Further Revelations on L.S.D.

In a recent paper the author showed that the distribution ofleading significant digits, l.s.d., resulting from successivemultiplications is logarithmic. In this paper these resultsare extended by establishing, still without any assumptionsof invariance to scaling, that this distribution remains invariantunder all further arithmetic operations—both multiplicativeand additive. The fact that 30% of decimal numbers have l.s.d.1 persists.     

SPECTROSCOPIC INVESTIGATION OF DIHYDRONICOTINAMIDES-I: CONFORMATION, ABSORPTION, AND FLUORESCENCE

Abstract— The 1(N)-(2,6-dichlorobenzyl)-1,4-dihydronicotinamide (I), N-methyl- and N,N-dimethyl-1(N)-(2,6-dichlorobenzyl)-1,4-dihydronicotinamide (II and III), respectively), and 1(N)-(2,6-dichloro-benzyl)-2-aminomethyl-1,4-dihydronicotinic acid lactame (IV) were synthesized as model compounds for natural coenzymes, and systematically studied by 1H NMR, UV/V1S absorption and fluorescence spectroscopy. The absorption at ∼ 340 nm argues for an effective conjugation between dihydropyridine and carboxamide π-system, and rules out any severely twisted conformation. For the natural coenzymes NADH and NMNH, as well as for I and II (with no or only one N-amide substituent), 1H NMR definitively establishes a transoid conformation in solution, with the carbonyl O close to 2-H of the dihydropyridine ring. N,N-dimethyl substitution effectively inverts the carboxamide orientation into the cisoid form. The 1H NMR data (as well as molar extinctions) for the fused-ring derivatives IV and V, with a fixed cisoid and transoid structure, respectively, provide final proof for the conformational assignment.
Absorption maxima are shifted to lower energies with increasing solvent polarity. In solvents which can act as hydrogen bond acceptors to the carboxamide N-H, absorption shows a general blue-shift of ∼ 10 nm. H-bond donor solvents do not affect absorption maxima but enhance molar extinction. Fluorescence maxima show a similar dependence on solvent polarity but no specific hydrogen-bonding effect. Fluorescence quantum yields appear increased tenfold in solvents donating H-bonds to the carboxamide C=O group. These results are interpreted in terms of the vinylogous amide resonance between C=O function and ring-N lone pair being the electronic interaction dominating in the ground state of dihydronicotinamides.     

Error estimates for generalized compound quadrature formulas

We define quadrature formulas for integrals with weight functionsby applying a given approximation method locally. This allowsthe generalisation of different quadrature formulas, e.g., thecompound Newton-Cotes formulas, Gauss summation formulas, orGregory's formulas, to the case of weighted integrals, as wellas to construct new quadrature formulas, and to derive errorestimates for all these quadrature formulas. The estimates consideredhere are mainly of the form |R[f]|c||f^(r)||, provided the underlyingapproximation method is exact for polynomials of degree <r(R[f] is the quadrature error). Explicit, asymptotically sharperror estimates are obtained for arbitrary integrable weightfunctions. Further, estimates are obtained for the case thatthe quadrature error is of higher order than the approximationerror.     

PHOTOPRODUCTS OF BROMOURACIL-LABELED DNA AND THE STRUCTURE OF 5-BROMODEOXYURIDYLYL-(3' → 5')-THYMIDINE PHOTOPRODUCT

Abstract— –An attempt was made to identify some of the ultraviolet (u.v.) photoproducts of 5-bromouracil-labeled DNA (BrU-DNA). Two synthetic dinucleotides, 5-bromodeoxyuridylyl-(3' →5 ')-thymidine (BrdUpT) and 5-bromodeoxyuridylyl-(3' → 5')-deoxycytidine (BrdUpdC), were prepared. Each gave a single u.v. photoproduct which in turn gave a single acid hydrolysis product. 2-¹⁴C-BrU-DNA. prepared from E. coli B3, was irradiated (275–280 nm), hydrolyzed, and paper chromatographed in four systems. Comparison with the two synthetic photoproducts showed that if present at all, BrdUpT and BrdUpdC photoproducts could account for no more than 10 and 3.5 per cent respectively of the total photoproducts. At 55 per cent conversion of BrU into photoproducts, the major ¹⁴C-photoproduct was uracil (78 per cent); the remaining 22 per cent was made up of at least six products, three of which were reversed by 232 nm irradiation.
The debrominated cyclobutane structure proposed by Haug for BrdUpT photoproduct has been shown to be incorrect. It was found to contain one atom of bromine per molecule. On the basis of nuclear magnetic resonance and u.v. spectra, two possible structures are proposed for the photoproduct, each containing an eight-membered ring.     

PLANNING MARINE PROTECTED AREAS: A MULTIPLE USE GAME

Abstract The EU Marine Strategy Directive (MSD) has a regional focus in its implementation. The directive obliges countries to take multiple uses and the marine strategies of neighboring countries into account when formulating marine strategies and when designating marine protected areas (MPAs). We use game theoretical analysis both to find the optimal size of MPAs with multiple uses by multiple countries and to investigate the influences of multiple uses on cooperation. To this end, we develop a model in which two specific uses, fisheries and nature conservation, by multiple countries are considered in a strategic framework. The results of the paper suggest that EU marine policy such as the MSD and the coming Maritime Policy may help to secure the highest possible benefits from these MPAs if these policies induce cooperation among countries, but only if policies force countries to consider all possible benefits of MPAs. In fact cooperation on a single issue may give a worse outcome than the noncooperative equilibrium. The results also indicate that cooperation may be hard to achieve because of defector incentives, and therefore policy measures should be strict in enforcing cooperation on all possible uses of MPAs.     

ROBUST NUMERICAL METHODS FOR TRANSONIC FLOWS

In this paper, numerical methods for solving the transonic full potential equation are developed. The governing equation is discretized by a flux-biasing finite volume method. The resulting non-linear algebraic system is solved by using a continuation method with full Newton iteration. The continuation method is based on solving a highly ‘upstream-weighted’ discretization and then gradually reducing the upstream weighting. A general PCG-like sparse matrix iterative solver is used to solve the Jacobians at each non-linear step. Various types of incomplete LU (ILU) preconditioners and ordering techniques are compared. Numerical results are presented to demonstrate that these methods are efficient and robust for solving the transonic potential equation in the workstation computing environment. © 1997 by John Wiley & Sons, Ltd.     

分子内敏化鎓盐的合成及光敏性研究

二芳基碘鎓盐和三芳基硫鎓盐是阳离子聚合的光引发剂和光敏产酸物,但他们在300nm以上的光吸收很低,限制了对紫外光的利用效率。为解决此问题,本文合成了一些新的碘鎓盐和硫鎓盐,并用凝胶时间方法考察了它们的光引发效率。实验结果表明,2-苯硫基甲基,2′,4′-二甲基二苯碘鎓盐和9-蒽丙基,二苯基硫鎓盐具有特别高的光引发效率,这归之于光照时这些鎓盐发生了分子内电荷转移反应,即发生了分子内敏化。9-蒽丙基二苯硫鎓盐分子中的蒽基(An)是电子给体也是敏化基团,光照时可发生如下反应: .     

Complexation in dense gases: concentrations of argon monomers,dimers and trimers

A classical statistical mechanical cluster formalism is presented for computing the thermodynamic properties and equilibrium state of aggregation of a fluid composed of structureless monomeric units which are capable of forming weakly bound van der Waals complexes. The general procedure is not restricted to any particular definition of the clusters, provided that the definition used satisfies certain reasonable criteria. The formalism is illustrated by applying it to two different cluster definitions. Calculations based on these definitions have been performed for the concentrations of argon monomers, dimers and trimers. It is found that gas imperfections due to cluster-cluster interactions can significantly affect the calculated values of these concentrations.