An extension of Krasnoselskii’s fixed point theorem and its application to nonlocal problems for implicit fractional differential systems with uncertainty

The traditional Krasnoselskii’s fixed point theorem in Banach spaces does not reproduce the rich and varied forms of operator equations in abstract spaces which are not linear structure. Consequently, its applications to integral equations and differential equations have met many obstacles. The present alternative Krasnoselskii’s fixed point theorem in generalized semilinear Banach spaces overcomes this deficiency and opens up for profitable investigation such as differential systems with uncertainty. An application to the existence of solutions of nonlocal problems for fuzzy implicit fractional differential systems under Caputo generalized Hukuhara differentiability with demonstrated example is given to validate the effectiveness of our theoretical results.     

Investigation of elastic moduli and constants of zinc-blende Al<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>Ga<Subscript>1-<Emphasis Type="Italic">y</Emphasis></Subscript>As alloy by statistical moment method

The elastic moduli and elastic constants of the ternary semiconductor alloy Al _y Ga_1-yAs at finite temperature have been investigated using the statistical moment method. The Young, shear, bulk moduli and elastic constants C₁₁, C₁₂, C₄₄ of the zinc-blende Al _y Ga_1?yAs crystal are calculated as functions of Al composition and temperature. Numerical calculations have been performed and compared with those of the experimental and other theoretical results showing the reasonable agreements. Our study shows that elastic moduli and C₁₁, C₁₂ constants of zinc-blende Al _y Ga_1?yAs alloy are decreasing functions of the temperature and Al composition; C₄₄ constant is a decreasing function of the Al composition.     

Effects of an absorptive coating on the dynamics of underwater laser-induced shock process

The effects of an absorptive coating on the dynamics of underwater laser-induced shock process have been observed from the end of laser pulse to hundreds of microseconds after irradiation by time-resolved imaging techniques. A laser pulse of 13 ns at 1,064 nm was focused by a 40-mm focal length lens onto the surface of epoxy-resin blocks immersed in water to induce the shock process in the confining regime. A custom-designed time-resolved photoelasticity imaging technique and a high-speed laser stroboscopic videography technique in photoelasticity mode were used to analyze the evolution of shock waves in the water phase, the strength of stress waves in the solid phase, the oscillation of cavitation bubbles, and the generation of bubble-collapse-induced shock waves. We showed that black paint coating enhances the strength of laser-induced stress wave inside the solid, drives faster shock waves traveling in the water phase, and produces higher-energy cavitation bubbles. We propose that even at power densities of 1 GW/cm² and above, an absorptive coating can intensify the shock process by enhancing the absorption of laser energy by plasma.     

Carbon nanohorns-coated microfibers for use as free-standing electrodes for electrochemical power sources

We report the first direct laser based synthesis of carbon nanohorns onto carbon microfibrous, for the straightforward fabrication, of free-standing (binderless) electrodes. These carbon nanohorns have diameters as small as 2–4 nm and were found to cover uniformly the microfibrous substrates. The carbon nanohorns-based electrodes developed here are shown to open new prospects for the development of advanced electrochemical power sources. In particular, their possible applications in either lithium-ion batteries or supercapacitors or fuel cell technologies are demonstrated.     

A Unified Monotonic Approach to Generalized Linear Fractional Programming

We present an efficient unified method for solving a wide class of generalized linear fractional programming problems. This class includes such problems as: optimizing (minimizing or maximizing) a pointwise maximum or pointwise minimum of a finite number of ratios of linear functions, optimizing a sum or product of such ratios, etc. – over a polytope. Our approach is based on the recently developed theory of monotonic optimization.     

New cytotoxic cucurbitacins from the pericarps of Trichosanthes tricuspidata fruits

An extract of the fruits of Trichosanthes tricuspidata collected in North Vietnam was found cytotoxic in KB cells. A bioassay-guided fractionation led to the isolation of a series of cucurbitacins of which two are new: tricuspidatin and 2-O-glucocucurbitacin J. Their isolation and structure determination are described.     

Dugundji’s theorem for cone metric spaces

In this work, we will prove the Dugundji extension theorem for the cone metric space. It is heavily reliant on the paracompactness of the cone topology that is proved by Ayse Sönmez in the paper Sönmez (2010) [11].