Controllability of the second-order differential inclusion in Banach spaces

The purpose of this paper is to study the controllability for the second-order differential inclusion in Banach spaces. We rely on a fixed point theorem for condensing maps due to Martelli. We consider the damping term x′(·) and find a control u such that the solution satisfies x(T)=x¹ and x′(T)=y¹.     

Amphiphilic Carbazole‐Containing Compounds with Lower Critical Solution Temperature Behavior for Supramolecular Self‐Assembly and Solution‐Processable Resistive Memories

The self‐organization and resistive memory performances of a series of newly synthesized water‐soluble amphiphilic carbazole derivatives have been explored. Temperature‐dependent UV/Vis absorption spectroscopy has been conducted to study the isodesmic self‐assembly mechanism of the carbazole‐containing compounds. This class of compounds also exhibits interesting lower critical solution temperature properties, which are sensitive to concentration and ionic additives. One of the compounds has been solution‐processed and utilized as an active material in the engineering of resistive memory devices, exhibiting a switching voltage of about 3.9 V, a constant ON/OFF current ratio of 10⁶, and a long retention time of 10⁴ s. The present work demonstrates the versatile potential applications of water‐soluble amphiphilic carbazole‐containing compounds in supramolecular chemistry and resistive memory devices.     

Recent progress in metal–organic framework/graphene-derived materials for energy storage and conversion: design,preparation, and application

Graphene or chemically modified graphene, because of its high specific surface area and abundant functional groups, provides an ideal template for the controllable growth of metal–organic framework (MOF) particles. The nanocomposite assembled from graphene and MOFs can effectively overcome the limitations of low stability and poor conductivity of MOFs, greatly widening their application in the field of electrochemistry. Furthermore, it can also be utilized as a versatile precursor due to the tunable structure and composition for various derivatives with sophisticated structures, showing their unique advantages and great potential in many applications, especially energy storage and conversion. Therefore, the related studies have been becoming a hot research topic and have achieved great progress. This review summarizes comprehensively the latest methods of synthesizing MOFs/graphene and their derivatives, and their application in energy storage and conversion with a detailed analysis of the structure–property relationship. Additionally, the current challenges and opportunities in this field will be discussed with an outlook also provided.

This review summarizes comprehensively the latest methods of synthesizing MOFs/graphene and their derivatives, and their application in energy storage and conversion with a detailed analysis of the structure–property relationship.     

Fixed points in {\mathcal{M}}-fuzzy metric spaces

In this paper, we give some common fixed point theorems for five mappings satisfying some conditions in -fuzzy metric spaces.     

A fast matrix–vector multiplication method for solving the radiosity equation

A “fast matrix–vector multiplication method” is proposed for iteratively solving discretizations of the radiosity equation (I — К)u = E. The method is illustrated by applying it to a discretization based on the centroid collocation method. A convergence analysis is given for this discretization, yielding a discretized linear system (I — K _n )u _n = E _n. The main contribution of the paper is the presentation of a fast method for evaluating multiplications K_n v, avoiding the need to evaluate K_n explicitly and using fewer than O(n ²) operations. A detailed numerical example concludes the paper, and it illustrates that there is a large speedup when compared to a direct approach to discretization and solution of the radiosity equation. The paper is restricted to the surface S being unoccluded, a restriction to be removed in a later paper. This revised version was published online in June 2006 with corrections to the Cover Date.     

Using group (or Loge) functions to explore the transferability of chemical bonds

The transferability of bonds in a set of small molecules has been explored. The molecular wave-functions have been calculated from the group (or loge) function method, via a construction based on Gaussian functions. The transferability is very good and the effect of lone pairs on adjacent bonds has been analysed. Furthermore, a very simple procedure has been proposed to estimate the frontiers of the bonds.     

Investigation of the dependence of Barkhausen noise on stress and the angle between the stress and magnetization directions

The dependence of Barkhausen noise amplitude on stress, and on the angle between the stress and magnetization directions, has been investigated in specimens of AISI/SAE 4340, HY-80 and ASTM A-36 steels. In all three materials it was found that the Barkhausen noise amplitude measured with the magnetic field applied at 60° to the stress axis is independent of stress. This result is compared with the theory of elasticity which indicates that under a uniaxial or a pure bending stress, the normal component of a strain in steel is zero along the direction approximately 61° from the direction of the applied stress. It was also found that the Barkhausen noise follows the same angle dependence as that of the normal strain. These findings strongly indicate that the Barkhausen noise amplitude is directly dependent on the normal strain along the direction of the magnetization and not on the shearing strain. An explanation for such a direct normal strain dependence is given based on magnetoelastic energy. Possible application of this finding to quantitative nondestructive stress measurements is also discussed.     

Copper-based nanowire materials: templated syntheses, characterizations, and applications

Well-aligned Cu(OH)2 nanoribbon and CuO nanorod arrays have been prepared on copper substrates by liquid-solid reactions. The effects of temperature, reaction time, solvent, and pH value on the morphology and composition of the products are systematically studied. Using the Cu(OH)2 nanoribbons array as a reactive and sacrificial template, we have successfully synthesized Cu2O, Cu9S8, and Cu nanoribbon/ nanowire arrays, demonstrating the versatility of the template. The extensive series of copper-based one-dimensional nanomaterials have been fully characterized by various structural, microscopic, and spectroscopic techniques. Moreover, the Cu nanowires are demonstrated to be an excellent surface-enhanced Raman scattering substrate with a sensitivity over an order of magnitude higher than that of a common roughened copper electrode.     

Effect of glycerol addition on phase inversion in horizontal dispersed oil-water pipe flows

The effect of interfacial tension on the phase inversion process during horizontal pipe flow of an oil-aqueous solution was investigated. Interfacial tension was varied by adding small amounts of glycerol in the water phase. At these glycerol concentrations the density and viscosity of the aqueous phase changed by 1% or less. Exxsol™ D140 (5.5 mPa s, 828 kg m⁻³) was used as the oil phase. The experiments were carried out in a 38 mm ID acrylic test pipe. The phase continuity and appearance of phase inversion were investigated using conductivity (wire and ring) probes and an Electrical Resistance Tomographic (ERT) system. The ERT also provided diagrams of the phase distribution in a pipe cross section. Drop size distribution was monitored using a dual impedance probe. It was found that starting from a water continuous flow with increasing oil fraction at constant mixture velocity the mixture inverted initially in the middle of the pipe (measured at 19 mm from the top pipe wall) while a higher oil fraction was required for inversion at the top (measured at 4 mm from the top pipe wall) and finally the rest of the pipe. The addition of glycerol did not affect the phase fraction where the initial inversion occurred but caused an increase in the oil fraction needed to complete the inversion. The drop size measurements were used to explain this behaviour. Pressure drop was found to decrease with increasing oil fraction but this trend reversed when inversion spread to the pipe wall and the oil continuous phase came in contact with it.