Rational surfaces having only a finite number of exceptional curves

We characterize the rational surfaces X which have a finite number of (-1)-curves under the assumption that -K_X is nef and having self-intersection zero.     

Simplification d’idéaux fractionnaires

Riassunto SianoI, J, N eL degli ideali frazionari di un dominioA. Mostriamo che se dueA-moduli moltiplicativi (I ⊕J, 〈,〉) e (L ⊕N, 〈,〉) sono isometrici suA alloraI è isomorfo aL (rispettivamenteJ≈N) o aN (rispettivamenteJ≈L); se ne deduce un criterio che permette di sapere se dueA-moduli quadratici, isotropici di rango 2, sono isometrici o no su un anello di Prüfer.

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Summary LetI, J, L andN be fractional ideals of a domainA. We prove that if two ?Multiplicative modules? (I⊕J, 〈,〉) and (L⊕N, 〈,〉) are isometric, thenI is isomorphic toL (respectivelyJ is isomorphic toN) or toN (respectively toL). As a consequence, we can know if two isotropic quadratic spaces of rank 2 are isometric on a Prüfer domain.

     

An improved high-performance liquid chromatographic determination of chlorpropamide in human plasma

Summary Samples were extracted with dichloromethane and the organic layer evaporated to dryness. The residue was dissolved in methanol, and 10 μl aliquot injected onto the column. Tolbutamide was used as the internal standard for chlorpropamide. The UV detector response was linear over the range 0–200 μg ml⁻¹ with a correlation coefficient of 0.999; detection limit: 0.002 μg ml⁻¹. Within-day and between-day assay variation was generally ≤7%. No interference from endogenous constituents was observed. The utility of the method was demonstrated by determining chlorpropamide in samples from six healthy volunteers following a single oral dose of 250 mg. The procedure is simple and requires small volumes of plasma.     

Dérivés de l'imidazo[2,l-b]thiazole. IX. Comportement du phénacyl-3 dihydro-5,6 imidazo[2,1-b]thiazole et du phénacylidène-3 tétrahydro-2,3,5,6 imidazo[2,1-b]thiazole vis-à-vis du chlorhydrate d'hydroxylamine

The reaction of hydoxylamine hydrochloride with two imidazothiazoles, having a ketonic carbonnyl group, leads to two types of compounds according to the quantity of the sodium acetate used. 3-Phenacyl-5,6-dihydroimidazo[2,1-b]thiazole hydrochloride gives logically the corresponding oxime, isolated in salt form or as a base depending upon the quantity of sodium acetate added. Furbase depending upon the quantity of sodium acetate added. Furthermore, a systematic allylic rearrangement was observed with migration of thiazole double bond to the adjacent nuclear position. 3-Phenacylidene-2,3,5,6-tetrahydroimidazo[2,1-b]thiazole gave directly in the absence of sodium acetate, a rearranged oxime salt. On the other hand, in the presence of sodium acetate, we obtained a hgydroxylamine which was characterized by a double bond in the 2,3-position of the thiazole ring. It is noteworthy that no transformation of the hydroxylamine into the oxime or vice-versa occurs whatever the pH of the solution. These different compounds have no fungistatic activity in contrast to the corresponding ketones.     

Hydrodynamic screening of ring copolymer solutions

The relaxation frequency of the dynamic correlation function for a diblock cyclic copolymer in solution in the zero average condition is calculated in the presence of hydrodynamic interaction. The latter is introduced through the screened Oseen tensor where the hydrodynamic screening length is used as a parameter to determine the range of screening. Substantial differences with the case of linear homopolymer are found, especially in the low q range where the dynamics are much faster and correspond to nondiffusive processes as usually is the case for copolymer systems. As the screening length decreases the dynamics approach the Rouse behavior and the minimum of the relaxation frequency shifts to lower values. The proportionality constant of the relaxation frequency in the intermediate q range Γ(q) → q³/(k_BTη₀) is also investigated as a function of the screening length. © 1994 John Wiley & Sons, Inc.     

Information theories for time-dependent harmonic oscillator

Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.     

Piecewise-linear,discontinuous Galerkin method for a fractional diffusion equation

We use a piecewise-linear, discontinuous Galerkin method for the time discretization of a fractional diffusion equation involving a parameter in the range − 1 < α < 0. Our analysis shows that, for a time interval (0,T) and a spatial domain Ω, the error in L_￥((0,T);L₂(W))L_\infty\bigr((0,T);L_2(\Omega)\bigr) is of order k ^2 + α , where k denotes the maximum time step. Since derivatives of the solution may be singular at t = 0, our result requires the use of non-uniform time steps. In the limiting case α = 0 we recover the known O(k ²) convergence for the classical diffusion (heat) equation. We also consider a fully-discrete scheme that employs standard (continuous) piecewise-linear finite elements in space, and show that the additional error is of order h ²log(1/k). Numerical experiments indicate that our O(k ^2 + α ) error bound is pessimistic. In practice, we observe O(k ²) convergence even for α close to − 1.     

A heuristic method for non-homogeneous redundancy optimization of series-parallel multi-state systems

This paper develops an efficient heuristic to solve the non-homogeneous redundancy allocation problem for multi-state series-parallel systems. Non identical components can be used in parallel to improve the system availability by providing redundancy in subsystems. Multiple component choices are available for each subsystem. The components are binary and chosen from a list of products available on the market, and are characterized in terms of their cost, performance and availability. The objective is to determine the minimal-cost series-parallel system structure subject to a multi-state availability constraint. System availability is represented by a multi-state availability function, which extends the binary-state availability. This function is defined as the ability to satisfy consumer demand that is represented as a piecewise cumulative load curve. A fast procedure is used, based on universal generating function, to evaluate the multi-state system availability. The proposed heuristic approach is based on a combination of space partitioning, genetic algorithms (GA) and tabu search (TS). After dividing the search space into a set of disjoint subsets, this approach uses GA to select the subspaces, and applies TS to each selected subspace. The design problem, solved in this study, has been previously analyzed using GA. Numerical results for the test problems from previous research are reported, and larger test problems are randomly generated. These results show that the proposed approach is efficient both in terms of both of solution quality and computational time, as compared to existing approaches.     

Stokes flow in a junction of two-dimensional orthogonal channels

The purpose of this study is to calculate Stokes flow structures in relation to flow rate distribution in a junction of four orthogonal channels. Particular attention was paid to the existence of recirculation flow inside the channels for low Reynolds numbers. The presence of this recirculation flow may be observed, but only when the flow rate is relatively low in at least one of the branches.