Iranian Journal of

Concept of Colon-Ideals in $Gamma$-Rings and its Application

N. Nabusawa introduced the concept of $Gamma$-rings in 1964, after that we find the development of this concept with parallel to the non-commutative ring theory. In this paper we are interested to study the concept of colon ideals in the $Gamma$-rings and study some of their properties. After that we will use the concept of colon ideal to introduce the notion of $S$-prime ideals, where $S$ is a multiplicative subset of $R$. Lastly we will introduce the Zeriski-type topology on $R$ with $S$-prime ideals in $Gamma$-rings.

Dr. Subrata Bhowmik

Ergodic Partial Actions

In the context of measurable partial dynamical systems, we prove the existence and uniqueness of measurable globalization. We define the notion of ergodicity for partial actions and prove a mean ergodic theorem in this context. For conservative partial $mathbb{Z}$-actions, we show that the measurable globalization is obtained using the Kakutani Skyscraper and give a criterion for such a globalization to have a finite invariant measure.

Prof Massoud Amini,Mr Mirnavid Razavi

The Köthe Teoplitz Duals of V_λ^0 (G)

In this study, we introduce the sequence space      of the sequence      consisting of modulus functions. Also we will show that      is a linear space and a solid AK-FK-space with an absolutely monotone F-norm. Furthermore, we will introduce the  Köthe-Toeplitz Duals of    .

Tuba DİNC, Cigdem A. BEKTAS

Approximate Controllability of fractional Stochastic Functional Differential Equations with Fractional Brownian Motion and Impulses under Infinite Delay

In this paper, by using Schaefer's fixed point theorem and fractional power of operators,  we study the approximate controllability
 of  impulsive fractional  stochastic functional differential equations with infinite delay driven  by fractional Brownian motion in a
 real separable Hilbert space. As application, an example is provided to illustrate the obtained results.
    

Hajji salah, Lahmoudi Ahmed, Lakhel El Hassan

STEFFENSEN’S TYPE INEQUALITIES FOR TRIGONOMETRICALLY CONVEX FUNCTIONS WITH APPLICATIONS

ŞENOL DEMİR, SAAD IHSAN BUTT

Cubic Interval Vague $R_0$ and Cubic Interval Vague $R_1$-Spaces

The main purpose of this paper is to present two novel classes of separation axioms called cubic interval vague-$R_0$  and cubic interval vague-$R_1$ in cubic interval vague topological spaces. The paper explores and analyzes some of the key characteristics and fundamental properties associated with these classes. Moreover, we give necessary and sufficient conditions for a cubic interval vague topological space to be classified as either a cubic interval vague-$R_0$ or cubic interval vague-$R_1$ space.

Alias Khalaf, Arsalan Haji

A NOTE ON GESSEL-STANTON THEOREM ${}_3F_{2}left(frac{3}{4}right)$ WITH APPLICATIONS IN DOUBLE HYPERGEOMETRIC FUNCTIONS

The main aim of this paper is  to establish a new general double-series identity, which involve some suitably bounded sequences of complex numbers, by using Gessel-Stanton hypergeometric summation theorem for terminating Clausen  series ${}_3F_2left(frac{3}{4}right)$ and series rearrangement technique. By using this general double-series identity, we have  derived four reduction formulas (numerically verified by using Mathematica software) for Srivastava-Daoust double hypergeometric functions  with the arguments  $left(z, frac{-3z}{~4}right)$, $left(frac{-3z}{(1-z)},frac{-3z^2}{(1-z)^2}right)$, $left(frac{-3z}{4(1-z)^2},frac{-z}{(1-z)}right)$ and $left(frac{-3z}{(1-z)^2},frac{3z^2}{(1-z)^2}right)$ in terms of the difference of two generalized hypergeometric functions of one variable, under
appropriate convergence conditions.

Mr. SHAKIR HUSSAIN MALIK,Prof. MOHAMMAD IDRIS QURESHI,Mr. JAVID MAJID

Constructing a symmetric doubly stochastic matrix with a certain spectrum

In this article, we first introduce an orthogonal matrix that leads to the construction of a new symmetric doubly stochastic matrix with the sufficient condition presented in the article by Gnacik and Kania. In fact, we prove that if $ sigma =lbrace1, lambda_{2},...,lambda_{n}rbrace$ is a list of real numbers such that  $ lambda_{i} leq 0 $ for  $ i in lbrace2,...,nrbrace $ and   $ sum_{i=2}^{n}lambda_{i} geq frac{-1}{2} $, then there is a symmetric doubly stochastic matrix with spectrum $ sigma $
 different from the article by Gnacik and Kania. Then we show that the graph and matrix  $ P_{n} $   selected in the mentioned article are not unique.
  Also, we show with an example that the   $ delta_{min} $    proposed in the mentioned article is incorrect.
  In addition, we present another sufficient condition for the construction of new symmetric doubly stochastic matrices. This time we consider the real list of
  $ lambda =lbrace1, lambda_{2},...,lambda_{n}rbrace$    in such a way that    $ lambda_{i} leq 0 $ for  $ i in lbrace2,...,nrbrace $     and      $ sum_{i=2}^{n}lambda_{i} geq frac{-1}{n} $     and we show that there is a new symmetric doubly stochastic matrix with spectrum     $ lambda $. We also provide examples of different algorithms.
 

Mohadese Raeisi Sarkhoni, Azim Rivaz, Hossein Momenaee, Somayeh Zangoei Zadeh

Effect of non-homegeneity in an initially stressed hygro-thermoelastic medium

In the present research article, the mechanical deformation of a non-homogeneous hygro-thermoelastic half space under hydrostatic initial stress with an overlying elastic layer of thickness d has been discussed. A mechanical force F of constant magnitude is applied along the layer. The non-homogeneous properties of functionally graded materials varies along x direction. The expressions for displacement, moisture concentration, temperature and force stress are computed analytically. The effect of non-homogeneous parameter and the initial pressure on the components are obtained and shown graphically by using MATLAB.

Praveen Ailawalia, Anchal sharma, Harish Nagar

Numerical solutions of two dimensional nonlinear integral equations by Müntz-Legendre Wavelet

In this paper, a two-dimensional Müntz-Legendre wavelet has been developed to approximate the solution of two different types of two-dimensional nonlinear integral equations, two-dimensional nonlinear Volterra-Fredholm integral equations and the second-kind nonlinear Volterra integral equations.  The present Müntz-Legendre method reduces these two-dimensional nonlinear integral equations to a system of nonlinear algebraic equations, and again these algebraic system has been solved numerically by Newton’s method. Convergence analysis of the present method has been discussed in this article. Illustrative examples have been included to demonstrate the validity and applicability of the technique.
Also, the results obtained by the present wavelet method have been compared with the results of the known methods. In addition, an application of the generalized Telegraph equation has been made.

Prof. Khosro Maleknejad,Dr. Masoud Dehkordi

Uniqueness of Meromorphic Functions Concerning Non-linear Differential Polynomials Sharing Certain Value CM and IM

In this article, we consider the uniqueness problem of the nonlinear differential polynomial $(f^{n}P(f)H[f])^{(k)}$, where $f(z)$ is a transcendental meromorphic function. With the concept of sharing certain  value CM and IM, we obtain some results which extend and improve some results due to Pulak Sahoo and Biswajit Saha [Vietnam Journal of Mathematics, 44:531–540, 2016].

Dr. Naveenkumar S. H,Dr. Jayarama H R H. R,Dr. Chaithra C. N

Approximation by Phillips type $q$-Bernstein Operators on Elliptic domain

In this paper  we  define univariate Phillips type  $q$-Bernstein operators $big(mathcal{B}^{zeta}_{s,q}Hbig)(zeta,v)$ and $big(mathcal{B}^{v}_{t,q}Hbig)(zeta,v),$ their Products $big(mathcal{P}_{st,q}Hbig)(zeta,v),$ $big(mathcal{Q}_{ts,q}Hbig)(zeta,v)$ and their Boolean sums     $big(mathcal{S}_{st,q}Hbig)(zeta,v)$, $big(mathcal{T}_{ts,q}H)(zeta,v) $  on the elliptic region with boundary. The Remainders of approximation formula have been calculated by Peano's theorem and modulus of continuity. Also rate of convergence for functions of Lipschitz class are estimated.

Dr. Mohammad Iliyas ,Dr. Asif Khan ,Mr. Mohd Arif ,Mr. Naved Alam ,Dr. Mudassir Rashid Lone

Packing chromatic number of $G$ and $G$ minus a cut edge of $G$

Given a graph $G$ and a positive integer $i,$ an {it $i!$-packing} in $G$ is a subset $X$ of $V(G)$ such that the distance $d_G(u, v)$ between any two distinct vertices $u,v,in,X$ is greater than $i.$ The {it packing chromatic number} $chi_{rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i,$ $iin {1,2,dots,k},$ where each $V_i$ is an $i!$-packing in $G.$ We compute $chi_{rho}(G),$ $chi_{rho}(G-e),$ and compare these two numbers, where $G$ is some connected graph and $e$ is a cut edge of $G.$
 

Dr Sampathkumar R,Dr Sivakaran T,Mr. Unnikrishnan R

THE SMARANDACHE VERTICES OF THE ANNIHILATING-IDEAL GRAPH OF A COMMUTATIVE RING

Let R be a commutative ring with 1 ̸= 0 and A(R) the set of annihilator
ideals of R. An ideal I of R is an annihilator ideal (= annihilating ideal) if there exists
a nonzero ideal J in R such that IJ = (0). The annihilating-ideal graph of R, denoted
by AG(R), is defined to be the graph with the vertex set A(R)*= A(R) {(0)} and two
distinct vertices I and J are adjacent if and only if IJ = (0). A vertex a in a simple
graph G is said to be a Smarandache vertex (or S-vertex for short) provided that there
exist three distinct vertices x, y, and b (all different from a) in G such that x—a, a—b,
and b—y are edges in G, but there is no edge between x and y. The main object of
this paper is to study the S-vertices of AG(R). We will show that a conjecture related
to the weakly perfectness of AG(R) is true when the graph has no S-vertices. It is
shown that how the existence of an S-vertex in Γ(R) implies the existence of an S-vertex
in AG(R). We characterize rings R when gr(AG(R)) ≥ 4, and so we characterize rings
whose annihilating-ideal graphs are bipartite. There is also a discussion on a relationship
between the diameter, Girth, and S-vertices of Γ(R) and AG(R).

Prof Elham Mehdinezhad,Prof Amir Rahimi

Normalized Adjacency Energy and Spectral Radius of Non-Commuting Graph for Group $U_{6n}$

The non-commuting graph is defined on a finite group $G$ with $G backslash Z(G)$ as the vertex set of $Gamma_G$ and $v_p neq v_q in G backslash Z(G)$ are adjacent whenever they do not commute in $G$. In this paper, we consider the problem of the energy and spectral radius of the non-commuting graph for group $U_{6n}$ corresponding to the normalized adjacency matrix. We highlight that the obtained energy is always equal to twice its spectral radius and it is hypoenergetic.

Mamika Ujianita Romdhini, Athirah Nawawi, Faisal Al-Sharqi, Ashraf Al-Quran

BOUND FOR CERTAIN HANKEL DETERMINANTS AND ZALCMAN CONJECTURE FOR A SUBCLASS OF MULTIVALENT ANALYTIC FUNCTIONS

n this paper, we consider certain subfamily of p- valent analytic functions, for which, we estimate sharp bound to certain generalised second Hankel determinant, the Zalcman conjecture and an upper bound to the third, fourth Hankel determinants. Further, we investigate an upper bound for the third and fourth Hankel determinants with respect to two-fold and three-fold
symmetric functions belongs to the same class. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carath´eodory class P.

Mr VIJAYA KUMAR CH.,Dr VAMSHEE KRISHNA D.,Dr BISWAJIT R.,Mr SANJAY KUMAR K.,Dr VANI N.

Asymptotically $(Delta^m,f)$-deferred statistical equivalent sequences of order $alpha$

In this paper, we introduce set of all $(Delta^m,f)$-deferred statistically convergent sequences of order $alpha$ and the concept of asymptotically $(Delta^m, f)$-deferred statistical equivalent sequences of order $alpha$ with the help of unbounded modulus function $f$ and deferred density of order $alpha$ by taking two sequences $(p_n)$ & $(q_n)$ of non-negative integers satisfy conditions $p_n

Dr. Sudhanshu Kumar,Dr. Arvind Kumar Verma

Rough Ideal convergence in 2-fuzzy 2-normed spaces

In this work, we define several fundamental results relating to the ideas of rough $I$-convergence and rough $I$-Cauchyness of sequences in 2-fuzzy 2-normed spaces. Furthermore, we define the rough$I$-limit and the rough $I$-cluster points of a sequence in a 2-fuzzy 2-normed linear space and look into the relationships between these ideas. In addition, we investigated various features of the concepts of rough ideal cluster point and rough ideal limit point of a sequence in 2-fuzzy 2-normed spaces. The rough ideal cluster point of a sequence in 2-fuzzy 2-normed space is also connected with an ordinary ideal convergence criteria, which we also obtain.

Prof. Dr. Mohammad Rashid

An Extension to Perturbation Iteration Method: Artificial Perturbation Iteration Method

An extension to the recently developed Perturbation Iteration Method (PIM) is suggested. The method employs an artificial parameter other than the perturbation parameter if it exists in the differential equation. If there is no existing perturbation parameter, the artificial parameter is not introduced to the equation for simplification purposes as is done in classical perturbation iteration methods. The method is called Artificial Perturbation Iteration Method (APIM) to distinguish in from the classical PIM. The PIM, APIM and exact solutions of a number of differential equation are contrasted with each other. The extended method increases the convergence rate with the cost of dealing with more complex iterative equations.
 

Prof Mehmet Pakdemirli,Dr Ihsan Timucin Dolapci

GENERALIZATION OF GR¨USS INEQUALITY ON TIME SCALES

In the present paper we derive a generalized Gru¨ss inequality on time scales & recapture several published results of different authors of various papers and thus unify coresponding discrete & continuous versions. Moreover, we use our obtained consequence to the case of quantum calculus.

Dr. Faraz Mehmood,Dr. Asif R. Khan,Dr. Muhammad Awais Shaikh

Log-Logistic Autoregressive Moving Average Model

The aim of this paper is to propose a class of models for time series which their dependent variable has a Log-Logistic distribution,
called the Log-Logistic Autoregressive Moving Average model (LLARMA). The Log-Logistic distribution has many applications in survival
analysis, for example in processes which are dependent on the time, including time of death in cancer and time of failure in industry, to name
a few. In this model , by using the median index , the dynamic structure of the autoregressive moving average is introduced, consisting, timedependent
variable, parameters, and link function. A new class for the model is introduced and there are discussions about methods to estimate
conditional likelihood of parameters and also the hypothesis testing, matrix of information, and forecasting have been explained. This model is
fitted using simulated and real data from the flow of Karun river, the parameters are estimated and then have been selected for the model

Dr. Behzad Reihaninia,Dr. Farshin Hormozinejad,Dr. Mohammad Khodamoradi,Dr. Mohammadreza Ghalani

Symplectic connection and metric-affine geometry‎: A ‎model‎ for gravity and dark matter

‎The standard theory of relativity is a ‎‎‎purely metric gravity ‎theory ‎and ‎it‎ neglects the ‎possible symplectic structure on space-time manifold‎. ‎With the help of a new concept called symplectic connection we try to extend this theory‎. ‎Then‎, ‎we reveal that this generalization coincides with metric-affine (Palatini) formalism of gravity‎. ‎Considering a special case for tensorial part of affine connection and using calculus of variations on a natural Lagrangian‎, ‎we find some new field equations‎ . ‎Finally‎, ‎we present an example which satisfies our field equations‎.

Dr Ghodratallah Fasihi-Ramandi,Dr Vahid Pirhadi,Dr Shahroud Azami

FRACTIONAL 2-POINT LEFT RADAU TYPE INEQUALITIES FOR DIFFERENTIABLE s-CONVEX FUNCTIONS

The concept of convexity is a fundamental principle in the field of analysis. Over the years, numerous important integral inequalities have been established for various classes of convex functions. This paper focuses on the establishment of 2-point left Radau type inequalities for functions whose first derivatives are s-convex in the second sense via Riemann-Liouville fractional integrals. Finally, we provide some application of our findings in the context of numerical integration.

saleh wedad, meftah badreddine, lakhdari abdelghani, Benchettah Djaber Chemseddine

Some 2-Designs Invariant Under the Group $S_9$

We consider a binary $[36,28,3]$ code invariant under the automorphism group $S_9$ which is obtained from a primitive permutation representation of degree 36 of the projective special linear group $PSL_2(8)$. We examine the stabilizers $(S_9)_omega$ and their structures, where $omega$ is a codeword of weight at most 10. Moreover, 1-designs $supp(omega)^{S_9}$ are constructed and we show that there exist 2-$(36,6,120)$, 2-$(36,6,20)$, 2-$(36,10,6480)$, 2-$(36,10,2160)$, 2-$(36,10,12960)$, 2-$(36,10,1620)$, 2-$(36,10,3240)$ and 2-$(36,10,360)$ designs among them.

Reza Kahkeshani

On Generalized Commutative John Quaternions

Generalized commutative quaternions generalize elliptic, parabolic and hyperbolic quaternions, bicomplex numbers, complex hyperbolic numbers and hyperbolic complex numbers. In this paper, we study the generalized commutative John, John-Lucas and Tribonacci quaternions and we derive some of their properties. Moreover, we determine the generating functions for them and we give their matrix generators.

Dr. Dorota Bród,Dr. Natalia Paja,Dr. Anetta Szynal-Liana

On the Center of Crossed Polysquares

‎In this paper‎, ‎we introduce the center of Cat$^2$-polygroups and the center of crossed polysquares‎, ‎by using the equivalence between the category of crossed polysquarse‎,

‎and category of cat$^2$-polygroups‎. Also, we give a new application of crossed squares‎. ‎This application is so impotant‎, ‎because we use the notion of polygroup to obtain center of crossed polysquares‎. Furthermore, to we consider a crossed polysquare and by using the concept of fundamental relation‎,‎ we obtain a center for crossed square.

Mohammad Ali Dehghanizadeh, Saeed Mirvakili

Controllability of Non-linear Generalized Impulsive Systems using Functional Analytic Approach

This article explores the exact controllability of the linear and nonlinear generalized impulsive evolution systems over the finite interval. Exact controllability results of the linear systems was achieved using the concept of semigroup of operators, and the concepts of linear functional analysis. The results of exact controllability for linear systems using the concept of semigroup of operators, nonlinear functional analysis, and generalized Banach fixed point theorem. To support the result, an application is included in this article.

Mr. Vishant Shah,Dr. Jaita Sharma

Estimation of functions with first derivatives in Hα,2 w [0, 1) class by first kind Chebyshev wavelet and solutions of Duffing type equations

In this paper, the first kind of Chebyshev wavelet has been studied. The class Hα,2 w [0, 1) of functions and the moduli of continuity of f − S2k−1,M(f) have been introduced, where S2k−1,M(f) is the 2k−1,M + 1th partial sums of the Chebyshev wavelet series of f. The moduli of continuity are sharper and better than approximations of f ∈ Hα,2 w [0, 1) by S2k−1,M(f). An algorithm for solving non-linear Duffing equations by first kind Chebyshev wavelet matrix integration has also been proposed. The damped and undamped Duffing oscillators have been solved by the proposed method in this paper. The solutions of these oscillators obtained by the proposed method coincide almost with their exact solutions. This shows the application and accuracy of the proposed method in this paper in obtaining the solution to scientific and engineering problems expressed in differential equations.

Prof. Shyam Lal,Ms. Abhilasha

An inverse problem for Burgers' equations with periodic boundary condition

 In this article, we tried to find the solution in Burgers' equations by iteration method. Also we have proposed a numerical method by using finite difference method.

Prof. Irem Baglan,Prof. Fatma Kanca,Prof. Vishnu Narayan Mishra

Total outer-connected domination number of middle graphs

 In this paper, we study the total outer-connected domination number of the middle graph of a simple graph and we obtain tight bounds for this number in terms of the order of the middle graph. We also compute the total outer-connected domination number of some families of graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total outer-connected domination number of middle graphs.

Farshad Kazemnejad, Benhaz Pahlavsay, Elisa Palezzato, Michele Torielli

HÖLDER AND CARLSON TYPE INEQUALITIES FOR THE INTERVAL-VALUED FUNCTIONS

In this paper, we have proved the indispensable inequalities of classical analysis for
interval value functions: Holder, Cauchy-Schwarz and Carlson inequalities. Additionally, we achieved
generalization for Carlson's inequality for interval-valued functions.

Necmettin Alp, Mehmet Zeki Sarıkaya, Hüseyin Budak

Triangular matrix extensions of ‎π‎-reguar rings

The aim of this paper is to study some extensions of abelian ‎π-regular rings. ‎ We prove that the class of abelian π‎-regular rings is closed under several triangular matrix extensions. ‎Also, a necessary and sufficient condition for a trivial extension to be an abelian ‎π‎-regular ring is obtained.‎‎

Dr Ali Shahidikia,Dr Morteza Ahmadi

On σ-classes of modules with applications

In this paper we introduce some lattices of classes of left
R-module relative to a preradical sigma. These lattices are generaliza-
tions of the lattices R-TORS, R-tors, R-nat, R-conat, of torsion theo-
ries, hereditary torsion theories, natural classes and conatural classes,
respectively. We define the lattices σ-(R-TORS), σ-(R-tors), σ-(R-nat),
σ-(R-conat), which reduce to the lattices mentioned above, when one
takes sigma as the identity. We characterize the equality between these
lattices by means of the (σ-HH) condition, which we introduce. We also
present some results about σ-retractable rings, σ-Max rings extending
results about Mod-retractable rings and Max rings.
 

Dr Hugo Alberto Rincón-Mejía,M. en C. Oscar Alberto Garrido-Jiménez

A new notions of quotient mappings and networks through $ P $-$ I $-convergence

In this paper, we procure the concepts of $ P $-$ I $-quotient mappings, $ P $-$ I $-$ cs $-networks,  $ P $-$ I $-$ cs' $-networks and $ P $-$ wcs' $-networks, and prove some properties of $ P $-$ I $-quotient mappings and $ P $-$ I $-$ cs' $networks, especially $ P $-$ J $-quotient mappings and $ P $-$ J $-$ cs $-networks on an ideal $ J $ of $ mathbb{N} $. With these notions, we obtain that if $ X $ is a $ P $-$ J $-$ FU $ space with a point-countable $ P $-$ J $-$ cs' $-network, then $ X $ is a meta-Lindelof space.  

Carlos Granados, Laxmi Rathour

Mercer type variants of the Jensen--Steffensen inequality-II

Jensen--Mercer's inequality for weights satisfying conditions as for the reversed Jensen-Steffensen inequality is proved. Several inequalities involving more than one monotonic function with reversed Jensen-Steffensen conditions are proved. Furthermore, a couple of general companion inequalities related to Mercer's inequality with reversed Jensen-Steffensen conditions are presented as well. Applications for the generalization of weighted Ky Fan's inequality, classical Power Mean, and classical Arithmetic--Geometric--Harmonic Mean inequalities are given as well

Dr. ASIF RAZA KHAN,Miss FAIZA RUBAB

The equivalency relation on Fusion Frames

Fusion frames have been recently introduced by some researchers. They are applied in the construction of global frames from local frames and on centralized reconstruction versus distributed reconstructions and their numerical differences. In this paper, fusion frames in Hilbert C8-modules with C ∗-valued bounds are presented. Equivalent fusion frames and their duals are considered. Finally, we investigate fusion frames in Hilbert C ∗-modules that are constructed on the same set with different C ∗-algebras.

Azadeh Alijani

Oscillation behavior for a n-dimensional system of coupled van der Pol oscillators with delays

In this paper, the oscillatory behavior of the solutions for a n-dimensional system of coupled van der Pol oscillators with delays is investigated. We extend the result in the literature from mathematical point of view. some sufficient condition to guarantee the oscillation of the solutions are provided and computer simulations are given to support the present criteria.

Chunhua Feng

Some Properties Of G**-Autonilpotent Groups

Let G be a group. In this paper, we first introduce a new series on the subgroups generated by G and IA(G) and define G**-autonilpotency in this series. Then we study some properties of these concepts and their relationships.

Miss Sara Barin,Dr Mohammad Mehdi Nasrabadi

Cubic Semisymmetric Graphs of Order 52p

A graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we prove that there are no connected cubic semisymmetric graphs of order 52p,  where p ≥ 17 is a prime.

Mrs Samira Fallahpour

Solution of a nonlinear boundary value problem in probabilistic metric space with minimum $t$-norm

In the context of probabilistic metric spaces, we obtain some sufficient conditions for the existence of best proximity points for the class Kannan type contraction mappings. As an application of our findings, we present a solution to a second-order boundary value differential equation.

S K Bhandari, S Chandok, S Guria

Parameter for Connectedness on the Generalized Topological Spaces

Connectedness and path connectedness are the important tools for discussing the intermediate value theorem in the real line as well as in the calculus of R^n. Convex set is also discussed via connected and path connected notions. In the connected spaces, it can't be separated by some subsets of the original space. In our paper, we are interested
to study the connection as well as path connection of a space by means of number of points on account of the connection. To do this we define nth order connection and a new type of path connection and discuss their detail properties. In this paper, we shall show that the huge change of the properties of these connection and path connection from original connection as well as path connection. Counter examples are also an important argument of this paper.

Shyamapada Modak, Kulchhum Khatun, Md. Monirul Islam

Algorithms for Computing the Adjacency and Distance Matrices of a Class of 3-Generalized Fullerenes

‎A 3-connected cubic planar graph $H$ is an $m-$generalized fullerene if its faces are two $m-$gons and all other faces are pentagons and hexagons‎. ‎Suppose $H$ is such a graph‎. ‎The adjacency matrix $A(H) = [a_{ij}]$ is a matrix in which entries are 0 or 1 such that $a_{ii} = 0$‎, ‎$1 leq i leq n$‎, ‎and $a_{ij} = 1$‎, ‎$i ne j$‎, ‎if and only if the $i$-th vertex of $H$ is adjacent to the $j$-th vertex of $H$‎. ‎The distance matrix $D(H) = [b_{ij}]$ is defined as $d_{ii} = 0$‎, ‎$1 leq i leq n$‎, ‎and $d_{ij} = d(v_i,v_j)$‎, ‎$i ne j$‎, ‎is the length of a shortest path connecting the $i$-th and $j$-th vertices of $H$‎. ‎The aim of this paper is to present algorithms for computing the adjacency and distance matrices of a ‎$‎‎‎m$-generalized fullerene graph $C_{12m+40}$ with exactly $12m‎ + ‎40$ vertices‎. ‎There are some exceptional cases in our calculations for $m leq 5$‎. ‎These cases are solved with the aid of Matlab and then we will present a recursive method for computing the adjacency and distance matrices of the sequence ${C_{12m+40}}(m geq 5)$ of 3-generalized fullerenes‎.

Hasan Barzegar , Omid nekoei , A. R. Ashrafi

Blow Up of Solutions for Coupled Nonlinear Klein-Gordon with Source Term

In this paper we will substantiation that the positive intial-energy solution for coupled nonlinear Klein-Gordon equations with source term. We prove, with positive initial energy, the global nonexistence of solution by concavity method.

Djamel Ouchenane, Fares Yazid, Fatima Siham Djeradi

Characterizations of super quasi-Einstein spacetimes

The main goal of this paper is to characterize an imperfect fluid spacetimes, named super quasi-Einstein spacetimes. We address some properties of such a spacetime satisfying covariant constant Ricci tensor and Killing Ricci tensor. Further, we characterize super quasi-Einstein Yang pure space. Moreover, super quasi-Einstein generalized Robertson-Walker spacetimes have been investigated. Finally, we have constructed an example of a super quasi-Einstein spacetime.

Emeritus Professor Uday Chand De,Mr. Dipankar Hazra

Investigations on Malmquist Type Delay Differential Equation over Non-Archimedean Field

In this article, we have established the analogue of famous Mokhon'ko lemma for the rational function of two non-linear differential operators. We also investigated on the existence of solutions of a system of Malmquist type delay differential equation over non-Archimedean field.

Dr. Sayantan Maity,Dr. Abhijit Banerjee

On the PUL-integral on Smooth Manifolds

    The notion of the PU integral was first formulated by Kurzweil and Jarnik. It is a Henstock type that utilizes the concept of a partition of unity in it covering system. They mentioned, without much details, that this integration process may be used in the formulation of the Henstock integral in manifolds. In this paper, the above query will be revisit and the Henstock integral of a function defined on a manifold will be presented including some of its fundamental properties.

Dr Greig Bates Flores

ON ROUGH φ CONVERGENCE

In this paper we introduce rough φ-convergence of real numbers as a generalization of rough convergence as well as φ-convergence. We study some of its basic properties and relations of the above convergence concept with already known different types of convergence.
In 2001, H.X.Phu proved that "The diameter of a r-limit set is not greater than 2r". We investigate the above result for rough φ-convergence by introducing r-φ limit set and surprisingly the result comes out to be not true.
So our main aim is to find out the different behaviour of the new convergence concept based on r-φ limit set.
 

Dr. Chiranjib Choudhury,Dr. Shymayal Debnath,Dr. Ayhan Esi

Vortex Solutions for the 2D Boussinesq Equations Under the Radial Gravity

Behruz Raesi, Mahdi Kamandar

Duality of FqFq[u]-additive skew cyclic codes

Li et al. (2021) obtained the generator polynomials and the minimal generating sets of FqFq[u]-linear skew cyclic codes, where q is a power of prime integer and u2 = 0. In this paper, we determine the structure of dual of these codes in terms of their generating polynomials and we illustrate the dual of some special FqFq[u]-additive skew cyclic codes.
 

Dr Saeid Bagheri,Dr Roghaye Mohammadi Hesari,Ms Elham Shahpouri,Dr Karim Samei

On Statistical Compactness

In the search of a topological property which lies somewhere between compactness and Lindelofness, we introduce the concept of statistical compactness in this paper. We have also searched for the preservation of statistical compactness under sub-space topology and open continuous surjection. Some nite intersection like properties are also addressed here.

Susmita Sarkar,Dr Prasenjit Bal,Dr Debjani Rakshit