009433   Kitagawa I (NO, Research Institute of Yokkaichi Univ, Yokkaichi 512-8512 Japan, Email: kitagawa@yokkaichi-u.ac.jp) : An exponential function on generalized fractional brownian motions and infinite dimensional laplacians. Far East J mathl Sci 2014, 87(2), 235-66.

In this paper, we introduce some stochastic processes induced from the fractional Brownian motion and discuss the Wiener integrals by the processes. Moreover, we give a relationship between the partial differentiations with respect to r and σ of an exponential functional of the generalized fractional Brownian motion and infinite dimensional Laplacians, i.e., the Gross Laplacian, the number operator, the adjoint of the generalized Gross Laplacian and the generalized Levy Laplacian, with an operator which is transferring the white noise B(t) to B(t). Also give a characterization of the exponential functional in terms of these infinite dimensional Laplacians.

12 ref

009432   Indira K P;Ramesha C;Mohandas (Mathematics Dep, Manipal Institute of Technology, Manipal-576 104, Email: indira.kp@manipal.edu) : On starlike functions and srivastava-attiya operator. Far East J mathl Sci 2013, 83(2), 223-32.

Let A denote the class of analytic functions f(z) defined in the unit disk satisfying the conditions /(0) = f'(0) - 1 = 0. The purpose of the present paper is to show that the subclasses S*_h and C_h are invariant under Srivastava-Attiya operator and to obtain certain subordination properties associated with the Srivastava-Attiya operator.

13 ref

009431   Hosny R A (Mathematics Dep, Faculty of Science, Zagazig Univ, P.O. 44519 Zagazig, Egypt) : Remarks of soft topological spaces with soft grill. Far East J mathl Sci 2014, 86(1), 111-28.

The classical mathematical theories have their difficulties which are pointed out in [16] for the solution complicated problems in engineering and environment. To overcome these difficulties, Molodtsov [16] introduced the concept of soft set as a new mathematical tool. Furthermore, Pei and Miao [20] showed that soft sets are a class of special information systems. The aim of this paper is to present new soft topology τ_G from old τ via soft grill G inducedby soft operators ϕ_G, Ψ_G. Authors investigate therein some behaviours and features of soft operators and the new topology.

25 ref

009430   Gunawan A A N (Physics Dep, Udayana at Bali Univ, Indonesia, Email: agung1962sp@yahoo.co.id) : Novel model determination of breast cancer stage using physical parameter. Far East J mathl Sci 2014, 87(1), 23-35.

This article determines the stage of breast cancer with a new method using mathematical equation models with physical parameters. To determine the stage of breast cancer, a model has been developed by the method of Tumor Node Metastasis (TNM) and Scarff-Bloom-Richardson. In this study, we have used mathematical equation models with physical parameters to determine the probability of gray-level pair at a certain distance. In a previous research, we managed to determine the histological type of breast cancer using the physical parameters. The proposed approach has been tested on 15 mammograms new patients of Dr. Soetomo Hospital, Indonesia. The results showed that the use of physical parameters was actually able to predict the stage of breast cancer with a sensitivity of 86,67% on the footage 5x5 cm and a = 5%.

1 illus, 1 table, 25 ref

009429   Exarchakos T G;Dimakos G M;Baralis G E (Mathematics and Informatics Dep, Faculty of Primary Education National and Kapodistrian Univ of Athens, Athens 10680, Greece, Email: gdimakos@primedu.uoa.gr) : On the automorphisms of finite p-groups. Far East J mathl Sci 2014, 87(1), 1-21.

27 ref

009428   Estuningsih R D;Guritman S;Silalahi B P (NO, Academy of Chemical Analysis of Bogor Jl. Pangeran Sogiri No 283 Tanah, Kota Bogor, Jawa Barat Indonesia) : Algorithm construction of hli hash function. Far East J mathl Sci 2014, 86(1), 23-36.

Hash function based on lattices believed to have a strong security proof based on the worst-case hardness. In 2008, Lyubashevsky et al. proposed SWIFFT, a hash function that corresponds to the ring R = Zp[α]/(α^{n + 1). We construct HLI, a hash function that corresponds to a simple expression over modular polynomial ring R_f,p = Z_p[x]/f(x). Authors choose a monic and irreducible polynomial f(x) = x" - x - 1 to obtain the hash function is collision resistant. Thus, the number of operations in hash function is calculated and compared with SWIFFT. Thus, the number of operations in hash function is calculated and compared with SWIFFT.}

1 illus, 3 tables, 8 ref

009427   Dong C Z;Zhang Y P;Song J M (NO, , School of Mathematics and Science Shijiazhuang Univ of Economics Shijiazhuang, Email: dongchangzh@sina.com) : Solving matrix equation MZM* = N with some constraint by eigenvalue decomposition. Far East J mathl Sci 2014, 86(1), 1-9.

Let P be a given Hermitian matrix satisfying P^{2 = I. Using the eigenvalue decomposition of P, we consider the Hermitian least squares solutions to the matrix equation MZM = N with the constraint PZ = ZP.}

9 ref

009426   Djue N R;Kramoh Y;Danho E;Asseke D B (College of Mathematics and Computer Sciences, Univ FHB of Abidjan-Cocody, 22 BP 582 Abidjan 22, Ivory Coast, Email: danhoemile@yahoo.com) : Linear stability of passive clouds flows. Far East J mathl Sci 2014, 84(1), 65-80.

The convective clouds experience complex mechanisms in their dynamics. Among these mechanisms, instabilities appear as the main factors that drive the clouds dynamics processes. Since it is important to follow those mechanisms that draw the cloud from its passive state to an active one characterized by raindrops formation and rainfalls, this paper aims to scrutinize the role of condensation on the instabilities enhancement in the passive cloud motion. It appears that the passive cloud remains stable to infinitesimal perturbations until the level of water vapor in the flow reaches the saturation threshold value. And from there, if the water contained in the cloud is sufficient enough for the condensation process to initiate, then droplets begin to form and the equilibrium state cannot be maintained so that the passive flow evolves to an active state. The flow becomes then unstable, and the instability increases along with the cloud ensemble velocity.

3 illus, 22 ref

009425   Djue N R;Kramoh Y;Danho E;Asseke B D (Laboratory of Mechanics, College of Mathematics and Computer Sciences, Univ FHB of Abidjan-Cocody 22 BP 582 Abidjan 22, Ivory Coast, Email: danhoemile@yahoo.com) : Entrainment of surrounding air effects on the stability of passive clouds containing water droplets. Far East J mathl Sci 2014, 84(1), 123-38.

In a previous work, authors investigated the stability of passive cloud flows at the stage of condensation and found that this process favored the instability of the flow. In the present paper, we diagnose the capacity of both gravity and entrainment to generate also instability mechanisms in passive cloud flows. The study shows that gravity waves cannot generate instability in the flow, whereas the entrainment is very destabilizing. Moreover, the amplification rate of the unstable modes is proportional to the entrainment rate and the flow becomes more and more unstable along with higher entrainment rate.

4 illus, 3 tables, 25 ref

009424   Dalal S;Chauhan S;Vujakovic J (NO, S.R. Institute of Education Asaudha, Haryana, Email: mathsqueen_d@yahoo.com) : Employing common property (E.A) on new contraction condition in menger spaces. Far East J mathl Sci 2013, 83(2), 145-65.

The object of this paper is to prove some fixed point theorems for weakly compatible mappings in Menger spaces satisfying new contraction condition with common property (E.A). We furnish an illustrative example to support our main result. We extend our results to four finite families of self mappings.

26 ref

009423   Choi J;Agarwal P (Mathematics Dep, Dongguk Univ, Gyeongju 780-714, Republic of Korea, Email: junesang@mail.dongguk.ac.kr) : Certain generating functions involving appell series. Far East J mathl Sci 2014, 84(1), 25-32.

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Here we aim at presenting (presumably) new generating functions for the Appells series. Since all the results derived here are of general character, it is noted that they can yield a number of (known and new) generating functions for certain simpler special functions which can be reducible from the Appell's series.

17 ref

009422   Chinram R (Mathematics and Statistics Dep, Faculty of Science Prince of Songkla Univ, Hat Yai, Songkhla 90112 Thailand, Email: ronnason.c@psu.ac.th) : Magnifying elements on Γ-semigroups. Far East J mathl Sci 2013, 83(1), 65-73.

The notion of a Γ-semigroup was introduced by Sen and Saha [16]. Many classical notions of semigroups have been extended to Γ-semigroups. The notion of a left (right) magnifying element of semigroups was introduced by Ljapin [10] in the year 1963. In this paper, we introduce left (right) magnifying and strongly left (right) elements of Γ-semigroups and give the existence of left (right) magnifying elements of left simple, right simple and bisimple Γ-semigroups without idempotent. Moreover, we show that the set of all non left (right) magnifying elements and the set of all strongly left (right) magnifying elements of Γ-semigroups S are sub Γ-semigroups of S if it is not empty.

18 ref

009421   Chasreeschai S;Sitthiwirattham T (Mathematics Dep, Faculty of Applied Science King Mongkut's Univ of Technology North Ban, Bangkok-10800, Thailand, Email: slc@kmutnb.ac.th ) : Independent and vertex covering number on strong product of complete bipartite graphs. Far East J mathl Sci 2013, 83(1), 41-8.

2 illus, 6 ref

009420   Chailos G (Computer Science Dep, Nicosia Univ, Nicosia 1700, Cyprus, Email: chailos.g@unic.ac.cy) : Convergence and complete continuum in plato's philosophy. Far East J mathl Sci 2013, 83(2), 185-22.

The main aim of this article is to defend the thesis that Plato apprehended the structure of incommensurable magnitudes in a way that these magnitudes correspond in a unique and well defined manner to the modern concept of the Dedekind cut. Thus, the notion of convergence is consistent with Plato's apprehension of mathematical concepts, and in particular these of density of magnitudes and the complete continuum in the sense that they include incommensurable cuts. For this purpose, I discuss and interpret, in a new perspective, the mathematical framework and the logic of the Third Man Argument (TMA) that appears in Plato's Parmenides as well as mathematical concepts from other Platonic dialogues. I claim that in this perspective the apparent infinite sequence of F-Forms, that it is generated by repetitive applications of the TMA, converges (in a mathematical sense) to a unique F-Form for the particular predicate. I also claim and prove that within this framework, the logic of the TMA is consistent with that of the Third Bed Argument (TBA) as presented in Plato's Republic. This supports Plato's intention for assuming a unique Form per Predicate; that is, the Uniqueness thesis.

34 ref

009419   Baik H G;Park C H (NO, Faculty of Information Technology Ulsan College, 101 Bong su-ro, Dong-gu Ulsan 682-715, Korea, Email: hgbaik@uc.ac.kr) : Filters of heyting algebras on vague set theory. Far East J mathl Sci 2013, 83(2), 269-80.

In this paper, author introduced the notion: of vague filter in Heyting algebras and investigate some properties. Also, gave conditions for a vague set to be vague filter and stated a characterization of Heyting algebra by vague filter.

9 ref

009418   Azis M I;Clement D L (NO, , Jurusan Matematika Fak. MIPA Universitas Hasanuddin, Indonesia) : On some problems concerning deformations of functionally graded anisotropic elastic materials. Far East J mathl Sci 2014, 87(2), 173-84.

Some problems concerning the deformation of a class of functionally graded anisotropic materials under generalised plane strain are considered. The elastic moduli of the materials vary quadratically with the spatial coordinates. Strip loading of a half-space, a slab on a rigid foundation and a simply supported slab are considered with particular attention to materials with a narrow strip of material with small elastic moduli along a plane boundary surface. Numerical results are obtained for some particular materials.

9 illus, 2 tables

009417   Ali F M;Nazar R;Arifin N M;Pop I (Mathematics Dep, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia, Email: fadzilahma@upm.edu.my) : Heat transfer characteristics of an unsteady shrinking sheet with mass transfer in a rotating fluid. Far East J mathl Sci 2014, 87(2), 225-34.

The problem of unsteady laminar boundary layer flow and heat transfer over a permeable shrinking sheet in a rotating fluid is considered. The transformed boundary layer equations are solved numerically using an implicit finite-difference scheme, namely the Keller-box method. Numerical results for different values of the Prandtl number, suction, unsteadiness and rotation parameters on the heat transfer characteristics are obtained and discussed.

5 illus, 1 table, 20 ref

009416   Ahmad M;Jae-Bok J;Shahid M H;Rizvi S (Mathematics Dep, Integral Univ, Kursi Road, Lucknow, 226026, Email: mobinahmad@rediffmail.com) : CR-submanifolds of a nearly hyperbolic kenmotsu manifold with a semi-symmetric non-metric connection. Far East J mathl Sci 2014, 84(1), 13-24.

We consider a nearly hyperbolic Kenmotsu manifold admitting a semi-symmetric non-metric connection and study CR-submanifolds of the nearly hyperbolic Kenmotsu manifold with semi-symmetric non-metric connection. We also study parallel distributions relating to ξ-vertical CR-submanifolds of a nearly Kenmotsu manifold with semi-symmetric non-metric connection.

15 ref

008524   Yamamoto K;Tahata K (Medical Innovation Dep, Osaka Univ Hospital, Japan) : Some symmetry models for the analysis of collapsed square contingency tables with ordered categories. Calcutta Statist Ass Bull 2012, 64(253-4), 21-36.

For the square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers some symmetry models for collapsed square contingency tables and proposes two new models which have the structure of global symmetry and that of quasi-symmetry for the collapsed square tables. Also this paper gives two kinds of decompositions of the symmetry model for collapsed square tables. The new models and decompositions are useful for analyzing the collapsed square tables. Examples are given.

3 tables, 19 ref

008523   Wu Z;Du H (Business School, Univ of Shanghai for Science and Technology, Shanghai 200093, China, Email: zkwu2011@gmail.com) : Some limit properties for the coefficients of the q-catalan numbers. Indian J pure appl Math 2014, 45(4), 469-78.

In the paper, some limit properties, such as, moderate deviation principle and law of large numbers, for the coefficients of the q-Catalan numbers and the generalized q-Catalan num-bers are obtained.

8 ref

008522   Vasanthakandasamy W B;Vasuki R;Thulukkanam K (Maths Dep, IIT(M), Chennai, Email: thulukkanamk@gmail.com) : Kosko hamming distance in the analysis of FCMs to study the problems of locals due to dumping of solid waste in Kodungaiyur. Ultra Scient phys Sci-Sect A 2014, 26(1), 55-62.

In this paper we for the first time define a new notion called Kosko - Hamming distance in the study of several experts using Fuzzy Cognitive Maps(FCMs)model. This new concept finds how two experts opinions differ using a distance function d_k between each of the individual experts. Here we study the health problems faced by the locals due to the dumping of solid waste. This study was carried out by taking a sample survey from around 40 persons living in and around the Kodungaiyur area. We have analysed the data using FCMs by taking 6 experts opinion.

7 tables, 8 ref

008521   VasanthaKandasamy W B;Vasuki R;Nedumaran P (Maths Dep, IIT(M), Chennai-600 036) : Study of influential nodes of fuzzy graphs in fuzzy models. Ultra Scient phys Sci-Sect A 2014, 26(1), 79-87.

In this paper author give the role of fuzzy graphs in fuzzy models like Fuzzy Cognitive Maps (FCMs) and Fuzzy Relational Maps (FRMs). Our study of these fuzzy graphs is different from the usual study as we have the nodes or edges of a fuzzy graph to be dependent on the fuzzy model in which they are used. In this paper we define different types of influential nodes of fuzzy graphs related with the fuzzy models like Fuzzy Cognitive maps (FCMs) models and Fuzzy Relational Maps (FRMs) models. This study of labeling the nodes as most influential, more influential, just influential, influential, less influential and least influential nodes of the fuzzy graphs associated with these fuzzy models is carried out in this paper. This study is new and innovative leading to several important observations on the nodes used in the fuzzy models. This answers the natural question whether the node which has the maximum number of edges incident to it is the most influential node in a fuzzy graph associated with fuzzy models. This is answered in the affirmative. This paper is organized into three sections. The first section is introductory in nature. In section two we define the types of nodes based on the fuzzy models defined, we also prove some results in this direction. The final section gives the conclusions based on our study.

2 illus, 12 ref

008520   Vasantha Kandasamy W B;Ebenezer H;Srinivasan K;Reuben Jonathan D (Mathematics Dep, Indian Institute of Technology-Madras, Chennai-600 036) : Health hazards of using endosulfan in the food sector: a fuzzy analisis. Ultra Scient phys Sci-Sect B 2014, 26(1), 33-42.

Endosulfan a well known pesticide has been used to preserve fruits, vegetables, pulses and food grains from infesting pests in the farming sector. Even after harvesting they are sprayed with it to avoid rotting. This pesticide enters into the body of human being through inhalation, skin and also by consumption of these food materials. This has a hazardous impact on the health conditions of anybody who comes in contact with it. The various effects caused by this organo-chlorine pesticide is analyzed by making use of the simple Fuzzy Cognitive Maps [FCMs].

2 illus, 28 ref

008519   Varshney R;Ahsan M J;Ansari A H (NO, , Statistics and Operations Research Dep, Aligarh Muslim Univ) : Compromise allocation based on the individual mixed allocations in multivariate straified sampling: a goal programming approach. Calcutta Statist Ass Bull 2012, 64(253-4), 98-113.

In the literature of stratified random sampling Equal, Proportional, Optimum and several other allocations are well known. Usually any one type of allocation is selected and is applied to all the strata. But, there are practical situations in which some of the strata differ significantly in one or the other respect from others. In such situations the strata can be classified in mutually exclusive and exhaustive groups that favour a par-ticular type of allocation. Different types of allocations may then be used in different groups. An allocation using the above criterion may be called a "Mixed Allocation". In the present paper we considered a multivariate stratified population where more than one (say p) characteristics arc defined on. every unit of the population and developed a procedure to work out a compromise allocation that can be used for all characteristics under study. The problem of obtaining a compromise allocation is formulated as a Mul-tiobjective Programming Problem that minimizes the deviation of all the sampling variances of the estimators of the p-population means from their respective optimum variances. The solution is obtained through Goal Programming Technique. A numerical example is also presented to illustrate the computational details.

5 tables, 30 ref

008518   Upadhyay V;Agrawal A K;Rajput J S;Singh N P (Physical Sciences Dep, MGCG, Vishwavidyalaya, Chitrakoot-485 780, Email: jsrajput2684@gmail.com) : Hydromagnetic convection flow with radiative heat and mass transfer past an infinite impulsively moving vertical plate in the presence of heat source/sink. Ultra Scient phys Sci-Sect A 2014, 26(1), 39-54.

In this study, an analysis has been performed for heat and mass transfer with radiation effect in transient laminar boundary layer flow of a viscous fluid past an impulsively moving infinite vertical flat plate in a homogenous porous medium in the presence of thermal diffusion and heat source/sink. Exact solution of momentum, energy and diffusion equations, under Boussinesq approximation, is obtained in closed form by use of Laplace transform technique. The variations in fluid velocity, temperature and concentration distribution are shown graphically, whereas numerical values of skin-friction, Nusselt number and Sherwood number are presented in tabular form and discussed.

12 illus, 3 tables, 33 ref

008517   Thomas P Y;Baiju K V (NO, , Statistics Dep, Kerala Univ) : Estimation of the scale parameter of skew-normal distribution using U-statistics based on order statistics. Calcutta Statist Ass Bull 2012, 64(253-4), 1-20.

In this work, author obtained the best linear unbiased estimator based on order statistics for the scale parameter of skew-normal distribution for some known values of the shape parameter. We also propose a technique estimating the scale parameter of skew-normal distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency comparison of the proposed U-statistics with the maximum likelihood estimator is also carried out.

3 tables, 17 ref

008516   Tanwar V K;Varshney N K (NO, , U-655, Jalvayu Vihar, Builders Area, Sector-p4, Greater Noida-201 308, Email: varuniit2000@gmail.com) : Pulsatile flow of blood through a stenosed artery with body acceleration. Ultra Scient phys Sci-Sect B 2014, 26(1), 19-28.

A mathematical model has been developed for the studying of pulsatile flow of blood through a stenosed artery with periodic body acceleration. Herschel - Bulkley fluid has been taken to represent the non-Newtonian character of blood. Perturbation method is used to solve the resulting system of non-linear partial differential equation with appropriate boundary condition to analyze the flow. Analytical expressions are obtained for axial velocity, volumetric flow rate and wall shear stress. Their variations with different flow parameters are plotted in figures. It has been observed that the axial velocity increases as body acceleration increases but the volumetric flow rate increases with the increase of body acceleration with time.

7 illus, 22 ref

008515   Sunoj S M;Linu M N (NO, , Statistics Dep, Cochin Univ of Science and Technology) : Cumulative measure of uncertainty for conditionally specified models. Calcutta Statist Ass Bull 2012, 64(253-4), 59-77.

Recently, Rao (2005) introduced an alternate measure of uncertainty called cumulative entropy that parallels Shannon entropy (see Asadi (2007)). Motivated by this, in the present paper, authors introduce cumulative entropies for two types of conditionally specified models. Finally, an application of the cumulative entropy using the maximum entropy principle is also illustrated.

19 ref

008514   Sujatha L;Sattanathan R (Mathematics Dep, Auxilium College (Autonomous), Vellore-632 006, Email: sujathajayasankar@yahoo.co.in) : Fuzzy longest path problem in an acyclic digraph. Int Rev Fuzzy Math 2014, 9(1-2), 1-9.

In traditional models, for finding the critical path in project networks, the durations of activities are represented as crisp numbers. But in real life situation, the operation time for each activity is uncertain which lead to the use of Fuzzy Numbers. The main aim of this study is to propose the algorithm for Fuzzy Longest Path Problem using Fuzzy Triangular Numbers where the Intersection Area is utilized to get the Longest Path.

3 illus, 1 table, 10 ref

008513   Sugantha G;Balakrishnan R (Mathematics Dep, Pope's College, Sawyerpuram-628 251, Email: sugi.trini@gmail.com) : β₂ near-rings. Ultra Scient phys Sci-Sect A 2014, 26(1), 63-8.

In this paper we introduce the notion of β₂ near-rings and study some of their properties. We furnish a complete characterization and also a structure theorem for such near rings.

4 ref

008512   Srivastava K;Bhardwaj R (IMD Unit, Civil Aviation Training College, Bamrauli, Allahabad-211 012, Email: rashmib22@gmail.com) : Impact of doppler weather radar data on numerical simulation of heavy rainfall. Indian J ind appl Math 2014, 5(1), 64-75.

In this paper, impact of Doppler Weather Radar (DWR) data has been examined for numerical simulation of heavy rainfall events using numerical weather prediction system Advance Regional Prediction System (ARPS) model at 3 km horizontal resolution. Weather radars transmit electromagnetic waves that receive and process backscattered signals and receive information of size, shape, class and precipitation rate. Fundamental variable measured by weather radars includes reflectivity and radial velocity. The reflectivity and radial velocity observations from DWR station Delhi are assimilated into ARPS model using ARPS Data Assimilation System (ADAS) and cloud analysis scheme. The main objective of this study is to evaluate the impact of Delhi DWR data on hydrometeor initialization (rain, snow and hail) of Numerical Weather Prediction (NWP) model, using hydrometeor analysis procedure within framework of ADAS and thence spin up problem. An initial results show that hydrometeor analysis procedure of ADAS is successfully able to convert observed reflectivity of Delhi radar to the model's precipitating hydrometeors (rain, snow and hail). The use of hydrometeor analysis for DWR data has significantly improved precipitation field in the initial conditions. It also significantly reduces spin up problem when model, has been initialized with improved initial conditions.

8 illus, 19 ref

008511   Srisailam A (Mathematics Dep, Osmania Univ, Hyderabad-500 007, Email: asmou22@yahoo.com) : Excluded energy and relative encircled energy plays an important role in the optical systems as point-image quality-assessment parameters. Ultra Scient phys Sci-Sect B 2014, 26(1), 43-8.

Encircled Energy Factor (EEF), Excluded Energy and Relative Encircled Energy are important corollaries of the Point Spread Function (PSF) of an optical system. In this paper, we have studied the Excluded Energy, Relative Encircled energy to understand their role as Point Image quality assessment parameters of Optical systems with amplitude apodised rotational symmetric filter functions.

2 illus, 2 tables, 13 ref

008510   Somran S;Sukparungsee S;Areepong Y (Applied Statistics Dep, Faculty of Applied Science King Mongkut's Univ of Technology North Ban, Bangkok 10800, Thailand, Email: ssophana@gmail.com) : Derivation and analysis of average run length for non-negative cumulative sum chart when observations are exponential distribution for the lower-sided case. Far East J mathl Sci 2013, 82(1), 65-78.

Purpose of this paper is to derive, the explicit expressions of the average run length (ARL) for non-negative cumulative sum (CUSUM) chart when observations are exponential distribution for the lower-sided case. Two methods are used for this research; the integral equation approach (IE approach) and numerical integral equation (NI approach). The efficiency of these methods is investigated by accuracy and computational times. The simulation results obtained by two methods show an excellent accuracy whereas the computational time for the numerical integral equation is significantly longer than the integral equation approach.

3 tables, 12 ref

008509   Som T;Choudhury B S;Das K (Applied Mathematics Dep, Institute of Technology, Banaras Hindu Univ, Varanasi-221 005, Email: som_tanmoy@yahoo.co.in) : Two common fixed point results in fuzzy metric spaces. Int Rev Fuzzy Math 2014, 9(1-2), 63-77.

In this paper authors have proved some fixed point results satisfying some R-weakly commuting conditions. We derive a corollary thier results with example.

12 ref

008508   Solanki A;Jindal P (Applied Mathematics Dep, Gautam Buddha Univ, Greater Noida, Uttar Pradesh, Email: anjana@gbu.ac.in) : Integrated inventory model with defective units involving controllable lead-time and backorder price discount. Indian J ind appl Math 2014, 5(1), 42-53.

Considered the integrated inventory model with defective units. The total related cost in the continuous review model is minimized by considering the order quantity, reorder point, lead-time and backorder price discount as decision variables. Moreover, we assume that the lead-time demand distribution is unknown but has known mean and variance of lead-time demand. The minimax distribution free procedure is applied to find the optimal solution considering that the buyer places an order, then the vendor produces m-times order quantity in each production cycles, to reduce setup cost. In addition, the buyer offers backorder price discount to the customers to motivate them for backorders. The arrival lot may contain some defective items, so its treatment is also incorporated in this paper. The effective iterative procedure for finding the optimal policy is developed.

3 tables, 13 ref

008507   Sohgaura B K;Pandey N (Mathematics Dep, Govt. P.G. Science College, Rewa, Madhya Pradesh) : Some new bilateral generating relations involving hypergeometric function and H-function of one and two variables. Ultra Scient phys Sci-Sect A 2014, 26(1), 35-8.

In this paper, we establish some new bilateral generating relations involving additional complete hypergeometric functions of three variables and H-function of one variable.

3 ref

008506   Sohgaura B K;Pandey N (Mathematics Dep, Govt. P.G. Science College, Rewa, Madhya Pradesh) : Some new linear generating relations involving H-function of one variables. Ultra Scient phys Sci-Sect A 2014, 26(1), 31-4.

The object of this paper is to evaluate some new generating relations involving H-function of one variable some special cases have also been derived.

4 ref

008505   Singh B;Rathore G P S;Dubey P;Singh N (School of Studies in Mathematics, Vikram Univ, Ujjain, Madhya Pradesh) : Unique common fixed point theorem on weak commuting mapping. Ultra Scient phys Sci-Sect A 2014, 26(1), 19-24.

The aim of this paper is to establish a new fixed point theorem on complete metric space for weak commuting mapping. Our results generalize several corresponding relations of weak commuting mapping in metric space.

11 ref

008504   Singh A P;Dixit M;Garg M (Mathematics Dep, P.G.D.A.V. College (Eve.), Nehru Nagar, New Delhi, Email: garg_manoj1972@yahoo.co.in) : On *g-closed sets in bitopological spaces. Ultra Scient phys Sci-Sect A 2014, 26(1), 88-96.

In this paper, we introduce *g-closed sets in bitopological spaces. Properties of these sets are investigated and we introduce the two new bitopoligical spaces (i, j)-*gT*_1/2 and (i, j)-*g*T_1/2 spaces as applications. Further we introduce and study *g-continuity^{13 in bitopological spaces.}

3 illus, 15 ref

008503   Samanta K P;Chandra B C;Bera C S (Mathematics Dep, Bengal Engineering and Science Univ, Shibpur, P.O.-Botanic Garden, Howrah-711 103) : On generating functions of modified Gegenbauer polynomials. Ultra Scient phys Sci-Sect A 2014, 26(1), 74-8.

In this note, author have obtained some novel bilateral generating functions involving modified Gegenbauer polynomials, C_n^{λ+n(x) which is converted into trilateral generating functions with Tchebycheff polynomials by group theoretic method.}

4 ref

008502   Samanta K P;Chandra B C;Bera C S (Mathematics Dep, Bengal Engineering and Science Univ, Shibpur, P.O.-Botanic Garden, Howrah-711 103) : On mixed trilateral generating functions of extended Jacobi polynomials. Ultra Scient phys Sci-Sect A 2014, 26(1), 69-73.

In this note we have obtained some novel result on mixed trilateral relations involving extended Jacobi polynomials by group theoretic method which inturn yields the corresponding results involving Hermite, Laguerre and Jacobi polynomials.

4 ref

008501   Rasulova M Y (NO, Advanced Analysis and modelling Laboratory, MIMOS BHD, Technology Park Malaysia, Bukit Jalil, 57000, KL, Malaysia, Email: rasulova@live.com) : Optimization problem for a cognitive network. Indian J ind appl Math 2014, 5(1), 10-16.

Present paper is devoted to the computation of the optimum signal-to-interference-plus-noise ratio (SINR) and signal-to-noise ratio (SNR) of a cognitive network with single primary (subscriber) and single secondary (anonymous) user. To solve this problem, an optimization method based on a theorem in matrix algebra; on the properties of the ratio of two Hermitian forms is used.

1 illus, 12 ref

008500   Ramana Reddy G V;Subrahmanyam S V;Satish Kumar D (Mathematics Dep, K L Univ, Guntur-522 502) : Soret effect on MHD mixed convection oscillatory flow over a vertical surface in a porous medium with chemical reaction and thermal radiation. Ultra Scient phys Sci-Sect B 2014, 26(1), 49-60.

This work deals with the study of thermal radiation and MHD on mixed convection flow of a viscous incompressible electrically conducting fluid through a porous medium with variable permeability in the presence of oscillatory suction. The influence of a first-order homogeneous chemical reaction, heat source and Soret effects are analyzed. The resultant governing boundary layer equations are highly nonlinear and coupled form of partial differential equations which are solved analytically using two-term harmonic and non-harmonic functions. The effects of different physical parameters on the velocity, temperature and concentration fields as well as skin-friction coefficient, Nusselt number and the Sherwood number with their amplitude and phase are discussed in detail. The results are presented graphically and discussed qualitatively.

15 illus, 20 ref

008499   Rakesh Kumar;Som B K;Jain S (School of Mathematics, Shri Mata Vaishno Devi Univ, Katra-182 320, Email: rakesh_stat_kuk@yahoo.co.in) : Optimizing service rate and the capacity of an M/M/1N queuing system and retention of reneged customers. Indian J ind appl Math 2014, 5(1), 54-63.

In this paper, authors present analysis of a single-server finite capacity Markovian queuing system with reneging and retention of impatient customers. It is assumed that arriving customers renege according to an exponential distribution and the reneged customers may be retained with some probability. The cost model of the system is made. The optimal values of service rate and the system capacity are obtained by using search and classical optimization algorithms. Further, the expected system size is compared with and without the optimization of the system. Some important comparisons are done to show the impact of optimization of parameters like system capacity, mean service rate, and the probability of retaining the reneged customers.

7 tables, 19 ref

008498   Qiang J;Zheng Q;Li M (Mathematics Dep, Huazhnog Univ of Science and Technology, Wuhan 430074, P.R. China, Email: qiangjingren@hotmail.com) : Representation of fractional powers of coercive differential operators. Indian J pure appl Math 2014, 45(4), 461-7.

In this paper, under the definition of fractional powers by Straub, we will give the representation of fractional powers of coercive differential operators by using pseudo differential operators.

13 ref

008497   Paul I (Mathematics Dep, Bharata Mata College, Thrikkakara, Kochi-682 021, Email: pibmct@gmail.com) : Exactness in L-module theory-I. Int Rev Fuzzy Math 2014, 9(1-2), 37-44.

Concepts of exact sequences, split exact sequences and the like form an important area in module theory. The notion of fuzzy modules and L-modules were introduced respectively by Negoita & Ralescu and Mashinchi & Zahedi as an extension of module theory in the fuzzy context. In this paper authors introduce and study the concepts of exact sequences and split exact sequences of L-modules. We obtain a necessary condition for a given sequence to be exact. Some related results also are proved.

12 ref

008496   Parsan Kaur;Bhardwaj R (Mathematics Dep, Guru Tegh Bahadur Institute of Technology, GGSIP Univ, New Delhi-110 064, Email: rashmib22@gmail.com) : Rotational oscillation of satellite in elliptic orbit under magnetic torque. Indian J ind appl Math 2014, 5(1), 17-24.

Magnetic disturbance torque results from interaction between spacecraft's residual magnetic field and geomagnetic field. The primary sources of magnetic disturbance torques are spacecraft magnetic moments, eddy currents and hysteresis. The instantaneous magnetic disturbance torque due to spacecraft effective magnetic moment is the product of geocentric magnetic flux density and sum of individual magnetic moments caused by permanent and induced magnetism and spacecraft generated current loops. Let us consider a rigid satellite S moving around the central body C and orbital plane of satellite coincides with equatorial plane of C. This paper deals with rotational oscillation of satellite under influence of magnetic torque in elliptic orbit. Non-linear planar equation of motion of model has been derived. Using BKM method, it is observed that resonances exist. The analysis regarding stability of stationary planar oscillation of satellite near resonance frequency shows that discontinuity occurs in amplitude of oscillation at frequency of external periodic force which is less than frequency of the natural oscillation. The half width of chaotic separatrix has been estimated by Chirikov's criterion. Through surface of section method, it has been observed that magnetic torque parameter, eccentricity and mass ratio play an important role in changing regular motion into chaotic one.

2 illus, 9 ref

008495   Parmar K S;Bhardwaj R (Non-Linear Dynamics Research Lab, Mathematics Dep, Guru Gobind Singh Indraprastha Univ, Dwaraka, New Delhi-110 078, Email: rashmib22@gmail.com) : Time series, trend and wavelet analysis of water parameters. Indian J ind appl Math 2014, 5(1), 1-9.

Time series, trend and wavelet analysis of water quality parameters Chemical Oxygen Demand (COD), Biochemical Oxygen Demand (BOD), Dissolved Oxygen (DO) monitored at Nizamuddin bridge mid-stream of river Yamuna in India have been studied. In Auto Regressive Integrated Moving Average (ARIMA) model (p, d, q) value of 'd' is zero thus process is stationary. It is observed that Root Mean Square Error (RMSE) value are comparatively very low thus dependent series is closed with the model predicted level. The Mean Absolute Percentage Error (MAPE), MaxAPE, MAE, MaxAE, normalized Bayesian Information Criterion (BIC) are calculated and have low value. Trend is calculated by using Auto correlation function (ACF), Partial auto correlation function (PACF) and lag. The predictive model is useful at 95% confidence limits. The 1 -D discrete and continuous Daubechies wavelet analysis explains that the parameters COD, BOD, DO have the maximum value 120, 50, 8; the value of a5 varies between 52 to 78, 10 to 30, 0.2 to 1.4 and the scale values of Db5, i.e., d5 ranges between -10 to 10; -5 to 5 and -0.5 to 0.5, respectively. It is concluded that as the value of COD, BOD increases and value of DO decreases, water is not fit for drinking, agriculture and industrial use.

3 illus, 2 tables, 16 ref

008494   Pardeep Kaur;Shelly;Potucek F (Mathematics Dep, Punjabi Univ, Patiala-147 002, Email: aroshelly@gmail.com) : Numerical solution of axial dispersion model using orthogonal collocation method. Indian J ind appl Math 2014, 5(1), 35-41.

Axial dispersion model involving Peclet number has been solved using the technique of orthogonal collocation. Lagrangian interpolation polynomial has been used to discretize the approximating function. This technique converts the set of partial differential equations into ordinary differential equations. The resulting system of differential algebraic equations has been solved using MATLAB with ode 15s system solver. Numerical values have been compared with analytic ones to check the efficiency of the method.

4 illus, 1 table, 6 ref

008493   Niyamathulia U;Elangovan R;Sathiyamoorthi R (Bio-Statistics Dep, Vinayaka Mission College of Nursing, Karaikal-609 609, Email: srelangovan@rediffmail.com) : Estimation of expected time to seroconversion of HIV infected when the antigenic diversity thresholds has SCBZ property. Ultra Scient phys Sci-Sect A 2014, 26(1), 1-8.

The likelitime at which the seroconversion of HIV infected takes place is a vital event indicating the progression of the infection. The antigenic diversity of the invading antigens due to successive contacts increases and similarly the virulence also increases. The seroconversion occurs if either the total antigenic diversity crosses the threshold level or the total virulence crosses the threshold level. Using the shock model approach the expected time to seroconversion has been derived by several authors. In this paper it is assumed that the antigenic diversity threshold is a random variable which has a distribution that has the change of parameter this is called the SCBZ property. The expected time to seroconversion is obtained using this concept numerical illustrations are also provided.

5 illus, 5 tables, 5 ref