关于负超几何分布期望与方差算法的注记

研究了非还原取样模型中负超几何随机变量的联合分布,得到了若干有用的推论.据此给出了负超几何分布的期望和方差的一种分解算法.     

Characteristic behaviour of plasma fluctuations inside a plasma bubble in presence of a magnetic field due to the formation of a potential well

Experiments were carried out to observe the effect of a magnetic field and grid biasing voltage in presence of a plasma bubble in a magnetized, filamentary discharge plasma system. A spherical mesh grid of 80% optical transparency was negatively biased and introduced into the plasma for creating a plasma bubble. Diagnostics via an electrical Langmuir probe and a hot emissive probe were extensively used for scanning the plasma bubble. Plasma floating potential fluctuations were measured at three different positions of the plasma bubble. The instability in the pattern showed the dynamic transition from periodic to chaotic for increasing magnetic fields. Time scale analysis using continuous wavelet transform was carried out to identify the presence of non‐linearity from the contour plots. The mechanisms of the low‐frequency instabilities along with the transition to chaos could be qualitatively explained. Non‐linear techniques such as fast Fourier transform, phase space plot, and recurrence plot were used to explore the dynamics of the system appearing during plasma fluctuations. In order to demonstrate the observed chaotic phenomena in this study, characteristics of chaos such as the Lyapunov exponent were obtained from experimental time series data. The experimentally observed potential structure is confirmed with numerical analysis based on fluid hydrodynamics.     

Spherical hollow mesoporous silica supported phosphotungstic acid as a promising catalyst for α-arylstyrenes synthesis via Friedel-Crafts alkenylation

This work presents a scalable approach for preparing spherical hollow mesoporous silica with high surface area/pore volume, serving as outstanding support for supported phosphotungstic acid catalyst with much superior catalytic performance to the one on previously reported spherical mesoporous silica toward diverse transformations, ascribed to the strengthened mass transfer and the enlarged exposure degree of acidic sites to reactants those resulting from unique hollow and mesoporous morphology.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Effect of rotation in magneto-thermoelastic transversely isotropic hollow cylinder with three-phase-lag model

This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted.     

The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.     

A Shell-by-Shell Approach for Synthesis of Mesoporous Multi-Shelled Hollow MOFs for Catalytic Applications

Over the past two decades, advanced materials with hollow interiors have received significant attention in materials research owing to their great application potential across a vast number of technological fields. Though with great difficulty, multi-shelled hollow metal–organic frameworks (MSHMs) have also been successfully synthesized in recent years. Herein, a rational shell-by-shell soft-templating protocol has been devised to fabricate highly uniform multi-shelled hollow cobalt-imidazole-based MOF (ZIF-67). For the first time, it has become possible to endow mesoporosity to this new type of functional material (i.e., mesoporous MOFs). When used as carrier materials in catalytic reactions, in principle, these mesoporous MSHMs with high surface area not only improve the dispersity of metal nanoparticles (NPs), but also efficiently facilitate the mass diffusion of the reactions, resulting in enhanced catalyst activity. Moreover, the obtained MSHMs/M nanocomposites serve as base-metal bifunctional catalysts for one-pot oxidation-Knoevenagel condensation cascade reaction, in which the MSHMs itself serves as a pristine active catalyst in addition to its role of catalyst support. The results demonstrate that excellent multifunctional catalysts can be achieved via preparing intrinsically microporous bulk MOFs into extrinsically mesoporous MSHMs which possess many structural merits that conventional bulk MOFs do not have.     

Smart Soft‐Templating Synthesis of Hollow Mesoporous Bioactive Glass Spheres

Hollow bioactive glass spheres with mesoporous shells were prepared by using dual soft templates, a diblock co‐polymer poly(styrene‐b‐acrylic acid) (PS‐b‐PAA) and a cationic surfactant cetyltrimethylammonium bromide (CTAB). Hollow mesoporous bioactive glass (HMBG) spheres comprise the large hollow interior with vertical mesochannels in shell, which realize large uptake of drugs and their sustained release. The formation of hydroxyapatite layer on the surface of HMBG particles shows the clear evidence for promising application in bone regeneration.     

托卡马克真空室内线圈水冷管道接头强化二次流的数值研究

基于计算流体力学(CFD)理论，研究了不同曲率半径的螺旋导流片的托卡马克真空室内线圈水冷管道接头。利用湍流数值模拟方法，分析了线圈管道接头导流片曲率半径比、冷却水入口流速对线圈管道内流体平均雷诺数分布的影响。结果表明，不同导流片曲率半径比的线圈管道内的流体雷诺数分布曲线相似，平均雷诺数随入口流速的增加而增大，管道接头出口雷诺数随导流片曲率半径比的增大而减小，导流片曲率半径比小的管接头更适用于线圈水冷曲线管的二次流强化。此外，还为导流片曲率半径比为0.2的管接头拟合了管接头出口雷诺数与入口流速的关系式，为进一步研究类似于托卡马克真空室内线圈管道的曲线管接头的二次流强化提供理论基础。