020126   Rajendra Prasad;Shukla S S;Rai A K (Mathematics Dep, University of Allahabad, Allahabad-211 002) : On semi-invariant submanifolds of nearly trans-sasakian manifolds. Bull Calcutta Mathl Soc 2006, 98(4), 347-66.

Deals with Nijenhuis tensor [φ, φ] of φ in a nearly Trans-Sasakian manifold. Integrability conditions for certain disributions on a semi-invariant submanifold of a nearly Kenmotsu and nearly Trans-Sasakian manifold, totally umbilical and totally geodesic sub-manifilds. Totally contact umbilical and totally contact geodesic submanifolds and certain parallel operators.

39 ref

020125   Rajan S;Bhatnagar P (Statistics Dep, Hindu Coll, Moradabad, Uttar Pradesh) : Fritz-John optimality and duality for multi-objective programs. Acta Cienc Indica-Math 2006, 32(2), 911-8.

It is proposed to study Fritz-John necessary Optimality and Duality conditions for a weakly efficient solution of the multiobjective programming problem without assuming any constraint qualification.

4 ref

020124   Prashanth Kumar P;Sharma S D;Ravindra Babu G (Sci and Humanities Dep, Sci Inst of Technol, Hyderabad, Andhra Pradesh) : Goal programming for health-care planning. Acta Cienc Indica-Math 2006, 32(2), 751-4.

In the complex financial environment, today's health-care industry requires administrators who are familiar with efficient method of allocating scare resources. Many health-care facilities have become similar to large business enterprises, which intend to achieve multiple and conflicting goals through integration and use of limited resources. The objective of this study was to develop the goal programming approach in the health care field, and to determine the optimal sequence for treatment of surgical patients that maximizes the total contribution to profit.

1 table, 21 ref

020123   Pidadi S S;Khobragade N W (Mathematics Dep, Nagpur University, MJP Educational Campus, Nagpur-440 010) : Inverse steady-state thermoelastic problem of a finite length hollow cylinder. Acta Cienc Indica-Math 2006, 32(2), 497-514.

Attempt is made to solve two inverse problems of thermoelasticity. In the first problem, an attempt is made to determine the temperature, displacement and stress functions on the outer curved surface in the finite isotropic hollow cylinder of length 2h occupying the space D: a ≤ r ≤ b,- h ≤ z ≤ h with the stated boundary conditions by applying finite Marchi-Fasulo integral transform technique. In the second problem, an attempt is made to determine the temperature, displacement and stress functions on upper plane sJlrface in the finite isotropic hollow cylinder of length 2h occupying the space D: a ≤ r ≤ b, 0 ≤ z ≤ h with the stated boundary conditions by applying finite Marchi-Zgrablich integral transform technique.

7 ref

020122   Pawar M (Mathematics Dep, K.G.K. College, Moradabad-244 001) : B-vexity and its generalizations. Acta Cienc Indica-Math 2006, 32(2), 565-7.

Deals with generalizations of b-vex functions. Some known property of convex functions are studied for b-vex function. The class of convex functions has been extended to a class of b-vex function by Bector and Singh which are quite similar to (α,λ). Concave functions introduced by Castognoli and Mazzoleni now defined functions and study some their properties.

4 ref

020121   Pawar M (Mathematics Dep, K.G.K. College, Moradabad-244 001) : Classical technique with single-variable and multivariable optimization with no constraints. Acta Cienc Indica-Math 2006, 32(2), 559-63.

Authors present the necessary and sufficient conditions in locating the optimum solution of single-variable function, a mutivariable function with no constraints.

5 illus

020120   Patel T;Mehta M N (Mathematics Sect A.S.H. Dep, S.V. National Inst of Technol, Surat-396 007) : Solution of non-linear problem arises into the two immiscible phase flow in porous media by using shooting method approach. Acta Cienc Indica-Math 2006, 32(2), 895-900.

Solution of nonlinear problem arises into the two immiscible phase flow in porous media have been obtained by using appropriate boundary condition with suitable assumption which physically consistent with the problem. Its solution have been obtained by using the shooting method approach and its graph have been obtained, under assuming standard relation. This problem has great importance in oil recovery process.

3 illus, 5 ref

020119   Pandey N A;Achari J (Mathematics Dep, Statistics and Computer Sciences, Science College, Nanded-431 605) : Generallized fixed point theorems for d-domplete topological spaces ll. Appl Sci Period 2006, 8(1), 55-62.

Hicks has proved some important fixed point theorems in more general setting for a large class of non-metric spaces, viz., d-complete topological spaces. Authors have generalized some of the basic ones in previous part-1 of the paper. Generalizes the extended versions of the related theorems.

4 ref

020118   Nashine H K;Dewangan C L (School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur-429 010) : Existence of best proximity pair theorem in H-space. Acta Cienc Indica-Math 2006, 32(2), 763-6.

Obtains an existence result on best proximity pair using the concept of KKM theory in H-space.

11 ref

020117   Mukherjee S;Sarkar D (Mathematics Dep, Dr. Meghnad Saha Coll, Itahar, Uttar Dinajpur, West Bengal) : Exact analysis of unsteady convective diffusion of solute in to-layered MHD flow through parallel plates. Acta Cienc Indica-Math 2006, 32(2), 659-72.

Unsteady dispersion of solute in two-layered MHD flow through parallel plates is studied using the generalized dispersion model of Gill and Sankarasubramanian. With this approach, the entire dispersion process is described with the effective diffusion coefficient as function of time. The model brings-out mainly the effect of plug flow region on the over all dispersion process. It is found that initially the dispersion coefficients decreases considerably with the increase of the value of plug flow region but becomes essentially a constant as time takes larger values. It is also seen that time required to reach the steady state depend on plug flow region. This study can be used as a starting first approximate solution for studying the dispersion in cardiovascular system.

5 illus, 6 ref

020116   Modi G;Tiwari R;Chandel R S (Mathematics Dep, Goverment Motilal Vigyan Mahavidayalaya, Bhopal-262 003) : Common fixed point theorem on D-metric space over topological semi field. Acta Cienc Indica-Math 2006, 32(2), 575-80.

Presentys the result of fixed point theorem in D-metric space over a topological semi field.

8 ref

020115   Mittal S K;Tyagi A;Gupta S (Maths Dep, M.M. P.G.College, Delhi Meerut Road, Modinagar(U.P)) : Mathematical modelling and reliability analysis of a complex system with waiting concept. Reflection Des Ra 2006, 1(1), 83-96.

In this paper, authors have considered a complex system, consisting of n-identical units in series. this system suffurs several types of falure viz, Partial, catastrophic, Critical human failure, Environmental failure, Networking failure an Software failure. This system goes to reduced efficiency state due to partial failure and failed state due to catastrophic failure. System also goes to complete failure due to critical human error, environmental failure, networking & software failure. System goes to complete break down if more than one units fail. All failures follow exponential time distribution, while repairs follow general time distribution except repair of environemntal failure. By Modelling and Reliability analysis, differential equations are formulated and solved by S.V. technique. L.T. of up and down state probabilities and M.T.T.F. are derived. Some numerical illustrations are given in the end.

5 illus, 6 ref

020114   Mittal S K;gupta R;Jain S (M.M.(PG) College, , Modinagar) : Operational availability of a standby redundant complex system with environmental effects under preemptive repeat repair discipline. Reflection Des Ra 2006, 1(1), 21-34.

Paper deals with operational behaviour of a 2-state complex system consisting of two sub-systems A and B in 1-out-of -2: f arrangement suffering from environmental effects. This system has three modes, viz: normal, dgraded and failed with environmental effects. This system has three modes, viz: normal, degraded and failed with environmental failure. All types of failure rates are exponential while repair rates are distributed quite generally except environmental repair rate, which is distributed exponentially. All the repairs follow Pre-emptive Repeat Repair Policy. Supplementary variable technique has been employed to obtain various state probabilities and then the expressions for operational availability, reliability and mean time to system failure are obtained by inversion process. Finally, the ergodic behaviour has been analyzed by some graphical illustrations to explain the practical utility of the model.

5 ref

020113   Mittal P K;Bojalwan M (Mathematics Dep, Govt. (P.G.) Coll, Rishikesh-249 201) : On some self superposable fluid motions in ellipsoidal ducts. Acta Cienc Indica-Math 2006, 32(2), 875-82.

Attempt has been made to find some self-superposable motiolls of incompressible fluid in the ellipsoidal ducts. No stress has been given on boundary conditions and the solutions thus determilled containing a set of constants. Pressure distribution of some of such flows has also been discussed. The curves along which the vorticity of the flow becomes constants have also been attempted. Attempts have also been made to determine the surfaces along the flows, which show the tendency of irrotationality. The object of the paper is to introduce a method for solving the basic equations of fluid dynamics in ellipsoidal coordinates by using the property of self superposability.

26 ref

020112   Meenakshi A R;Krishnamoorthy S (Mathematics Dep, Annamalai Univ, Annamalai Nagar-608 002) : Reverse order law for k-EP martices. Appl Sci Period 2006, 8(1), 50-4.

For any two non-singular matrices A, B ∈ Cnxn, (AB)<^>-1 = B<^>-1 A<^>-1 holds. However, it is not true for generalized inverses of matrices. In general, (AB)<^><187> ≠ B<^><187>A<^><187>, for any two matrices A and B. Authors say that reverse order law holds for Moore-Penrose inverse of the prodcut of A and B, if (AB)<^> = B<^><187>A<^><187>. In this paper, authors discussed, the necessary and sufficient conditions for the reverse order law (AB)<^><187> = B<^><187>A<^><187> to be hold, for a pair of K-EPr matrices A and B.