015834   Bagwan A;Sharma S (Tidal Hydraulics Div, Central Water and Power Research Station, Khadakwasla, Pune-24) : Gregus type common fixed point theorems on normed sapce. Acta Cienc Indica-Math 2005, 31(4), 1135-40.

Authors prove a common fixed point theorem of Gregus type under the condition of compatible mappings of type (a). Which is a generalization of various common fixed theorems on normed space and Banach space.

14 ref

015833   Avadayappan S;Santh P;Sridevi R (Mathematics Dep, V.H.N.S.N. College, Virudhunagar-626 001) : Some results on neighbourly irregular graphs. Acta Cienc Indica-Math 2006, 32(3), 1007-12.

Let G be a finite simple connected graph. G is said to be a neighbourly irregular graph (or simply NI graph) if any two adjacent vertices have distinct degrees. It has been proved that in a NI graph number of vertices of degree i is at most n-i, for 1 ≤≤n-1. Considers some special cases. Also discusseds the case when there is at least one vertex of degree i for each, i, 1≤i≤n - 1. Moreover, obtains the maximum size of any NI graphs of order n and list all the NI graphs with at most six vertices.

5 illus, 6 ref

015832   Athisaya Ponmani S;Lellis Thivagar M (Mathematics Dep, Jayaraj Annapackiam College for Women, Periyakulam, Theni-625 601) : δgr-mappings associated with δ-generalised regular closed sets. Acta Cienc Indica-Math 2006, 32(3), 1333-40.

Aim is to introduce a new class of sets called δ-generalized regular closed sets and δ-generalized regular T_1/2-spaces and to introduce δgr-continuous and δgr-irresolute maps.

25 ref

015831   Anitha M;Thangavelu P (Mathematics Dep, Govindammal Aditanar College for Women, Tiruchendur-628 215) : On pre-generated pre-regular-closed sets. Acta Cienc Indica-Math 2005, 31(4), 1035-40.

In 2002, Veerakumar defined pre-semi-closed sets in topological spaces and investigated their properties. The purpose of this paper is to introduce pre-generalized pre-regular closed (briefly pre-gpr closed) sets and to study their properties. This class of sets is properly placed between the class of pre-closed sets and the class of pre-semi-closed sets. In this paper, we characterize pre-gpr-T1/2 spaces and gpr-T1/2 spaces and discuss their properties.

11 ref

015830   Alagar R (Mathematics Dep, Asan Memorial College of Engineering and Technology, Chengalpattu-603 105) : Finite product topologies with respect to ideals. Acta Cienc Indica-Math 2005, 31(4), 1125-8.

Given a topological space (X, τT) and an ideal ℑ al3 in X, a finer topology τ* in X can be associated with τ and ℑ. Given two topological spaces (X, τ₁), (Y, τ2) and ideals ℑ, φ in X, Y respectively, an ideal ℑ x ?? in X x Y, called the product ideal of ℑ and φ, in X x Y. author investigated inclusion relations between τ₁ X τ₂ and (τ1x τ₂)* and the conditions under which τ1x τ₂ = (τ1x τ₂)*.

5 ref

015829   Agrawal N;Jain R C (NO, Rajiv Gandhi Produyogiki Vishwavidyalaya, Bhopal, Madhya Pradesh) : New approach to approximate reasoning using fuzzy logic. Acta Cienc Indica-Math 2006, 32(3), 1127-32.

4 illus, 10 ref

015828   Acharya D P;Maji C (NO, , 109/3, Kailash Roy Chowdhury Road, Barrackpore, Kolkata-120) : Effect of rotation on the propagation of plane waves and surface waves in solid media under the couple-stress theory of elasticity. Acta Cienc Indica-Math 2006, 32(3), 969-84.

Studies the effect of rotation on plane waves and surface waves in solid media which rotates with a uniform angular velocity Ω under the couple-stress theory of elasticity. The linearised asymmetric theory of couple-stress elasticity, presented by Mindlin and Tiersten, has been used to investigate the elastic waves in a rotating solid medium. Two additional parts of acceleration, namely centripetal and Cariolis acceleration, have been considered. In the propagation of surface waves, special attention has been given to Rayleigh, Lave and Stoneley type of waves which are the particular cases of general surface waves. Wave velocity equations are deduced for different cases. The formulas and results presented in this investigation may be considered as more general ones in the sense that the results obtained by previous authors may be deduced from our results as particular cases. Some numerical calculations and graphs have been presented for the propagation of plane waves and Rayleigh waves to highlight the combined effect of rotation and couple-stress. It is observed that Love waves are not effected by rotation and the effect of couple-stress is also small.

4 illus, 1 table, 23 ref

011409   Yeung K S;Mulhollan T;Lee K H (NO, , ) : New test for SPR functions using Routh's array. J Computnl Math optimiz 2006, 2(3), 217-14.

Alternate methods for testing the strict positive realness of a function have recently been introduced in the literature. Presents another method to identify whether a function is strictly positive real (SPR) based entirely on Routh's array.

9 ref

011408   Xiaoji L (Mathematics Dep, College of Computer and Information Sciences, Guangxi University for Nationalities, Nanning 530 06, P.R. China, Email: xiaojiliu@yahoo.com.cn) : Partial ordering of the generalized nonnegative definite normal matrics. J appl Algebra Discrete Structs 2006, 4(3), 129-38.

Partial ordering of generalized definite nonnositive normal matrices are studied and the existing results are extended.

8 ref

011407   Tripathi B C;Et M;Altin Y;Mahanta S (Mathematical Science Div, Institute of Advanced Study in Science and Technology, Paschim Boragaon, Garchuk, Guwahati 781 035, Email: tripathybc@yahoo.com) : Generalized difference paranormed sequence spaces defined by orlicz function in a locally convex space. Indian J Math 2006, 48(2), 187-99.

Generalized difference paranormed sequence spaces c(Δⁿ, M, p, q), co(Δⁿ, M, p, q) and l∞ (Δⁿ, M, p, q) defined over a semi-normed sequence spaces (X, q) has been introduced. Different properties of them like completeness, solidity, symmetricity has been studied. Obtain some relations between these spaces as well as prove some inclusion results.

22 ref

011406   Tang G;Gao Y;Fu X (School of Mathematics and Computational Science, Hunan Univ of Sci and Technol, Xiangtan, Hunan 411201, Email: tang0326@163.com) : Note to solution for mixed problems realted to the time dependent wave equation. J Computnl Math optimiz 2006, 2(3), 175-9.

Conditions of existence and uniqueness of solutions for mixed problems related to the time dependent wave equation in [1] and [2] is weakened.

2 ref

011405   Tang G;Gao Y;Fu X (School of Mathematical and Computational Sciences, Hunan Univ of Science & Technology, Xiangtan, Human 411 201, Email: tang0326@163.com) : Note of solution for mixed problems related to the time dependent wave equation. J Computnl Math optimiz 2006, 2(3), 175-9.

2 ref

011404   Talukder H M;Santosh Kumar;Jones B C (Faculty of Mathematics, Open University in the South East St. James House, 150 London Road, East Grinstead, West Sussex UK RH19 1HG, Email: ht755@open.ac.uk) : Information recycling mathematical methods: analysis of link weighted protean communication flow network. Indian J Math 2006, 48(2), 221-38.

Flow of information in communication network may not be successful through some links due to technical faults or due to saturation of capacity, resulting in a state of no connectivity, which defined as a no communication state. This phenomenon of temporary non-availability or availability of a link changes the logical topology of the network. Such a network has been defined as a protean communication flow network. Intended to develop a mathematical model to find the flow capacity of such a communication network. There are two cases that could be considered. In one link changes their state but nodes are always in an operational state. In the other, nodes change their state but links are always in the operational state. In this investigation the case where link changes their state but nodes are always in the operational state has been considered. When a link fails, it is possible that it will fail to transmit flow. This also means that required flow may not reach the destination intended for the time period that the failed link remains un-repaired. Assumed that the communication has the capacity to store information during this failure. Analyzed and find the reliability of a two-state communication flow network in which the link is either in a communication state or in no communication network.

1 illus, 18 ref

011403   Spearman B K (Mathematics and Statics Dep, British Columbia Okanagan Univ, Kelowna, B.C. Canada VIV 1V7, Email: blair.spearman@ubc.ca) : Trinomials x<. J appl Algebra Discrete Structs 2006, 4(3), 149-55.

Rational parametrization is given for sextic trinomials which define sextic fields containing a cyclic cubic subfield.

3 ref

011402   Soybas D;Argun Z (Mathematics Dep, Faculty of Education, Gazi Univ, Teknikokular, 065 00, Ankara, Turkey, Email: danyal@gazi.edu.tr) : On the relationship beteen the week philip property and arens regularity. Indian J Math 2006, 48(2), 139-52.

Relationship between the Arens regularity of bilinear operators and the weak Phillips property has been investigated. A result, the weak Phillips property implies Arens regularity for Banach algebras not containing a copy of ι₁. Space K (X) of compact operators on a reflexive Banach space X with the approximation property has the weak Phillips property, although it fails to have the Grothendieck property. Under the same conditions, every bounded bilinear operator m : K(X) x K(X) → K(X) is Arens regular.

36 ref

011401   Sekigawa K;Yamada A (Mathematics Dep. Faculty of Science, Niigata University, Niigata-950 2181) : A note on the integrability of a class of almost quaternionic manifolds. Indian J Math 2006, 48(2), 239-48.

8 ref

011400   Qi J (Department of Mathematics, Ningbo University, Zhejiang, Ningbo 315211, P.R. China, Email: qwljgol@sohu.com) : Periodic solutions and stability to nonlinear autonomous impulsive differential equations. Indian J pure appl Math 2006, 37(2), 99-110.

Existence and stability of periodic solutions for nonlinear impulsive differential equations with impulse at variable moments has been studied. Sufficient and necessary conditions are obtained for the existence and stability of periodic solutions by using Ponecare mapping with impulse. Two examples are given to illustrate the main results.

7 ref

011399   Natarajan P N;Sakthivel S (NO, , Old No. 2/3 New No. 3/3, Second main Road, R A Puram, Chennai 600 028, Email: pinnangudinatarajan@gmail.com) : Weighted means for double sequences in non-archimedean fields. Indian J Math 2006, 48(2), 201-20.

Weighted means for double sequences in complete, non-trivially valued, non-archimedean fields and extend theorems for weighted means for double sequences has been defined.

7 ref

011398   Nam K B (Mathematical and Computer Sciences Dep, Wisconsin-Whitewater Univ, Whitewater, WI 53190, Email: namk@uww.edu ) : ALgebras on localizations of a stable algebra I. J appl Algebra Discrete Structs 2006, 4(3), 123-7.

Using a stable algebra in the formal power series ring, many authors defined a Lie and non-associative algebras. Author define a Lie and non-associative algebra using a localization of a stable algebra in the formal power series ring.

11 ref

011397   Mladenovic P (NO, University of Belgrade, Faculty of Mathematics, Studentski trg 16, 110, Serbia, Email: paja@matf.bg.ac.yu) : On extreme steps of a random function of finite sets. Indian J pure appl Math 2006, 37(2), 89-98.

Possible limiting distributions of extreme steps of a random function on finite sets as numbers of elements of these sets tend to infinity has been determined.

11 ref

011396   Lin S;Zhu J C;Ge Y;Gu J S (Department of Mathematics, Zhangzhou Teachers' College, Zhangzhou, Fujian 363 000, Peoples' Republic of China, Email: linshou@public.ndptt.fj.cn) : Almost-open maps, sequence-covering maps and SN-networks. Indian J pure appl Math 2006, 37(2), 111-9.

Some relationships among the images of metric spaces under almost-open maps or sequence-covering maps and spaces determined by certain sn-networks have been established, and some mapping theorems about generalized metric spaces have been obtained.

15 ref

011395   Li S;Wulan H (Mathematics Dep, Jia Ying Univ, 514 015 Meizhou, GuangDong, China, Email: jyulsx@163.com) : Besov space on the unit ball of C<. Indian J Math 2006, 48(2), 177-86.

Higher dimensional version of the Stroethoff characterization of the besov space on the unit ball of Cⁿ, as well as another new characterization has been obtained.

10 ref

011394   Kohaupt J (TFH Berin FB II, Luxemburger Str. 10, D-13353 Berlin, Germany, Email: kohaupt@tfh-berlin.de) : Computation of optimal two-sided bounds for the asymptotic behavior of free linear dynamical system with application of the defferential calculus of norms. J Computnl Math optimiz 2006, 2(3), 127-73.

Linear dynamical system x = A(t)x, t ≥ t0, x(t0) = x0, which is essentially restricted to the special cases of a constant system matrix A(t) = A = const and of a periodic system matrix A(t) = A(t + t_p) has been discussed in this paper. These cases are the ones which are most important and best investigated in technical problems. As theoretical background for the lower bounds, first we study the left regularity and left derivatives of norms of vector and matrix functions. Based on this and the corresponding facts on right regularity and right derivatives, new two-sided bounds for the asymptotic behavior of the solution x(t) and of the pertinent fundamental matrix Φ(t,to) are deduced. The main result is a two-sided bound based solely on the spectral abscissa v[A] if A(t) = A = const and on v[R] if A(t) = A(t + t_p) where R = (1/t_p) in Φ (t0 + t_p, t0). The bounds are applied to a vibration problem with periodic system matrix. The minimal constants in the asymptotic two-sided bounds can be determined numerically by the differential calculus of norms. The obtained results are especially of interest in engineering; they cannot be obtained by the methods used so far.

17 illus, 33 ref

011393   King J P (Mathematical Sciences Dep, Lehigh University, 14 E Packer Avenue, Bethlehem, Pennsylvania 18015 3174, USA) : Summability methods and bormann series expansions. Indian J Math 2006, 48(2), 249-58.

Burmann series are used to generate matrix methods of summability. Conditions for regularity and for summability of the geometric series are presented.

5 ref

011392   Jeon W;Nam K B (Natural & Applied Sciences Dep, Wisconsin-Green Bay Univ, Green Bay, Wisconsin 54311 7001, Email: jeonw@uwgb.edu) : Generalized contenct lie algebra of cartan type. J appl Algebra Discrete Structs 2006, 4(3), 165-75.

Cartan type K algebras over F, a field of characteristic 0, are generalized by extending the polynomial algebras to the Laurent polynomial algebras and the algebras of rational functions. These are infinite dimensional Lie algebras. There is the minimal ideal of this type of algebras and it is generated by a nonzero polynomial element. Simple subalgebras of these generalized algebras have also been seen.

6 ref

011391   Jeon W;Lee K S;Nam K B (Natural & Applied Sciences Dep, Wisconsin-Green Bay Univ, Green Bay, Wisconsin 54311 7001) : Algebras on localizations of a stable algebra II. J appl Algebra Discrete Structs 2006, 4(3), 157-63.

Lie and non-associative algebra are defined using a localization of a stable algebra in the formal power series ring in the paper. Using, a additive groups, author define a stable algebra. Further, Lie algebra and a non-associative algebras are defined using the stable algebra.

15 ref

011390   Jarvis A F;Larcombe P J;French D R (Pure Mathematics Dep, Sheffield Univ, Hicks Building, Sheffield S3 7RH, UK, Email: A.F.jarvis@sheffield.ac.uk) : Short proof of the 2-adic valuation of the Catalan-Larcombe-French number. Indian J Math 2006, 48(2), 135-8.

Short proof of the 2-adic valuation of the general term of the Catalan-Larcombe-French sequence has been presented. Following its initial dissemination by Eugene Catalan in the late 19th century, has been recovered formally in two different ways in previous papers.

3 ref

011389   Hanawa K;Kuga K I (Department of Mathematics and Informatics, Faculty of Science, Chiba University, 1-33 Yayoi-Cho, Inageku-Ku, Chiba City 263-8522, Japan) : On some formulas in combinatorial computation of uni-trivalent graphs. Indian J pure appl Math 2006, 37(2), 75-88.

Combinatorial computation of uni-trivalent diagrams with n fixed external points A (fixed n-pts) is considered. Some formulas for the combinatorial computation of Vassiliev-Kontsevich invariants of-such diagrams evaluated with rank 2 simple Lie algebras are obtained. Specifically, explicit base diagrams in A (fixed 4-pts) evaluated with the simple Lie algebras B₂ and G₂ are determined. These results are consequences of an explicit bound for the dimension of the image of the weight system W : A (fixed n-pts) → g^⊗n. These explicit bounds are provided for simple Lie algebras and affine Lie algebras as an application of Weyl-Kac character formula.

10 ref

011388   Gupta P;Arora H (Statistics Dep, Maharshi Dayanand Univ, Rohtak-124 001, Email: hari_arora@hotmail.com) : Generalized performance function for (r,s) entropy of DMC under single and multiple constraints. Indian J Math 2006, 48(2), 153-65.

Channel capacity is a key concept in information theory and its usefulness has been widely discussed in the literature. It is an important measure of channel performance but it requires a free choice of the input distribution. Brijpaul and Sharma [3] gave a direct method of computing the performance function of a discrete memoryless communication channels. They obtained the performance function for discrete channels by using Shannon entropy which is additive in nature, but in some situations additivity does not hold good. In such situations, non-additivity prevails. Algorithm for computing the performance function for generalized (r, s) entropy of discrete memoryless communication channel under single and multiple constraints has been given. Entropy has been defined by Sharma and Mittal [8] which is non-additive in nature.

10 ref

011387   Guo W (Mathematics Dep, Xuzhou Normal Univ, Xuzhou 221 116, P.R. China, Email: wbgeo@xznu.en) : Formations determined by hall subgroups. J appl Algebra Discrete Structs 2006, 4(3), 139-47.

It is proved that the class of all soluble groups in which every F-Projector contains some Hall π-subgroup as its normal subgroup is a local formation. In addition, the structure of the formation function of the formation is given.

8 ref

011386   Chandrakala P;Antony Raj S (Department of Mathematics, Presidency College, Chennai-600 005) : Radiation effects on MHD flow past an impulsively started infinite vertical plate with variable temperature. Indian J Math 2006, 48(2), 153-65.

Thermal radiation effects on MHD flow past an impulsively started infinite vertical plate in the presence of variable temperature is considered. The temperature near the plate is made to rise linearly with time. The fluid considered is a gray, absorbing-emitting radiation but a non-scattering medium. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity and temperature are studied for different parameters like Magnetic field parameter, time and radiation parameter. It is observed that the velocity slightly decreases with increasing the value of the radiation parameter.

3 illus, 1 table, 5 ref

011385   Agarwal M;Pandey P (Department of Mathematics and Astronomy, Lucknow University, Lucknow-226 007) : Combined harvesting of two competitive species having a resource dependent carrying capacity. Indian J pure appl Math 2006, 37(2), 63-73.

Non linear mathematical model is proposed and analyzed to study the combined harvesting of a system involving two competitive species having a resource dependent carrying capacity. Bounds for existing solutions of the system and criteria for the existence and stability of positive equilibria are obtained. The dynamical behavior of the system is studied in both the local and global senses. Also obtain the optimal harvesting policy for sustainable development of the species.

8 ref

012490   Shinde R L;Mahale M M (North, Maharashtra Univ, Maharashtra) : On the distribution of the number of failed components in a consecutive k-out-of-n: F system. IAPQR Trans 2006, 31(1), 19-26.

In a consecutive-k-out-of-n F system, Papastavridis obtained the distribution of W the number of failed components at the moment of system failure. Two exact formulae have been drived for the pmf of W using an urn model and minimaTi-cutsequence approaches.

8 ref

012489   Narain L;Bagga P C (NO, Delhi Univ, Delhi) : Bicriteria in nxm flowshop problem. IAPQR Trans 2006, 31(1), 57-71.

The paper provides the procedure for obtaining sequence(s) in special n x m flowshop problems which gives minimum possible mean flowtime while minimizing total elapsed time.

4 tables, 10 ref

012488   Maiti S S (NO, Visva-Bharati Univ, India) : On estimation of P (X ≤ Y) for discrete distributions useful in life testing. IAPQR Trans 2006, 31(1), 39-46.

Estimation of R = P (X ≤ Y) has been considered when X and .Y follow discrete distributions (like Geometric, Poisson). Both UMVUE of R and estimator of R using ML estimators of parameters involved have been found out. Simulation has been conducted to examine the .MSE's of these two estimators.

3 tables, 3 ref

012487   Jain J L;Meitei A J (NO, Delhi Univ, Delhi) : Computational study of the transient solution of M/M/1 queue by takacs. IAPQR Trans 2006, 31(1), 27-37.

Author discusses the computational efficiency of the Takacs expression for the transient solution to M/M/1 Queueing System, for different values of the parameters in comparison with the other expressions using the Mathematica 4 Package.

8 tables, 19 ref

012486   Hanagal D D (NO, Pune Univ, Pune) : Gamma frailty regression model in bivariate survival data. IAPQR Trans 2006, 31(1), 73-83.

Genetic epidemology propose maximum likelihood estimation procedure for a bivariate fraility regression model in which dependence is generated by a gamma distribution. Authors bivariate survival data follow bivariate Weibull of Hanagal (1996) and distribution of censoring variable is independent of the two life times. There are some interesting situations like survival times in genetic epidemiology, survival times of dental implants of patients and survival times of twin births (both monozygotic and dizygotic) where genetic behaviour (which is unknown and random) of patients follows gamma frailty distribution. These are the situations which motivate to study this particular model.

16 ref

012485   Dutta A K (Stat-Math Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata-700 108, Email: amartya@isical.ac.in) : Aryabhata and axial rotation of earth. Resonance 2006, 11(5), 58-72.

Brief historical account of some of Aryabhata's views on axial rotation of Earth has been given.

10 ref

012484   Ali M M;Woo J;Nadarajan S (NO, Ball State Universite, Muncie, USA) : Parametric and non-parametric estimation for right truncated exponential distribution. IAPQR Trans 2006, 31(1), 47-55.

Foright truncated exponential distribution, the estimation of the truncation parameter, mean parameter, right tail probablity and the left tail probablity are considered. Various parametric and non-parametric estimators are used and their performance compared in terms of the mean squared error.

1 illus, 1 table, 5 ref

012483   Aggarwal M L;Roy Chowdhury S;Bansal A;Mital N (NO, Memphis Univ, Memphis, USA) : Hidden projection property for 4<. IAPQR Trans 2006, 31(1), 1-18.

Hamada and Wu studied .16-run and 24-run Plackett-Burman designs for estimation of some two-factor interactions along with main effects'. Hidden projections for 4'2" (n = 3,4) non-regular fractional factorial designs were studied using l6 run and 24-run non-regular Hadamard matrices.

5 tables, 17 ref

010435   Zhu P;Wang Z;Zhao J (School of Science, Southern Yangtze University, Wuxi, Jiangsu 214122, P.R. China, Email: zptl2002@yahoo.com.cn) : Quasi-Rings and Clifford Quasi-regular semirings. J appl Algebra Discrete Structs 2006, 4(2), 99-107.

By using quasi-groups, introduced the concept of quasi-rings and present, a construction theorem for an arbitrary quasi-ring. Also defined the so-called Clifford quasi-regular semirings. Combining the relationship between Clifford, quasi-regular semigroups and Clifford quasi-regular semirings, discussed some properties of Clifford quasi-regular semirings and give some necessary and sufficient conditions for them.

7 ref

010434   Yang S J;Shi B;Gai M J (NO, Institute of Applied Mathematics, Naval Aeronautical Engineering Insti, Yantai, Shandong 264001, People's Republic of China, Email: baoshi781@sohu.com) : Boundary value problems for functional differential systems. Indian J pure appl Math 2005, 36(12), 685-705.

Concerns with the existence of solutions of two-point singular boundary problems for second-ordet functional differential systems.

15 ref

010433   Xiaoji L (Department of Mathematics, College of Computer and Information Science, Guangxi University for N, Nanning 530006, P.R. China, Email: xiaojiliu72@yahoo.com.cn ) : On the inverse order rule for weighted generalized inverse. J appl Algebra Discrete Structs 2006, 4(2), 85-92.

Some new sufficient and necessary conditions for inverse order rule for weighted generalized inverse are given using the weighted singular-value decomposition.

6 ref

010432   Wang Q W;Qin F (Mathematics Dep, Shanghai Univ, Shanghai-200444, Peoples' Republic of China) : Common solution to matric equations over a reglur ring with applications. Indian J pure appl Math 2005, 36(12), 655-72.

Common solutions of the matrix equations X B₁ = C₁ X B₂ = C₂, A₃ X B₃ = C₃, A₄ X B₄ = C over ℜ an arbitrary von Neumann regular ring with identity, are considered. A necessary and sufficient condition for the existence and the representation of the common solution to system mentioned above are given. As an application, a necessary and sufficient condition for the existence and the expression of the centrosymmetric solution to the system X B ₁ = C₁, A₃ X B₃ = C₃ over ℜ with char ℜ ≠ 2 are given. Furthermore, some auxiliary results on the othersystems of matrix equations over ℜ are also obtained.

28 ref

010431   Verma K L (Mathematics Dep, Government Post Graduate College, Hamirpur (H.P.)-177 005, Email: klverma@sancharnet.in) : Normal mode expansion method for generalized thermoelastic Lamb waves in transversely isotropic thin plates. Int J appl Math Statist 2006, 4(J06), 68-83.

A quantitative theory for modeling the generalized thermoelastic Lamb waves, which propagates in transversely isotropic plates with thermal relaxation, is presented by employing normal mode expansion method of generalized Lamb wave modes. The displacement and temperature fields are expressed by a summation of the symmetric and antisymmetric thermoelastic modes in the surface thermal stresses and thermal gradient free transversely isotropic plate, and therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin plates. The results show that the theory provides a quantitative analysis to characterize anisotropic elastic stiffness properties of transversely isotropic plates by Lamb wave detection. Numerical calculations have been presented for a zinc plate. However, the methods can be used for other materials as well.

4 illus, 40 ref

010430   Torres D F M (Mathematics Dep, University of Aveiro, 3810-193 Aveiro, Portugal) : Simple proof of the constancy of the Pontryagin Hamiltonian for autonomous problems. Int J appl Math Statist 2006, 4(J06), 23-4.

Author provide a new, simpler, and more direct proof of the well known fact that for autonomous optimal control problems the Pontryagin extremals evolve on a level surface of the respective Pontryagin Hamiltonian.

7 ref

010429   Suresh V (Math Statist Dep, Univ Hyderabad, P.O. Central Univ, Goachibowli, Hyderabad-500 046, Email: vssm@uohyd.ernet.in) : Discriminants of involutions. Indian J pure appl Math 2006, 37(1), 3-7.

Work of Knus, Parimala and Sridharan on the discriminants of involutions is described.

10 ref

010428   Srinivasan A;Thiagarajan M (Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, Email: mathsrinivas@yahoo.com) : M/M/1/K Interdependent queueing model with controllable arrival rates. Int J Mgmt Syst 2006, 22(1), 23-34.

M/M/1/K interdependent queueing model with controllable arrival rates is considered. The steady state solutions and the system characteristics are derived and analyzed for this model. Numerical examples are given for a better understanding.

3 tables, 4 ref

010427   Silverman J H;Stephens N (Mathematics Dep, Box 1917, Brown University, Providence, RI 02912 USA, Email: jhs@math.brown.edu) : Sign of an elliptic divisibility sequence. J Ramanujan Mathl Soc 2006, 21(1), 1-17.

An elliptic divisibility sequence (EDS) is a sequence of integers (W_n) _n≥0 generated by the nonlinear recursion satisfied by the division polyomials of an elliptic cureve. A formula for the sign of W_n for unbounded nonsingular EDS, a typical case being Sing (W_n) = (-1)^[nβ] for an irrational number β ∈ R given. As an application, it has been shown that the associated sequence of absolute values (<157>W_n<157>) cannot be realized as the fixed point counting sequencde of any abstract dynamical system.

20 ref

010426   Shukla D;Trivedi M (Department of Mathematics and Statistics, Dr. H.S.Gour University, Sagar, MP-470 003, Email: diwakarshukla@rediffmail.com) : Examining stability of variability ratio with application in post-stratification. Int J Mgmt Syst 2006, 22(1), 59-70.

Suppose a survey is repeated over several occasions on the same population to learn the rate of change over time. A ratio of mean squares reveals a tendency of stability if the span of time between occasions is not very large. Explores and examines the characteristics on various data sets and presents an example of application for the estimation of population mean under the post-stratified set-up. A database study is incorporated to support the results and a study for robustness property has been also carried out.

5 tables, 16 ref