014968   Farhang Y;Fattahi H (NO, Faculty of Computer Science and Information System, Teknologi Malaysia, Skudai, 81310, Johor Bahru, Malaysia, Email: yfarhang@yahoo.com) : Theory of rough set and fuzzy set in granular computing. Far East J mathl Sci 2012, 64(1), 97-104.

Granular computing is powerful strategies for expressing and solving problems. Fuzzy set theory and rough set theory, as two very main patterns of granular computing, are frequently used to process unclear information in data mining. Granular computing is a name of techniques, methodologies, and machines that make use of granules in the progression. The idea of granular computing has exposed in many parts, and it is usually playing the main role in data mining. Mixing fuzzy set and rough set theory, a flexible technique is for processing flawed information systems. Nowadays, the usage of the rough set theory compared to other theories is more importance, and its rapid growth of popularity is undeniable.

2 illus, 26 ref

014967   El-Shehawy S A;Abdel-Salam E A B (Mathematics Dep, College of Science, Qassim Univ, P.O. Box 6644, Buraidah 51452, Kingdom of Saudi Arabia, Email: shshehawy64@yahoo.com) : On deformation technique of the hyperbolic secant distribution. Far East J mathl Sci 2012, 64(1), 37-49.

Based on the deformation technique for the hyperbolic secant (HS) function, the p-deformed hyperbolic secant (p-DHS) distribution is presented. This technique is used to deform the balance between exponential growth and decay parts in the hyperbolic secant (HS) distribution. Some fundamental properties of the constructed p-DHS distribution are discussed. Our study aims to derive some important corresponding functions in closed forms, to explain some fundamental measures and to summarize some results for the mentioned distribution.

3 illus, 12 ref

014966   Dias D P;Melo S T (NO, Instituto de Matematica e Estatistica, Sao Paulo Univ, Rua do Matao 1010, 05508-090 Sao Paulo, Brazil, Email: dpdias@ime.usp.br) : Chern-connes character for pseudodifferential operators on the sphere. Far East J mathl Sci 2012, 64(2), 269-80.

Compound the Chern-Connes character (a map from the K-theory of a C' -algebra under the action of a Lie group to the cohomology of its Lie algebra) for the L -norm closure of the algebra of all classical zero-order pseudodifferential operators on the sphere under the action of SO(3). Authors show that its image is R if the trace is the integral of the principal symbol.

15 ref

014965   Diankha O;Deme C B (Mathematics and Computer Science Dep, Cheikh Anta Diop of Dakar Univ, Senegal, Email: odiankha@ucad.sn) : Connection between classification and minimum polynomial of multiplexed sequences. Far East J mathl Sci 2012, 64(1), 105-20.

Linear recurrent sequences are used in many areas like cryptology, electronics, coding theory, where they play an important role. However, they suffer a great weakness before Berlekamp-Massey algorithms attacks. This is the motivation of the creation of the multiplexed sequences constituted by two maximal period sequences with respective periods 2^k -1 and 2^m -1, k and m being their respective orders. Here is devised a method to determine the complexities k and m of maximal period sequences constituting a multiplexed sequence in certain conditions. It is also given a connection between the classification of the multiplexed sequences and their minimum polynomial of a multiplexed sequence.

10 ref

014964   Corona G C (Area de Analisis Matematico y sus Aplicaciones, Autonoma Metropolitana-Azcatpotzalco Univ, Av. San Pabl;o Xalpa 180, Col. Reynosa Tamaulipas, Azcaptozalco D.F., C.P. 02200, Mexico, Email: ccg@correo.azc.uam.mx) : Schrodinger unbound eigenfunctions. Far East J mathl Sci 2012, 64(2), 297-306.

All eigenfunctions of the one-dimensional Schrodinger spectral problem system over the complex numbers are bound except for a finite number of them.

6 ref

014963   Chen J;Yang S (NO, College of Applied Sciences, Beijing Technology Univ, Beijing-100 124, P.R. China) : Algebra automorphisms of two-parameter quantum superalgebras U_r,s (osp(1,2,c)). Far East J mathl Sci 2012, 64(1), 63-80.

A new kind of two-parameter quantum superalgebra U_r,s (osp(l, 2, c)) which is a Hopf superalgebra, is investigated. All the algebra automorphisms are determined. Furthermore, the Hopf automorphisms are also obtained as an application.

10 ref

014962   Chauhan K;Roy S N (P.G. Mathematics Dep, V.K.S. Univ, Ara, Bihar, Email: kavitachauhan908@gmail.com) : Effect of perturbations in coriolis and centrifugal forces in the motion of infinitesimal mass around L₄ in the photogravitational restricted three body problem. Invertis J Sci Technol 2014, 7(1), 12-22.

Lagrangian formula for the three dimensional motion of a satellite in the vicity of the non collinear points of the photogravitational circular restricted three body problem is considered. It is shown that the motion around L4 gets influenced by radiation pressure and perturbation in centrifugal force. It is observed that the motion around L4 does not get affected by the perturbation in coriolis force.

7 illus, 1 table, 18 ref

014961   Chao-Ping C (Applied Mathematics and Informatics Dep, Research Institute of Applied Mathematics, Henan Polytechnic Univ, Jiaozuo City, Henan-454 003, China) : Note on monotonicity of the extended mean values. J Analysis Computn 2013, 9(1), 1-3.

Provide another proof of monotonicity for the extended mean values. 2000 Mathematics Subject Classification, 26A48.

6 ref

014960   Changphas T (Mathematics Dep, Faculty of Science, Khon Kaen Univ, Khon Kaen 40002, Thailand) : On the decomposition of prime ideals of ordered N-semigroups into three N-classes. Far East J mathl Sci 2012, 64(1), 121-7.

Author show that every ideal of an N-class of an ordered N-semigroup does not contain proper prime ideals. Similar results on ordered semigroups were presented by Kehayopulu and Tsingelis in [2] and on semigroups can be founded in [3, II.2.11].

5 tables, 5 ref

014959   Cerin Z;Gianella G M (NO, , Kopernikova 7, 10010 Zagreb, Croatia, Email: cerin@math.hr) : On the fermat problem for ellipse. Far East J mathl Sci 2012, 64(2), 213-27.

Extended a curious observation by Fermat about points on a semicircle on a side of a special rectangle to a theorem that holds for all points on an ellipse.

5 illus, 6 ref

014958   Caro-Lopera F J (Basic Sciences Dep, Medellin Univ, Carrera 87 No. 30-65, Medellin, Colombia, Email: fjcaro@udem.edu.co) : Family of formulae for Pi. Far East J mathl Sci 2012, 64(2), 157-81.

Simple circle method for constructing rational points and tangents with straightedge and compass is introduced; taking the limit, this leads to a family of N formulae for π. The whole process is based on the derivation of a Pythagorean triple and the construction of the circle by irregular inscribed polygons with rational area.

1 ref

014957   Caristi G;Stoka M (S.E.A. Dep, Messina Univ, Italy) : Laplace type problem for lattice with the axial symmetry and different types of obstacle (II). Far East J mathl Sci 2012, 64(2), 281-95.

Authors consider a lattice with the cell composed of three rectangles as in Figures 1, 3 and 5 or of 3n rectangles as in Figure 7, 8 and 9 and with obstacles of different types and, authors compute the probability that a segment of random position and constant length intersects a side of the lattice.

9 illus, 4 ref

014956   Bijendra Singh;Jain S;Johri A (NO, School of Studies in Mathematics, Vikram Univ, Ujjain, Madhya Pradesh) : Sir model with mass incidence and modified death rate. J Indian Acad Math 2012, 34(1), 1-7.

Using the concept of Gao and Hethcote a model with mass action incidence is analyzed by Han et at. Investigated the problem by using a modified general death rate of prey species. One general threshold quantity has also been derived. Using Lemma 1 of Han et al. %, the model can be reduced to four differential equations of which the analysis can be done independently. The model being of general form, the result obtained by Han et al. follows as a special case.

18 ref

014955   Bageerathi K;Thangavelu P (Mathematics Dep, Govindammal Aditanar College for Women, Tiruchendur-628 215, Email: sivarathi2006@yahoo.in) : Remarks on fuzzy boundary and fuzzy semi boundary. J Indian Acad Math 2012, 34(1), 49-59.

Athar and et al. studied the properties of Fuzzy boundary and Fuzzy semi boundary in fuzzy topological spaces. Proved new results on fuzzy boundary and fuzzy semi boundary, by the way of establishing that the some of the results listed are not true.

7 ref

014954   Badshah V H;Pariya A (NO, School of Studies in Mathematics, Vikram Univ, Ujjain, Madhya Pradesh, Email: vhbadshah@yahoo.com) : Common random fixed point theorem for six random operators satisfying a rational inequality. J Indian Acad Math 2012, 34(1), 301-17.

The purpose of this paper is to establish a common random fixed point theorem for six random operators satisfying a rational inequality using the concept of semi-compatibility, weak compatibility and commutativity of random operators in Polish spaces.

17 ref

014953   Aly F S;Mestady M O A;Alghazzawi D A (Mathematics Dep, Faculty of Science King Abdulaziz Univ, P.O. Box 80203, Jeddah 21589, Saudi Arabia, Email: farahata@yahoo.com) : Semisymmetric rings. Far East J mathl Sci 2012, 64(1), 141-9.

Right semisymmetric rings are introduced as a generalization of symmetric rings. Some properties of this class are given. It is shown that R is strongly regular if and only if every right R-module is flat and right semisymmetric if and only if every cyclic right R-module is flat and right semisymmetric if and only if R is regular and right semisymmetric.

11 ref

014952   Aiyub Khan;Tak S S;Sharma N (Mathematics & Statistics Dep, Jai Narain Vyas Univ, Jodhpur-342 003, Email: draiyubkhan@gmail.com) : Effect of hall current on gravitational stability of an interstellar medium with radiation. J Indian Acad Math 2012, 34(1), 189-203.

The effects of radiation pressure, finite conductivity and Hall currents on the gravitational instability of infinite homogeneous rotating self gravitating plasma in a horizontal magnetic field are investigated. The streaming motion is also assumed to be horizontal. Under necessary MHD linearized equations and applying normal mode analysis the dispersion relation has been derived and solved numerically. It is found that the rotation and the magnetic field have stabilizing influence while finite conductivity and Hall currents have destabilizing influence on the growth rate of unstable mode of system.

4 illus, 14 ref

014951   Adiga C;Shrikanth A S;Shivakumar Swamy C S (Studies in Mathematics Dep, Mysore Univ, manasagangothri, Mysore-570 006, Email: c_adiga@hotmail.com) : 1-edge balance index set. Int J mathl Combinatorics 2012, 3(Sept), 113-7.

Let G be a graph with vertex set V and edge set E, and Z₂ = (0, 1). Let f be a labeling from E to Z₂, so that the labels of the edges are 0 or 1. The edges labelled 1 are called 1-edges and edges labelled 0 are called 0-edges. The edge labeling f induces a vertex labeling f* : V → Z₂ defined by f*(v) = {[1 if the number of 1-edges incident on v is odd], [0 if the number of 1-edges incident on v is even]}. For i ∈ Z₂ let e_f(i) = e(i) = |{e ∈ E : f(e) = i}| and v_f(i) = v(i) = |{v ∈ V : f*(v) = i}|. A labeling f is said to be edge-friendly if |e(0) - e(1)|≤1. The 1- edge balance index set (OEBI) of a graph G is defined by {|v_f(0) - v_f(1) : the edge labeling f is edge-friendly}. The main purpose of this paper is to completely determine the 1-edge balance index set of wheel and Mycielskian graph of a path.

1 illus, 6 ref

014950   Adachi Y (NO, , 12-29 Kurakuen 2 ban-cho, Nishinomiya, Hyogo 662-0082, Japan, Email: fwjh5864@nifty.com) : Addendum to the previous paper "on a schur stable set of algebric equations". Far East J mathl Sci 2012, 64(1), 151-5.

In the previous paper, we proved that every connected component of a Schur stable set is simply connected. We studied the number of connected components of it. But there was an incorrect figure and left a problem behind. We correct it and study the problem.

3 illus, 2 ref

014949   Abhishek Singh;Banerji P K (Mathematics Dep, Faculty of Science, J.N.V. Univ, Jodhpur-342 005, Email: abhijnvu@gmail.com) : Dunkl transform of tempered boehmians. J Indian Acad Math 2012, 34(1), 9-18.

In this paper the Dunkl transform is extended on the space of tempered Boehmians. Properties of the Dunkl transform are studied and also an inversion formula for this transform on the extended tempered distribution is derived.

9 ref

014948   Abdullah (NO, Atma Ran Sanatan Dharma College, Delhi Univ, Dhaula Kuan, New Delhi-110 021, Email: abdullah2008@rediffmail.com) : Periodic orbits around lagrangian points of the circular restricted four body problem. Invertis J Sci Technol 2014, 7(1), 29-38.

In this paper we study the periodic orbits generated by Lagrangian solutions of the circular restricted four body problem in three cases. In the first case, Authors consider all the three primaries as spherical in shape. In the second case, we consider one of the primaries as oblate body. In the third case, we consider two of the primaries as oblate body and all the three primaries are source of radiation pressure. In all the three cases, we find the equations of motion in the Cortes/on form, the tangents and normal form of equations and then we illustrate the periodic orbits by giving displacements along the tangent and normal to the mobile coordinates and also show the effect of oblateness and radiation pressure in the second and third cases respectively.

12 illus, 17 ref

013813   Yuksel S;Simsekler T H (Mathematics Dep, Science Faculty, Selcuk University, Konya, Turkey, Email: syuksel@selcuk.edu.tr) : Strongly θ-1-continuous functions. Far East J mathl Sci 2011, 58(2), 223-33.

Strongly θ-I-continuous functions are defined. The aim of this paper is to investigate this type of continuity and to obtain the new results.

18 ref

013812   Ying-Ying W;Jian-Ping F;Song-Hua M (Physcd Dep, Zhejiang Lishui University, Lishui 323 000, P.R. China, Email: zjlsfjp@yahoo.com.cn) : Application of homotopy perturbation method in the Benjamin-Boma-Mahony equation. Far East J mathl Sci 2011, 58(2), 193-8.

Using the Riccati mapping method to get the simple exact solutions of Benjamin-Boma-Mahony (BBM) equation and choosing one of the solutions as the initial condition of the approximate homotopy solutions of the BBM equation, we get the third order approximate solutions of the equation.

21 ref

013811   Wani S S;Thakar S (Applied Mathematics Dep, Pillai's Institute of Information Technology, Sector 16, Plot No. 10, New Panvel, Dist. Raigad, Navi Mumbai-410 206, Email: sachin.swani@gmail.com) : Linear method for two dimensional burgers equation. Ultra Scient phys Sci-Sect A 2013, 25(1), 156-68.

Linear method is constructed for numerical solution of two dimensional non-linear Burgers equation. The scheme is derived from Crank-Nicolson finite difference scheme for linear terms and averaging for nonlinear terms. The method is shown to be consistent and second order accurate in time and space. The numerical solutions are obtained for two test problems at different time t and Reynolds number Re. The numerical solutions are compared with exact solution and other existing methods. Though the method is linear numerical solutions are compatible with ADM and Crank-Nicolson method.

14 tables, 24 ref

013810   Tripathi A;Sharma A K;Singh K K (Mathematics Dep, K.K. (P.G.) College, Etawah, Uttar Pradesh, Email: atkkdc@gmail.com ) : MHD flow of a conducting visco-elastic Rivlin-Ericksen (1955) fluid through porous medium in a long uniform rectangular duct due to an impulsive pressure gradient acting at the central part of a section. Ultra Scient phys Sci-Sect A 2013, 25(1), 73-80.

The aim of present problem is to study the unsteady flow of a conducting visco-elastic Rivlin-Ericksen type fluid through porous medium in a long uniform rectangular duct under the influence of an impulsive pressure gradient acting at the central part of a section and uniform magnetic field applied normally to the flow of fluid. The analytical expressions for velocity profile and flux have been determined by the application of transform technique. Some particular cases have been discussed in detail. The results for the flow of ordinary viscous fluid have also been deduced by taking parameter μ1→0.

15 ref

013809   Tian Y;Fan M;Meng F (Basic Courses Dep, Qingdao Technological Univ (Linyi), Feixian-273 400, Shandong, P.R. China, Email: tianyazhou369@163.com) : New oscillation criteria for second order neutral equations with distributed deviating argument. Far East J mathl Sci 2012, 63(2), 253-68.

11 ref

013808   Tang S;Thadapani E;Li T (NO, School of Information and Control Engineering, Weifang Univ, Weifang, Shandong-261 061, P.R. China, Email: wfxytang@163.com) : Oscillation theorems for second-order neutral differential equations of mixed type. Far East J mathl Sci 2012, 63(1), 75-85.

Some oscillation criteria are presented for the second-order nonlinear neutral differential equations of mixed type [x(t) + P₁x(t - τ₁) + P₂x(t + τ₂))^γ]ⁿ = q₁(t) x^γ(t - σ₁) + q₂(t)x^γ(t + σ₂), t ≥ t₀, where γ ≤ 1 is the ratio of odd positive integers. These criteria generalize and complement the results given in the literature.

17 ref

013807   Tanaka M;Yanagishita M (Mathematics and Informatics Dep, Fundamental Science Div, Graduate School of Science, Chiba Univ, 1-22 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan, Email: emblem-yp5@graduate.chiba-u.jp) : Minimal thinness fo parabolic functions. Far East J mathl Sci 2012, 63(1), 1-10.

In this paper, authors introduce the notion of minimal thinness for parabolic functions and characterize subsets of the slab with respect to positive parabolic functions on the slab. Also consider the boundary limit theorem related to this notion for positive parabolic functions on the slab.

6 ref

013806   Suwastika E;Alamsyah I M;Irawati (Faculty of Mathematics and Natural Sciences, Institute Teknologi Bandung, Bandung, 40132, Indonesia) : Polynomials over G-Dedekind prime rings. Far East J mathl Sci 2011, 58(2), 173-8.

Let R be a G-Dedekind prime ring with an automorphism s of finite order. Akalan proved that R[x, σ] is also a G-Dedekind prime ring. In this paper, proved that if the skew polynomial ring R[x, σ] is a G-Dedekind prime ring with enough invertible ideals, then R is also s-G-Dedekind prime ring.

4 ref

013805   Srivastava S S;Singh A (Mathematics Dep, Govt. P.G. College, Shahdol, Madhya Pradesh) : Temperature in the prism involving I-fnction of two variables. Ultra Scient phys Sci-Sect A 2013, 25(1), 207-9.

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013804   Sophiaporchelvi R;Vanitha R (Mathematics Dep, ADM College for Women, Nagapattinam-611 001, Email: sophiaporchelvi@gmail.com) : On studying antibiotic in the bloodstream by the method of dynamical model. Ultra Scient phys Sci-Sect A 2013, 25(1), 135-8.

Primarily the antibiotics-the group drugs intended to inhibit or destroy bacteria, should be used only against bacterial infection. The antibiotic Norfloxacin is prescribed for treating bacterial infections, including urinary tract infections, prostatitis, and gonorrhea infections of the urethra or cervix. This antibiotic works to kill bacteria by interfering with specific enzymes, which prevents the bacteria from multiplying. When taking an antibiotic, it is important to keep the amount of the bloodstream fairly constant. If the amount gets too low, they can begin to regrow. If the amount gets too high, it could cause other Complications. In this paper, a dynamical model has been constructed to find the amount of the Norfloxacin in the blood stream.

7 ref

013803   Song-Hua M;Qing-Bao R;Jian-Ping F (NO, College of Mathematics and Physics, Lishui Univ, Lishui-323 000, P.R. China, Email: qingbaoren@hotmail.com) : Soliton excitations and fractal behaviours for A (2+1)-dimensional nonlinear physical model. Far East J mathl Sci 2012, 63(1), 87-95.

Starting from a projective equation approach and a linear variable separation approach, some solitary wave solutions with arbitrary functions for the (2 + 1) -dimensional Bogoyavlenskii-Schiff system (BS) is derived. Based on the derived solution and by selecting appropriate functions, some novel localized excitations such as propagating solitons and fractal solitons are investigated.

3 illus, 21 ref

013802   Soleymani F (Mathematics Dep, Islamic Azad University, Zahedan Branch, Zahedan, Iran, Email: fazlollah.soleymani@gmail.com) : On a novel optimal quartically class of methods. Far East J mathl Sci 2011, 58(2), 199-206.

Following the existing trend in providing optimal derivative-free methods for finding simple roots; this paper suggests a general class of two-step iteration methods, which are consistent with the optimality conjecture of Kung-Traub [1] for constructing multi-point iterative without memory methods. The theoretical results show the fourth-order convergence using only three evaluations of the function per full cycle. This developed class of iterations is totally free from derivative evaluation, which is so much fruitful for engineering and optimization problems.

1 table, 22 ref

013801   Singh S P;Bahl S (Statistics Dep, MDU, Rohtak, Email: 76satinderpal@gmail.com) : Estimation of population mean using auxiliary information in stratified sampling on successive occasion using ratio method. Ann agric Res 2013, 34(4), 366-73.

In this paper tools of sampling theory have been developed and used for estimation of population mean. With the help of double sampling an effort has been made to improve the estimation in stratified sampling on successive occasion. The available information of the last occasion is used in improving the estimated mean in the current situation in stratified sampling. In case the population mean X(bar) of an auxiliary character X is known then a variety of estimators including ratio/regression and difference estimators are available for estimation of Y(bar) which is the mean of the character under study. Variance for ratio and double ratio estimators using ratio method has been derived. Also, an attempt has been made to study such an estimator under general sampling ways and even with specific sampling procedure.

10 ref

013800   Singh G P;Tyagi A (Mathematics Dep, Pacific Institute of Engineering, Pacific Academy of Higher Education, Udaipur-313 001, Email: gajendrasingh237@gmail.com) : LRS bianchi type II bulk viscous stiff fluid cosmological models with variable G and A. Ultra Scient phys Sci-Sect A 2013, 25(1), 85-94.

It is investigated the Bianchi type II bulk viscous stiff fluid cosmological models with variable gravitational constant G and cosmological constant A. To obtain the deterministic model, it is assumed that the expansion 6 in the model is proportional to the shear τ. Various physical and geometrical features of the models are also discussed.

34 ref

013799   Singh A;Mathur P K (Mathematics Dep, Rajeev Gandhi Engieering College, Salliya, Kolar Bhopal, Madhya Pradesh) : On the mixed boundary value problem of steady state heat conduction in a domain formed by cementing two plano-convex solids. Ultra Scient phys Sci-Sect A 2013, 25(1), 188-98.

The contact problem of two conducting plano-convex solids having different conductivities is considered assuming that steady state heat conduction takes place. The problem is formulated so as to involve a pair of dual integral equations having Legendre functions with complex index. These equations are reduced to a single integral equation which is then solved iteratively. Lastly, the quantities of physical interest are found out.

1 illus, 8 ref

013798   Seong-Hoon C;Jee-Won L;Jong-Sook B;Kwang-Soo N (Mathematics Dep, Hanseo Univ, Chungnam-356 706, South Korea, Email: shcho@hanseo.ac.kr) : Common fixed point theorems for generalized contractive type and generalized quasi-contractive type mappings on cone metric spaces. Far East J mathl Sci 2012, 63(2), 181-202.

Some new generalized contractive type and generalized quasi-contractive type conditions for a pair of mappings in cone metric spaces are defined and certain common fixed point theorems for these mappings are established.

3 ref

013797   Sebastian S;Mendez A;Divya Mary Daise S (Mathematics Dep, St. Albert's College, Ernakulam, Kochi-682 018) : On the maximal lattice of finite cyclic groups. Ultra Scient phys Sci-Sect A 2013, 25(1), 47-54.

In this paper author introduced the notion of a maximal lattice of groups. Also proved some theorems regarding maximal lattices and based on them developed a method to construct the maximal lattice of any finite cyclic group.

4 illus, 2 tables, 10 ref

013796   Sarangi A;Nath G;Swain S K (Physics Dep, Veer Surendra Sai University of Technology, Burla, Sambalpur-768 018, Email: anesh_nath99@yahoo.co.in) : Compatibility study of binary mixture for surface modifications of natural fibers using ultrasonic technique at different frequencies. Indian J pure appl Phys 2014, 52(1), 30-4.

The ultrasonic wave can be used to study the compatibility between the solvent mixtures. The selective mixture of organic compounds minimizes the lignin present in the surface of the natural fibers by which the modified fibers may enable to be filler for making of composites. Date palm leave (DPL) has been chosen as natural fiber whose surface is modified with mixture of methanol and acetone. The ultrasonic velocities are determined in binary mixtures of acetone and methanol with different frequencies (1 MHz, 3 MHz and 5 MHz) at temperature of 303 K. The different acoustic parameters like acoustic impedance, bulk modulus, intermolecular free length and compressibility are computed from the ultrasonic velocities and densities. The variations of these parameters are discussed in terms of different intermolecular interactions present in the solvent mixture. The compatibility of solvent mixtures is determined from the nature of excess values of thermo dynamical acoustic parameters. The interactions of selected solvent mixture with surface of the fiber have been investigated by Fourier transform infrared (FTIR) spectroscopy and field emission scanning electron.

8 illus, 16 ref

013795   Saluja A S;Dhakde A K;Magarde D (NO, J.H. Govt. P.G. College, Betul-460 001, Email: alkeshdhakde@gmail.com) : Fixed point theorem for expansion mappings of rational type on a implicit relation. Ultra Scient phys Sci-Sect A 2013, 25(1), 55-8.

In this note a fixed point theorems on expansion mappings is established in a complete metric space under certain conditions. Further a common fixed point theorem for pair of weakly compatible expansion mappings is established. In this theorem the completeness of space is replaced with a set of four alternative conditions for functions satisfying implicit relations. These theorems extended and improve results of S.M. Kange, M.A. Khan et a/e.,³, B.E. Rhoades and T. Taniguchi.

9 ref

013794   Reddy V S;Kiran Babu E (NO, G. Pulla Reddy Engineering College, Kurnool, Andhra Pradesh-518 007, Email: ebabukiran1982@gmail.com) : Combinatorial aspects of the generalized unitaroy Euler's totient. Ultra Scient phys Sci-Sect A 2013, 25(1), 15-8.

Generalized unitary Euler's totient is defined as a Dirichlet convolution of a power function & a product of the Souriau -Hsu-Mobius function with a completely multiplicative - function. Two combinatorial aspects of the generalized unitary Euler's totient, namely its connect totients and its relations with counting formulas are investigated.

2 ref

013793   Rawat K S;Uniyal N (Mathematics Dep, H.N.B. Garhwal Campus Univ, Badshahi Thaul, Tehri, Garhwal-249 199, Email: nitinuniyadlddn@gmail.com) : Decomposition of curvature tensor fields in a tachibana recurrent space of first order. Ultra Scient phys Sci-Sect A 2013, 25(1), 43-6.

In the present paper, author have studied the decomposition of curvature tensor field R_ijk^h in terms of two vectors and a tensor field. Also several theorems have been established therein.

8 ref

013792   Rana S (Mathematics Dep, Govt. College of Teacher Education, Dharamshala, Email: sureshrana428@gmail.com) : Free convection effects on the oscillatory flow past a vertical porous plate in the presence of radiation for an optically thin fluid. Indian J pure appl Math 2013, 44(6), 757-70.

The purpose of this work is to study the effect of transverse sinusoidal suction velocity on the flow and mass transfer on free convective oscillatory viscous and optically thin grey fluid over a porous vertical plate in the presence of radiation. The flow becomes three-dimensional due to the variation of suction velocity in the transverse direction. Analytical expressions for velocity and temperature fields are obtained using the perturbation technique. The governing equations has been transformed to ordinary differential equations. Numerical solutions are obtained for different values of radiation parameter, Grashof number and Schmidt number. It is found that non-dimensional velocity decreases with increase of radiation parameter, increases with increase of Grashof number, decreases with increase of Schmidt number and non-dimensional temperature decreases with the increase of radiation parameter.

4 illus, 16 ref

013791   Qiao S (NO, School of Applied Math., Guangdong Technology Univ, Guangzhou-510 006, P.R. China, Email: qshqsh513@163.com) : Weakly S-supplemented subgroups and P-nilpotency of finite groups. Indian J pure appl Math 2013, 44(6), 795-808.

Subgroup H of a group G is said to be weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ H_sG, where HSG is the maximal s-permutable subgroup of G contained in H. In this paper, investigated the influence of weakly s-supplernented subgroups on the structure of finite groups. Some recent results are generalized.

19 ref

013790   Pushpandra Kumar;Nadeem A (NO, , 94, North City, Near Airforce Gate, Pilibhit Road, Bareilly-243 122, Email: drpkgangwar03@gmail.com) : Product form in networks of queues with negative customers. Ultra Scient phys Sci-Sect A 2013, 25(1), 1-4.

In this paper, author introduced a new classes of queueing networks with "negative customers". A negative customer arriving to a queue reduces the total customers count in that queue by one negative customer donot receive service applications for such negative customer queueing networks include certain transaction models and certain neural network models. Even though the underlying equations of the models to be described can be nolinear they do have a product form solution for the equilibrium state probabilities.

11 ref

013789   Park J (Mathematics Dep, Hanseo Univ, Seosan-si, Chungnam-do-356 706, Korea, Email: jkpark@hanseo.ac.kr) : Generalizations of Hermite-Hadamard-like type inequalities for co-ordinated convex and concave mappings. Far East J mathl Sci 2012, 63(2), 235-51.

Obtained a new identity which gives more generalized results and using this equality, the generalizations of inequalities for differentiable co-ordinated convex, concave and s-convex mappings in the second sense in two variables which are related to the left side of Hermite-Hadamard type inequality for co-ordinated convex mappings in two variables are obtained.

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013788   Park J (Mathematics Dep, Hanseo Univ, Seosan-si, Chungnam-do-356 706, Korea, Email: jkpark@hanseo.ac.kr) : Hermite-hadamard-like and simpson-like type inequalities for co-ordinated convex mappings. Far East J mathl Sci 2012, 63(1), 105-25.

In this paper, author gives a new identity for partial differentiable mappings, and using this identity, establishes the estimates between two special terms for differentiable co-ordinated convex and coordinated s-convex mappings in the second sense.

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013787   Park J (Mathematics Dep, Hanseo Univ, Seosan-si, Chungnam-do-356 706, Korea, Email: jkpark@hanseo.ac.kr) : Some generalized inequalities for differentiable co-ordinated s-convex mappings in the second sense. Far East J mathl Sci 2012, 63(1), 57-74.

Several new inequalities which are related to the left side of Hermite-Hadamard inequality for partial differentiable co-ordinated s-convex mappings in the second sense on the rectangles from the plane are obtained.

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013786   Park J (Mathematics Dep, Hanseo University, Seosan-si, Chungnam-do, 356-706 Korea, Email: jkpark@hanseo.ac.kr) : On the Hermite-Hadamard-type inequalities for co-ordinated s-r-convex mappings. Far East J mathl Sci 2011, 58(2), 207-21.

In this article, author provided a new definition of co-ordinated s-r-convex mappings and establish some Hadamard-type inequalities for these mappings.

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013785   Park J (Mathematics Dep, Hanseo University Seosan-si, Chungnam-do, 356-706 Korea, Email: jkpark@hanseo.ac.kr) : On the left-side inequality of Hermite-Hadamard inequality for differentiable α, m)-convex mappings. Far East J mathl Sci 2011, 58(2), 179-91.

In this article, the author establishes new results related to the left hand side inequality of the Hermite-Hadamard inequality for differentiable (α, m)-convex mappings whose first derivative in absolute value aroused to the q-th (q ≥1) power is (α, m)-convex. Some applications to special means of positive real numbers are also given.

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