Degenerate polynomial patches of degree 11 for almostGC 2 interpolation over triangles

We consider the problem of interpolating scattered data in ³ by analmost geometrically smoothGC ² surface, where almostGC ² meansGC ² except in a finite number of points (the vertices), where the surface isGC ¹. A local method is proposed, based on employing so-called degenerate triangular Bernstein-Bézier patches. We give an analysis of quintic patches forGC ¹ and patches of degree eleven for almostGC ² interpolation.     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

The regioselectivity of the formation of 2-pyrazolylthiazoles and their precursors from the reaction of 2-hydrazinothiazoles with 4,4,4-trifluoro-1-hetaryl-1,3-butanediones

Reaction of 2-hydrazinothiazoles 1 with 1-thienyl- and 1-furyl-1,3-butanediones 2a,b in methanol in the presence of hydrochloric acid mainly leads to a mixture of pyrazoles 3 and pyrazolines 4 or pyrazoles 3 and 5 in strong acidic conditions. Isomeric hydrazones 6 and pyrazolines 4 were formed and isolated in these reactions in the absence of hydrochloric acid. It has been shown that the regioselectivity in the reaction of diketones 2 with hydrazine 1 is governed by both the concentration of acid and the nature of substituents in the 1,3-diketones 2. Cyclization of hydrazones 6 is shown to occur under milder conditions than dehydration for pyrazolines 4. The new heterocyclic compounds were prepared and fully characterized by NMR spectra and by X-ray analysis for 3c.     

Molecular structure and spectral properties of thionaphthalimides

The molecular structure and absorption spectra of monothio- and dithio-naphthalimides were compared to their naphthalimide analogues using AM1, PM3 and ZINDO/S semiempirical quantum chemical methods. The substitution of the 4R-naphthalimide oxygen atoms by sulphur atoms resulted in a red-shift of the absorption spectra by Δλ_max60-65 and 100-140 nm, respectively. The thionated naphthalimide derivatives do not show observable fluorescence due to intersystem crossing to the triplet -states localised at the CS groups. The -absorption bands of monothioimides are located at 525-580 nm (ε=60-80) and those for dithioimides at 535-560 nm (ε=140-390) and 628-686 nm (ε=34-68). None of these transitions are solvent sensitive. The -transitions of N-phenylthioimides have also a small contribution from -states due to a partial conjugation between CS group and π-electronic system of the N-phenyl ring. As a result, the bands of aromatic substituted N-phenylthioimides are red-shifted as compared to those of the aliphatic N-methyl-thioimides.     

Use of Local Lagrange Interpolation for calculation of retention indices in linear temperature-programmed gas chromatrography

Summary The influence of the isothermal temperature, program rate, initial temperature and flow rate on retention indices was studied. The methods of Kováts, Van Den Dool and Local Lagrange Interpolation are compared. Ten experimental measurements were carried out on a capillary column coated with OV-101 stationary phase.     

Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation

Consider a kind of Hermit interpolation for scattered data of 3D by trivariate polynomial natural spline,such that the objective energy functional (with natural boundary conditions) is minimal.By the s...     

On the signal degradation induced by the interpolation and the sampling rate reduction in aeroacoustics hybrid methods

Taking place within more extensive work that focuses on hybrid methods in aeroacoustics, the present study is devoted to the data transfer operations that are to be performed between two stages of a hybrid calculation. More precisely, the article focuses on two typical operations that usually accompany such data transfer, which are (i) the sampling rate reduction and (ii) the interpolation of the unsteady perturbations to be transmitted from one stage to the other. First part of the paper analyzes the two main issues of such operations, which are the spuriousing and the aliasing phenomena. For doing so, the usual notions of the interpolation theory are revisited before they are synthesized within an original approach. The here proposed formalism allows to understand better both the spuriousing and the aliasing phenomena, as well as to accurately predict the impact of the latter on the data to be transmitted in terms of signal degradation. Second part of the paper provides an illustration and a validation of these theoretical developments via a direct application to a typical aerodynamic noise problem (aeroacoustic emission by a 2D cylinder cross flow). There, it is further shown how the here proposed formalism can help in improving aeroacoustics hybrid calculations by predicting (and thus possibly minimizing) the bias to be induced on the acoustic extrapolation stage because of the aliasing and/or spuriousing effects inherited from the sampling rate reduction and/or interpolation of CFD data—which is likely to occur in any hybrid scenario. Copyright © 2012 John Wiley & Sons, Ltd.     

“多角度欣赏面心立方晶胞”教学设计*

尝试利用“火花学院”App等在线交互资源,引导学生从立体几何及密置层堆积模型视角,观察、描述、绘制面心立方晶胞的正四面体填隙、正八面体填隙、三视图和沿体对角线投影图像,加深学生对以面心立方晶胞结构为基础的CaF₂→金刚石晶胞、NaCl→钙钛矿晶胞结构的理解;再结合新型材料透明镁铝尖晶石晶体结构的探讨,了解晶体制备中的掺杂改性等常用方法,发展学生的微观探析能力和科学创新意识。     

Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element.