Invertibility of a linear combination of two matrices and partial orderings

In this paper, we present some results relating different matrix partial orderings and the invertibility of a linear combination of EP matrices.     

3D Organic–Inorganic Perovskite Ferroelastic Materials with Two Ferroelastic Phases: [Et3P(CH2)2F][Mn(dca)3] and [Et3P(CH2)2Cl][Mn(dca)3]

Organic–inorganic hybrid perovskite-type multiferroics have attracted considerable research interest owing to their fundamental scientific significance and promising technological applications in sensors and multiple-state memories. The recent achievements with divalent metal dicyanamide compounds revealed such malleable frameworks as a unique platform for developing novel functional materials. Herein, two 3D organic–inorganic hybrid perovskites [Et₃P(CH₂)₂F][Mn(dca)₃] ( 1 ) and [Et₃P(CH₂)₂Cl][Mn(dca)₃] ( 2 ) (dca=dicyanamide, N(CN)₂⁻) are presented. Accompanying the sequential phase transitions, they display a broad range of intriguing physical properties, including above room temperature ferroelastic behavior, switchable dielectricity, and low-temperature antiferromagnetic ordering (T_c=2.4 K for both 1 and 2 ). It is also worth noting that the spontaneous strain value of 1 is far beyond that of 2 in the first ferroelastic phase, as a result of the precise halogen substitution. From the point view of molecular design, this work should inspire further exploration of multifunctional molecular materials with desirable properties.     

Almost Fuzzy Compactness in L-fuzzy Top ological Spaces

In this paper, the notion of almost fuzzy compactness is defined in L-fuzzy topological spaces by means of inequality, where L is a completely distributive DeMorgan algebra. Its properties are discusse...     

Thermodynamic aspects of carbon redistribution during ageing and tempering of Fe–Ni–C alloys

Carbon redistribution is known to occur during martensite ageing. The two associated processes most discussed in the literature are spinodal decomposition and carbon segregation to defects. In order to elucidate the topic, the ageing and tempering of two Fe–Ni–C alloys have been characterised by means of atom probe tomography and synchrotron radiation diffraction. Upon ageing at room temperature, carbon redistribution is clearly observed, where the process of carbon segregation to defects appears to be most likely to occur. Nevertheless, the possibility of spinodal decomposition is not entirely discarded, and the current work presents a series of discussion points that challenge our current understanding of the thermodynamic of ferrite in steels.     

Characterizing and Generating Bivariate Empirical Rank Distributions Satisfying Certain Positive Dependence Concepts

Abstract

This article introduces an approach for characterizing the classes of empirical distributions that satisfy certain positive dependence notions. Mathematically, this can be expressed as studying certain subsets of the class S_N of permutations of 1, …, N, where each subset corresponds to some positive dependence notions. Explicit techniques for it-eratively characterizing subsets of S_N that satisfy certain positive dependence concepts are obtained and various counting formulas are given. Based on these techniques, graph-theoretic methods are used to introduce new and more efficient algorithms for constructively generating and enumerating the elements of various of these subsets of S_N. For example, the class of positively quadrant dependent permutations in S_N is characterized in this fashion.     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.     

Synthesis and Liquid Crystalline Behavior of Random Copolymer of Poly(ethylene oxide) Macromonomer and Liquid Crystalline Monomer by the Photon Transmission Technique

Random copolymers of poly(ethylene oxide) macromonomer with p‐vinylbenzyl end‐functional group (PEOVB) and liquid crystalline monomer, namely 6‐(4‐cyanobiphenyl‐4′‐oxy)hexyl acrylate (COA), were prepared by conventional free radical polymerization. A living anionic polymerization technique was employed for the synthesis of PEO macromonomers bearing p‐vinylbenzyl moiety at one end. The photon transmission method was also applied to study the phase transitions of COA monomer and its random copolymer with PEO. It was found that, for both samples, the nematic‐smectic A transition is continuous, but the critical fluctuation regions do not allow to obtain 3D XY values. Instead, we have obtained the values close to mean field regime. Scaling of thermal hystersis for random copolymer sample near the nematic‐isotropic transition was studied as well. Thermal hysteresis loops were produced under linearly varying temperature. It was shown that the areas of the hysteresis loops scale with the temperature scanning rate with an exponent being equal to 0.614 which is in good agreement with the field‐theoretical value.     

Flow-induced ordering of particles and flow velocity profile transition in a tube flow of graphene oxide dispersions

We measured the S- and P-order parameters of flow-induced ordered graphene oxide (GO) particles and the flow velocity profiles for a flowing aqueous GO dispersion in a tube, by using an optical method. The order parameters clearly exhibit increasing concentric biaxial ordering as the flow velocity increases, with the exception of a disordered centre. Newtonian to non-Newtonian transition in the flow velocity profile is found, changing from a parabolic shape to a fuller shape at very low Reynolds numbers less than 10. This is attributed to the shear thinning effect (i.e., an ordering-induced reduction in viscosity). In the Newtonian flow, a uniaxial ordering was dominant; whereas a biaxial ordering sharply increased in the non-Newtonian flow, indicating that both the ordering of GO particles and the interparticle interactions influence the flow profile transition.