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In this paper, a fuzzy random minimum cost flow problem is presented. In this problem, cost parameters and decision variables are fuzzy random variables and fuzzy numbers respectively. The object of the problem is to find optimal flows of a capacitated network. Then, two algorithms are developed to solve the problem based on Er-expected value of fuzzy random variables and chance-constrained programming. Furthermore, the results of two algorithms will be compared. An illustrative example is also provided to clarify the concept  

In this paper, we will discuss two special classes of mathematical programming models with fuzzy random variables. In the first model, a linear programming problem with fuzzy decision variables and fuzzy random coefficients is introduced. Then an algorithm is developed to solve the model based on fuzzy optimization method and fuzzy ranking method. In the second model, a fuzzy random quadratic spanning tree problem is presented. Then the proposed problem is formulated and solved by using the scalar expected value of fuzzy random variables. Furthermore, illustrative numerical examples are also given to clarify the methods discussed in this paper  

In this paper, a fuzzy approach is applied to special classes of integer programming problems with all diierent constraints. In the rst model, a fuzzy integer programming model is developed to represent the all-diierent constraints in mathematical programming. In order to solve the proposed model, a new branching scheme for the Branch and Bound algorithm is also presented. In the second model, a special class of large-scale multi-objective fuzzy integer programming problems with all-diierent constraints is introduced. A solution method for the proposed model is also developed by using the decomposition technique, weighting method and Branch and Bound algorithm. An illustrative numerical... 

In this paper, a fuzzy random minimum cost flow problem is presented. In this problem, cost parameters and decision variables are fuzzy random variables and fuzzy numbers respectively. The object of the problem is to find optimal flows of a capacitated network. Then, two algorithms are developed to solve the problem based on Er-expected value of fuzzy random variables and chance-constrained programming. Furthermore, the results of two algorithms will be compared. An illustrative example is also provided to clarify the concept  

This is a variation on a theme of Bayer-Fluckiger, Shapiro, and Tignol related to hyperbolic involutions. More precisely, criteria for the hyperbolicity of involutions of quadratic extensions of simple algebras and involutions of the form σ ⊗ τ and σ ⊗ ρ, where σ is an involution of a central simple algebra A, τ is the nontrivial automorphism of a quadratic extension of the center of A, and ρ is an involution of a quaternion algebra are obtained  

The aim of this article is to provide a characterization of quadratic forms of low dimension such that the canonical involutions of their Clifford algebras are hyperbolic  

Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated  

For every rotation (Formula presented.) of the Euclidean space (Formula presented.) ((Formula presented.)), we find an upper bound for the number (Formula presented.) such that (Formula presented.) is a product of (Formula presented.) rotations by an angle (Formula presented.) ((Formula presented.)). We also find an upper bound for the number (Formula presented.) such that (Formula presented.) can be written as a product of (Formula presented.) full rotations by an angle (Formula presented.). © 2017 Australian Mathematical Publishing Association Inc  

For every rotation of the Euclidean space ℝ(n≥3), we find an upper bound for the number such that is a product of rotations by an angle α( 0<≤π). We also find an upper bound for the number such that ρ can be written as a product of full rotations by an angle α. © 2017 Australian Mathematical Publishing Association Inc  

This article aims to present a geometric interpretation of the simplicity of the rotation group of three-dimensional Euclidean space. Some historical remarks on the subject and an overview of a collection of different proofs of this result are also given  

We investigate the structure of normal subgroups of the unit group of a quaternion algebra over a pythagorean field. © 2019, Iranian Mathematical Society  

To improve the hydrogen kinetics of magnesium hydride, TiCr1.2Fe0.6 alloy was prepared by vacuum arc remelting (VAR) and the alloy was co-milled with MgH2 to process nanostructured MgH2–5 at.% TiCr1.2Fe0.6 powder. The hydrogen desorption properties of the composite powder were studied and compared with pure magnesium hydride. X-ray diffraction (XRD) analysis showed that the composite powder prepared by VAR/mechanical alloying (MA) procedure consisted of β-MgH2, γ-MgH2, bcc Ti–Cr–Fe alloy, and small amount of MgO. The average size of particles and their grain structure after 4 h MA were determined by a laser particle size analyzer and XRD method and found to be 194 nm and 11 nm, respectively.... 

In this paper we develop a fuzzy system to obtain the demand based on input variables of price, warranty length and lead time of order delivery. We use linguistic terms to illustrate the situation of input and output variables and construct a fuzzy rule base. The fuzzy rule base is integrated with a genetic algorithm to construct a hybrid solution method. The best value of price, warranty length and lead time are obtained by maximizing the manufacturer profit. Finally a numerical example is presented to show the performance of proposed approach  

In this article, we propose a bi-objective model for the pricing-queuing problem under a fuzzy environment. We consider two objectives: maximizing the profit function and minimizing the waiting time in queue. Imagine a firm which sells a product in a channel providing after sales services. The sales price and warranty length affect customer demand. We formulate the demand function as a fuzzy system considering the sales price and warranty length. The firm optimizes the sales price and warranty length, as well as waiting time, in the queue of after sales services, to maximize its revenues and minimize waiting time. To solve the derived model, we develop a hybrid solution method of a fuzzy... 

Nanofibrous structures that mimic the native extracellular matrix and promote cell adhesion have attracted considerable interest for biomedical applications. In this study, GO-modified nanofibrous biopolymers (GO) were prepared by electrospinning blended solutions of chitosan (80 vol%), polyvinyl pyrrolidone (15 vol%), polyethylene oxide (5 vol%) containing GO nanosheets (0–2 wt%). It is shown that GO nanosheets significantly change the conductivity and viscosity of highly concentrated chitosan solutions, so that ultrafine and uniform fibers with an average diameter of 60 nm are spinnable. The GO-reinforced nanofibers with controlled pore structure exhibit enhanced elastic modulus and... 

This paper introduces the energy-constrained multi-visit traveling salesman problem with multiple drones considering non-customer rendezvous locations (EM-TSPDs). A ground vehicle equipped with multiple drones that can serve multiple customers per trip performs deliveries. Before solving the EM-TSPDs, the non-customer rendezvous location subproblem (NRLP) is addressed to locate candidate non-customer rendezvous nodes so that all drone customers can be covered by drones. The importance of this full coverage is that all drone customers can reap the benefits of drone delivery by receiving fast delivery or being served in areas that are inaccessible by road network. We propose MILP formulations...