Caspian Journal of Mathematical Sciences
Volume:11 Issue: 1, Winter Spring 2022

In this paper, as an extension of Pareto optimality concepts for multi objective programming problems to fuzzy multi objective linear programming (FMOLP) problems, different types of Pareto optimal solutions (POSs), namely, weakly, strictly, and properly POSs are defined on the basis of α-cuts of fuzzy numbers. Then a method for solving FMOLP problems is proposed to obtain them. It is shown that they can be obtained by solving some non fuzzy multi objective linear programming problems. A numerical example is solved to illustrate the method.

We study on Jacobsthal and Jacobsthal-Lucas generalized octonions over the algebra O(a,b,c) where a,b and c are real numbers. We present Binet formulas for these types of octonions. Furthermore, we give some well-known identities such as Catalan's, Cassini's, d'Ocagne's identities and other special identities for Jacobsthal and Jacobsthal-Lucas generalized octonions.

In this paper we intend to extract some types of generalized topologies from a topological space. To do this, we first generalize the derived set operator and the closure operator of a topological space using a class of subsets of the space, this collection is called the hereditary family since it is closed under the operation subset. The generalized closure operator induces a structure that is our desired generalized topology.

The edge neighborhood graph N_{e}(G) of a simple graph G is the graph with the vertex set E ∪ S where S is the set of all open edge neighborhood sets of G and two vertices u,v ∈ V (N_e{}(G)) adjacent if u ∈ E and v is an open edge neighborhood set containing u. In this paper, we determine the domination number, the total domination number, the independent domination number and the 2-domination number in the edge neighborhood graph. We also obtain a 2-domination polynomial of the edge neighborhood graph for some certain graphs.

In this paper we study about IF binary operations on some IF sets, at first. Then we introduce IF groups, IF modules and IF homo- morphisms under IF binary operations. We present some properties of IF groups rings and modules under binary operation. IF modules and IF homomorphisms over this kind of IF rings are introduced and investigated.

We consider the sl(2,R)-module structure on the spaces of n−ary differential operators acting on the spaces of weighted densities. We classify sl(2,R)-invariant n−ary differential operators acting on the spaces of weighted densities.

In this paper, we investigate the Hermite-Hadamard inequality for the Riemann-Liouville integral transformations for uniformly convex functions from a geodesic perspective in the Hadamard spaces. This inequality is widely used in some fractional integral approximations.

‎The golden ratio $phi=frac{1+sqrt{5}}{2}=1/61803398874...$ is the root of the polynomial $x^2-x-1=0$‎, ‎and is the one of the important numbers in mathematics‎. ‎The golden ratio is also used in many fields of science‎. ‎The golden ratio appears in some patterns in nature‎, ‎including the spiral arrangement of leaves and other plant parts‎. ‎In this paper‎, ‎we present a sequence of golden numbers ${phi_n}_n$ and study their properties‎.

In this paper, singularly perturbed differential equations having delay on the convection and reaction terms are considered. The highest order derivative term in the equation is multiplied by a perturbation parameter epsilon taking arbitrary values in the interval (0; 1]. For small epsilon, the problem involves a boundary layer on the left or right side of the domain depending on the sign of the coefficient of the convective term. The terms involving the delay are approximated using Taylor series approximation. The resulting singularly perturbed boundary value problem is treated using exponentially fitted upwind finite difference method. The stability of the proposed scheme is analysed and investigated using maximum principle and barrier functions for solution bound. The formulated scheme converges independent of the perturbation parameter with rate of convergence O(N−1). Richardson extrapolation technique is applied to accelerate the rate of convergence of the scheme to order O(N−2). To validate the theoretical finding, three model examples having boundary layer behaviour are considered. The maximum absolute error and rate of convergence of the scheme are computed. The proposed scheme gives accurate and parameter uniformly convergent result.

We construct some types of universal closure operations induced by certain collection of morphisms. For this purpose, we use Lawvere-Tierney topologies and universal closure operations that correspond to each other to establish the equivalent conditions over the collection of morphisms. In this way we use multiple sieves instead of principal sieves for constructing results. Examples are also given to illustrate the established results.

In this paper, the first and second variation formulas of the Sacks-Uhlenbeck bienergy functional is obtained. As an application, instability and non-existence theorems for Sacks-Uhlenbeck biharmonic maps are given.

The aim of this paper is to introduce the concepts of $alpha$-continuity, $eta$-admissible pair for fuzzy set-valued maps and define a notion of fuzzy $eta-(psi, F)$-contraction. The existence of common fuzzy fixed points for such contraction is investigated in the setting of a complete metric space. The ideas presented herein complement the results of Wardowski, Banach, Heilpern and other results on point-to-point and point-to-set-valued mappings in the comparable literature of metric and fuzzy fixed point theory. A few important of these consequences of our results are highlighted and discussed. Some nontrivial examples and an application to a system of integral inclusions of Fredholm type are considered to support our theorems and to illustrate a usability of the results obtained herein.

‎In this paper for two given sets of eigenvalues‎, ‎which one of them is the eigenvalues of circulant matrix and the other is the eigenvalues of skew-circulant matrix‎, ‎we find a nonnegative matrix‎, ‎such that the union of two sets be the spectrum of nonnegative matrices‎.

In this article, we construct a new computational algorithm for solving multiobjective linear programming problem in  intuitionistic fuzzy environment. The resources and technological coefficients are taken to be intuitionistic fuzzy numbers. Here, the intuitionistic fuzzy multi-objective linear programming problem is transformed into an equivalent crisp multi-objective linear programming problem. By using fuzzy mathematical programming approach, the transformed multiobjective linear programming problem is reduced into a single objective nonlinear and non-convex programming problem. Stepwise algorithm is given for solving an intuitionistic fuzzy multiobjective linear programming problem and it is checked with a numerical example using intuitionistic fuzzy decisive set method.

The power graph P(G) of a finite group G is a graph whose vertex set is the group G and distinct elements x; y are adjacent if one is a power of the other. Suppose that G = P * Q, where P (resp. Q) is a finite p-group (resp. q-group) of exponent p (resp. q) for distinct prime numbers p < q. In this paper, we determine necessary and sufficient conditions for existence of Hamiltonian cycles in P(G).

In this paper, we consider a generalization of $alpha$-$phi$-Geraghty contractive type operators and investigate the conditions for the existence and uniqueness of fixed point in a $S$-complete Hausdorff uniform space equipped with a $E$-distance. Our results extend, improve and generalize some related works in the literature. We illustrate the validity of the results with examples.

The notion of the Schur multiplier of a pair of groups was introduced by Ellis.Authors generalized the concept of the Schur multiplier of a pair of groups to the c-nilpotent multiplier of a pair of groups.In this paper , we prove some inequalities for the order of the c-nilpotent multiplier of a pair of groups.

‎This paper is devoted to the notion digital pseudocovering map introduced by Han cite{H4}‎. ‎We show that considered conditions in definition of digital pseudocovering map are incompatible unless the map be a covering map‎. ‎Then we will modify the definition so that the results remain true‎.

Let $f$ be a convex function on $I$ and $a,$ $bin I$ with $a<b.$ If $p:% left[ a,bright] rightarrow lbrack 0,infty )$ is Lebesgue integrable and symmetric, namely $pleft( b+a-tright) =pleft( tright) $ for all $tin % left[ a,bright] ,$ then we show in this paper that begin{align*} 0& leq frac{1}{2}int_{a}^{b}leftvert t-frac{a+b}{2}rightvert pleft( tright) dtleft[ f_{+}^{prime }left( frac{a+b}{2}right) -f_{-}^{prime }left( frac{a+b}{2}right) right]  \ & leq int_{a}^{b}pleft( tright) fleft( tright) dt-left( int_{a}^{b}pleft( tright) dtright) fleft( frac{a+b}{2}right)  \ & leq frac{1}{2}int_{a}^{b}leftvert t-frac{a+b}{2}rightvert pleft( tright) dtleft[ f_{-}^{prime }left( bright) -f_{+}^{prime }left( aright) right] end{align*} and begin{align*} 0& leq frac{1}{2}int_{a}^{b}left[ frac{1}{2}left( b-aright) -leftvert t-frac{a+b}{2}rightvert right] pleft( tright) dtleft[ f_{+}^{prime }left( frac{a+b}{2}right) -f_{-}^{prime }left( frac{a+b}{% 2}right) right]  \ & leq left( int_{a}^{b}pleft( tright) dtright) frac{fleft( aright) +fleft( bright) }{2}-int_{a}^{b}pleft( tright) fleft( tright) dt \ & leq frac{1}{2}int_{a}^{b}left[ frac{1}{2}left( b-aright) -leftvert t-frac{a+b}{2}rightvert right] pleft( tright) dtleft[ f_{-}^{prime }left( bright) -f_{+}^{prime }left( aright) right] . end{align*}.

In this paper, by using a modified forward-backward splitting method, the author introduces and studies an iterative algorithm for finding a common element of the set of fixed points of demicontractive mappings and the set of solutions of variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings in real Hilbert spaces.,The author proves that the sequence $x_n$ which is generated by the proposed iterative algorithm converges strongly to a common element of two sets above. Finally, some applications are given.

In this paper, considering the $k$th shape loop space $check{Omega}_{k}^{mathbf{p}}(X,x)$, for an HPol$_*$-expansion $mathbf{p}:(X,x)rightarrow ((X_{lambda},x_{lambda}),[p_{lambdalambda'}],Lambda)$ of a pointed topological space $(X,x)$, first we prove that  $check{Omega}_{k}$ commutes with the product under some conditions and then  we show that $check{Omega}_k^{mathbf{p}}(X,x)cong displaystyle{lim_{leftarrow}check{Omega}_k^{mathbf{p}}(X_i,x_i)}$, for a pro-discrete space $(X,x)=displaystyle{lim_{leftarrow}(X_i,x_i)}$ of compact polyhedra. Finally,  we conclude that these spaces are metric, second countable and separable.

Let $B$ be a Banach $A-bimodule$. We introduce the weak topological centers of left module action and we show it by $tilde{{Z}}^ell_{B^{**}}(A^{**})$. For a compact group, we show that $L^1(G)=tilde{Z}_{M(G)^{**}}^ell(L^1(G)^{**})$ and on the other hand we have $tilde{Z}_1^ell{(c_0^{**})}neq c_0^{**}$. Thus the weak topological centers are different with topological centers of left or right module actions. In this manuscript, we investigate the relationships between two concepts with some conclusions in Banach algebras. We also have some application of this new concept and topological centers of module actions in the cohomological properties of Banach algebras, spacial, in the weak amenability and $n$-weak amenability of Banach algebras.

The aim of this paper is to introduce the notions of the length and the mean of a hyper structure in UP-algebras. The notions of length fuzzy UP-subalgebras and mean fuzzy UP-subalgebras of UP-algebras are introduced, and related properties are investigated. Characterizations of length fuzzy UP-subalgebras and mean fuzzy UP-subalgebras are discussed. Relations between length fuzzy UP-subalgebras (resp., mean fuzzy UP-subalgebras) and hyperfuzzy UP-subalgebras are established. Moreover, we discuss the relationships among length fuzzy UP-subalgebras (resp., mean fuzzy UP-subalgebras) and upper level subsets, lower level subsets, and equal level subsets of the length (resp., mean) of a fuzzy structure in UP-algebras.

In this work, we study the Hadamard-type k-step Pell sequence modulo m and then, we obtain the cyclic groups which are generated by the multiplicative orders of the Hadamard-type k-step Pell matrix when read modulo m. Then we extend the Hadamard-type k-step Pell sequence to groups and we redefine the Hadamard-type k-step Pell sequence by means of the elements of groups. Finally, we obtain the periods of the Hadamard-type 3-step Pell sequence in the semi-dihedral group SD2m and the quasi-dihedral group QD2m.

As usual, the ring of continuous real-valued functions on a frame $L$ is denoted by $mathcal{R}L$. We determine the relation among strongly $z$-ideals, strongly divisible ideals and uniformly closed ideals in the ring $mathcal{R}L$. We characterize Lindel"of frames based on strongly fixed ideals in $mathcal{R}L$. We observe that a weakly spatial frame $L$ is Lindel"of if and if every strongly divisible ideal in $mathcal{R}L$ is strongly fixed; if and only if every closed ideal in $mathcal{R}L$ is strongly fixed.

The manuscript deals with the fractional optimal control problems (FOCPs) based on the Caputo fractional derivative by the Ritz method. To use this method, we transform the FOCPs into an optimization problem and obtain the system of nonlinear algebraic equations. By polynomial basis functions, we approximate solutions. Then, we have the coefficients of polynomial expansions by solving the system of nonlinear equations. Numerical examples are presented which illustrate the performance of the method.

A two-criteria user-optimized route choice problem is proposed, in which each user of a network system seeks to determine his/her optimal route of travel between an origin-destination (O-D) pair considering two-criteria simultaneously. In this problem, the two-criteria of travel, time and cost, between an O-D pair are fuzzy, in the sense that, time and cost of which links are chosen for traveling are uncertain. Applying the concept of $alpha$-cut level, a fuzzy vector disutility function on a path is computed. Furthermore, the fuzzy vector equilibrium principle as a generalization and extension of the Wardrop equilibrium principle is defined. Finally, by reducing this fuzzy principle to a crisp one, the relationship between the vector equilibrium flow and the solution of a vector variational inequality problem is discussed.

For an integer $kgeq1$, a $k$-distance enclaveless number (or $k$-distance $B$-differential) of a connected graph $G=(V,E)$ is $Psi^k(G)=max{|(V-X)cap N_{k,G}(X)|:Xsubseteq V}$. In this paper, we establish upper bounds on the $k$-distance enclaveless number of a graph in terms of its diameter, radius and girth. Also, we prove that for connected graphs $G$ and $H$ with orders $n$ and $m$ respectively, $Psi^k(Gtimes H)leq mn-n-m+Psi^k(G)+Psi^k(H)+1$, where $Gtimes H$ denotes the direct product of $G$ and $H$. In the end of this paper, we show that the $k$-distance enclaveless number $Psi^k(T)$ of a tree $T$ on $ngeq k+1$ vertices and with $n_1$ leaves satisfies inequality $Psi^k(T)leqfrac{k(2n-2+n_1)}{2k+1}$ and we characterize the extremal trees.

In this paper, we introduce the concept of Sequential Henstock integrals for interval valued functions and discuss some of their properties.