Error expansions for multidimensional trapezoidal rules with Sidi transformations

In 1993, Sidi introduced a set of trigonometric transformations x = ψ(t) that improve the effectiveness of the one-dimensional trapezoidal quadrature rule for a finite interval. In this paper, we extend Sidi's approach to product multidimensional quadrature over [0,1] ^N . We establish the Euler–Maclaurin expansion for this rule, both in the case of a regular integrand function f(x) and in the cases when f(x) has homogeneous singularities confined to vertices. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of the reaction of OH radicals with t-amyl methyl ether revisited

The kinetics of the reaction of OH radicals with t-amyl methyl ether (TAME) have been reinvestigated using both absolute (flash photolysis resonance fluorescence) and relative rate techniques. Relative rate experiments were conducted at 295 K in 99 kPa (740 torr) of synthetic air using ethyl t-butyl ether, cyclohexane, and di-isopropyl ether as reference compounds. Absolute rate experiments were performed over the temperature range 240–400 K at a total pressure of 4.7 kPa (35 torr) of argon. Rate constant determinations from both techniques are in good agreement and can be represented by k₁=(6.32 ± 0.72) × 10^?12 exp[(?40 ± 70)/T] cm³ molecule^?1 s^?1. Quoted errors represent 2σ from the least squares analysis and do not include any estimate of systematic errors. We show that results from the previous kinetic study of reaction (1) are in error due to the presence of a reactive impurity. Results are discussed in terms of the atmospheric chemistry of TAME. © 1993 John Wiley & Sons, Inc.     

Preconditioners for Ill-Conditioned Toeplitz Matrices

This paper is concerned with the solution of systems of linear equations A _N x = b, where denotes a sequence of positive definite Hermitian ill-conditioned Toeplitz matrices arising from a (real-valued) nonnegative generating function f C ₂ with zeros. We construct positive definite Hermitian preconditioners M _N such that the eigenvalues of M _N ^–1 A _N are clustered at 1 and the corresponding PCG-method requires only O(N log N) arithmetical operations to achieve a prescribed precision. We sketch how our preconditioning technique can be extended to symmetric Toeplitz systems, doubly symmetric block Toeplitz systems with Toeplitz blocks and non-Hermitian Toeplitz systems. Numerical tests confirm the theoretical expectations.     

Synthesis of 3,4-bis-Acetoxymethyl-Furan

There are available in the literature^1–3 a very limited number of useful routes for the preparation of 3,4-bis-acetoxymethyl-furan in general purpose manufacturing plant because they are either too long and/or they use specialized reagents or techniques. Our attempts to provide a solution to this problem have provided a simple short practical route to the title compound which may have more general application in the synthesis of furans. Additionally both starting materials and reagents are cheap and readily available.     

Inclusion of thiazyl radicals in porous crystalline materials

The incorporation of benzodithiazolyl (BDTA) and methylbenzodithiazolyl (MBDTA) radicals into porous hybrid frameworks via gas phase diffusion revealed that inclusion appeared selective for the MIL53(Al) framework against a range of other potential hosts. Both PXRD and EPR studies are consistent with retention of a π*-π* dimer motif for BDTA in MIL53(Al)@BDTA whereas MBDTA in MIL53(Al)@MBDTA appears to be monomeric. The guests are readily released by the addition of solvent (CH(2)Cl(2)).     

THE PHOTOADDITION OF NUCLEOPHILES TO URACIL

Abstract— Quantum yields for 254 nm ultraviolet photoaddition of the nucleophiles hydrazine, HCN, HSO₃^-, methyl amine, and BH₄^- to uracil have been measured; the quantum yields for hydrazine, HCN, and HSO₃^- additions are pH-dependent. The nucleophiles sulfide, azide, chloride, bromide, iodide, nitrite and thiocyanate failed to photo–add under similar conditions. These reactions are interpreted as 1,4-additions to the conjugated enone system of the anti-aromatic compound, uracil; as suggested by S. Y. Wang (Wang and Nnadi, 1968). The nuclear magnetic resonance (NMR) spectrum of the photohydrate of uracil-5-d-showed that the proton was added to the 5-position in a stereochemically random manner. The photoaddition of HSO₃^- takes place at much lower concentrations than required for the thermal addition of this anion and is also stereochemically random.     

Mesoionic compounds—XIX: Mass spectral fragmentation patterns for some five-membered systems containing oxygen,nitrogen and sulfur

Mesoionic compounds of the s-triazole, 1,3,4-oxadiazole, 1,3,4-thiadiazole, 1,2,3-thiadiazole, 1,3-thiazole and 1,3-dithiole systems all underwent deep-seated decomposition on electron-impact to small stable ions, determined to a large extent by the nature of the peripheral heteroatoms and the exocyclic substituent. In some instances fragmentation most probably involved an open-chain isomer of the cyclic system.     

连续波锁模P_r~（3＋）：YLF激光器

本文报导了采用氩离子激光器来泵浦Ｒｒ￣（３＋）：ＹＬＦ晶体，应用声光调制器实现了主动锁模；同时应用振动─高反射平面镜也实现了被动锁模，两种锁模均得到了ｐｓ光脉冲。据作者了解这是这种晶体材料的第一次锁模运转。