichur district. Biosci Res Bull 2005, 21(1), 63-5.

Malaria incidence of Raichur district for the last ten years in studied. Polynomial equation is fitted to the data and seasonal variation and relationship in the incidences of malaria in dry and irrigated areas is also analyzed.

1 illus, 4 tables, 6 ref

005465   Sivakumar B;Arivarignan G;Perumal V (Math and Statist Dep, Madurai Kamaraj Univ, Madurai) : Inventory model with multiple rates of production. Opsearch 2005, 42(2), 126-33.

In production inventory systems, there are situations, in which it is not possible to have single rate of production throughout the production period. Items are produced at different rates during sub periods so as to meet various constraints that arise due to change in demand pattern, market fluctuations etc. Such a situation is modelled by assuming constant rate of demand a and varying rates of productio Pi, during the time when the inventory level goes from (i - 1)Q to iQ (i=1,2,3...,n) where Q is prefixed level. The production is stopped when the inventory level reaches nQ. Thereafter the stock is consumed by demand alone. The production is started immediately when the inventory level reaches zero. For this model the total cost per unit time as a function Q and n is derived. The optimal decision rules for Q and n, when the production rates Pi form a decreasing sequence, are computed. Special cases are discussed. Results are illustrated by numerical examples.

1 illus, 14 ref

005464   Sinha S (Inst of Math Sci, , Taramani) : Spatiotemporal consequences of random coupling. Proc Indian Natn Sci Acad-Pt A 2005, 71(1-2), 97-111.

Discusses the spatiotemporal dynamics of networks of diffusively coupled chaotic maps, with varying degrees of randomness in coupling connections. In such systems, while strictly nearest neighbour coupling never allows spatiotemporal synchronization, randomly rewiring some of those connections stabilises entire networks at x*. where x* is the strongly unstable fixed point solution of the local chaotic map. Shows both analytically and numerically, that the range of coupling over which synchronization is achieved increases monotonically with p. It also studies the effects of random connections on chaotic maps with threshold activated coupling. Shows how randomness in spatial connections yields synchronized networks in threshold regimes where a large number of unsynchronized attractors occur under regular connections. However, in contrast to diffusively coupled maps, the dependence of the synchronized fraction on p is typically non-monotonic. Further the mean time to reach synchronization with respect top also indicates an optimum randomness for which synchronization is most efficiently achieved.

16 illus, 16 ref

005463   Sinha J K;Mishra R N;Verma A (Government of Bihar, , Patna) : Optimisation in repair and replacement of multicomponent engineering system subject to shocks that form interdependent geometric process. IAPQR Trans 2004, 29(2), 147-52.

The paper considers a repair-replacement policy for an engineering system subject to shocks that form interdependent geometric process.

^ssc8 ref

005462   Singh S P (Dep of Math, T D P G Coll, Jaunpur-222 002) : Certain transformations involving q-series. Proc Natn Acad Sci India-Sect A 2005, 75(1), 39-43.

Certain transformations for basic hypergeometric series have been established by making use of a known identity.

4 ref

005461   Singh J;Koul C L (Dep of Math, Malaviya Natn Inst of Technol, Jaipur-302 017) : Application of fractional calculus. Proc Natn Acad Sci India-Sect A 2005, 75(1), 33-8.

Applications of the generalized Lagrange's expansion of a function f(z), provided by Osler in the theory of fractional calculus, six useful results are derived.

6 ref

005460   Sharma P R;Mishra U (Dep of Math, Univ of Rajasthan, Jaipur-302 004) : Unsteady flow and heat transfer along a porous vertical surface bounded by porous medium. Proc Natn Acad Sci India-Sect A 2005, 75(1), 45-9.

Unsteady flow and heat transfer along a porous vertical surface bounded by porous medium in the presence of variable free stream and permeability is investigated. The expressions of velocity and temperature distributions are derived, discussed numerically and shown through graphs. The expressions for skin-friction coefficient and rate of heat transfer in terms of Nusselt number at the surface are derived, discussed numerically and their values are presented.

2 illus, 1 table, 11 ref

005459   Sengupta P R;Paul S (Dep of Math, Univ of Kalyani, Kalyani-741 235) : Unsteady hydromagnetic flow of higher order visco-elastic fluid through a circular cylinder. Indian J Theor Phys 2004, 52(4), 327-36.

Paper is to investigate the laminar flow of unsteady hydromagnetic higher order visco-elastic fluid through a circular cylinder under the influence of exponentially decreasing pressure gradient. The magnetic field is acting in the azimuthal direction. The z-axis is taken along the axis of the cylinder. In solving the problem, the electrical and induced fields are neglected because of its smallness. The problem has been solved in the generalised visco-elastic model and the velocity field has been derived analytically in the closed form. Then several special cases corresponding to Maxwell, Oldroyd, Rivlin-Ericksen models and ordinary viscous fluids are obtained for velocity field.

17 ref

005458   Saxena S K (Dep of Phys, Upadhi P.G. Mahavidyalaya, Pilibhit-262 001, Bihar) : An abstract mathematical approach for existence of linear wave operator under time fall-off conditions. Acta Cienc Indica-Phys 2005, 31(2), 273-7.

Derived the existence of Linear wave operators W₊ (H, H₀; J) under fall off conditions on (v, e^itH (HJ-JH₀) e^-itH₀ u) in t.

11 ref

005457   Said S M (Dep of Math and Informatic Fac of Sci, Univ of Ouargla, Ouargla 30000, Algeria, Email: smedsaid@yahoo.com) : (NULL). Far East J mathl Sci 2005, 17(1), 121-35.

The adjoin problem controlled by the system of Lame affected by a weight function in an open limited field at polygonal border with the boundary conditions of Dirichlet has been studied. It is shown that this weight function plays a very important role in the study of the existence of solutions of these problems, in the traditional case. The existence of solutions of these problems depends on the openings of the angles of the polygon, i.e., for certain values of the angles, the solution of the direct problem cannot exist in classical spaces of Sobolev. This results in the fact that the image of the operator of the direct problem is not closed for certain values of the angles of the polygon, this influences the kernel of the adjoin operator and thereafter the existence of the solution of the adjoin problem. It has been shown that the solution of the adjoin problem controlled by the Lame operator affected by a weight function is in a functional space with weight, richer than traditional spaces of Sobolev, and that the existence of the solution in these spaces does not depend any more on the angles in the polygon. This study is more original and it covers the traditional case.

13 ref

005456   Saibah;Darus M (Sch of Math Sci Fac of Sci and Technol, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor D E, Malaysia, Email: saibahvirgo@yahoo.com) : Unified treatment of p-valently analytic functions. Far East J mathl Sci 2005, 17(1), 69-79.

The unified class U[p,n, α β], p, n ∈ N := {1, 2, 3, ...}; 0 ≤ α <60> 1/p; β ≥ 0; of p-valently starlike and p-valently convex functions of order α in the open unit disk E have been introduced and studied. Some properties of functions belonging to μ[p,n, α, β] are obtained which include radii of starlikeness and radii of convexity involving Hadamard products (or convolution).

2 ref

005455   Sahu J K (Dep of Math, Gangadhar Meher Coll, Sambalpur-768 004) : Projective motion admitting recurrent vector in flat Finsler space. Proc Natn Acad Sci India-Sect A 2005, 75(1), 57-9.

The vector field v'(x') has an important role in the infinitesimal transformation in Riemannian as well as Finsler space which gives rise to lie derivative. The vector field v' in both spaces is considered as a function of position. Yano has treated the various possibilities of covariant derivative of v' in non-Reiemannian spaces and they are named centra-vector field, recurrent vector field and concircular vector field. Okumura generalizes the idea of concircular vector field which he called as torse-forming vector field. The concepts of different types of recurrent vector of v in a flat Finsler space admitting projective motion has been introduced and explored certain results.

12 ref

005454   Saha L M;Sarma T P;Erjaee G H;Dixit P (Dep of Math, Zakir Husain College, J L N Marg, New Delhi-110 002) : Hill's stability problem criteria in the oblate restricted three-body problem. Proc Natn Acad Sci India-Sect A 2005, 75(1), 51-5.

Hill's problem stability criteria in the outer planetary orbit encircling binary stars has been investigated. The result for restricted problem, when one of the primaries is an oblate spheroid body has been discussed through Hill's analytical method by varying the mass parameters μ = m₂/(m₁ + m₂), 0 ≤ μ ≤ 0.5.

3 illus, 1 table, 5 ref

005453   Ramanath K;Lakshmi P (NO, Sch of Math Madurai Kamaraj Univ, Madurai-21) : Performance analysis of the M/G/c retrial queueing systems using the theory of Markov Regenerative Stochastic Petrinets. Opsearch 2005, 42(2), 134-51.

A method of modeling and analsing the M/G/c retrial queueing system with the help of Markov Regenerative Stochastic Petrinets (MRSPN) has been exhibited. It has been indicated as to how this representation could be used to obtain the transient and the steady state probabilities of the retrial queueing system. The methodology is illustrated with a simple example.

3 illus, 26 ref

005452   Pandey M;Chandra N (Banaras Hindu Univ, , Varanasi) : Bayes estimation of reliability of a component under Burr model. IAPQR Trans 2004, 29(2), 105-19.

Paper provides Bayes estimator of reliability of a component under stress-strength set up in accelerated life testing. The comparison of Bayes and quasi-Bayes estimators has been done on the basis of their relative efficiencies and absolute bias. The variation in each of the Burr and prior parameters has been considered for numerical computation by generating 200 samples for a Monte-Carlo study.

7 tables, 8 ref

005451   Pal M;Ghosh S K (Calcutta Univ, , ) : An inventory model for deteriorating items allowing shortages. IAPQR Trans 2004, 29(2), 121-8.

An inventory model has been developed for an item that deteriorates with time. Demand for the item is assumed to occur in a Poisson fashion and the lifetime of the item follows an exponential distribution.

6 ref

005450   Ojha J P N (Dep of Math, M L V Government Coll, Bhilwara) : Heat conduction in a truncated wedge of semi-infinite height with circular boundaries. Indian J Theor Phys 2004, 52(4), 277-85.

The problem of finding the temperature at any point of a truncated wedge of semi-infinite height with circular boundaries, when there are sources of heat within it and for boundary conditions of the radiation type is considered. different types of integral transforms are employed to solve the problem.

5 ref

005449   Moukoko D;Dzoumba J (Dep de Mathematiugues Faculte des Sci, Universite Marien Ngouabi, Congo) : Newton form of Hermite interpolation polynomial. Far East J mathl Sci 2005, 17(1), 107-20.

The Hermite interpolation polynomial is often given as linear combination of polynomials of the same degree. It has been given in the form Σ C_jW_j(x), where W_j(x) is a monic polynomial of degree j, product of powers x-x_i. The cofficients C_j can be computed using divided differences.

3 ref

005448   Mitra S;Chatterjee A K (NO, Indian Inst of Mgmt, Kolkata-700 104) : An efficient lot-sizing heuristic for a periodic-review inventory system under non-stationary stochastic demand. Opsearch 2005, 42(2), 168-77.

The lot-sizing problem has been considered in a periodic-review inventory system under non-stationary stochastic demand. A heuristic has been proposed and its performance compared with the optimal solution given by dynamic programming for 90 problem instances. Across all the problem instances the heuristic averages 1.96% error, and is found to be at least 30 times faster than dynamic programming.

4 tables, 10 ref

005447   Mandal P K;Gupta M (Dep of Math, Jadavpur Univ, calcutta-700 032, Email: pravat3112@yahoo.co.in) : Parametric amplification of acoustic waves in a piezosemiconducting medium. Indian J Theor Phys 2004, 52(4), 345-54.

Investigation is made of the energy gain or loss of acoustic wave, due to the non-linear parameteric interaction in a piezosemiconducting medium. In the study, Author has consider the amplitude of the initial pump wave is not very much larger than that of acoustic wave. Using the hydrodynamic model of plasma, the relative change of energy of signal wave is computed for different propagation distances, assuming the interaction to be of degenerate type and the drift velocity of electrons is exactly equal to the sound wave. Numerical investigations reveal that the change of energy of signal wave is slow due to the non-linear parametric interaction with the initial pump wave in a piezosemiconducting medium.

3 illus, 1 table, 9 ref

005446   Makarov I S (Independent Researcher, , P O B 1656, Tel Aviv 61015, Israel) : The neutron becoming the atom. Indian J Theor Phys 2004, 52(4), 337-43.

New method of research, the self-developing logical analysis and the adequate mathematical description, has enabled to reveal the contradiction in the structure of the neutron, which leads to its eventual spontaneous transformation into the structure of the hydrogen atom. The latter proves to be a linear system with lumped parameters and is described by a system of linear differential equations with constant coefficients, its solution defining the structural function of the atom. The hydrogen atom constitutes a perfect discrete model of the vacuum, is immune to its influence and hence absolutely stable. It is an organic system containing three interdependent subsystems, so-called quarks; the latter implementing collective interaction of virtual electrons and positrons inside the atom, and its photon exchange interaction with the vacuum. These quarks are described by square matrices with real entries and may be called, in a generalized sense, the subsystems of inertia, elasticity, and dissipation. The vectors of the dynamic variables of the above equations, their first and second time derivatives are the agents of the above processes and correspond to so-called gluons.

2 ref

005445   Liu Y;Yuhan D (Dep of Math, Hanshan Teachers's Coll, Chaozhou, Guangdong, 521041, China, Email: cz_liuyu@126.com) : Some characterizations of reverse order law of matrices over skew fields. Far East J mathl Sci 2005, 17(1), 59-68.

The reverse order law of group inverse and generalized inverses of the product of matrices over skew fields have been considered. Some necessary and sufficient conditions of these problems are given and the decomposition theorem is obtained.

9 ref

005444   Karanjai S (Dep of Math, North Bengal Univ, West Bengal-734 430) : Solution of the equation of transfer in finite atmosphere using eddington's approximation for the intensity of radiation. Indian J Theor Phys 2004, 52(4), 355-9.

Equation of liner transport has been converted to equation for the radiative transfer problem and it is then solved using Eddington's approximation for the intensity of radiation which provides some quantitative insight into the mechanism of the radiation and gives quite appreciable results.

2 ref

005443   Hur K;Jang S Y;Jun Y B (Div of Math and Informational Statistic and Inst of Basic Nat Sci, Wonkwang Univ, Iksan, Chonbuk, Korea 570-749, Email: kulhur@wonkwang.ac.kar) : Intuitionistic fuzzy congruences. Far East J mathl Sci 2005, 17(1), 1-29.

The concept of an intuitionistic fuzzy congruences on a semigroup have been studied some of its properties has been introduced. Some properties under semigroup homomorphisms have been investigated.

23 ref

005442   Ghosh K (Dep of Appl Math, Univ of Calcutta, 92, A P C Road, Kolkata-700 009, Email: koushikg123@yahoo.co.uk) : On brown dwarfs under the consideration of their internal rotation. Indian J Theor Phys 2004, 52(4), 295-303.

Rotation is expected to play a vital role in the process of estimating the characteristics of gravitationally collapsing stellar configurations as all of them are rotating. If the rate of internal rotation is of high magnitude, the observed characteristics under the consideration of rotation will certainly show distinct changes from their old estimations. The observed radius of the completely degenerate brown dwarf configuration under the consideration of the internal rotation is significantly higher than the previous estimation while the newly calculated central density and central pressure at the stage of complete degeneracy show prominent decrease from their old estimations. In the present paper, deriving the radius, central density and central pressure for the fully degenerate brown dwarf models under the consideration of internal non-rigid rotation, some remarks are placed by the author on the rotational instability of the brown dwarf configurations. In this paper, it is suggested that for the highly rotating brown dwarfs with low mass rotational instability most probably will not arise and the configuration will remain rotationally stable roughly throughout the whole life-span while for the highly rotating brown dwarfs with higher mass rotational instability will arise after a small contraction.

1 table, 15 ref

005441   Ganguly A;Arondekar P (Dep of Appl Math and Computational Sci, Shri G S Inst of Technol and Sci, 23 Park Road, Indore-452 003) : Hyperbolic class of Bezier-like curves. Far East J mathl Sci 2005, 17(1), 45-57.

A Hyperbolic class of Bezier basis is constructed by an integral approach, generated over space Ω_n = span{l, t. ..., t^n-2, sinh(mt), cosh(mt)}, where n is an integer and m is a real number not equal to zero. It has been shown that the basis behaves like a Bernstein basis in the limiting case of our definition and defined hyperbolic class of Bezier-like curves. This curve shares the most of the properties as those of Bezier curve over polynomial space (Hyperbolic polynomials). An example to represent the remarkable curve such as hyperbola and caternary has been given.

6 illus, 5 ref

005440   Gadre M P;Rattihalli R N (Madhoji Coll, , Phaltan) : Group runs control chart for identifying increases in fraction nonconforming. IAPQR Trans 2004, 29(2), 129-45.

Authors has proposed a control chart, called the 'Group Runs' (GR) chart to detect an increase in fraction nonconforming. It is verified that the proposed chart significantly reduces the out of control. 'Average Time to Signal' (ATS) as compared to most of the well-known compatible attribute control charts including Bernoulli CUSUM chart and synthetic chart. Though in some situations the performance of GR chart is poor as compared to the Run-Length CISIM chart (Bourke [1]), there is not much difference between the corresponding out of control ATS values.

3 illus, 6 tables, 10 ref

005439   El Saady K (Math Dep, Coll of Sci, Taif, P O Box 5700, Saudi Arabia, Email: el-saady@lycos.com) : Completeness and completions of objects in the category of fuzzy neighborhood groups. Far East J mathl Sci 2005, 17(1), 31-44.

The notion of I-fuzzy neighborhood groups was introduced by Ahsanullah and it forms a category lies between the category of topological groups and the category of stratified I-topological groups. Within this category the completeness notions have been introduced the group completion of its objects have been constructed.

13 ref

005438   Datta S;Pandya N (Dep of Math and Astronomy, Lucknow Univ, Lucknow-226 007) : Axial symmetric translational motion of a half submerged sphere in a liquid with a surfactant layer. Proc Natn Acad Sci India-Sect A 2005, 75(1), 61-72.

Studies the translational motion of a half-submerged sphere in viscous fluid bounded by a plane surface covered by a monomolecular layer of sufactant fluid. The Stokes flow solution is presented for the quasistatic case and the effect of surfactant layer on the drag determined and discussed. Numerical results in tabnular and graphical forms reveal that in general the effect of surfactant layer is to increase the values of drag opver those of O'Neill et al.

2 illus, 1 table, 8 ref

005437   Chauhan D S;Jain R (Dep of Math, Univ of Rajasthan, Jaipur-302 004) : Three-dimensional MHD flow and heat transfer in the presence of a naturally permeable boundary of very small permeability. Indian J Theor Phys 2004, 52(4), 311-26.

Heat transfer in MHD steady three-dimensional flow of a viscous incompressible and electrically conducting fluid over a naturally permeable bed of very small permeability is considered with transverse sinusoidal suction. The effects of magnetic field and permeability on the velocity and temperature fields, co-efficient of skin-friction and on the rate of heat transfer are investigated and discussed.

2 illus, 3 tables, 12 ref

005436   Caltenco J H;Lopez-bonilla J;Pena rivero R (Seccion de Estudios de Posgrado e Investigation, Escuela Superior de Ingenieria Mecanica y Electrica Instituto Politecn, Edif. z, 3er Piso, Col. Lindavista, C P 07738, Email: lopezbjl@hotmail.com ) : R₄ embedded into E₅ with perfect fluid. Indian J Theor Phys 2004, 52(4), 271-6.

005435   Binder A;Zhai X (Univ of Appl Sci, , Wurzburg, Germany) : A not on productivity, quality and reliability and the aspect of uncertainty. IAPQR Trans 2004, 29(2), 83-95.

Productivity through quality and reliability is the motto of IAPQR and consequently it has been engaged in "pursuit, propagation and promotion of concepts, methods and practices to enhance productivity in manufacturing and services organisations." The main obstacle to arrive at quality and reliability is uncertainty about future developments. Any effort made in the realm of quality and reliability targets at reducing uncertainty and arriving at stable processes, product behaviour and services. Thus, uncertainty and an appropriate mathematical description must be the foundation of any procedure applied to achieve better quality and reliability. Clearly, an appropriate description of uncertainty assumes that its sources and its structure are identified and taken into account. Unfortunately, the traditional approach for developing mathematical models of uncertainty fails and yields mathematical models which blatantly violate reality. Paper introduces a general approach for mathematically describing uncertainty as basis for developing a new generation of effective procedures to be applied for improving quality and productivity.

11 ref

005434   Arora S R;Ravi Shanker;Malhotra N (Math Dep, Hans Raj Coll Univerity of Delhi, Delhi-110 007) : A goal programming approach to solve linear fractional multi-objective set covering problem. Opsearch 2005, 42(2), 112-25.

A goal programming approach to find a prime cover solution of the Linear Fractional Multi-Objective Set Covering Problem is discussed. A Goal Programming Problem equivalent to the given problem is formulated. It is illustrated with the help of an example.

14 ref

005433   Aggarwal M L;Deng L Y;Mazumder M D (Univ of Memphis, , USA) : Optimal fractional fractorial plans using finite projective geometry. IAPQR Trans 2004, 29(2), 97-104.

Dey and Suen [4] obtained optimal fractional plans for estimating mean, all main effects and specified two factor interactions using finite projective geometry. Authors has obtained two new optimal fractional factorial plans, one for estimating mean, all main effects, specified two factor interactions and another for estimating mean, all main effects, specified two factor interactions and specified three factor interaction using finite projective geometry. It has also provided tables of optimal fractional factorial plans.

2 tables, 8 ref

004360   Wu S;Debnath L (Department of Mathematics, Longyan College, Longyan Fujian 364012, People's Republic of China, Email: wushanhe@yahoo.com.cn) : Generalizations of aczel's inequality and popoviciu's inequality. Indian J pure appl Math 2005, 36(2), 49-62.

Authors has given new generalizations of Aczel's inequality and Popoviciu's inequality, which has broad applications to mathematical analysis. Authors improve a number of algebraic inequalities and obtain some new ones. Furthermore, authors has also pointed out that a new generalization of Aczel's inequality by Mitrinovic (2), Wang (7) and Kuang (8) is not true in general. In the end, authors has given an analogue of Popoviciu's inequality.

10 ref

004359   Wang Y Y;Jiang Y L (School of Science, Xi'an Jiaotong University, Xi'an, People's Republic of China, Email: yywang@mail.xjtu.edu.cn) : Transient analysis of large systems with complex parameters. Indian J pure appl Math 2005, 36(2), 89-108.

An improved waveform relaxation (WR) is proposed for solving initial value problem for ordinary differential equations with complex parameters. Firstly, the convergence conditions are given. Secondly, the initial waveforms are produced by using the Chebyshev collocation method instead of constant waveforms. Thirdly, model-reduction is performed for iterative systems to reduce computational cost. An illustrative example is also provided.

2 illus, 19 ref

004358   Vinocha O P;Narula R K (Department of Mathematics, S.G.N. Khalsa College, Sri Ganganagar-335 001) : Bounds of undetected error probability of linear code. Math Educ 2005, 39(1), 12-7.

The undetected error probability P_ue(C,ε) of linear code used to detect error on asymmetric channel is a function of symbol error probability ε of the channel and involve the weight distribution of the code. The code is proper, if P_ue(C,ε) increase monotonously in ε have been found.

6 ref

004357   Vershney N K;Dharmvir Singh (Math Dep, S.V. Coll, Aligarh, U. P) : Three dimensional free convective flow with heat and mass transfer through a porous medium with periodic permeability. Bull Calcutta Mathl Soc 2005, 97(2), 95-106.

The effect of mass transfer on three dimensional free convective flow of a viscous incompressible fluid through a highly porous medium has been studied. The porous medium is bounded by an infinite vertical porous plate. assuming the free stream velocity to be uniform, approximate solutions are obtained for the velocity field, the temperature field, the concedntration field, the skin friction and the rate of heat and mass transfer.

3 illus, 3 tables, 9 ref

004356   Veerapandi T;Mariappan M (NO, P M T College, Melaneelithanallur-627 953) : Fixed point theorem for mappings in complete metric spaces. Math Educ 2005, 39(1), 9-11.

6 ref

004355   Thengane K D (R.S. Bidkar Arts Comm and Sci Coll, , Hinganghat-442 301) : Existence of [√y<. Bull Calcutta Mathl Soc 2005, 97(2), 147-52.

The bimetric relativity of Rosen admits [√y²+z² - √ t²₁+t²₂]-type and [√ t²₁+t²₂ / √y²+z²]-type plane gravitational waves in n-dimensional space-time V_n having two time axes where in the later case the space-times can be reduced to conformal one.

3 ref

004354   Sun J;Edmunds D E;Wang A (Department of Mathematics, Inner Mongolia University, Huhhot 010021 P R China, Email: masun@imu.edu.cn) : The number of Dirichlet solutions and discreteness of spectrum of differential operators with middle deficinecy indices. J Analysis Applic 2005, 3(1), 55-66.

The relationship between the essential spectrum, the deficiency index and the number of solutions of My = λy in L₂[a, ∞), where a <62> 0 and M is a symmetric ordinary differential operator of order 2N have been analysed. The results extend Weidmann's work to the case of differential operators with middle deficiency indices. It has been found that if I is an interval in the real line and the number of Dirichlet solutions of My = λy is N for every λ ← I (the defieiency indices may be in the middle case), then the continuous spectrum of any self-adjoint extension H of the minimal operator associated with M in L₂[a, ∞) has empty intersection with I. Furthermore, if the point spectrum of H has no accumulation point in I, then the essential spectrum of H is also disjoint from I.

8 ref

004353   Stein A;Teske E (Math Dep, Univ of Wyoming, P.O. Box 3036, 1000 E, University Asve., Laramie, WY 82071-3036, USA) : Optimized baby step-giant step methods. J Ramanujan Mathl Soc 2005, 20(1), 27-58.

Shanks' baby step-giant step alogrithm is known to be a generic method for computing element orders and discrete logarithms in any finite abelian group. Authors has shown how this method can be optimized in various applications where more is known about the underlying group than just the group operation itself. Additional information incluedes situations when the disttribution of the solution in a given search interval is known, when symmetries in the search interval or less expensive inversions exist, and when baby steps are less expensive than giant steps. In each case, this additional information can be readily used to obtain a speed-up of the algorithm. The optimized methods have been applied to the computation of invariants of hyperelliptic function fields. Hereby one is able to verify the speed-up in an important application.

5 tables, 24 ref

004352   Srivastava J P;Rakesh Kumar (Math Dep, Univ of Jammu, Jammu-180 006) : Submanifolds of codimension 2 on a special paracontact riemannian manifold. Bull Calcutta Mathl Soc 2005, 97(2), 131-6.

Adati and Miyazawa (1977, 1980) studied Para contact manifold and a special Para contact Riemannion manifold. Submanifolds of codimension-2 of a special Para contact Riemannian manifold M have been studied. As particular cases, submanifold of condimension-2 of M tangent to te structure vector field and submanifold of codimension-2 of M normal to the structure vector field have been studied. Also, some basic properties of an invariant submanifold of codimension-2 of special Para contact Riemannian manifold M by using concurrent vector field are studied.

5 ref

004351   Srivastava A C;Srivastava P K (Math and Astronomy Dep, Lucknow Univ, Lucknow-226 007) : Stagnation point flow of a second order dusty fluid near an oscillating plate. Bull Calcutta Mathl Soc 2005, 97(2), 107-16.

The laminar boundary layer of a second order dusty fluid on an infinite plate normal to an incoming stream, the plate making trasnsverse oscillations in its own plane, has been discussed. The velocity of the fluid as well as that of dust partcles consists of two parts, one steady and other unsteady; hence skin friction on the oscillating plate has steady and unsteady part. The effect of non-Newtonian terms in the constitutive equation is to increase the steady part and decrease the amplitude of oscillations of unsteady part of the skin friction. It has been found that dust particles slip on the plate and steady part of the slip velocity increases with the increase of non-Newtonian parameter. The increase of the radius of dust particles increases the skin friction as well as slip velocity of the dust particles on the plate.

2 illus, 2 tables, 8 ref

004350   Srinivas V;Raja Shekar M N (Department of Mathematics, Sree Nidhi Institute of Science and Technology, Ghatkesar-5001 301) : A note on a fixed point theorem of Brian Fisher. Math Educ 2005, 39(1), 24-5.

A generalization of Brian Fisher fixed point theorem for a compact metric space has been proved.

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004349   Sinha A K;Thakur P J (Department of Chemistry, L S College, Muzaffarpur-842 001) : Two colour theory for an open sphere. Math Educ 2005, 39(1), 46-8.

7 ref

004348   Sen S (Math Dep, Cornell Univ, Ithaca NY, 14853, U.S.A., Email: ss70@cornell.edu) : The galois theory of the p-adic complex numbers. J Ramanujan Mathl Soc 2005, 20(2), 147-53.

The Galois theory of the p-adic complex numbers (completion of an algebraic closure of Q_p) has been discussed and, in particular, its closed subfields have been characterised as completions of algebraic extensions of Q_p.

6 ref

004347   Sen M K;Weinert H J (Pure Mathematics Dep, Univ of Calcutta, 35 Ballygunge Circular Road Kolkata-700 019, Email: senmk@cal3.vsnl.net.in) : Completely simple semirings. Bull Calcutta Mathl Soc 2005, 97(2), 163-72.

It is well known that a semigroup S is a completely simple semigroup if and only if S is isomorphi to a Rees matrix semigroup over a group with sandwich matrix P and index sets I and Λ. This important result is extended to semirings by showing that a semiring S is a completely simple semiring if and only if S is isomorphic to a rees matrix semiring over a skew-ring with sandwich matrix P and index sets I and Λ which are bands under multiplication.

5 ref

004346   Satish Chandra;Agarwal A K (Department of Mathematics, Hindu College, Moradabad-244 001) : On certain structure in tangent and cotangent bundles. Math Educ 2005, 39(1), 18-23.

Almost contact and almost complex structures in the tangent bundle have been studied by K. Yano & S. Ishihara. GF-Structure was studied by Mishra & Singh. Niwas & Ali studied generalized contact structure & GF-structure in the tangent bundle & obtained interesting results involving Nijenhuis tensor & Lie derivative. Srivastava, extended certain results on the lifts of quartic structure. Generalised cohtact-structure and GF-structure & quartic-structure in tangent & cotangent bundles have been studies.

9 ref

004345   Sarangi K C;Jose C B (Math Dep, Univ of Rajasthan, Jaipur-302 004) : Unsteady free convective MHD flow and mass transfer past a vertical porous plate with variable temperature. Bull Calcutta Mathl Soc 2005, 97(2), 137-46.

3 illus, 1 table, 11 ref