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In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\mathbb{R})$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area

In this paper, by employing Ricceri variational principle, we prove the existence of infinitely many weak solutions for fourth-order problems depending on two real parameters. We also provide some particular cases and a concrete example in order to illustrate the main abstract results of this paper.

In this paper, we establish coincidence point and common fixed point theorems involving two pairs of weakly compatible mapping satisfying contraction condition with complex coefficient are proved in complex valued metric space. The presented theorems generalize, extend and improve many existing results in the literature. An example is given at the end of the paper.

In this paper we introduce and study the notion of d-continuity continuity on mixed fuzzy topological spaces. We have investigated this notion in the light of the notion of q-neighbourhoods, q-coincidence, fuzzy d-closure, fuzzy d-interior. In this paper we have established the relationship between fuzzy continuity and fuzzy d-continuity in mixed fuzzy topological spaces.

In this paper we introduce a new concept for Riesz almost lacunary $\Gamma^{3}$ sequence spaces strong $P-$ convergent to zero with respect to an Musielak-Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of Riesz almost lacunary $\Gamma^{3}$ sequence spaces and also some inclusion theorems are discussed.

This paper is devoted to the existence of solutions for a class of Kirchhoff type systems involving critical exponents. The proof of the main results is based on concentration compactness principle related to critical elliptic systems due to Kang combined with genus theory.

In this paper we study different weak forms of open multifunctionsfrom a fuzzy topological space into a fuzzy $m$-space. Further we study the same from a fuzzy bitopological space into a fuzzy bitopological spaces.

In this paper, we will introduce new sequence Hilbertian space and for it we will show boundedness of composition operators.

Recently, a large number of integral formulas involving Bessel functions and their extensions have been investigated. The objective of this paper is to establish four classes of integral formulas associated with the Struve functions, which are expressed in terms of the Fox-Wright function. Among a variety of special cases of the main results, we present only six integral formulas involving trigonometric and hyperbolic functions.

In this paper, we introduce the paranormed sequence space $\mathcal{M}_{u}(t)$ corresponding to the normed space $\mathcal{M}_{u}$ of bounded double sequences. We examine general topological properties of this space and determine its alpha-, beta- and gamma-duals. Furthermore, we characterize some classes of four-dimensional matrix transformations concerning this space and its dual spaces.

In this paper, we introduce the concepts of fuzzy rare α continuous,fuzzy rarely continuous, fuzzy rarely pre-continuous, fuzzy rarely semi-continuous are introduced and studied in light of the concept of rare set in a fuzzy setting. Some interesting properties are investigated besides giving some examples

In this paper, we present and analyze the upper and lower bounds on the Hyper Zagreb index $\chi^2(G)$ of graph $G$ in terms of the number of vertices $(n)$, number of edges $(m)$, maximum degree $(\Delta)$, minimum degree $(\delta)$ and the inverse degree $(ID(G))$. In addition, we give a counter example on the upper bound of the second Zagreb index for Theorems 2.2 and 2.4 from \cite{ranjini}. Finally, we present lower and upper bounds on $\chi^2(G)+\chi^2(\overline G)$, where $\overline G$ denotes the complement of $G$.

The aim of this paper is to investigate some properties of almost bcontinuous function in a bitopological space. Relationships with some other types of functions are also investigated.

In this paper first of all, we introduce the mapping : [0;1) X [0;1) R,called the simulation function and the notion of Z-contraction with respect to which generalize several known types of contractions. Secondly, we prove certain xed point theorems using simulation functions in G-Metric spaces. An example is also given to support our result.

In this paper we introduce a new concept for generalized almost (λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}) convergence in χ_{R_{λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}}}³-Riesz spaces strong P- convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of generalized almost (λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}) convergence in χ_{R_{λ_{m_{i}}μ_{n_{ℓ}}γ_{k_{j}}}}³-Riesz space and also some inclusion theorems are discussed.

A hereditary class on a set X is a nonempty collection of subsets closed under heredity. The aim of this paper is to introduce and study strong forms of u-compactness in generalized topological spaces with respect to a hereditary class, called SuH-compactness and S- SuH-compactness. Also several of their properties are presented. Finally some eects of various kinds of functions on them are studied.

We generalized the concepts in probability of rough lacunary statistical by introducing the diference operator of fractional order, where is a proper fraction and = (mnk ) is anyxed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related triple diference sequence spaces. The main focus of the present paper is to generalized rough lacunary statistical of triple diference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator

The purpose of the present paper is to introduce and study upper and lower nearly I-continuous multifunctions. Basic characterizations, several properties of upper and lower nearly I-continuous multifunctions are investigated.

In this paper we investigate the influence of some subgroups of Sylow subgroups with semi cover-avoiding property and $E$-supplementation on the structure of finite groups. Some recent results are generalized and unified.

In this paper, we introduce and investigate a new class of sets called A -open sets which are weaker than co-zero sets. Moreover, we obtain characterizations and preserving theorems of quasi compact spaces.

In this paper we introduce a new sequence space $bv(\hat{F})$ by using the Fibonacci band matrix $\hat{F}.$ We also establish a few inclusion relations concerning this space and determine its $\alpha-,\beta-,\gamma-$duals. Finally we characterize some matrix classes on the space $bv(\hat{F}).$

In this paper , we derive asymptotic expansion of the wavelet transform for large values of the dilation parameter a by using Lopez and Pagola technique. Asymptotic expansion of Mexican Hat wavelet and Morlet wavelet transform are obtained as a special cases.

In this paper we study of the existence of solutions for a class of elliptic system with nonlocal term in R^{N}. The main tool used is the variational method, more precisely, the Mountain Pass Theorem.

In this paper we define Bertrand curves of constant precession with a new approach and obtain their characterizations by using a moving alternative frame.

Let $k\geq 1$ be an integer and let $P=k+2,Q=k$ and $D=k^{2}+4$. In this paper, we derived some algebraic properties of quadratic ideals $I_{\gamma}$ and indefinite quadratic forms $F_{\gamma }$ for quadratic irrationals $\gamma$, and then we determine the set of all integer solutions of the Diophantine equation $F_{\gamma }^{\pm k}(x,y)=\pm Q$.

In this paper we introduce stable subgroup graph associated to the group $G$. It is a graph with vertex set all subgroups of $G$ and two distinct subgroups $H_1$ and $H_2$ are adjacent if $St_{G}(H_1)\cap H_2\neq 1$ or $St_{G}(H_2)\cap H_1\neq 1$. Its planarity is discussed whenever $G$ is an abelian group, $p$-group, nilpotent, supersoluble or soluble group. Finally, the induced subgraph of stable subgroup graph with vertex set whole non-normal subgroups is considered and its planarity is verified for some certain groups.

In this paper, we study an existence result of entropy solutions for some nonlinear parabolic problems in the Musielak-Orlicz-Sobolev spaces.

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan c1.

In this paper, we propose a numerical scheme to solve multi-dimensional Black-Scholes equation using the global radial basis functions-based dierential quadrature (RBFs-DQ) method. Before applying the method, it is needed to remove mixed derivatives from the Black-Scholes equation by making an appropriate change of variables . Then, any spatial derivatives are approximated by a linear weighted sum of all the function values in the whole physical domain. In the RBFs-DQ method the weighting coecients are computed by RBFs. The method is very easy to implement and the non-singularity is ensured. The proposed method com bines the advantages of the conventional DQ method and the RBFs. It also remains mesh-free feature of RBFs.

In this paper, we study inextensible flows of evolute curve of curves in E³. We research inextensible flows evolute curves of in the E³.

In this paper, a new numerical method for solving the optimal control problems with payoff term or fixed state endpiont by quadratic performanceindex is presented. The method is based on Bezier polynomial. The properties of Bezier polynomials in any intervel as [a; b] are presented. The operational matrices of integration and derivative are utilized to reduce the solution of the optimal control problems to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.

In this paper, the authors introduce a generalized Sakaguchi type spiral-likefunction class S(\lambda, \beta, s, t) and obtain sharp upper bound to thesecond Hankel determinant |H_{2}(1)| for the function f in the above class.Relevances of the main result are also briefly indicated.

In this paper, it is shown that if $\mathcal {A}$ is a CSL subalgebra of a von Neumann algebr and $\phi$ is a continuous mapping on $\mathcal {A}$ such that $(m+n+k+l)\phi(A^{2})-(m\phi(A)A+nA\phi(A)+k\phi(I)A^2+l A^2 \phi(I))\in \mathbb{F}I $ for any $A\in \mathcal {A}$, where $\mathbb{F}$ is the real field or the complex field, then $\phi$ is a centralizer. It is also shown that if $\phi$ is an additive mapping on $\mathcal {A}$ such that $(m+n+k+l)\phi(A^{2})=m\phi(A)A+nA\phi(A)+k\phi(I)A^2+l A^2 \phi(I) $for any $A\in\mathcal{A}$, then $\phi$ is a centralizer.

The main aim of this paper is to introduce the necessary and sufficient condition for a particular type of transformation of the form A: (a......) be regular from a triple sequence space to another triple sequence space.

‎Stochastic fractional differential equations (SFDEs) have been used for modeling many physical problems in the fields of turbulance‎, ‎heterogeneous‎, ‎flows and matrials‎, ‎viscoelasticity and electromagnetic theory‎. ‎In this paper‎, ‎an‎ efficient wavelet Galerkin method based on the second kind Chebyshev wavelets are proposed for approximate solution of SFDEs‎. ‎In ‎this ‎app‎roach‎‎, ‎o‎perational matrices of the second kind Chebyshev wavelets ‎are used ‎for reducing SFDEs to a linear system of algebraic equations that can be solved easily‎. ‎C‎onvergence and error analysis of the proposed method is ‎considered‎.‎ ‎Some numerical examples are performed to confirm the applicability and efficiency of the proposed method‎.

In this paper, the quadratic B-spline collocation methodis implemented to find numerical solution of theBenjamin-Bona-Mahony-Burgers (BBMB) equation. Applying theVon-Neumann stability analysis technique, we show that the method is unconditionally stable. Also the convergence of the method is proved. The method is applied on some testexamples, and numerical results have been compared with theexact solution. The numerical solutions show theefficiency of the method computationally.

In this paper we use a family of Muntz polynomials and a computational technique based on the collocation method to solve the calculus variation problem. This approach is utilizedto reduce the solution of linear and nonlinear fractional order dierential equations to the solution of a system of algebraic equations. Thus we can obtain a good approximation evenby using a smaller of collocation points.

The aim of this paper is to introduce the concept of lambda operator of a fuzzy set in a fuzzy bitopological space. Then we study (i, j)-fuzzy Lembda Gamma- set and its properties. Moreover we define (i, j)-fuzzy Lembda-closed set, (i, j)-fuzzy Lembda Gamma-closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts (i, j)-fuzzy Lembda-closed set and (i, j)-fuzzy generalized closed set are independent to each other but jointly they gives the taui-fuzzy closed set. To this end as the application of (i, j)-fuzzy Lembda Gamma-closed set we shall study (i, j)-fuzzy Lembda Gamma continuity and (i, j)-fuzzy Lembda Gamma-generalized continuity and their properties.

In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of a linear operator. Some of our results improve and generalize previously known results.

The purpose of the paper is to obtain a new bi-unique range sets, as introducedin [4] with smallest cardinalities ever for derivative of meromorphic functions. Our results will improve all the results in connection to the bi-unique range sets to a large extent. A number of examples have been exhibited to justify our certain claims. At last an open question have been posed for future investigations.

In the present paper the Tarig transform of fractional order is studied by employing Mittag - Leffler function. Properties of Tarig transform are proved using the same fractional Tarig transform.

In this paper we study Bertrand and Mannheim partner -curves on parallel surface. Using the definition of parallel surfaces, first we find images of two curves lying on two different surfaces and satisfying the conditions to be Bertrand partner -curve or Mannheim partner -curve. Then we obtain relationships between Bertrand and Mannheim partner -curves and their image curves.

In this paper, we define and study a new class of generally locally closed sets called $\I$-locally-$\tau_g^\star$-closed sets in ideal topological spaces. We also discuss various characterizations of $\I$-locally-$\tau_g^\star$-closed sets in terms of $g$-closed sets and $\I_g$-closed sets.

In this paper, generalizations of adherence and convergence of nets and filters on a bi-GTS are introduced and studied. Several properties and interrelations among such adherence and convergence of nets and filters on a bi-GTS are discussed and characterized using graphs of functions. Finally, these results are applied to investigate the behaviour of a generalization of compactness, known as $g_{ij}$-$closedness$ of a bi-GTS.

In this paper we present and discuss a new numerical scheme for solving fractional delay differential equations of the generalform:$$D^{\beta}_{*}y(t)=f(t,y(t),y(t-\tau),D^{\alpha}_{*}y(t),D^{\alpha}_{*}y(t-\tau))$$on $a\leq t\leq b$,$0

In this paper, we give the first kind and second kind osculating curves in the lightlike cone. In addition we characterize osculating curves in terms of their curvature functions.

In this paper we have examined the approximate point spectrum, defect spectrum and compression spectrum of the operator D(r, 0, 0, s)on the sequence spaces c0, c, ℓp and bvp.

WOS: 000410590900001 In this paper, we analyzed the problem of consructing a family of surfaces from a given some special Smarandache curves in Euclidean 3-space. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame, and derive the necessary and sufficient conditions for coefficents to satisfy both the asymptotic and isoparametric requirements. Finally, examples are given to show the family of surfaces with common Smarandache curve.

The aim of this paper, is to study the limit behavior of the solution of a convex elasticity problem with negative power type, of a containing structure, an elastic thin oscillating layer of thickness depending of a small enough parameter. The epi-convergence method is considered to nd the limit problems with interface conditions.

In this paper we introduce the notion of $\lambda_{mn}-\chi^{2}$ and $\Lambda^{2}$ sequences. Further, we introduce the spaces $\left[\chi^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)}$ and $\left[\Lambda^{2q\lambda}_{f\mu },\left\|\left(d\left(x_{1},0\right),d\left(x_{2},0\right),\cdots, d\left(x_{n-1},0\right)\right)\right\|_{p}\right]^{\textit{I}\left(F\right)},$ which are of non-absolute type and we prove that these spaces are linearly isomorphic to the spaces $\chi^{2}$ and $\Lambda^{2},$ respectively. Moreover, we establish some inclusion relations between these spaces.