004138   Heydari A P D (Dep of Stats, Mazandaran Univ, Babolsar, Iran) : On flow-shop scheduling problem with processing of jobs in a string of disjoint job-blocks : fixed order jobs and arbitrary order jobs. J Indian Soc Statist Ops Res 2003, 24(1-4), 39-43.

A flow-shop 2xn scheduling problem where processing of jobs is done in a string of disjoint job-blocks has been considered : An optimal solution procedure minimizing the total elapsed/production time has been given.

3 ref

004137   He L (Math Dep, Harbin Inst of Technol, Harbin, 150001, P.R. China) : Version's inner product of π-partial characters for π-separable groups. Far East J mathl Sci 2003, 11(2), 147-51.

A form of inner product of π-partial characters of π-separable groups has been given and a weak version of the corresponding Frobeniux reciprocity has been obtained and one application is exhibited.

9 ref

004136   Han J H;Son J W (Math Dep, Univ of Mysore, Manasagangothri, Mysore-570 006) : q-Distribution operator. Far East J mathl Sci 2003, 11(2), 207-14.

A q-distribution operator and as been defined some properties of it have been investiated under two cases. One when χ is not tocally constant and another when it is locally constant but not the trivial character, The T-invariant subspace Fq has been found.

10 ref

004135   Gupta P;Arora G K;Tuteja R K (NO, M D University, Rohtak-124 001) : R-divergence for continuous probability distributions. J Indian Soc Statist Ops Res 2002, 23(1-4), 45-51.

Two parametric genralizations of R-divergence for the continuous probability distribution have been provided. A unified expression of these generalizations is obtained and its properties are also studied.

10 ref

004134   Gupta K C;Taneja A K (Dep of Math, M D U P G Reg Cen, Rewari) : Comparative study of two models for a Two-unit cold standby system with instructions and two types of repairman. J Indian Soc Statist Ops Res 2002, 23(1-4), 23-39.

A two-unit cold standby system is investigated with two types of repairman one expert and the other his assistant. Two models are discussed with the concept of instructions in the second model and no instruction in the first model. Various measures of system effectiveness are obtained using semi-Markov processes and regenerative point technique. Comparative study of the two models is made through graphs.

7 illus, 5 ref

004133   Gungor M;Et M (Math Dep, Firat Univ, 23119-Elazig, Turkey) : Δ<. Indian J pure appl Math 2003, 34(8), 1141-51.

Introduces the space of sequences that are Δ^r-strongly almost summable with respect to an Orlicz function. Some relations related to these sequence spaces have been given. It is also shown that if a sequence is Δ^r-strongly almost summable with respect to an Orlicz function, then it is Δ^r-almost statistically convergent.

23 ref

004132   Gandhi B K;Reddy M J (Math Dep, Jawaharlal Nehru Technological Univ Coll of Engng, Kukatpally, Hyderabad-500 072) : Triangular numbers in the generalized associated Pell sequence. Indian J pure appl Math 2003, 34(8), 1237-48.

4 tables, 6 ref

004131   Edmunds D E;Kokilashvili V (Cen for Math Analysis and its Applic, Univ of Sussex, Brighton BN1 9QH, United Kingdom) : On Fourier multipliers. J Analysis Applic 2003, 1(3), 143-55.

Deals with two-weighted inequalities for multipliers of the Fourier transform which is considered in the framework of S'-distributions. Optimal conditions for other pairs of weights ensuring two-weight estimates for general multipliers in Trieble-Lizorkin spaces are established. Two-weighted boundedness criteria for integral operators with positive kernel are essential for the arguments. The method of proof consists in the representation of the multiplier operator in the form of compositions of certain "elementary" transformations. (L^p_w, L^q_v) multiplier statements are derived. An example of pair of power weights goerning two-weight estimates for Fourier ultipliers in presented.

7 ref

004130   Diagana T (Dep of Math, Howard Univ, 2441 6th Street, N.W. Washington, DC 20059, U S A) : On the algebric sum of Unbounded normal operatots. Far East J mathl Sci 2003, 11(1), 89-94.

Characterizes the algebric sum of unbounded normal operators.

4 ref

004129   Datta S;Shukla M (Math and Astronomy Dep, Lucknow Univ, Lucknow-226 007) : Slow steady rotation of a DISC with slip in a viscous fluid. Indian J pure appl Math 2003, 34(10), 1459-68.

The problem considered is concerned with the determination of the viscous couple on a uniformly rotating disc with angular velocity Ω about its axis in an infinite extent of viscous fluid. The problem is then formulated as the mixed boundary value problem and solved by finding the azimuthal component of velocity υ for the case of rotational symmetry, satisfying the mixed boundary conditions. To obtain the couple on the disc atempt is first made for both large and small values of the slip parameter β through the method of perturbation. For small values of β the perturbation method fails. Therefore n approximate solution has been assumed which provides the couple not only for small β but also agrees qualitatively with the perturbation value for large β. It is seen that the effect of slip coefficient β is to decrease the couple on the disc.

2 tables, 15 ref

004128   Charles V;Dutta D (Dep of Math & Humanities, REC Warangal-506 004, ) : Two level linear stochastic fractional programming problem with discrepancy vector. J Indian Soc Statist Ops Res 2002, 23(1-4), 59-67.

Two level linear stochastic fractional programming problem with discrepancy vector involves two subsidiary optimization problems where the decision variable of the first level problem is implicitly determined by another optimization problem. Two level linear stochastic fractional programming problem (TLLSFPP) in which the objective function of the first level is fractional with non-stochastic constraints, whereas the objective function of the second level is linear function subject to stochastic constraints was considered. In the second level the objective function which is the product of discrepancy and penalty vector was minimized in order to maximize the first level problem.

4 illus, 3 ref

004127   Chakrabarti A;Ahluwalia D S;Manam S R (Math Dep, Indian Inst of Sci, Bangalore-560 012) : A note on surface water waves for finite depth in the presence of an ice-cover. Indian J pure appl Math 2003, 34(11), 1631-44.

A class of boundary value problems involving propagation of two-dimensional surface water waves, associated with water of uniform finite depth, against a plane vertical wave maker is investigated under the assumption that the surface is covered by a thin sheet of ice. It is assumed that the ice-cover behaves like a thin isotropic elastic plate. Then the problems under consideration lead to those of solving the two-dimensional Laplace equation in a semi-infinite strip, under Neumann boundary conditions on the vertical boundary as well as on one of the horizontal boundaries, representing the bottom of the fluid region, and a condition involving upto fifth order derivatives of the unknown function on the top horizontal ice-covered boundary, along with the two appropriate edge-conditions, at the ice-covered corner, ensuring the uniqueness of the solutions. The mixed boundary value problems are solved completely, by exploiting the regularity property of the Fourier cosine transform.

6 tables, 12 ref

004126   Cammaroto F;Chinni A (Dep of Math, Univ of Mesina, 98166 Sant Agata-Messina, Italy) : Infinitely many solutions for a Two points boundary value problem. Far East J mathl Sci 2003, 11(1), 41-51.

Conditions on the continuous function ƒ : R → R have been discussed ensuring that the Dirichlet problem related to the equation - uⁿ = →(u) admits infinitely many classical solutions in W₀^1,2([0,1]).

4 ref

004125   Borkar M S;Karade T M (Math Dep, Nagpur Univ, Mahatma Jotiba Phule Educational Campus, Amravati Road, Nagpur-440 010) : On singularity of spherically symmetric space times. Indian J pure appl Math 2003, 34(8), 1219-24.

The definition of the singularity is proposed on the basis of the characteristic system of a spherically symmetric space time containing two orthogonal vectors and nine scalars and then concluded that the so called Schwarzschild singularity is physical.

1 table, 19 ref

004124   Bhowmik B B;Rajput A (NO, Netaji Subhas Vidyaniketan Higher Secondary School, Basugaon-783 372, Dist. Kokrajhar, Assam) : Five-dimensional Brans-Dicke cosmology with constant deceleration parameter. Indian J pure appl Math 2003, 34(8), 1189-93.

It has been shown that (for k = 0) a five-dimensional Brans-Dicke cosmology with creation of matter does not admit of any model with non-zero energy-density if the deceleration parameter is assumed to be constant. This leads to the corollary that no corresponding four-dimensional Brans-Dicke cosmology can evolve out of such a five-dimensional cosmology.

24 ref

004123   Bhave N S;Deshpande C M (Math Dep, Univ of Pune, POune-411 007) : Range of diameters of a bipartite graph and its generalized 2-partite complement. Indian J pure appl Math 2003, 34(8), 1209-18.

11 illus, 2 tables, 10 ref

004122   Bhavanari S;Kuncham S P (Math Dep, Nagarjuna Univ, Nagarjuna Nagar-522 510) : An isomorphism theorem on directed hypercubes of dimension n. Indian J pure appl Math 2003, 34(10), 1453-7.

In graph theory, hypercubes of fimension n were well known. Directed hypercubes have been introduced. Four properties P₁, P₂, P₃, P₄ of directed graphs were identified and finally proved that a directed graph is a directed hypercube of dimension n if and only if it satisfies properties P₁-p₄.

3 ref

004121   Baljeet Singh (Math Dep, Govt Coll, Sector 11, Chandigarh) : Wave propagation in an anisotropic generalized thermoelastic solid. Indian J pure appl Math 2003, 34(10), 1479-85.

The plane wave propagation in a homogeneous transversely isotropic thermally conducting elastic solid is studied with two thermal relaxation times. Three types of plane waves, quasi-P, quasi-S ad thermal waves, are shown to exist. The analytical expressions for their velocities of propagation are obtained. The velocities of these waves are found to depend on the angle of prpagation and frequency. This dependence of velocities on the direction of propagation and frequency is shown graphically. Effects of thermal parameters and anisotropy upon these velocities are observed.

2 illus, 14 ref

004120   Bahl S;Nain M (Dep of Statist, M D University, Rohtak-124 001) : Post-stratified estimation in two stage design using multivariate auxiliary information. J Indian Soc Statist Ops Res 2000, 21(1-4), 19-30.

Post-stratification is often used to increase the precision of survey estimation and multi-auxiliary information is used for improving the efficiency of the estimators. An attempt has been made to develop the estimator of population parameter in a post-stratified two-stage design using multi-auxiliary information under the assumption that the population mean of multi-auxiliary characters (X_ikh) as well as stratum size (M_in) are known. It has been demonstrated that the suggested procedure not only provides estimators of the character under study according to strata variables but also improves the precision of the estimator pooled over the strata compared to the conventional unstratified two-stage procedure.

6 ref

004119   Amroune A;Gheboli M;Zedam L (Dep of Math, Univ of Med Boudiaf, P. Box 166 Ichbilia 28003 M'sila, Algeria) : Priestley duality and representation of Heyting algebra. Far East J mathl Sci 2003, 11(1), 65-74.

Gives a topological representation for the Heyting algebras by means of Priestley spaces.

7 ref

003132   Yaoqing Z (Dep of Math and Phy, Wuyi Univ, Jiangmen, Guangdong 529 020 P.R. China) : On supplements of maximal subgroups of a Finite group. J appl Algebra Discrete Structs 2003, 1(3), 181-8.

Supplements of maximal subgroups of a finite group have been discussed. A result of O.H. Kegel is strengthened and a result which proved a conjecture raised by W.E. Deskins is improved. Some theorems which characterize the supersolvability of a finite group have been obtained.

10 ref

003131   Yalavigi C C (NO, , Sai Deep Hts. Pai Lay Out, Bangalore-560 016) : Proof for a 'Generalised FLT with different indices'. Math Educ 2003, 37(3), 145-9.

The title abbrevation is well-known to Number Theorists, and this paper concerns the proof for Generalised Fermat's Last Theorem with different indices.

6 ref

003130   Vinocha O P; (Dep of Math, S.G.N. Khalsa College, Sri ganganagar-335 001) : On the non-existence of perfect double hamming error correcting codes on q=11 symbols. Math Educ 2003, 37(3), 123-9.

By generalizing and extending the techniques developed by Alter (1968) diophantine equation 2y² = (11)^k+7 for k<62>2 has been solved the existence of no perfect double Hamming-error-correcting codes on q=11 symbols have been justified.

3 tables, 4 ref

003129   Verma S M;Reddy E M K (Department of Operations Research and SQC, Sri Krishnadevaraya University P G Centre, Kurnool-518 002, Andhra Pradesh) : Reliability indices for 2-component non-identical system. J Instn Engrs-Pt ID 2003, 84(Nov), 30-2.

Determination of reliability characteristics, eg, reliability function and mean time between failures (MTBF) which reveals the important measures of the effectiveness of the system in the reliability analysis has been dealt with. The model considers the 2-component non-identical system, which is under the influence of lethal shocks in addition to individual failures as well as non-lethal common cause shock failures. The emphasis is on the Markovian approach in order to derive the reliability characteristics mentioned. These measures are compared in the presence of lethal common cause shock failures with that of the situation when only individual failures are affecting the system. The numerical illustration is also discussed.

1 illus, 1 table, 5 ref

003128   Thiyagarajan M;Santhi B (Math Dep, Shanmugha Arts, Sci Techno & Res Acad, Thanjavur-613 402) : Linear algebraic representation of wavelet coefficients. Math Educ 2003, 37(3), 154-60.

With the advent of the digital age, many opportunity have arisen for the collection, analysis and dissemination of information. Dealing with such massive amounts of data presents difficulties. All of this digital information must be stored and be retrievable in an efficient manner. One approach to deal with these problems is to use wavelets. Haar wavelets have the property that zero everywhere except on a small interval. These can be used to expand any function of the compact support using the connection between Haar wavelet and Linear algebra. Signals can be decomposed into wavelet coefficients and recompose the signal from the wavelet coefficients. This idea can be extended to any kind of signal processing.

3 ref

003127   Shankar P N (Computational and Theoretical Fluid Dynamics Div, National Aerospace Laboratories, Bangalore-560 017) : On the use of biorthogonality relations in the solution of some boundary value problems for the biharmonic equation. Curr Sci 2003, 85(7), 975-9.

If a function <>(x,y), biharmonic in the semi-infinite strip {-1/2<60>x<60>1/2, y<60>0}, be such that the function and its normal derivative vanish on the side walls x=±1/2. The problem of determining this function is considered when given <>(x,0) and <>²2<>(x,0) one is on the short edge y = 0. First, a direct method of obtaining a biorthogonality relation among the elgenfunctions is given and then a formal solution of the boundary value problem using this relation. Next it is shown that if one attempts to use this solution using a finite number of terms of series, it is inferior to a solution where the expansion coefficients are calculated using a least squares procedure. This is a surprising result considering that for Fourier series, the Fourier coeffcients are always optimal.

2 illus, 2 tables, 9 ref

003126   Shankar P (Dep of Computer Science and Automation, Indian Institute of Science, Bangalore-560 012) : Codes and decoding on graphs. Curr Sci 2003, 85(7), 980-8.

Graphical descriptions of block codes known as trellises, which illustrate connections between algebra and graph theory, and can be used to develop powerful decoding algorithms have been looked into. Trellises for linear block codes are known to grow exponentially with the code parameters and hence decoding on such objects is often infeasible. Of considerable interest to coding theorists therefore, are more compact descriptions called tail-biting trellises which in some cases can be much smaller than any ordinary trellis for the same code. Some interesting properties of tail-biting trellises and have been derived an optimal maximum likelihood decoding algorithm that performs rather well in terms of decoding complexity even at low signal-to-noise ratios is presented.

9 illus, 27 ref

003125   Sarkar J (NO, , ) : Principles of traffic forecasting. Indian Ports 2002, 34(1), 9-12.

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003124   Rajesh Kumar;Ajay Kumar;Nirbhay Kumar;Jha K N (Dep of Math, L.N. Mithila Univ, Darbhanga- 846 004) : On existence properties of reverse recursion theory. Math Educ 2003, 37(3), 164-6.

Examines the existence and non-existence properties of recursively enumerable sets under Σ₂ induction. M. Mytilenacos and T.A. Slaman have shown that all recursively enumerable sets satisfy existence properties under finite injury method. It has been shown here that the ∀∃ theory of recursively enumerable degrees under Σ₂ collection is different from Peano's aximons.

6 ref

003123   Prathap G;Mukherjee S (NO, CSIR Centre for Mathematical Modelling and Computer Simulation, Bangalore-560 037) : The engineer grapples with theorem 1.1 and lemma 6.3 of Strang and Fix. Curr Sci 2003, 85(7), 989-94.

The best-known statements on error analysis of the finite element method are derived using rigorous mathematical abstractions which are difficult for the average engineer (who remains the biggest user) to grasp. There is much merit in being able to re-derive these using the energy, virtual work and least action principles that the engineer or physicist is more familiar with. An attempt has been made to obtain Theorem 1.1 and Lemma 6.3 of Strang and Fix, perhaps the most valuable of all error statements ever made of finite element elastostatics and elastodynamics. Some interesting atypical problems which arise when errors that appear when finite element discretization is used to solve problems of interest in engineering and applied science are studied have been looked into. The formal mathematical theorems and lemmas which have been identified in the seminal work of Strang and Fix, are now re-examined for these atypical situations using an engineering approach.

16 ref

003122   Nam K B;Wang M O (Dep of Math, Univ of Wisconsin-Whitewater, Whitewater, WI 53190 U.S.A.) : Notes of some Non-associative algebras. J appl Algebra Discrete Structs 2003, 1(3), 159-64.

The non-associative N_n,m,s is introduced in the papers [1], [7]. All the derivations of the non-associative simple N_0,0,1 algebra is found in the paper [1]. All the derivations of the non-associative algebras and the automorphism group have been found.

8 ref

003121   Nam K B (Math Dep, Univ of Wisconsin-Whitewater, Whitewater, WI 53190 U.S.A.) : Graded radical W-type Non-associative algebras I. J appl Algebra Discrete Structs 2003, 1(3), 211-8.

Non-associative algebra N_√m,e (∂) which is simple and Lie admissible has been found. Also the automorphism group has been defined Aut(N_o,1,1) of N_0,1,1 has been found.

9 ref

003120   Maitra S N (Math Dep, Natn Def Acad, Khadakwasla, Pune-411 023) : Analytical solution to relativistic rocket motion. J Aerospace Sci Technol 2003, 55(2), 153-6.

Basing on classical dynamics, motion of rocket called Newtonian Rocket is contemplated in the sense of framing its differential equations of motion. These differential equations of motion of rocket have modified in the light of theory of relativity applying Lorentz's transformation and have velocity of rocket but considerably less than the velocity of light to determine its propellant mass, velocity and distance travelled. A tabled with numerical has been prepared comparing the performance of the relativistic rocket with its Newtonian counterpart. Rocket dynamics in vacuum and gravitationless space, coupled with continuous decrease in mass due to the propellant consumption and due to relativistic effects have been dealt.

3 ref

003119   Mahurpawar V; (Dep of Math, Govt. Auto. P.G. College, Chhindwara-480 001) : Nil contribution of cosmic string to Bianchi type VI₀ cosmological model in bimetric relativity. Math Educ 2003, 37(3), 142-4.

A homogeneous and isotropic Bianchi type VI₀ cosmological model does not accomodate cosmioc strings coupled with perfect fluid distribution in bimetric relativity. Further it has been observed that the resulting space-time is free from singularity.

4 ref

003118   Li H C;Shum K P (Fac of Sci, The Chinese Univ of Hong Kong, Shatin, N.T. Hong Kong China (SAR)) : On a problem of Spctral posets. J appl Algebra Discrete Structs 2003, 1(3), 203-9.

In studying the conditions for a poset to be a spectral space, Lewis and Ohm asked in 1976 that if the ordered disjoint union of posets X_λ's is spectral, are the Xλ also spectral? There is so far no answer to this question in the literature. It has been proved that under certain cases, the answer to this question is affirmative.

4 ref

003117   Khairnar S M;Kulkarni S R (Dep of Math, Anuradha Coll of Enging, Chikhli-443 201) : A class of analytic functions with subordination. Math Educ 2003, 37(3), 130-2.

There are many criterion for univalency in the unit disk E. One criterion has been given for the function. f(z) = z + a₂z² + a₃z³ + ... to be univalent in <157>z<157> <60> 1 and which is subordinate to g(z); i.e. f(z)⊂g(z); g(z) be anlytic in the unit disk E =<123> z;<157>z<157> <60> 1 <125>. More have been found about differential subordination on the lines of Miller and Mocanu.

4 ref

003116   Joshi D C (Dep of Math, South Gujarat Univ, Surat-395 007) : Approximate solution of the miscible fluid flow through porous media using collocation method. Math Educ 2003, 37(3), 133-6.

Discusses the general solution of the miscible fluid flow through porous media in the form of concentration of the fluid. The mathematical formulation of the miscible fluid flow through porous media gives a non-linear partial differential equation which is transformed into ordinary differential equation (ode) by using a similarity variable. An alternative general solution is obtained by Galarkin's collocation method for odes. The phenomenon of longitudinal dispersion is discussed by regarding the cross-sectional flow velocity as time dependent in a specific form.

5 ref

003115   Jha D C (Univ Dep. of Math, L.N. Mithila Univ., Darbhanga-846 004) : On fixed point theorem in quasi-metric space. Math Educ 2003, 37(3), 150-3.

Generalises the results on fixed point theorem on quasi-metric space of Kelly and Wison. It has been shown here that a self-mapping on a quasi-metric space has unique fixed point in a non-empty set.

7 ref

003114   Dep S D (Dep of Math, N.S. Sci. Coll., Bhadrawati-442 908 Dist.-Chandrapur) : Uniform anisotropic vacuum solutions in bimetric relativity. Math Educ 2003, 37(3), 161-3.

4 ref

003113   Crnkovic D;Rukavina S (Dep of Math, Fac of Philosophy, Omladinska 14, 51000 Rijeka, Croatia) : On Hadamard (35,17,8) designs and their automorphism groups. J appl Algebra Discrete Structs 2003, 1(3), 165-80.

All symmetric Hadamard (35,17,8)-designs admitting automorphism groups of order 17,7,5 or cyclic automorphism groups of order 6 have been classified. Also, all Hadamard (35,17,8)-designs with an automorphism of order 3 having 8 fixed points and Hadamard (35,17,8)-designs admitting a standard action of an automorphism of order 4 have been constructed. The full automorphism groups of the designs obtained have been studied.

12 ref

003112   Chen H;Chen M (Dep of Math, Zhejiang Normal Univ, Jinhua, Zhejiang 321 004 People's Republic of China) : On unit 1-stable range. J appl Algebra Discrete Structs 2003, 1(3), 189-96.

For an ideal I of a ring R, R will be considered to satisfie unit 1-stable range for 1 in case ax + b = 1 with a ∈ I, x,b ∈ R implies that there exists a u ∈ U(R) such that x + ub ∈ U(R). If R satisfies unit 1-stable range for I, then M_n(R) satisfies unit 1-stable range for M_n(I).

11 ref

003111   Biswal T;Patra P K (Dep of Math, Samanta Chandra Sekhar College, Puri-752 001) : Flow of a visco elastic maxwell fluid through a rectilinear pipe of paral. lelogram crossectional area. Math Educ 2003, 37(3), 137-41.

The unsteady flow of visco-elastic Maxwell fluid through a rectilinear pipe having its cross-section as a parallelogram with a time dependant pressure gradient has been discussed. To solve the problem, variable separable method has been used. The solution of two particular cases have also been obtained insisting upon the condition m⁴λ²+1 =0. The solution so obtained matches with the those solutions for a viscous fluid as a particular case.

6 ref

003110   Behravesh H;Shahbazpour K (Dep of Math, Univ of Urmia, Urmia, Iran) : Quasi-permutation representations of sporadic groups. J appl Algebra Discrete Structs 2003, 1(3), 197-22.

The quantities c(G), q(G), and p(G) were defined by H. Behravesh for finite groups. c(G), q(G) and p(G) have been computed for sporadic groups.

4 ref

002191   Zhongxue L (Basic Sci Dep, Sci of Technol Coll, Xuzhou Normal Univ, Jiangsu-221 011, People's Republic of China) : Note on "new generalizations of hardy's integral inequality". Indian J pure appl Math 2003, 34(6), 831-40.

Some new generalizations of Hardy's integral inequalities have been given.

5 ref

002190   Zhang X (Math and Sys Sci Dep, Shandong Univ, Jinan, Shandong 250 100, People's Republic of China) : Global solutions of nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces. Indian J pure appl Math 2003, 34(6), 873-89.

A new comparison result and the Monch's fixed point theorem have been used to study the existence of global solutions of initial value problems for nonlinear second order impulsive integro-differential equations of mixed type in Banach spaces. As applications, the existence of global solutions of two classes of mixed boundary value problems for fourth order impulsive equations is given.

7 ref

002189   Yoon D W (Math Dep, Coll of Edu, Gyeong Sang Nat Univ, Chinju=660 701, Republic of Korea) : Some properties of the clifford torus as rotation surfaces. Indian J pure appl Math 2003, 34(6), 907-15.

Rotation surfaces in the 4-dimensional Euclidean space IE⁴ have been studied. Complete classification theorems for the flat rotation surfaces with pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. Flat rotation surfaces of finite type immersion have been characterized with Gauss map and the mean curvature vector field, namely the pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surface with respect to the induced metric.

21 ref

002188   Yegnanarayanan V (Sci and Humanities Dep, Arulmigu Meenakshi Omman Coll of Engng, Vadamavandal Kanchipuram) : A note on nordhaus-gaddum class. Indian J Math 2003, 45(1), 117-9.

The determination of the upper and lower bounds (Preferably sharp bounds) ƒ(G) + ƒ(G^c) and ƒ(G) ƒ(G^c) where G is a graph of order p is called the Nordhaus-Gaddum problem for a given graph theoretic parameter ƒ and a positive integer p. The sums and products of values of the vertex partition number over the factors of a decomposition have been studied.

4 ref

002187   Yajnik K S;Sharada M K (NO, CSIR Centre for Mathematical Modelling and Computer Simulation, Wind Tunnel Road, Bangalore-560 037) : Ammonium inhinition of nitrate uptake by phytoplankton: a new relation based on similarity and hyperbolicity. Curr Sci 2003, 85(8), 1180-9.

A theoretical formulation based on the properties of similarity and hyperbolicity is given for ammonium inhibition of nitrate uptake by phytoplankton. It leads to a new kinetic relation for ammonium inhibition, which is found to represent the data of nitrogen kinetics experiments of McCarthy et al.In the northwest indian ocean more accurately than the earlier relations of Wrobleski and O'Neill et al.Analysis of the f-ratio (new production/the sum of new and regenerated production) implied by the three relations shows that there is a qualitative difference among the three. The relation of Wroblewsk tends to underestimate the new production,while that of O'Neill et al. tends to overestimate it.

6 illus, 3 tables, 28 ref

002186   Warade R W;Deshmukh K C (Mathematics Dep, G.S. College, Khamgaon, Dist. : Buldana-444 303) : Inverse quasi-static transient thermoelastic problem in a thin annular disc-I. Acta Cienc Indica-Math 2003, 29(3), 611-17.

Inverse quasi-static transient thermal stress and displacement function in an annular disc are investigated by determining the heat flux at the upper face of an annular disc defined as D: a ≤ r ≤ b, 0 ≤ z ≤ h, using the technique of integral transform derives the expression of a temperature function. The results are obtained in a series form in terms of Bessel functions and illustrated graphically.

7 ref

002185   Warade R W;Deshmukh K C (Mathematics Dep, , Khamgaon, Distt-Buldana-440 303) : Mathematical modelling on transient thermal stresses in an annular fin. Acta Cienc Indica-Math 2003, 29(3), 507-16.

Deals with the generalization and obtain the exact solution and investigate the transient thermal stresses in an thin annular fin defined as D : a≤r≤b, -l/2≤z≤l/2, by using integral transform technique. The results are obtained in a series form in terms of Bessel's functions and illustrated graphically.

14 illus, 16 ref