006971   Wongsaijai B;Sukantamala N (Mathematics Dep, Faulty of Science, Chiang Mai Univ, Chiang Mai-502 00, Thailand, Email: gaia2556@gmail.com) : Convexity properties for generalized q-integral operators of p-valent funtions involving the ruscheweyh derivative and the generalized salagean operator. Far East J mathl Sci 2015, 96(4), 437-62.

Making use of a certain operator of fractional q-derivative with Ruscheweyh derivative and the generalized Salagean operator, we define two new generalized q-integral operators of p-valent functions. Also, we introduce two new comprehensive subclasses of analytic functions with respect to q-differentiation and obtain the convexity properties of these integral operators of p valent functions on two new classes. We also briefly indicate the relevant connections of our presented results to the formerly reported results. Furthermore, special cases of the main results are also mentioned.

41 ref

006970   Wang X;Yang F (Mathematics Dep, Zhejiang Univ, Hangzhou 310027, People's Republic of China, Email: wxg688@163.com) : Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps. Proc Math Sci 2014, 124(4), 551-62.

Authors gives an asymptotic formula of the Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps f_λ(z) = z^{d + λ/zd, where d ≥ 3 and λ is small.}

2 illus, 16 ref

006969   Ting-Bin C;Liu K;Xu N (Mathematics Dep, Nanchang Univ, Nanchang, Jiangxi 330031, People's Republic of China, Email: tbcao@ncu.edu.cn) : Zeros and uniqueness of Q-difference polynomials of meromorphic functions with zero order. Proc Math Sci 2014, 124(4), 533-49.

In this paper, authors investigate the value distribution of q-difference polynomials of meromorphic function of finite logarithmic order, and study the zero distribution of difference-differential polynomials [f^{n (z)f(qz + c)](k) and [fn (z)(f(qz + c) - f(z))](k), where f(z) is a transcendental function of zero order. The uniqueness problem of difference-differential polynomials is also considered.}

15 ref

006968   Subburam S (Mathematics Dep, SASTRA Univ, Thanjavur-613 401, Email: ssubburam@maths.sastra.edu) : Lenstra theorem in numer fields. Proc Math Sci 2014, 124(4), 481-5.

In this paper, authors present a number field version of the celebrated result of Lenstra (Math. Comp. 42(165) (1984) 331-340) in 1984. Also, this result allows us to improve a result of Wikstrom (On the l-ary GCD-algorithm in rings of integers (2005) pp. 1189-1201).

5 ref

006967   Sethuraman G;Sankar K (Mathematic Dep, Anna Univ, Chennai-600 025, Email: sethu@annauniv.edu) : One vertex union of shell graphs with a path at any common levels is cordial. Far East J mathl Sci 2015, 96(4), 485-95.

We recall from [3], a shell graph of size n, denoted C(n, n - 3), is the graph obtained from the cycle C_n<193>v₀, v₁, v₂, ..., v_{n_l}) by adding n-3 consecutive chords incident with a common vertex, say V0, called apex of the shell graph C(n, n - 3). The vertex v/ of the shell graph C(n, n -3) is said to be at level l. In this paper, we consider a new family of graphs called one vertex union of shell graphs with a path at any common level, denoted G(NI, NI - 3, k, I), is obtained from k shell graphs C(n_i, n_i - 3) 's NI ≥ 4, for 1 ≤ i <≤ k by merging them with their apex together and joining k of vertices each chosen from a distinct shell graph in a particular level / by a path P_k. We show that G(n_i, n_i, -3, k, /) is cordial for n_t = n ≥ 4, for 1 ≤ i ≤ k, k ≥ 1.

3 illus, 2 table, 12 ref

006966   Selvakumaran K A;Balachandar G;Rajaguru P (Mathematics Dep, R M K College of Engineering and Technology, Puduvoyal-601 206, Email: selvaal1826@gmail.com) : Coefficient inequalities for a class of p- Valent analytic functions defined by using fractional calculus operators. Far East J mathl Sci 2015, 96(4), 463-74.

By using the extended fractional differintegral operator, we introduce a new subclass of p-valent analytic functions in the open unit disk. We provide coefficient bounds for the newly defined class of functions. Also, we point out some new and known consequences of our work.

12 ref

006965   Sagiroglu Y (Mathematics Dep, Science Faculty, Karadeniz Technical Univ, 610 80 Trabzon, Turkey, Email: sagiroglu.yasemin@gmail.com) : Global defferential invariants of affine curves in R<. Far East J mathl Sci 2015, 96(4), 497-515.

In this paper, the complete system of affine global differential invariants of affine curves in R^{2 is obtained. The problem of affine equivalence of affine curves is reduced to that of paths. Conditions of affine-equivalence of curves are given in terms of the affine invariants. It is obtained that the generating affine invariants are independent.}

16 ref

006964   Nasrabadi M M;Gholamian A (Mathematics Dep, Birjand Univ, Birjand, Iran, Email: mnasrabadi@birjand.ac.ir) : On a-nilpotent abelian groups. Proc Math Sci 2014, 124(4), 517-25.

Let G be a group and A=Aut(G) be the group of automorphisms of G. Then, the element [g,α] = g^{-1 α(g) is an autocommutator of g ∈ G and α ∈ A. Hence, for any natural number m the m-th autocommutator subgroup of G is defined as K_m(G) = {[g, α₁, ..., α_m]|g ∈ G, α₁, ..., α_m ∈A}, where [g, α₁, α₂, ..., α_m] = [[g,α₁, ..., α_m-1], α_m]. In this paper, we introduce the new notion of A-nilpotent groups and classify all abelian groups which are A-nilpotent groups.}

8 ref

006963   Li Y;Zhong X (NO, Lijiang College of Guangxi Normal Univ, Guangxi, Guilin 541006, People's Republic of China, Email: xgzhong@mailbox.gxnu.edu.cn) : Finite groups all of whose minimal subgroups are NE*-subgroups. Proc Math Sci 2014, 124(4), 501-9.

Let G be a finite group. A subgroup H of G is called an NE-subgroup of G if it satisfies H^{G ∩ NG (H) = H. A subgroup H of G is said to be a NE*-subgroup of G if there exists a subnormal subgroup T of G such that G=H T and H ∩ T is a NE-subgroup of G. In this article, we investigate the structure of G under the assumption that subgroups of prime order are NE*-subgroups of G. The finite groups, all of whose minimal subgroups of the generalized Fitting subgroup are NE*-subgroups are classified.}

17 ref

006962   Jin H;Yuan S (Mathematics Dep, Suzhou Univ of Science and Technology, Suzhou, 215009, China, Email: ahjhl@sohu.com) : Sharp rogers-shephard type inequality for orlicz-difference body of planar convex bodies. Proc Math Sci 2014, 124(4), 573-80.

In this paper, we prove a sharp Rogers-Shephard type inequality for the Orlicz-difference body of planar convex bodies, which extend the works of Bianchini and Colesanti (Proc. Amer. Math. Soc. 138(7) (2008) 2575-2582).

22 ref

006961   Hua Y;Qi F (Information Engineering Dep, Weihai Vocational College, Weihai City, Shandong Province 264210, China, Email: xxgcxhy@163.com) : Double inequality for bounding toader mean by the centroidal mean. Proc Math Sci 2014, 124(4), 527-31.

15 ref

006960   Guo P;Wang J;Zhang H (School of Mathematics and Information Engineering, Lianyungang Normal College, Lianungang 222006, People's Republic of China, Email: guopf999@163.com) : Complete classification of minimal non-PS-groups. Proc Math Sci 2014, 124(4), 511-16.

Let G be a finite group. A subgroup H of G is called s-permutable in G if it permutes with every Sylow subgroup of G, and G is called a PS-group if all minimal subgroups and cyclic subgroups with order 4 of G are s-permutable in G. In this paper, we give a complete classification of finite groups which are not PS-groups but their proper subgroups are all PS-groups.

16 ref

006959   Geetha R;Pamela A A J;Selvaraj C (Mathematics Dep, RMKCET, Puduvoyal, Chennai, Tamil Nadu, Email: gbala89@yahoo.com) : Certain properties of a subclass of univalent functions. Far East J mathl Sci 2015, 96(4), 475-84.

By making use of the familiar concepts of neighbourhoods of analytic functions, the authors prove several inclusion relations associated with the 5-neighbourhoods of certain subclasses of univalent functions. Also, some other interesting properties of these classes are investigated.

11 ref

006958   Gaketem T (Mathematics Dep, School of Science, Phayao Univ, Phayao-560 000, Thailand, Email: newtonisaac41@yahoo.in) : On (m,n)-Regular in LA-semigroup. Far East J mathl Sci 2015, 96(4), 409-18.

The purpose of this paper is to define (m, n) -regular in LA-semigroup.

7 ref

006957   Fosner M;Rehman N U;Vukman J (Faculty of Logistics, Maribor Univ, Mariborska cesta 7, 3000 Celje, Slovenia, Email: maja.fosner@uni-mb.si) : Engel condition with a additive mapping in semiprime rings. Proc Math Sci 2014, 124(4), 497-500.

Main purpose of this paper is to prove the following result: Let n <62> 1 be a fixed integer, let R be a n!-torsion free semiprime ring, and let f:R → R be an additive mapping satisfying the relation [f(x),x]_n = [[...[[f(x),x],x],...], x] = 0 for all x ∈ R. In this case [f(x), x] = 0 is fulfilled for all x ∈ R. Since any semisimple Banach algebra (for example, C* algebra) is semiprime, this purely algebraic result might be of some interest from functional analysis point of view.

17 ref

006956   Dorsett C (Mathematics Dep, Texas A&M Univ-Commerce, Texas-75429, USA) : Regularly open sets and normal and T₄ spaces. Far East J mathl Sci 2015, 96(4), 517-24.

Within this paper, recent discoveries concerning regularly open and regularly closed sets are used to further investigate and characterize normal and T₄ spaces.

8 ref

006955   Chung J;Chang J (Mathematics Dep, Kunsan National Univ, Kunsan, 573-701, Korea, Email: jychung@kunsan.ac.kr) : On two functional equations originating from number theory. Proc Math Sci 2014, 124(4), 563-72.

Reducing the functional equations introduced in Proc. Indian Acad. Sci. (Math. Sci.) 113(2) (2003) 91-98 and in Appl. Math. Lett. 21 (2008) 974-977 to equations in complex variables and quaternions, we find general solutions of the equations. We also obtain the stability of the equations.

5 ref

006954   Chaubey S;Lanius M;Zaharescu A (Mathematics Dep, Illinois Univ, 1409 West Green Street, Urbana, IL 61801, USA, Email: chaubey2@illinois.edu) : Irrational factor races. Proc Math Sci 2014, 124(4), 471-9.

Investigated the behavior of the sum of the irrational factor function over arithmetic progressions. Author first establish a general asymptotic formula for such a sum, and then obtain some further results in the case of arithmetic progressions 3n±1.

10 ref

006953   Chakraborty S;Mukherjea A (Mathematics Dep, Univ of Texas-Pan American, 1201 West Univ Drive, Edinburg, Texas 78539, USA, Email: arunava.mukherjea@gmail.com) : Limit distributions of random walks on stochastic matrices. Proc Math Sci 2014, 124(4), 603-12.

Problems similar to Ann. Prob. 22 (1994) 424-430 and J. Appl. Prob. 23 (1986) 1019-1024 are considered here. The limit distribution of the sequence X_n X_n-1 ... X₁, where (X_n)_{n ≥ 1} is a sequence of i.i.d. 2 x 2 stochastic matrices with each X_n distributed as μ, is identified here in a number of discrete situations. A general method is presented and it covers the cases when the random components C_n and D_n (not necessarily independent), (C_n, D_n) being the first column of X_n, have the same (or different) Bernoulli distributions. Thus (C_n, D_n) is valued in {0, r}^{2, where r is a positive real number. If for a given positive real r, with 0 <60> r ≤ 1/2, r-1 C_n and r-1 D_n are each Bernoulli with parameters p₁ and p₂ respectively, 0 <60> p₁, p₂ <60> 1 (which means C_n <126> p₁δ_(r) + (1 - p₁)δ_{0} and D_n <126> p₂δ_{r} + (1-p₂)δ_{0}), then it is well known that the weak limit λ of the sequence μn exists whose support is contained in the set of all 2 x 2 rank one stochastic matrices. We show that S(λ), the support of λ, consists of the end points of a countable number of disjoint open intervals and we have calculated the λ-measure of each such point. To the best of our knowledge, these results are new.}

4 ref

006952   Biswas I;Heu V (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay-400 005, Email: indranil@math.tifr.res.in) : Meromorphic connections on vector bundles over curves. Proc Math Sci 2014, 124(4), 487-96.

Authors gives a criterion for filtered vector bundles over curves to admit a filtration preserving meromorphic connection that induces a given meromorphic connection on the corresponding graded bundle.

6 ref

006951   Basu A;Basu S;M J M (Quantitative Methods and Information Systems Area, Indian Institute of Management, Bangalore-560 076, Email: arnab.basu@iimb.ernet.in) : Nash equilibria via duality and homological selection. Proc Math Sci 2014, 124(4), 581-602.

Given a multifunction from X to the k-fold symmetric product Sym_k (X), we use the Dold-Thom theorem to establish a homological selection theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincare duality in addition to the Dold-Thom theorem.

16 ref

006950   Aman A;Nurisma;Hanum F;Bakhtiar T (Mathematics Dep, Bogor Agricultural Univ, JI. Raya Darmaga, Bogor-168 80, Email: amril.aman@gmail.com) : Buses dispatching problem in Urban transport system. Far East J mathl Sci 2015, 96(4), 393-8.

The complexity of transport system in urban area will significantly increase in accordance with demographic development, transport demand growth, life style change and transport policy. Inadequate transport management system implies a higher transport cost incuried by fuel wasting due to traffic jam, productivity deterioration and environment degradation. Busway as one of transport modes in Bus Rapid Transit (BRT) system is commonly adopted by local government to circumvent such kind of drawbacks, since it may reassign the use of private cars into public transport. However, in some cases, the implementation of busway system is not optimal due to poor planning. This paper develops a deterministic mathematical framework to model the operation of Transjakarta, busway transport system in the metro city of Jakarta. An integer programming is established to determine the optimum number of dispatched buses from the initial shelter under minimum operational cost. Optimum dispatching leads to a minimum waiting time and assures passengers' comfort.

4 table, 8 ref

006949   Ali T M;Kamil A A;Karim M F A (Mathematics Section, School of Distance Education, Univ Sains Malaysia, 118 00 USM, Penang, Malaysia) : Deterministic mathematical model of dengue disease spread. Far East J mathl Sci 2015, 96(4), 419-36.

In this paper, a mathematical model is formulated to simulate the dynamics of dengue disease spread and to investigate the effect of Toxorhynchites mosquitoes as biocontrol strategy to reduce dengue disease propagation. The human populations were portioned out into three different compartments of the susceptible, infected, and recovered humans. Whereas the mosquito's populations were portioned out into three classes of the aquatic stage, susceptible, and infected mosquitoes. Stability analysis of the equilibrium points was carried out. Numerical simulations results revealed that applying Toxorhynchites splendens larvae as biological control measure can effectively reduce the dengue spread in the community.

6 illus, 1 table, 16 ref

005992   Zhong-Cheng W;Li L (School of Funddamental Studies, Shanghai Univ of Engineering Science, Longteng Road 333, Shanghai 201620 P.R. China, Email: wzcsues@163.com) : Hermitian reflexive solution for a class of matrix equations. Far East J mathl Sci 2015, 96(6), 735-41.

In this paper, we investigate the solvability of the Hermitian reflexive solution for a class of matrix equations. The findings of this paper extend some known results in the literature.

11 ref

005991   Zakaria Z A;Shabri A;Mamat M (NO, Faculty of Informatics and Computing Univ Sultan Zainal Abidin K. Tere, Malaysia, Email: zahrahtulamani@unisza.edu.my) : Parameter estimation based on partial L-moments method for censored samples. Far East J mathl Sci 2015, 96(6), 671-84.

Estimation of flood magnitude is a crucial component in planning, designing, and managing of water resources projects. The main focus in hydrologic design is the estimation of high flow quantile. L-moments, popular among hydrologist in flood estimation is known to be oversensitive towards the lower part of the distribution and gives insufficient weight to large sample values. As an alternative, the method of partial L-moments (PL-moments) is proposed to give weightage to the upper part of distribution and large values in censored sample. In this paper, three widely used distributions are selected namely; generalized extreme value (GEV), generalized logistic (GLO) and generalized Pareto (GPA) distribution, for the analysis of censored flood samples. Monte Carlo simulations are conducted to illustrate the performance of PL-moments compared to simple L-moments in fitting each distribution to its samples. Finally, both simple L-moments and PL-moments are used to fit the GLO distribution to two data sets of annual maximum flow series of River Ketil in Kedah and River Gemencheh in Negeri Sembilan, Malaysia.

3 illus, 1 table, 13 ref

005990   Tyagi A (Mathematics Dep, M.M. Univ, Sadopur, Ambala) : Optimal vacation period with cost analysis of an interdependence fuzzy queue model to a communication system. Arya Bhatta J Math Inf 2015, 7(1), 41-6.

Mathematical study of queue model provides the basic frame work in communication system as there is a close resemblance between queue networks and communication systems. This paper deals with the application of an interdependence fuzzy queue model to a communication system which have the voice packetized statistical multiplexing. The objective of the paper is intended to review the state of affairs of analytical methods, queuing analytical techniques essential to modeling of communication system. By approximating the arrival of packets, transmission and the covariance between them under a bi-variate Poisson process, the performance of statistical multiplexing is measured. The steady state solution and system characteristics are derived. The model mechanism reduces the idle time of transmitter and enhances the system utilization capacity. A unified treatment of buffer storage over flow problem has been discussed as an application example in which we call attention to the analogy between buffer problem and waiting time. The ratio of the cost associated with shifting the transmitter from voice buffer to data buffer and the cost associated with waiting time of voice packets is compared with idle time of transmitter in consideration of the dependence between arrival of messages and service transmission. The vacation period has been calculated with respect to cost ratio and change in interdependence between arrival of packets and number of transmission completion.

1 table, 13 ref

005989   Sunita Rani;Rajeev Kumar (Mathematics Dep, M. D. Univ, Rohtak, Haryana, Email: kakoriasunita@gmail.com) : Reliabilty and profit analysis of a water process system considering none switching of redundant units and proper/improper repairs of minor faults. Arya Bhatta J Math Inf 2015, 7(1), 175-86.

Water process system in a Thermal Power Plant comprises of several redundant and non-redundant subsystems wherein the redundant subsystems are of two types, namely 1-out-of-2 (Type-I) and 2-out-of-3 (Type-II). On occurrence of a minor fault, the system goes to partial failure whereas on occurrence of a major fault the system goes to complete failure. Further on partial failure of the system, the available single repairman first inspects the subsystems to judge which subsystem has the minor fault and accordingly carries out the online repair of the infected subsystem, i.e. without halting the operation of the system, to avoid losses including loss of power generation etc. Even when a fault occurs in a redundant subsystem, switching of a redundant unit, being non-instantaneous and costly, is not done. However improper online repair of the infected subsystem sometimes results in to complete failure of the system. The present paper investigates a stochastic model developed for the system for the above practical situations. Various measures of system effectiveness for the model are obtained using Markov process and regenerative point technique. Using these measures, profit incurred to the system is also computed. The reliability and cost analyses of the system is presented through graphs for a particular case.

12 illus, 13 ref

005988   Singh S R;Daheriya R D (mathematics Dep, J.H. Govt. P.G. College Betul, Madhya Pradesh, Email: srsinghgaur@gmail.com) : Some common fixed point theorems for three mappings in G-metric spaces. Arya Bhatta J Math Inf 2015, 7(1), 127-34.

Objects in this paper is to obtain some common fixed point theorems for three mappings using the setting of generalized metric spaces. It is worth mentioning that our results that do not rely on the notion of continuity, weakly commuting or compatibility of mappings involved therein. These results generalized well known comparable results in the literature.

13 ref

005987   Singh R P;Nagar S (Maths Dep, Lajpat Rai (PG) College, Sahibabad, Ghaziabad-201 005, Email: drrpsingh2010@gmail.com ) : Upper bounds on the probability of error and weighted means divergence measures. Arya Bhatta J Math Inf 2015, 7(1), 69-80.

In the present communication, we have considered some weighted means such as weighted arithmetic, weighted harmonic, weighted geometric, weighted root- square means and mixed weighted means. The difference of these means has been considered as the divergence and the resulting divergence is convex function. Some upper bounds for the probability of error in terms of weighted means divergence measures have been proved exploring weighted f-divergence.

17 ref

005986   Sharma M (Mathematics Dep, Marudhar Engineering College, Bikaner-334 001, Email: mukesh2004.1729@rediffmail.com) : Note on undefined integral. Arya Bhatta J Math Inf 2015, 7(1), 159-62.

In the literature various workers obtained the values of some typical integration with the help of Watson, Whipple and Dixon theorem. In this research note we obtain the value of an undefined integral with the help of a result of Watson's theorem.

7 ref

005985   Sharma M (Mathematics Dep, Marudhar Engineering College, Bikaner-334 001, Email: mukesh2004.1729@rediffmail.com) : Result on watson's summation theorem for the series ₃F₂. Arya Bhatta J Math Inf 2015, 7(1), 135-8.

In the theory of hypergeometric and generalized hypergeometric series, Watson's summation theorem for the series ₃F₂ plays an important role. The aim of this short research note is to add one more result in the literature.

7 ref

005984   Senthil Kumar P;Mohamed Harif B;Nithya A (Mathematics Dep, Rajah Serofji Government College, Thanjavur, Tamil Nadu, Email: senthilscas@yahoo.com) : Forecasting the free cortisol levels after awakening based on high-order fuzzy logical relationship. Arya Bhatta J Math Inf 2015, 7(1), 13-22.

People usually use many methods to predict the weather, the temperature, the stock index, the enrollments, the earthquake, the economy, etc. A growing body of data suggests that a significantly enhanced salivary cortisol response to waking may indicate an enduring tendency to abnormal cortisol regulation. Based on these forecasting results, our objective was to apply the response test to a population already known to have long-term hypothalamo-pituitary-adrenocortical (HPA) axis dysregulation. We hypothesized that the free cortisol response to waking, believed to be genetically influenced, would be elevated in a significant percent age of cases, regard less of the afternoon Dexamethasone Suppression Test (DST) value based on high-order fuzzy logical relationships. First, the proposed method fuzzifies the historical data into fuzzy sets to form high-order fuzzy logical relationships. Then, it calculates the value of the variable between the subscripts of adjacent fuzzy sets appearing in the antecedents of high-order fuzzy logical relationships. Then, it lets the high-order fuzzy logical relationships with the same variable value form a high-order fuzzy logical relationship group. Finally, it chooses a high-order fuzzy logical relationships group to forecast the free cortisol response to walking and the short day time profile.

2 illus, 3 tables, 12 ref

005983   Senthil Kumar P;Abirami R (Mathematics Dep, Rajah Serfoji Government Arts College, Thanjavur, Tamilnadu, Email: senthilscas@yahoo.com) : Stochastic model for the yule process and estimation of the convex function of GIP secretion in response to oral glucose tolerance test. Arya Bhatta J Math Inf 2015, 7(1), 81-6.

To evaluate the Glucose dependent insulinotropic polypeptide (GIP) gastrointestinal peptide hormone regulating postprandial insulin release from pancreatic Beta-cells. The standardized oral glucose tolerance test was performed between n=52 patients and n-28 healthy controls. GIP levels were measured sequentially for 120 minutes, after glucose administration. GIP secretion was unchanged. There is no difference in GIP secretion between patients and healthy controls. In this paper, the problem is investigated considering Yule process and estimation of convex function with focus on exponential or Markovian case.

2 illus, 14 ref

005982   Sarmah B K;Chakrabarty D (Statistics Dep, Bholanath College, Dhubri, Assam) : Testing of randomness of the numbers generated by fisher yates. Arya Bhatta J Math Inf 2015, 7(1), 87-90.

Proper randomness of the numbers generated by Fisher and Yates has been examined by D. Chakrabarty in 2010 by computing the probability of occurrence of each digit in the table of generated numbers and then applying the theoretical probabilistic concept of randomness. The same has been tested by B.K Sarmah and D. Chakrabarty (Nov. 2014 IJESRT) by applying the Chi-square test for testing the significance of difference between observed frequency of each of the digit in the table and the corresponding theoretical (expected) frequency. In this paper, the randomness of the digits have been tested by applying t-test for amount of deviation of the observed number of occurrence and the theoretical(expected) number of occurrences of the respective digits and hence the numbers. The test shows that the numbers generated by Fisher and Yates deviated significantly from proper randomness.

1 table, 17 ref

005981   Rizwan S M;Padmavathi N;Taneja G (Mathematics & Statistics Dep, Caledonian College of Engineering, Sultanate of Oman, Email: rizwan@caledonian.edu.om) : Performance analysis of a desalination plant as a single unit with mandatory shutdown during winter. Arya Bhatta J Math Inf 2015, 7(1), 195-202.

Aim of this paper is to present a reliability and availability analysis of a desalination plant as a single unit. The plant operates round the clock for water production and the complete plant is under shut down state for 30 days during winter season for annual maintenance. The water supply during the shutdown period is maintained through ground water and storage system. Any failure or annual maintenance brings the plant to a complete halt and the plant goes under forced outage state. Tripping statesare also noted which requires only servicing. For the present analysis, seven years failure data has been extracted from operations and maintenance reports of a desalination plant in Oman. Measures of the plant effectiveness have been obtained using semi-Markov processes and regenerative point techniques.

1 illus, 7 ref

005980   Ramesh Kumar A;Deepa S (Mathematics Dep, Srimad Andavan Arts and Science College (Autonomous), T.V. Kovil, Trichy-5, Email: rameshmaths@ymail.com) : New method of 1'S interval linear assignment problems. Arya Bhatta J Math Inf 2015, 7(1), 91-6.

This paper deals with the Assignment problems arise in different situations where we have to find an optimal way to assign n jobs to m other objects as per their efficiency using maximizes and Alternate optimal assignment models. Using ones interval linear assignment methods and the existing Hungarian method a numerical example has been solved and compared. We consider interval analysis concept for solving interval linear assignment problems.

5 ref

005979   Rajeev Kumar;Vinod Kumar;Reena (Mathematics Dep, M.D. Univ, Rohtak, Haryana, Email: drrajeevmdu@gmail.com) : Performance and cost-benefit analysis of a system having bath-tub curve shaped failure pattern with provision of two types of replacement. Arya Bhatta J Math Inf 2015, 7(1), 139-50.

Present paper deals with a stochastic model for a system having bath-tub curve shaped failure patternt. The system having bath-tub curve shaped failure pattern is catogarised in to three stages of operation which have different failure rates, i. e. corresponding to testing/ burn-in process, useful life period and wear-out period. After burn-in stage, on failure of the system, the available repairman first inspects whether fault is minor or major and if the fault is minor he repairs the system. In case, fault is major then he carries out further inspection of the system to judge whether replacement has to be done by an old one unit of same operational stage or by a new one and accordingly carries out the replacement Various measures of the system effectiveness are obtained at different stages of operation of the system using Markov process and regenerative point techniques. The system is analysed with respect to its reliability, availabilty and profit. Various conclusions have been drawn for the system on the basis of graphical study.

10 illus, 13 ref

005978   Rahman S;Jae-Bok J;Ahmad A (Mathematics Dep, Maulana Azad National Urdu Univ, Polytechnic Darbhanga (Branch), Bihar-846 001, Email: shamsur@rediffmail.com) : On semi-invariant submanifolds of a nearly lorentzian para-sasakian manifold. Far East J mathl Sci 2015, 96(6), 709-24.

Object of the present paper is to study semi-invariant submanifolds of a nearly Lorentzian para-Sasakian manifold. Nijenhuis tensor in a nearly Lorentzian para-Sasakian manifold is calculated. Integrability conditions for some distributions on a semi-invariant submanifold of a nearly Lorentzian para-Sasakian manifold are investigated.

12 ref

005977   Rahman A;Chakrabarty D (Statistics Dep, Pub Kamrup College, Baihata Chariali, Kamrup, Assam, Email: rahman.atwar786@gmail.com) : Elimination of parameters and principle of least squares: fitting of linear curve to average maximum temperature data in the context of Assam. Arya Bhatta J Math Inf 2015, 7(1), 23-8.

Principle of least squares, innovated by the French mathematician Legendre, when applied to observed data in order to fit a mathematical curve yields normal equations. The parameters involved in the curve are estimated by solving the normal equations. The number of normal equations becomes larger when the number of parameters associated to the curve becomes larger. In this situation, the solution of the normal equations for estimating the parameters becomes more complicated. For this reason, one more convenient method has been search for computing the estimates of the parameters. The method has been developed by the stepwise application of the principle of least squares. The method innovated here consists of the elimination of parameters first and then the minimization of the sum of squares of the errors. In this paper, the method has been described with reference to the estimation of parameters of a linear curve based on observed data on monthly average maximum temperature at Guwahati.

2 tables, 12 ref

005976   Panwar A (Mathematics Dep, M.D. Univ, Rohtak, Email: anjupanwar15@gmail.com) : Stability of jungck iteration process in complete metric spaces. Arya Bhatta J Math Inf 2015, 7(1), 47-50.

Aim of this paper is to establish w^{2-stability of Jungck iteration procedure for some contractive conditions. It is generalization of some well known results in the literature.}

5 ref

005975   Nirmala G;Sinthamani P (Research Advisor and Convenor, Government Arts College, Melur, Madurai District, Tamil Nadu, Email: nirmalamanokar11@yahoo.com) : Fuzzy regular graph properties with IF-then rules. Arya Bhatta J Math Inf 2015, 7(1), 97-108.

In this paper derivation and approaches are worked on the basis of IF-THEN rules in regular fuzzy graphs and totally tegular fuzzy graphs. Some amazing facts with peculiar results for new parameters, by analyzing IF-THEN rule in fuzzy graphs are received. Fuzzy strongest path for the parameters are derived by presenting the fuzzy graph concept.

12 illus, 12 ref

005974   Mittal M;Singh T P;Gupta D (Mathematics Dep, M.M. Univ, Mullana) : Threshold effect on a fuzzy queue model with batch arrival. Arya Bhatta J Math Inf 2015, 7(1), 109-18.

Objective of the paper is to model the performance measures of a simple queue system with batch arrival. The arrival and service rates both are considered to be in fuzzy parameters. The mathematical description of the model has been presented for two and three parameters The various queue characteristics are extracted from the fuzzy state probability junction governing the behaviour of the system. α - cut and Zadeh extension principle has been applied to transfer the trapezoidal queue system into crisp queue measures. The batch size follows geometrical distribution. The evaluation of thresholding is applied to eliminate small membership values to avoid unnecessary computations.

3 illus, 1 table, 10 ref

005973   McKibben M A;Webster M (Mathematics Dep, West Chester Univ, 25 Univ Avenue West Chester, PA, 19383, U. S. A., Email: mmckibben@wcupa.edu) : Abstract stochastic integrodifferential delay equations driven by fractional brownian motion. Far East J mathl Sci 2015, 96(6), 757-800.

Investigated a class of abstract delay stochastic integrodifferential delay equations driven by a fractional Brownian motion (fBm) dependent upon a family of probability measures in a separable Hilbert space. We establish the existence and uniqueness of a mild solution and various convergence and approximation results. Finally, the analysis of two examples with numerical experiments is presented to provide numerical evidence of weak convergence.

36 ref

005972   Kalanov T Z (NO, Home of Physical Problems, Pisatelskaya 6a, 100200 Tashkent, Uzbekistan, Email: tzk_uz@yahoo.com) : Critical analysis of the foundations of the theory of negative numbers. Arya Bhatta J Math Inf 2015, 7(1), 3-12.

Critical analysis of the foundations of the theory of negative numbers is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of the theory of negative numbers contradict practice and contain formal-logical errors. The main results are as follows: a) the concept "number sign" is inadmissible one because it represents a formal-logical error; b) all the numbers are neutral ones because the number "zero" is a neutral one; c) signs "plus" and "minus" are only symbols of mathematical operations. The obtained results are the sufficient reason for the following statement. The existence of logical errors in the theory of negative numbers determines the essence of the theory: the theory is a false one.

12 ref

005971   Kalanov T Z (NO, Home of Physical Problems, Pisatelskaya 6a, 100200 Tashkent, Uzbekistan, Email: tzk_uz@yahoo.com) : On the formal-logical analysis of the foundations of mathematics applied to problems in physics. Arya Bhatta J Math Inf 2015, 7(1), 1-2.

Results of the critical analysis of the standard foundations of mathematics applied to problems in physics are discussed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. The main result is as follows: the concept of "mathematical quantity" - central concept of mathematics - is meaningless, erroneous, and inadmissible one because it represents the following formal-logical and dialectical-materialistic errors: negation of the existence of the essential sign of a concept (i.e., negation the existence of the essence of the concept) and negation of the existence of measure of material object. The obtained results lead to the conclusion that the generally accepted foundations of mathematics should be reconsidered.

005970   Im Y B;Lee J S;Cho Y D (NO, College of Dharma Dongguk Univ, Seoul 100-715, Korea, Email: philpen@dongguk.edu) : Fuzzy pairwise α-precontinuous mappings. Far East J mathl Sci 2015, 96(6), 743-55.

Defines and characterize a fuzzy pairwise α-precontinuous mapping and a fuzzy pairwise α-preopen mapping on a fuzzy bitopological space. Besides, some interesting properties of these mappings are given.

10 ref

005969   Gonzalez E G;Villegas M C;Garcia S I O;Rojas L A H;Garcia A C (NO, UPIICSA - Instituto Politecnico Nacional Av. Te 950, 08400 Mexico, D.F., Email: egutierrezg@ipn.mx) : Parametric bootstrap test for generalized extreme value distribution. Far East J mathl Sci 2015, 96(6), 693-708.

In this article a goodness of fit bootstrap test for generalized extreme value distribution (GEVD), taking the sample correlation coefficient as a statistic test is proposed. That the proposed test is consistent is shown and through Monte Carlo simulation size and power of the test for various alternative distributions is calculated. The test and GEVD are applied to the annual maximum values of rainfall in Alto-Grijalva basin, which belongs to the hydrographic region No. 30 of Mexico. * The distribution parameters were estimated by maximum likelihood, and the asymptotic properties of these pstimators were used to calculate confidence intervals for the parameters. The test verified that maximum annual values meet GEVD for the particular case of the Frechet distribution, and with this distribution, the return periods for various levels of extreme precipitation were calculated.

1 illus, 6 tables, 14 ref

005968   Geetha T;Karthika K (Mathematics PG & Research Dep, K.N.Govt. Arts College for Women, Thanjavur, Tamilnadu) : Mathematical model of gamma family on cortisol associated with chronic back pain. Arya Bhatta J Math Inf 2015, 7(1), 151-8.

One of the most important way to get a new probability distribution in applied probability is the mixture distribution. Because of this reason, we get a new mixed distribution namely MGG distribution and it is obtained by mixing GG and LGG. The MGG distribution is useful of modelling bathtub-shaped hazard rate, and also it includes some special submodels of gamma and exponential family. In application part, the hormonal level of Cortisol due to chronic back pain is discussed. It has been identified that maladaptive physiological responses of the organism with a recurrent stressor maintain the chronic pain. The associations between basal levels of Cortisol collected over seven successive days, the hippocampal volumes & brain activation to thermal stimulations is also examined by administering in 16 patients with chronic back pain (CBP) and 18 healthy control subjects. Finally, it is found that patients with CEP have higher levels of Cortisol than control subjects.

7 illus, 16 ref

005967   Duraivel T;Bhaskara Rao B;Premkumar K (Mathematics Dep, Pondicherry Univ, Pondicherry-605 014, Email: tduraivel@gmail.com) : Primary extension filtration of modules. Far East J mathl Sci 2015, 96(6), 685-92.

5 ref

005966   Bhardwaj R;Vijay Kumar;Singh T P (Mathematics Dep, Amity Univ, Punchgaon, Manesar, Gurgaon, Email: bhardwajreeta84@gmail.com) : Mathematical modeling of feedback bitandem queue network with linkage to common channel. Arya Bhatta J Math Inf 2015, 7(1), 187-94.

Present paper makes an attempt to model a network of queues in which a common service channel is linked with each of two biserial channels along with a feedback from common channel i.e., arrival and service pattern both follow poisson distribution. All the activity in the system is performed under stochastic environment. The differential difference equations have been framed for the model and steady state behavior of the system has been studied. The system performance characteristics have been determined by using generating function technique, laws of calculus, statistical formulae of marginal distribution etc. Numerical illustration has been given to demonstrate the result. The model finds its application in industries, banking system, administrative setup, computer network, super markets and many other business service systems.

9 ref