Numerical solution of reaction–diffusion equations by compact operators and modified equation methods

A system of reaction–diffusion equations which governs the propagation of an ozone decomposition laminar flame in Lagrangian co-ordinates is analysed by means of compact operators and modified equation methods. It is shown that the use of fourth-order accurate compact operators yields very accurate solutions if sufficient numbers of grid points are located at the flame front, where very steep gradients of temperature and species concentrations exist. Modified equation methods are shown to impose a restriction on the time step under certain conditions. The solutions obtained by means of compact operators and modified equation methods are compared with solutions obtained by other methods; good agreement is obtained.     

Dual-purpose gas chromatographic injection device for pressurized liquid and gas injection

A dual-purpose gas chromatographic injection device, capable of injecting pressurized liquid sample of up to 5000 psig and gas sample with a volume as high as 5000 μL, has been successfully developed and implemented. The injection device is synergized by the effectiveness of a classical flash vaporization of a syringe injection and the reliability of a proven rotary valve. Depending on the matrix involved, this injection device employs either a commercially available four-port internal valve for liquid sampling or a six-port external valve for gas sampling, a modified removable needle used in standard liquid syringe, and an auxiliary flow stream that can be either mechanical or electronic flow controlled for solute transfer. For pressurized liquid, the device was found suitable of up to nC₁₆ hydrocarbon with no observable carry-over despite the injection device was operating at ambient temperature. A relative standard deviation of less than 2% (n = 20) was obtained for hydrocarbon compounds ranging from nC₈ to nC₁₆. For gas injection, the device performed well even under difficult chromatographic conditions such as with a low column inlet pressure of less than 1 psig. A relative standard deviation of less than 0.5% (n = 10) was obtained for reactive sulfur compounds such as alkyl mercaptans. The device can be operated manually or automated with pneumatic or electrical actuator, is platform neutral, and can be moved amongst instruments without hardware modification as well as implemented for on-line or in situ applications. In this paper, the utility of the device was also demonstrated with selected GC applications of industrial significance.     

非线性双曲型积分微分方程有限元逼近的误差分析

考虑非线性双曲型积分微分方程半离散有限元格式，得到H^1超收敛和最优阶L^∞和W^1,∞模误差估计，结果丰富了有限元方法的理论。     

Randomized approximation of Sobolev embeddings, III

We continue the study of randomized approximation of embeddings between Sobolev spaces on the basis of function values. The source space is a Sobolev space with nonnegative smoothness order; the target space has negative smoothness order. The optimal order of approximation (in some cases only up to logarithmic factors) is determined. Extensions to Besov and Bessel potential spaces are given and a problem recently posed by Novak and Woźniakowski is partially solved. The results are applied to the complexity analysis of weak solution of elliptic PDE.     

Grab vs. composite sampling of particulate materials with significant spatial heterogeneity—A simulation study of “correct sampling errors”

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.     

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana’s (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to J, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.      

非负整数格上元素的性质及其在刻画@-Fuzzy关系方程解集中的作用

首先讨论了非负整数格上元素的性质. 从而完全地刻画了非负整数格上@-Fuzzy关系方程(其中@表示inf-α合成)的解集.     

Stability of localized operators

Let ?p, 1?p?∞, be the space of all p-summable sequences and Ca be the convolution operator associated with a summable sequence a. It is known that the ?p-stability of the convolution operator Ca for different 1?p?∞ are equivalent to each other, i.e., if Ca has ?p-stability for some 1?p?∞ then Ca has ?q-stability for all 1?q?∞. In the study of spline approximation, wavelet analysis, time-frequency analysis, and sampling, there are many localized operators of non-convolution type whose stability is one of the basic assumptions. In this paper, we consider the stability of those localized operators including infinite matrices in the Sjöstrand class, synthesis operators with generating functions enveloped by shifts of a function in the Wiener amalgam space, and integral operators with kernels having certain regularity and decay at infinity. We show that the ?p-stability (or Lp-stability) of those three classes of localized operators are equivalent to each other, and we also prove that the left inverse of those localized operators are well localized.     

沿海软粘土取土质量的对比分析

本文在简要介绍固定活塞式薄壁取土器取土技术基础上，详尽分析了在连云港、赤湾港和广深路所进行的软粘土取土技术对比试验结果。试验结果表明，土样扰动对于室内所测定的力学性指标影响极大，但对物理性指标影响不大。研究结果还有力地证明，只要操作正确，采用薄壁取土器能取得高质量土样，而采用敞口式厚壁取土器取出的土样扰动较大。     

SRK equation of state: Predicting binary interaction parameters of hydrocarbons and related compounds

The parameter mixing rules of the Soave–Redlich–Kwong (SRK) equation of state are rewritten as Huron–Vidal mixing rules, where infinite-pressure activity coefficients are predicted by group contributions. Alkanes are treated as composed by one group type and aromatics by two types, aliphatic and aromatic. Hydrocarbon mixtures can be treated using one universal interaction parameter. Light compounds like methane, N₂, CO₂, H₂S, etc. are treated as separate groups; each one requires a pair of parameters for its interactions with aliphatic and aromatic groups. Group interaction parameters were determined from experimental VLE data. From them, binary interaction constants of the classical quadratic mixing rules can directly be derived.