bluuebunny/crossref_metadata_2025 huggingface dataset:
Existence Theorems for Solutions to Set-Valued Stochastic Differential Equations and Applications
Authors: Ho Vu , Ngo Van Hoa
Published: August 2015

In this paper, a class of new stochastic differential equations on semilinear Hausdorff space under Hukuhara derivative, called set-valued stochastic differential equations (SSDEs) driven by a Wiener process. Moreover, some corresponding properties of SSDEs are discussed such as existence, uniqueness of solution. Finaly, we give some applications to models of interval-valued stochastic differential equations such as stock prices model and the Langevin equation.
An Analytic Approach of some Conjectures Related to Diophantine Equations
Authors: Ghanouchi Jamel
Published: August 2015

Our purpose in this paper is to show how much diophantine equations are rich in analytic applications. Effectively, those equations allow to build sequences, series and numbers. The question of the analytic proof of some theorems remains of course, we will see it in this communication. We will make also an allusion to the Fermat numbers (x2i) and will see how this problem of the proof is actual and how it can be solved using the sequences and series.
Relations between Schmidt's, Miller-Moreno's Groups and Groups with Basis Property
Authors: Alkadhi M.
Published: August 2015

In this paper we prove that a Schmidt's group forms a group with basis property if and only if it is a Miller- Moreno's group of type G(p,q) such that (p≠q(p,q are primes). Therefore doesn’t group with basis property if it is a Miller- Moreno's group of type G(p,qv), vϵN, v>1.
Π*-Regular Semigroups
Authors: Luo Xiao Qiang
Published: August 2015

Π*-regulur semigroups are promotion of Π* -regular semigroups. In the paper we show that a semigroup with some characterizations is Π* - regular, futhermore it is completely Π* -regular.
A Proof of Pillai’s Conjecture
Authors: Ghanouchi Jamel
Published: August 2015

Catalan theorem has been proved in 2002 by Preda Mihailescu. In 2004, it became officially Catalan-Mihailescu theorem. This theorem stipulates that there are not consecutive pure powers. There do not exist integers stricly greater than 1, X>1 and Y>1, for which with exponants strictly greater than 1, p>1 and q>1, YP=Xq+1 but for (X,Y,p,q) = (2,3,2,3) . We can verify that 32=23+1 Euler has proved that the equation Y2=X3+1 has this only solution. We propose in this study a general solution. The particular cases already solved concern p=2, solved by Ko Chaoin 1965, and q=3 which has been solved in 2002. The case q=2 has been solved by Lebesgue in 1850. We solve here the equation for the general case. We generalize the proof to Pillai’s conjecture YP=Xq+a and prove that it has always a finite number of solutions for a fixed a.
Exploration of Fibonacci Function
Authors: Gandhi K. Raja Rama
Published: August 2015

In this paper, I define Fibonacci function (probably unknown) on Real number field, for all x∈R, F:R → R,э F (x+n) = ∫nF(x+1)+∫n-1F(x). Also, I defined the limit value of Fibonacci function, which is closed to 1.618… where x tends to infinity. Including, Fibonacci sum as well.
Separation Axioms Inquad Topological Spaces
Authors: Tapi U.D. , Sharma Ranu , Deole Bhagyashri A.
Published: August 2015

In this paper, we introduce separation axioms in quad topological space (q topological spaces) and study some of their properties.
On âg Compact Spaces
Authors: Senthilkumaran V. , Krishnakumar R. , Palaniappan Y.
Published: August 2015

We introduce and study some subsets of a topological space X called âg compact sets; âg compact spaces are defined and their properties are studied.
Estimation of Technogenic Danger Risk of Technico Economic Systems
Authors: Petrov Nikolay
Published: August 2015

The article considers the study of technogenic danger risk of technico-economic systems in daily operation on the part of a human operator. In the techno-economic systems consist of a specified quantity of functional elements, United parallel or sequentially.
A Criterion for (Non-)Planarity of The Block-Transformation Graph Gαβγ when αβγ = 101
Authors: Basavanagoud B. , Veeragoudar Jaishri B.
Published: August 2015

The general concept of the block-transformation graph Gαβγ was introduced in [1]. The vertices and blocks of a graph are its members. The block-transformation graph G101 of a graph G is the graph, whose vertex set is the union of vertices and blocks of G, in which two vertices are adjacent whenever the corresponding vertices of G are adjacent or the corresponding blocks of G are nonadjacent or the corresponding members of G are incident. In this paper, we present characterizations of graphs whose block-transformation graphs G101 are planar, outerplanar or minimally nonouterplanar. Further we establish a necessary and sufficient condition for the block-transformation graph G101 to have crossing number one.
On some Multidimensional Fractional Integral Operators Involving Multivariable I-Function
Authors: Singh Yashwant , Kulkarni Nanda
Published: August 2015

In the present paper, we study certain multidimensional fractional integral operators involving a general I-function in their kernel. We give five basic properties of these operators, and then establish two theorems and two corollaries, which are believed to be new. These basic theorems exhibit structural relationships between the multidimensional integral transforms. The one- and two-dimensional analogues of these results, which are new and of interest in themselves, can easily be deduced. Special cases of these latter theorems will give rise to certain known results obtained from time to time by several earlier authors.
Index Summability of an Infinite Series Using δ-Quasi Monotone Sequence
Authors: Misra Mahendra , Padhy B.P. , Nayak Santosh Kumar , Misra U.K.
Published: August 2015

A result concerning absolute indexed Summability factor of an infinite series using δ-Quasi monotone sequence has been established.
Bivariate Stochastic Modelling of Glucose and Insulin Regulatory System among Type-2 Diabetes Mellitus Patients
Authors: Paidipati Kiran Kumar , Padi Tirupathi Rao
Published: August 2015

In this paper, a bivariate stochastic model for glucose and insulin regulatory system is developed. Difference Differential equations are derived from the processes of arrival and consumption of glucose molecules and insulin granules in blood plasma. Probability generating functions and linear differential equations are obtained, through which statistical measures on glucose and insulin levels are derived. Numerical illustrations are provided with suitable sensitivity analysis. Model behaviour is analyzed while using the derived measures. Indicators on health care and management of Type-2 Diabetes can be obtained with this study.
The Proof of the Fermat-Beal Theorem
Authors: Guła Leszek W.
Published: August 2015

The proof of The Beal’s Conjecture.
Non-Unit Bidiagonal Matrices for Factorization of Vandermonde Matrices
Authors: Purushothaman Nair R.
Published: August 2015

A non-unit bidiagonal matrix and its inverse with simple structures are introduced. These matrices can be constructed easily using the entries of a given non-zero vector without any computations among the entries. The matrix transforms the given vector to a column of the identity matrix. The given vector can be computed back without any round off error using the inverse matrix. Since a Vandermonde matrix can also be constructed using given n quantities, it is established in this paper that Vandermonde matrices can be factorized in a simple way by applying these bidiagonal matrices. Also it is demonstrated that factors of Vandermonde and inverse Vandermonde matrices can be conveniently presented using the matrices introduced here.
Proof of the Beal Conjecture through the Fundamental Theorem of Arithmetic
Authors: Watson Eric S.
Published: August 2015

This paper gives a proof of the Beal conjecture through the Fundamental Theorem of Arithmetic.
Beal’s Conjecture - Counter Examples
Authors: Saravanan S.B.E.
Published: August 2015

In [1-4], proof for Beal’s Conjecture has been presented. Counter examples for Beal’s Conjecture are presented in this paper.
A Study of the Zarisky Topology through Functors
Authors: Rana Pravanjan Kumar
Published: August 2015

The aim of this paper is to study the Zarisky topology through a functor. In this paper we construct i) Zarisky topology in Kn and a functor associated with this topology; ii) Spec(R) is a Zarisky topology in a ring R, where Spec(R) denotes the set of all prime ideals of R and construct a functor ‘Spec’ associated with Zarisky topology; and finally iii) we study the functor ‘Spec’ associated with Zarisky topology.
Solving the Navier Stokes Flow Equations of Micro-Polar Fluids by Adomian Decomposition Method
Authors: Adanhounmè Villevo , de Paule Codo François , Adomou Alain
Published: August 2015

In this paper we investigate the Navier Stokes flow equations of micro-polar fluids by peristaltic pumping through the cylindrical tube. Taking into account the slip boundary conditions at the wall and using the suitable change of variables, we transform these equations into the ordinary differential equations for which we apply the Adomian decomposition method. Doing so we obtain the stream function, the axial velocity, the micro-polar vector and the pressure.
Note on Perfect Numbers and their Existence
Authors: Gandhi K. Raja Rama
Published: August 2015

This paper will address the interesting results on perfect numbers. As we know that,perfect number ends with 6 or 8 and perfect numbers had some special relation with primes. Hereone can understand that the reasons of relation with primes and existence of odd perfect numbers. If exists, the structures of odd perfect numbers in modulo.
Reliability for Lindley Distribution with an Outlier
Authors: Khamnei Hossein Jabbari
Published: August 2015

In this paper, we consider the problem of estimating R=P(Y<X) , when Y has lindleydistribution with parameter a and x has lindley distribution with presence of one outlier withparameters b and c , such that X and Y are independent. The maximum likelihood estimator of R isderived and some results of simulation studies are presented.
An Unorthodox Parametric Measure of Information and Corresponding Measure of Intutionistic Fuzzy Information
Authors: Jha P. , Mishra Vikas Kumar
Published: August 2015

A new parametric function va(p)= log (1+a) - Σlog((1+api)/pi)-1,a>o is proposed for the probability distribution p1p2p3… … … pn and its properties are studied. In this paper the given functions is twice differentiable and is used to obtain the related measure of directed divergence, measure of intutionistic fuzzy entropy, measure of intutionistic fuzzy directed divergence. We also investigate the monotonic character of the proposed function.
Existence and Uniqueness of Fuzzy Control Integro-Differential Equation with Perturbed
Authors: Phuong N. , Phung N.N. , Vu H.
Published: August 2015

In the paper, we discuss the existence and uniqueness solution of fuzzy control integrodifferential equation with perturbed. The method of successive approximations is utilized toestablish these results.
A Statistical Analysis of the Nigerian External Reserveand the Impact of Military and Civilian Rule
Authors: Ohakwe J. , Odo I.V. , Nwosu C.
Published: August 2015

In this paper, the Nigerian External Reserve (ER) for the period 1960 – 2010 was modeled using descriptive time series technique and Box-Jenkins (ARIMA) model. Prior to the analysis the logarithm transformation was found to be the most appropriate to stabilize the variance of the data after the Bartlett's test of homogeneity of variance suggested non-constant variance. Applying the descriptive time series technique on the transformed data, a linear trend was found adequate which suggest an exponential trend for the untransformed data. However, the seasonal indexes were found to be insignificant which implies that the data is completely dominated by the trend. Furthermore, considering that the model obtained using the descriptive time series technique was found inadequate as suggested by the autocorrelation function (ACF) of the irregular component and therefore cannot be used for forecasting, a Box-Jenkins model was then fitted and was found adequate as suggested by the p-value = 0.00 for the modelsignificance. Furthermore using the Relative Percentage Change (RPC) to assess the impact ofthe various regimes on the ER data, it was found that the regimes of General Yakubu Gowon (Rtd) and Alhaji Shehu Shagari respectively had the most positive and negative impact on the ER data. Finally using the cumulative RPC in assessing the impact of civilian and military regimes on the ER data, it was discovered that the military had a higher positive impact than the civilian regimes.
An Elementary Identity with Cotangent Hyperbolic Function
Authors: Gandhi Raja Rama , Guedes Edigles
Published: August 2015

In this paper, we introduced and proved some important and intresting results on Cotangent Hyperbolic function. Also discussed an important remark at the end of the paper.
Decomposition in Finite Series for Dedekind Sum and some Hardy Sums by Trigonometric Functions
Authors: Gandhi Raja Rama , Guedes Edigles
Published: August 2015

In this paper, we introduced and proved some important and intresting results on Finite series for Dedekind sum and some Hady sums by using T-rations.
On Andrica’s Conjecture, Cramér’s Conjecture, Gaps between Primes and Jacobi Theta Functions III: A Simple Proof for Andrica’s Conjecture
Authors: Gandhi Raja Rama , Guedes Edigles
Published: August 2015

We will use the notation of Armitage and Eberlein, [see 1, p. 103]: k is a real number such that 0< k < 1; k' = (1 - k2)1/2 is the complementary modulus, K = K(k) =∫2π0 (dψ)/(1 - k2 sin2ψ), K' = K(k'). τ = iK' / K, q=exp(πiτ).
About some Transcendental Numbers
Authors: Ghanouchi Jamel
Published: August 2015

Everyone knows that π, e or the Champernowne number are transcendentals, but what about π+e or πe ? In this paper, we demonstrate a method in order to know if they also are.
The Second Proof of the Fermat's Last Theorem (Elementary Aspect)
Authors: Gandhi K. Raja Rama , Tint Reuven
Published: August 2015

We give a second proof of Fermat’s Last theorem without reference to the closure of numerical systems with respect to the operation of superposition.
Investigations on the Theory of Riemann Zeta Function II: On the Riemann-Siegel Integral and Hardy’s Z-Function
Authors: Guedes Edigles , Gandhi Raja Rama , Anapu Srinivas Kishan
Published: August 2015

We create new formulas for Riemann-Siegel Integral and Hardy's Z-function.
About an even as the Sum or the Difference of Two Primes
Authors: Ghanouchi Jamel
Published: August 2015

The present algebraic development begins by an exposition of the data of the problem. The definition of the primal radius r>0 is : For all positive integer x≥3 exists a finite number of integers called the primal radius r>0, for which x+r and x-r are prime numbers. The corollary is that 2x=(x+r)+(x-r) is always the sum of a finite number of primes. Also, for all positive integer x≥0, exists an infinity of integers r>0, for which x+r and r-x are prime numbers. The conclusion is that 2x=(x+r)-(r-x) is always an infinity of differences of primes.
The Reproductive Solution for Fermat’s Last Theorem (Elementary Aspect)
Authors: Gandhi K. Raja Rama , Tint Reuven
Published: August 2015

We give a proof of the solvability in a natural numbers for Fermat’s Last theorem and the equations ax+by=cz and Xn11 + Xn22 + ... + Xnk-1k-1 = Xnkk has not been found earlier, significantly different from known, and allow us to obtain infinite set of solutions in natural numbers, and examples.
A Proof of the Riemann Hypothesis
Authors: Ghanouchi Jamel
Published: August 2015

In this paper, we present the Riemann problem and define the real primes. It allows to generalize the Riemann hypothesis to the reals. A calculus of integral solves the problem. We generalize the proof to the integers.
On the Complete Elliptic Integrals and Babylonian Identity III: An Approximation for the Complete Elliptic Integral of the First Kind
Authors: Guedes Edigles , Gandhi Raja Rama
Published: August 2015

Using the Corollary 3 of previous paper (http://www.bmsa.us/admin/uploads/Mn95aZ.pdf), we evaluate the complete elliptic integral of the first kind in an approximately equal analytical closed form, by means of Bessel functions.
On the Complete Elliptic Integrals and Babylonian Identity IV: The Complete Elliptic Integral of First Kind as Sum of Two Gauss Hypergeometric Functions
Authors: Guedes Edigles , Gandhi Raja Rama
Published: August 2015

I evaluate the complete elliptic integral of first kind as the sum of two Gauss hypergeometric functions.
Proof of Goldbach Conjecture
Authors: Xue Ren Yong , Yi Ren
Published: August 2015

This paper through the creation of "double rectangular coordinate system", within the I quadrants, each coordinate axis coordinates all constitute the infinite sets. Coordinates with infinite sets one toone correspondence between the elements within and equal relationship. With any of the sum of two odd prime Numbers (a + b) to form a square area, length for a quarter of a square area A1 "square" diagonal integration method, a quarter of a square area A1 equation is derived with the definite integral equation; A1 area value of the argument as infinite generalized integral value, and deduce the equations, the Goldbach conjecture.
An Investigation on the Beta Function I: New Versions of the Euler Beta Function
Authors: Guedes Edigles , Gandhi Raja Rama
Published: August 2015

We developed new versions of the Euler beta function.
A New Hilbert-Type Inequality with the Homogeneous Kernel of Degree - 2 and with the Integral
Authors: Zheng Zeng , Gandhi Raja Rama , Xie Zi Tian
Published: August 2015

By using the weight functions and by means of Hadamard's inequality, we present a new Hilbert-type inequality with the integral in whole plane, a best constant factor and a homogeneous kernel of degree-2.
An Elementary Proof of Fermat-Wiles and Catalan-Mihailescu Theorems and Generalization to Beal Conjecture
Authors: Ghanouchi Jamel
Published: August 2015

We begin with Fermat, Catlan and Fermat-Catalan equations and solve them.
An Integral Representation for the Polylogarithm Function and some Special Values
Authors: Guedes Edigles , Gandhi Raja Rama
Published: August 2015

We proved a new integral representation for the polylogarithm function.
Elegant Solutions to Famous Conjectures on Fermat Pseudoprimes - II
Authors: Gandhi Raja Rama , Murty D. Narasimha
Published: August 2015

In this paper, we will solve two conjectures posed by M. coman on Fermat Pseudoprimes (base-2) or Poulet numbers by producing elegant proofs.
A Proof to Beal’s Conjecture
Authors: Thiagarajan Raj C.
Published: August 2015

In this paper, we provide computational results and a proof for Beal’s conjecture. We demonstrate that the common prime factor is intrinsic to this conjecture using the laws of powers. We show that the greatest common divisor is greater than 1 for the Beal’s conjecture.
Static Deformation due to a Long Tensile Fault of Finite Width in an Isotropic Half-Space Welded with an Orthotropic Half-Space
Authors: Godara Yogita , Sahrawat Ravinder Kumar , Singh Mahabir
Published: August 2015

Closed-form analytical expressions for displacements and stresses at any point of a two-phase medium consisting of a homogeneous, isotropic, perfectly elastic half-space in welded contact with a homogeneous, orthotropic, perfectly elastic half-space caused by a tensile fault of finite width located at an arbitrary distance from the interface in the isotropic half-space are obtained. The Airy stress function approach is used to obtain the expressions for the stresses and displacements. The vertical tensile fault is considered graphically. The variations of the displacements with the distance from the fault and with depth for various cases have been studied graphically. Also horizontal and vertical displacement of the surface are presented graphically.
Magic Graphoidal on Class of Trees
Authors: Murugan A. Nellai
Published: August 2015

B.D.Acharya and E. Sampathkumar [1] defined Graphoidal cover as partition of edge set of a graph G into internally disjoint paths (not necessarily open). The minimum cardinality of such cover is known as graphoidal covering number of G.
Particle Knots in Toric Modular Space
Authors: de Wet J.A.
Published: August 2015

The goal of this contribution is to relate quarks to knots or loops in a 6-space CP3 that then collapses into a torus in real 3-space P3instantaneously after the Big Bang, and massive inflation, when 3 quarks unite to form nucleons.
Common Fixed Point Theorem in Semi-Metric Space with Compatible Mapping of Type (E)
Authors: Rajopadhyaya U. , Jha K. , Imdad M.
Published: August 2015

In this paper, we establish a common fixed point theorem in semi-metric space with compatible mapping of type (E) which improves and extends similar known results in the literature.
Strongly Connectedness in Closure Space
Authors: Tapi U.D. , Deole Bhagyashri A.
Published: August 2015

A Čech closure space (X, u) is a set X with Čech closure operator u: P(X) → P(X) where P(X) is a power set of X, which satisfies u𝝓=𝝓, A ⊆uA for every A⊆X, u (A⋃B) = uA⋃uB, for all A, B ⊆ X. Many properties which hold in topological space hold in closure space as well. A topological space X is strongly connected if and only if it is not a disjoint union of countably many but more than one closed set. If X is strongly connected, and Ei‟s are nonempty disjoint closed subsets of X, then X≠ E1∪E2∪. We further extend the concept of strongly connectedness in closure space. The aim of this paper is to introduce and study the concept of strongly connectedness in closure space.
On Conformal Mapping in the Quasi-Einstein Manifolds
Authors: Dhair Prasanta , Jana Sanjib Kumar
Published: August 2015

In this paper we have shown the existence of conformal mapping from quasi-Einstein Manifold to Einstein manifold.
Continuity of Partially Ordered Soft Sets via Soft Scott Topology and Soft Sobrification
Authors: Sayed A.F.
Published: August 2015

This paper, based on the concept of partially ordered soft sets (possets, for short) which proposed by Tanay and Yaylali [23], we will give some other concepts which are developing the possets and helped us in obtaining a generalization of some important results in domain theory which has an important and central role in theoretical computer science. Moreover, We will establish some characterization theorems for continuity of possets by the technique of embedded soft bases and soft sobrification via soft Scott topology, stressing soft order properties of the soft Scott topology of possets and rich interplay between topological and soft order-theoretical aspects of possets. We will see that continuous possets are all embedded soft bases for continuous directed completely partially ordered soft set (i.e., soft domains), and vice versa. Thus, one can then deduce properties of continuous possets directly from the properties of continuous soft domains by treating them as embedded bases for continuous soft domains. We will see also that a posset is continuous if its soft Scott topology is a complete completely distributive soft lattice.
Stability Analysis of a Three Species Syn-Eco Dynamical System with a Limited Alternative Food for all the Three Species
Authors: Rao K. Kondala , Narayan K. Lakshmi
Published: August 2015

The present paper is devoted to an analytic investigation of a three species syn-eco system comprising two mutually helping species, both amensol on a third species. All possible equilibrium points are identified and their stability criteria is discussed by using Routh-Hurwitz criteria. Further, the analytical results are supported by numerical simulation using Mat Lab.
Common Due-Date Assignment and Job Scheduling on Single Machine and Parallel Machines
Authors: Mane Janardhan K. , Ghadle Kirtiwant P.
Published: August 2015

In this paper we consider a total penalty for the n job, one machine scheduling problem in which all jobs have a common due date. This penalty function is based on the due date value and on the earliness or the lateness of each job in the selected sequence. The main objective is to determine the optimal value of this due date and an optimal sequence to minimize a total penalty function. We prove that the optimal due date result can be generalized to the parallel machine problem. The problem of simultaneously available jobs on several parallel and identical machines. The problem is to find the optimal due date, assuming this to be the same for all jobs and we present a simple heuristic to find an approximate solution. On the basis of a limited experiment, we observe that the heuristic is very effective solution.
DIO 3 - Tuples for Special Numbers - I
Authors: Gopalan M.A. , Geetha V. , Vidhyalakshmi S.
Published: August 2015

We search for three distinct polynomials with integer coefficients such that the product of any two members of the set added with their sum and increased by a non-zero integer (or polynomial with integer coefficients) is a perfect square.
Special Dio 3 - Tuples
Authors: Gopalan M.A. , Geetha K. , Somanath Manju
Published: August 2015

We search for three distinct polynomials with integer coefficient such that the product of anytwo members of the set minus their sum and increased by a non-zero integer (or polynomial withinteger coefficient) is a perfect square.
Stochastic Modeling of Inter & Intra Stage Dependent Cancer Growth under Chemotherapy through Trivariate Poisson Processes
Authors: Rao P. Tirupathi , Kumar B.N. Naveen , Jayabharathiraj J.
Published: August 2015

This study has proposed a Stochastic Model for cancer growth under chemotherapy with the assumptions of the growth, transition and loss parameters of different stages are inter and intra dependent. A trivariate Poisson process approach has been adopted for modeling the three stage cancer growth by considering the stages of cells in the tumor namely normal cell, mutant cell and malignant cell in the presence and absence of chemotherapy during time 't'. Stochastic differential equations were obtained and the three dimensional joint probability functions along with related statistical measures were derived. Model behavior was analysed through numerical data.
A Connection between Hardy-Ramanujan Number and Special Pythagorean Triangles
Authors: Darbari Mita
Published: August 2015

Special Pythagorean Triangles are obtained in relation with the Hardy-Ramanujan Number 1729. Some special cases are also discussed. A few interesting results are obtained.
Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using Compatible Mappings of Type (K)
Authors: Manandhar K.B. , Jha K. , Cho Y.J.
Published: August 2015

In this paper, we introduce the notion of compatible mappings of type (K) in intuitionistic fuzzy metric space and obtain a common fixed point theorem for self mappings on complete intuitionistic fuzzy metric space with example. Our result generalizes and improves other similar results in literature.
N Positive Integers Whose Product is Equal to M-Times of their Sum
Authors: Kumar Satish , Kishan Hari
Published: August 2015

In this article, the problem proposed by Hitesh Jain (2014) has been solved and generalized.
An Outline of Cosmology Based on Interpretation of the Johannine Prologue
Authors: Christianto Victor
Published: August 2015

As we know there are two main paradigms concerning the origin of the Universe: the first is Big-Bang Theory, and the other is Creation paradigm. But those two main paradigms each have their problems, for instance Big Bang Theory assumes that the first explosion was triggered by chance alone, therefore it says that everything emerged out of vacuum fluctuation caused by pure statistical chance. By doing so, its proponents want to avoid the role of the Prime Mover (God). Of course there are also other propositions such as the Steady State theory or Cyclical universe, but they do not form the majority of people in the world. On the other side, Creation Theory says that the Universe was created by God in 6x24 hours according to Genesis chapter 1, although a variation of this theory says that it is possible that God created the Universe in longer period of thousands of years or even billions of years. But such a proposition seems not supported by Biblical texts. To overcome the weaknesses of those main paradigms, I will outline here another choice, namely that the Universe was created by Logos (Christ in His pre-existence). This is in accordance with the Prolegomena of the Gospel of John, which says that the Logos was there in the beginning (John 1:1). I describe 3 applications of the classical wave equation according to Shpenkov, i.e. hydrogen energy states, periodic table of elements, and planetary orbit distances. For sure, Shpenkov derived many more results beside these 3 phenomena as discussed in his 3 volume books and many papers, but these 3 phenomena are selected to give clear examples of what can be done with the classical wave equation. And then I extend further the classical wave equation to fractal vibrating string. While of course this outline is not complete, this article is written to stimulate further investigations in this direction.
An Exact Solution of Modified KdV (mKdV) Equation as a Reduction of Self-Dual Yang-Mills Theory
Authors: Christianto Victor
Published: August 2015

It is known for quite a long time that Self-Dual Yang Mills (SDYM) theory reduce to Korteweg-DeVries equation, but recently Shehata and Alzaidy have proved that SDYM reduces to modified KdV equation. Therefore, this paper discusses an exact solution of modified Korteweg-DeVries equation with Mathematica. An implication of the proposed solution is that it is possible to consider hadrons as (a set of) KdV soliton.
Blow-Up Phenomena and Global Existence to a Weakly Dissipative Shallow Water Equation
Authors: Zhou Jiang Bo , Chen Jun De , Zhang Wen Bing
Published: August 2015

We first establish the local well-posedness for a weakly dissipative shallow water equation which includes both the weakly dissipative Camassa-Holm equation and the weakly dissipative Degasperis-Procesi equation as its special cases. Then two blow-up results are derived for certain initial profiles. Finally, We study the long time behavior of the solutions.
The Proof of the Beal’s Conjecture
Authors: Guła Leszek W.
Published: August 2015

The truly marvellous proof of The Fermat's Last Theorem (FLT). Two false proofs of FLT for n = 4. The incomplete proof of FLT for odd prime numbers n ∈ Ρ. The proof of The Beal's Conjecture. The Beal's Theorem.
An Elementary Proof of Fermat-Wiles Theorem and Generalization to Beal Conjecture
Authors: Ghanouchi Jamel
Published: August 2015

A proof of Fermat theorem is presented and a generalization to Beal conjecture is proposed. For this, we begin with Fermat and Fermat-Catalan equations and solve them.
A Note on Multiplicative Triple Fibonacci Sequences
Authors: Kumar Satish , Kishan Hari , Gupta Deepak
Published: August 2015

In this paper, multiplicative triple Fibonacci sequences have been discussed. Here the results obtained by Singh et.al [3] have been extended. Some new theorems have been established.
An Inventory Model with Power Demand Pattern, Weibull Distribution Deterioration and without Shortages
Authors: Krishnaraj R. Babu , Ramasamy K.
Published: August 2015

An inventory problem can be solved by using several methods starting from trial and error methods to mathematical and simulation methods. Mathematical methods help in deriving certain rule and which may suggest how to minimize the total inventory cost in case of deterministic demand. Here an attempt has been made for obtaining a deterministic inventory model for power demand pattern incorporating two-parameter Weibull distribution deterioration and without shortages.
Recent Progress about the Conjecture of Erdös-Straus
Authors: Gueye Ibrahima , Mizony Michel
Published: August 2015

In this paper we present our recent progress about the conjecture of Erdös-Straus by using Diophantine equations and the irreducible twin Pythagorean triples of the first type.
Intuitionistic Fuzzy Semiboundary and Intuitionistic Fuzzy Product Related Spaces
Authors: Thiripurasundari V. , Murugesan S.
Published: August 2015

In this paper intuitionistic fuzzy semi boundary is introduced and its properties are investigated. Intuitionistic fuzzy semi continuous functions are characterized via intuitionistic fuzzy semi boundary.
Approching the Twin Prime Constant
Authors: Gueye Ibrahima
Published: August 2015

In this article I highlight some curiosities about the primes. Through a new conjecture, I think that the twin prime constant can be approached with an easy method.
About the Images and Inverse Images of Intuitionistic or Vague Fuzzy Subsets
Authors: Vasanti G.
Published: August 2015

In this paper an exclusive study of some standard (lattice) algebraic properties for Intuitionistic fuzzy (inverse) images of Intuitionistic fuzzy subsets is done. Further as in crisp setup, characterizations for injectivity and surjectivity of maps in terms of some (lattice) algebraic properties of Intuitionistic fuzzy images and Intuitionistic fuzzy inverse images are performed.
Comparative Effectiveness of Inductive Inquiry and Transmitter of Knowledge Models on Secondary School Students’ Achievement on Circle Geometry and Trigonometry
Authors: Ihedioha Silas A. , Osu Bright O.
Published: August 2015

In this study, the effectiveness of Inductive Inquiry and Transmitter of Knowledge models on students’ academic achievement on Circle Geometry and Trigonometry is explored. The main objectives of the study are to expose the groups to Inductive Inquiry and Transmitter of Knowledge models and compare the effectiveness of these modes of teaching in the teaching of circle geometry and trigonometry. The pre-test-post-test experimental design is chosen for this work. It is hypothesized that there would be significant difference between mean achievement scores of these experimental groups on the post-test. The population of the study consisted of all the students of senior secondary two (SS2) class studying in Govt. Sec. School, Bwari, Federal Capital Territory( FCT) Abuja, Nigeria from which a sample of 60 students is drawn using random sampling technique. They were divided into two groups formed through matching on the basis of their pre-test scores; each group consisting of 30 students. One of the groups is randomly chosen as the Inductive Inquiry group and the other as Transmitter of Knowledge group. The independent variable is mode of teaching and the dependent variable is the academic achievement of students. The dependent variable is measured through a 50-item achievement test items generated using the West African Examination Council’s (WAEC) past questions. These questions are used as both pre-test and post-test items. It is found that Inductive Inquiry group performed better than the Transmitter of Knowledge group. This result may be investigated for further confirmation. It is recommended that Inductive Inquiry model be used by teachers of mathematics while teaching the subject to senior secondary classes. A blend of models may be used because there is no single model that is exclusively best for teaching all the topics at all levels to all students, considering individual differences among students.
Solving Nonsmooth Equations Using Derivative-Free Methods
Authors: Bahgat M.S.M. , Hafiz M.A.
Published: August 2015

In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.
A Multiplicative Seasonal Arima Model for Nigerian Unemployment Rates
Authors: Etuk Ette Harrison
Published: August 2015

Time series analysis of Nigerian Unemployment Rates is done. The data used is monthly from 1948 to 2008. The time plot reveals a slightly positive trend with no clear seasonality. A multiplicative seasonal model is suggestive given seasonality that typically tends to increase with time. Seasonal differencing once produced a series with no trend nor discernible stationarity. A non-seasonal differencing of the seasonal differences yielded a series with no trend but with a correlogram revealing stationarity of order 12, a nonseasonal autoregressive component of order 3 and a seasonal moving average component of order 1. A multiplicative seasonal autoregressive integrated moving average (ARIMA) model, (3, 1, 0)x(0, 1, 1)12, is fitted to the series. It has been shown to be adequate.
On the Application of Stochastic Optimal Control to Pension Fund Management
Authors: Osu Bright O. , Ijioma Onwukwe
Published: August 2015

In this paper, we apply the stochastic optimal control theory to the pension fund management before and after retirement in the defined contribution and defined benefit pension schemes, where benefits are paid as investment returns for a period or duration of time. The goal of the management problem is to optimize the long-term growth of expected utility of returns. We consider different types of power law utility function of the form U(X)=γ-1Xγ, γ<1, γ≠0 to examine the different investment schemes. Our result shows the advantage of the defined contribution scheme over the defined benefit scheme before and after retirement.
Primes of the form x2 + ny2
Authors: Gandhi K. Raja Rama
Published: August 2015

We know that, Fermat Showed a prime can be expressed as a sum of two squares if and only if it is a multiple of four plus one and its decomposition is unique. This paper will discuss the similar writings of primes as a sum of squares and multiple of another square.
Comparison of Solution of 3x3 System of Linear Equation in Terms of Cost
Authors: Ubale P.V.
Published: August 2015

The solution of a linear system is one of the most frequently performed calculations in computational mathematics. Many numerical methods are involved to solve the system of linear equations. There are two basic approaches elimination approaches and iterative approaches are used for the solution. In this paper we describe the comparison of two popular elimination procedure simple Gauss Elimination and Gauss Jordan elimination method on to the solution of 3x3 system of linear equation and find out the cost required to implement this procedures.
Modules with ⊛(⊛’ or ⊛’’) Condition
Authors: Hadi Inaam Mohammed Ali , Humod Ghaleb Ahmed
Published: August 2015

In this paper we introduce and study modules with ⊛(⊛’or ⊛’’) condition. We give several properties of these types of modules and some relationships between them.
Twin Prime Numbers and Diophantine Equations
Authors: Gueye Ibrahima
Published: August 2015

For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. Starting from Wilson's theorem, Clement’s theorem and the corollary of Clement’s theorem [1], I came to find Diophantine equations whose solution could lead to theproof of the infinitude of twin primes.
A Study of Service in Restaurant by Using Queuing Model
Authors: Mishra G.D. , Singh Chauhan Vijiya , Chandra Nikita
Published: August 2015

The restaurants want to avoid losing their customers due to a long wait on the line. This shows a need of a numerical model for the restaurant management to understand the situation better. This paper aims to show that queuing theory satisfies the model when tested with a real-case scenario. We obtained the data from a restaurant. We then derive the arrival rate, service rate, utilization rate, waiting time in queue and the probability of potential customers to balk based on the data using Little’s Theorem and M/M/1 queuing model. We conclude the paper by discussing the benefits of performing queuing analysis to a busy restaurant.
Conjecture in Additive Twin Primes Numbers Theory
Authors: Gueye Ibrahima
Published: August 2015

For two millennia, the prime numbers have continued to fascinate mathematicians. Indeed, a conjecture which dates back to this period states that the number of twin primes is infinite. In 1949 Clement showed a theorem on twin primes. For the record, the theorem of Clement has quickly been known to be ineffective in the development of twin primes because of the factorial. This is why I thought ofusing the additive theory of numbers to find pairs of twin primes from the first two pairs of twin primes. What I have formulated as a conjecture. In same time i presentmy idea about the solution of the Goldbach’s weak conjecture.
Solution of some Problems in Hungarian Mathematical Competition - IV
Authors: Gandhi K. Raja Rama
Published: August 2015

In this work, we continue to present some interesting problems in the Transylvanian Hungarian Mathematical Competition held in 2012. In this article, one can find very interesting proofs of [1].
Investigations on the Theory of Riemann Zeta Function III: A Simple Proof for the Lindelöf Hypothesis
Authors: Gandhi K. Raja Rama , Guedes Edigles , Anapu Srinivas Kishan
Published: August 2015

We create new formulas for proving Lindelof Hypothesis from Zeta Function.
Conjecturing Constant Cross-Ratio Loci of a Pencil in E2
Authors: Narasimham G.L.
Published: August 2015

It is sought to find a locus of a variable point having constant cross-ratio of a pencil of rays emanating from it and connecting to four fixed points in order to relate its cross-ratio to a conic property.
The Beal’s Conjecture (Disproved)
Authors: Gandhi K. Raja Rama , Sarma E.A.S.
Published: August 2015

In this paper, we disprove the Beal’s conjecture by two different proofs.
An All-Inclusive Proof of Beal’s Conjecture
Authors: Marshall Stephen M.
Published: August 2015

This paper presents a complete and exhaustive proof of the Beal Conjecture. The approach to this proof uses the Fundamental Theorem of Arithmetic as the basis for the proof of the Beal Conjecture. The Fundamental Theorem of Arithmetic states that every number greater than 1 is either prime itself or is unique product of prime numbers. The prime factorization of every number greater than 1 is used throughout every section of the proof of the Beal Conjecture. Without the Fundamental Theorem of Arithmetic, this approach to proving the Beal Conjecture would not be possible.
Common Fixed Point Results in Random Fuzzy Metric Space
Authors: Shukla Manoj , Dubey R.P. , Patel Shailendra Kumar
Published: August 2015

In this paper we have proved some fixed point theorems in random fuzzy metric space for three mappings which satisfying some contractions. Also here we consider rational expression in contraction.
Common Fixed Point Theorem for Three Self Mappings
Authors: Singh Oinam Budhichandra
Published: August 2015

The aim of this paper is to study the concept of compatible mappings of type (R) and discussed a common fixed point theorem for three compatible mappings of type (R) satisfying contractive conditions.
Oscillation Criteria for a Class of Discrete Nonlinear Fractional Equations
Authors: Sagayaraj M. Reni , Selvam A. George Maria , Loganathan M. Paul
Published: August 2015

In this paper, we study the oscillatory behavior of the fractionaldifference equations of the following form (see in paper) denotes the Riemann-Liouville difference operator and η>0 is a quotient of odd positive integers. We establish some oscillation criteria forthe equation by using Riccati transformation technique and some inequalities. Anexample is shown to illustrate our main results.
Some Properties of the Harmonic Quadrilateral
Authors: Patrascu Ion , Smarandache Florentin
Published: August 2015

In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles.
General Keplerian Dynamics (GKD): A Testable Grand Unified Theory
Authors: Jarvis Brent Lee
Published: August 2015

Newton Generalized Kepler's Laws of Planetary Motion when he Developed his Laws of Universal Gravitation. Additional Generalizations are Submitted and an Auspicious Unified Model that can Be Tested Experimentally is Disclosed.
Time Discreteness & Wave Function Aliasing
Authors: Zaslavsky Alexander
Published: August 2015

The conditions of arising and some effects of physical phenomenon that may be found in the process of observing high energy particles are considered in this work. This phenomenon is consequence of time discreteness. When the repetition frequency of a particle discrete state proves to be commensurable with its own frequency (energy), the aliasing effect of its wave function may take place. The wave function aliasing limits the particle energy spectrum giving rise to the uninvestigated abnormal modes of movement. In view of the fact the discreteness of particle states at a time is a prerequisite for aliasing, the effect under consideration, in case of its experimental verification, may serve a proof of this discreteness.
Matter as Gravitational Waves-Dark Energy
Authors: López González Ernesto
Published: August 2015

Background In several previous papers [1,2] it was exposed the hypothesis that matter could be considered as consisting of gravitational pulses in a six-dimensional space with anisotropic curvature. These pulses interact between them through various mechanisms, one of which is based on time velocity gradient due to gravitational time dilation. As time dilation can also be achieved by speed, physical consequences of this effect are explored. Results Universe expansion, which can be expressed as Hubble's law, v=Ho causes a frame-dragging and an effective time velocity gradient, resulting in a repulsive force between any particle-pulsation. This force is mass-independent and causes an acceleration that can be expressed by the relationship. d2r/dt2=Ho2r+Ho2r(1-Ho2r2/c2)-1≈2Ho2r (approximation valid for distances up to 1000 Mpc) Since our best estimate of Hubble's constant value is 71 km/s/Mpc we can estimate the present value of the cosmological constant L at a value of 1.178 10-52 m-2 . This number is consistent with current observations.
On Soft Totally Bounded Sets
Authors: Surendranath Reddy B. , Jalil Sayed
Published: August 2015

In this paper, we investigate some result on soft bounded and soft totally bounded sets and derive relation among them. We investigate some necessary conditions on soft totally bounded sets. We also prove soft totally bounded set is separable.
Icosahedral Supersymmetry
Authors: de Wet J.A.
Published: August 2015

The Exceptional Lie Algebra E6 used by the Author as a basis forthe Standard Model of the Elementary Particles is a subalgebra of the Lie algebra E8 which in turn is the Lie algebra of the icosahedral group by the McKay correspondence. It is possible to introduce a mass proportional toan entropy given by the the number of permutations of the elements of E6, E8 labeled by the Weyl group W. In this way the masses of the top-quark pair uu and electron are derived without any appeal to QCD and a mass of approximately 19 TeV is predicted for supersymmetric particles.
A New Approach for Parameters of Nucleon-Nucleon Scattering at Low Energies in One and Two Dimensions
Authors: Shojaei Mohammad Reza , Amini Maryam , Zoghi-Foumani Niloufar
Published: August 2015

Many of the important properties of multi-nucleon systems can be found by studying the nucleon- nucleon interactions. In this work, a suitable central and an appropriate noncentral potential have been used to study nucleon- nucleon scattering in one and two dimensions. The phase shift, scattering cross section, length and amplitude are calculated using the Nikiforov-Uvarov (NU) method and WKB approximation. Comparison between the results of the suggested model in this article and the experimental reported values indicates that there is a good consistency between them.