Minimal Solution of Complex Fuzzy Linear Systems

This paper investigates the complex fuzzy linear equation Cz~=w~ in which C is a crisp complex matrix and w~ is an arbitrary LR complex fuzzy vector. The complex fuzzy linear system is converted to equivalent high order fuzzy linear system Gx~=b~. A new numerical procedure for calculating the complex fuzzy solution is designed and a sufficient condition for the existence of strong complex fuzzy solution is derived in detail. Some examples are given to illustrate the proposed method

Complex fuzzy linear systems

In paper the complex fuzzy linear equation nbspnbspin which nbspis a crisp complex matrix and nbspis an arbitrary complex fuzzy numbers vector, is investigated. The complex fuzzy linear system is converted to a equivalent high order fuzzy linear system . Numerical procedure for calculating the complex fuzzy solution is designed and thenbsp sufficient condition for the existence of strong complex fuzzy solution is derived. A example is given to illustrate the proposed method.nbs

Three-Leaf Dart-Shaped Single-Crystal BN Formation Promoted by Surface Oxygen

Two-dimensional hexagonal boron nitride (h-BN) single crystals with various shapes have been synthesized by chemical vapor deposition over the past several years. Here we report the formation of three-leaf dart (3LD)-shaped single crystals of h-BN on Cu foil by atmospheric-pressure chemical vapor deposition. The leaves of the 3LD-shaped h-BN are as long as 18 {\mu}m and their edges are smooth armchair on one side and stepped armchair on the other. Careful analysis revealed that surface oxygen plays an important role in the formation of the 3LD shape. Oxygen suppressed h-BN nucleation by passivating Cu surface active sites and lowered the edge attachment energy, which caused the growth kinetics to change to a diffusion-controlled mode.Comment: 7 pages,6 figure

Method for manufacturing of three-dimensional freestanding porous thin-graphite with hierarchical porosity

The present invention includes an apparatus and a method of making a three dimensional graphite structure with a controlled porosity comprising: plating a metal layer on at least one of a nickel, an iron or a cobalt foam substrate; annealing the metal and the nickel, iron or cobalt foam into a porous metal-nickel, iron or cobalt catalyst, wherein the catalyst has a smooth and a porous surface; etching the smooth surface of the annealed porous metal-nickel, iron or cobalt catalyst; growing a carbonaceous layer on the porous surface of the annealed porous metal-nickel, iron or cobalt catalyst; and completely etching the porous metal-nickel, iron or cobalt catalyst to obtain the graphite layer.Board of Regents, University of Texas Syste

Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

The fuzzy symmetric solution of fuzzy matrix equation A X = B, in which A is a crisp m × m nonsingular matrix and B is an m × n fuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method

Approximate Solution of n

The approximate solution of nth-order fuzzy linear differential equations in which coefficient functions maintain the sign is investigated by the undetermined fuzzy coefficients method. The differential equations is converted to a crisp function system of linear equations according to the operations of fuzzy numbers. The fuzzy approximate solution of the fuzzy linear differential equation is obtained by solving the crisp linear equations. Some numerical examples are given to illustrate the proposed method. It is an extension of Allahviranloo's results