Shockwave Visualization Using Holographic Interferometer

High-speed holographic interferometry was employed to visualize and record Shockwave phenomena. We performed three kinds of holographic interferometry for visualization and recording of the propagation of a Shockwave: a real-time holographic interferometer with a high-speed framing camera, a real-time holographic interferometer with a high-speed streak camera and a double-pulse laser holographic interferometer with a dual-reference-beam module. The experimental results were compared and their advantages and disadvantages are discussed. The experimental results clearly show the high-speed Shockwave propagation and give the feasibility of quantitative interpretation of high-speed gas-dynamics.     

Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation

Using the fixed point method, we prove the generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation.     

Nearly (k, s)-Fibonacci functional equations in β-normed spaces

In this paper, we solve the (k, s)-Fibonacci functional equation $$f_{k,s}(x)=kf_{k,s}(x-1)+sf_{k,s}(x-2).$$ Moreover, we prove the Hyers–Ulam stability of the (k, s)-Fibonacci functional equation in β-normed spaces.     

稀土氧化物修饰的富勒烯-二氧化钛复合材料光催化降解亚甲基蓝(英文)

Rare earth oxide-treated fullerene and titania composites (Y-fullerene/TiO2) were prepared by the sol-gel method. The products had interesting surface compositions. X-ray diffraction patterns of the composites showed that the Y-fullerene/TiO2 composites contained a single and clear anatase phase. The surface properties were observed by scanning electron microscopy, which gave a characterization of the texture on the Y-fullerene/TiO2 composites and showed a homogenous distribution of titanium particles. The ...     

Regioselective Bridging Calix[6]arenes: Synthesis and X-ray Structure of Trisbridged Calix[6]arene

The preparation and characterization of gold nanoparticles (～6 nm in diameter) modified with mono-6-thio-β-cyclodextrin (II) is described. The resulting monolayer-protected gold nanoparticles are water-soluble and more stable. The concentration of II plays a crucial role for the distribution of the modified nanoparticles. When the ratio of concentration of II to HAuCl₄,[II]/[HAuCl₄] ≥ 0.93, a stable gold nanoparticle with uniform distribution and diameter of 6.0 ± 0.9 nm will be obtained. The recognition of modified gold nanoparticles to organic guest molecule is researched. The modified gold nanoparticles can make the electrochemical reduction current of nitrobenzene decrease and can be self-assembled in three-dimensional to form spherical clusters with ligand of methylene green.     

Fixed point method for set-valued functional equations

In this paper, we introduce a set-valued cubic functional equation and a set-valued quartic functional equation and prove the Hyers-Ulam stability of the set-valued cubic functional equation and the set-valued quartic functional equation by using the fixed point method.     

The Caputo–Fabrizio time-fractional Sharma–Tasso–Olver–Burgers equation and its valid approximations

Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma–Tasso–Olver–Burgers (STOB) equation in the Caputo–Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for $\varphi \left(x,t;u\right)$ as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.     

Iterative Deconvolution Algorithm for Improving Range Resolution of a CO2-Laser Based Lidar System

An iterative deconvolution algorithm for improving range resolution of long-pulse lidars is proposed, and can be applied to the lidar data obtained with the typical pulse of a CO₂-laser which consists of a gain-switching peak and a long tail. The lidar signal itself with certain temporal shift is set to be the start profile for the unknown maximally resolved profile in the proposed technique, and then is corrected in proportion to the difference between the lidar return calculated with the assumption and the real one. The same process is repeated until the correction is smaller than tolerance. Simulations are made to test the performance of the proposed algorithm. We investigate the errors in the vicinity of data boundary in the retrieved profile when a part of lidar data is absent. The sensitivity of the iteration algorithm to noise in the lidar signals and the laser pulse profile is also numerically determined.     

Functional inequalities in non-Archimedean normed spaces

In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers–Ulam stability of the functional inequalities in non-Archimedean Banach spaces.