The Laplace transform on time scales revisited

In this work, we reexamine the time scale Laplace transform as defined by Bohner and Peterson [M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, 2001; M. Bohner, A. Peterson, Laplace transform and Z-transform: Unification and extension, Methods Appl. Anal. 9 (1) (2002) 155-162]. In particular, we give conditions on the class of functions which have a transform, develop an inversion formula for the transform, and further, we provide a convolution for the transform. The notion of convolution leads to considering its algebraic structure—in particular the existence of an identity element—motivating the development of the Dirac delta functional on time scales. Applications and examples of these concepts are given.     

MODELING A RIGHTS‐BASED APPROACH FOR MANAGING HABITAT IMPACTS OF FISHERIES

ABSTRACT. Limiting adverse consequences of fishing on essential fish habitat has emerged as a key fishery management objective. The conventional approach to providing habitat protection is to create MPAs or marine reserves that prohibit all or certain types of fishing in specific areas. However, there may be more cost‐effective and flexible ways to provide habitat protection. We propose an individual habitat quota (IHQ) system for habitat conservation that would utilize economic incentives to achieve habitat conservation goals cost‐effectively. Individual quotas of habitat impact units (HIU) would be distributed to fishers with an aggregate quota set to maintain a target habitat “stock.” HIU use would be based on a proxy for marginal habitat damage. We use a dynamic, explicitly spatial fishery and habitat simulation model to explore how such a system might work. We examine how outcomes are affected by spatial heterogeneity in the fishery and the scale of habitat regulation. We find that the IHQ system is a highly cost‐effective means of ensuring a given level of habitat protection, but that spatial heterogeneity and the scale of regulation can have significant effects on the distribution of habitat protection.     

子系统为S≥3的非线性大系统在近平衡区内的稳定性

本文采用文[1,2]中提出的平衡结构法研究子系统s≥3的非线性大系统在近平衡区内的稳定性;得到了判别这类大系统稳定性的两个一般性准则.     

Reactivity of a Ti–45.9Al–8Nb alloy in air at 700–900°C

A Ti–45.9Al–8Nb (at%) alloy with a lamellar structure (γ+α₂) was oxidised in air at 700, 800, 850 and 900°C in isothermal and thermal cycling conditions. The reaction progress was followed by thermogravimetric measurements. In isothermal conditions the oxidation kinetics followed approximately a parabolic rate law and the rate constants ranged from about 10^–12 kg² m^–4 s^–1 at 700°C to 10^–10 kg² m^–4 s^–1 at 900°C. The oxide scales were built of Al₂O₃ and TiO₂, the former being the main component of the outermost layer. The oxidation behaviour of Ti–45.9Al–8Nb was referred to a commercial titanium alloy, WT4 (Ti–6Al–1Mn), and selected oxidation-resistant alloys.     

Transient free‐surface flow of a viscoelastic fluid in a narrow channel

The interplay between inertia and elasticity is examined for transient free‐surface flow inside a narrow channel. The lubrication theory is extended for the flow of viscoelastic fluids of the Oldroyd‐B type (consisting of a Newtonian solvent and a polymeric solute). While the general formulation accounts for non‐linearities stemming from inertia effects in the momentum conservation equation, and the upper‐convected terms in the constitutive equation, only the front movement contributes to non‐linear coupling for a flow inside a straight channel. In this case, it is possible to implement a spectral representation in the depthwise direction for the velocity and stress. The evolution of the flow field is obtained locally, but the front movement is captured only in the mean sense. The influence of inertia, elasticity and viscosity ratio is examined for pressure‐induced flow. The front appears to progress monotonically with time. However, the velocity and stress exhibit typically a strong overshoot upon inception, accompanied by a plug‐flow behaviour in the channel core. The flow intensity eventually diminishes with time, tending asymptotically to Poiseuille conditions. For highly elastic liquids the front movement becomes oscillatory, experiencing strong deceleration periodically. A multiple‐scale solution is obtained for fluids with no inertia and small elasticity. Comparison with the exact (numerical) solution indicates a wide range of validity for the analytical result. Copyright © 2004 John Wiley & Sons, Ltd.     

钢卷尺刻度在线测量系

本文介绍了一种钢卷尺刻度在线测量系统 ,它采用了高速摄像及计算机数据处理技术 ,文章阐述了系统的非接触动态测量原理 ,描述了光电信号的处理方法 .     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

超高真空中银表面垂直谐波电流的实验测量

在超高真空的条件下,测量了清洁、自由银表面产生的光学二次谐波随基波电矢量与入射面之间夹角(?)的变化,从而通过理论公式,求得由Rudnick和Stern引入的,用于衡量垂直面电流密度的唯象参数a的值,在入射基频光波长为1.064μm时,被测定为-4.0±0.8.     

Improved accuracy of quantitative XPS analysis using predetermined spectrometer transmission functions with UNIFIT 2004

The accuracy of quantitative XPS analysis can be improved using predetermined transmission functions. Two different calibration methods are used for estimating the transmission function T(E) of a photoelectron spectrometer, applying a survey spectra approach (SSA) and a quantified peak‐area approach (QPA) to minimize the quantification error. For the SSA method, Au, Ag and Cu spectra measured with the Metrology Spectrometer II have been used. The new QPA method was built up from Au 4f, Au 4d, Au 4p_3/2, Ag 3d, Ag 3p_3/2, Cu 3p, Cu 2p_3/2, Ge 3p and Ge 2p_3/2 standard peak areas, applying adequate ionization cross‐sections and mean free path lengths for different pass energies (10 and 50 eV), lens modes (large area, large area XL, small area 150) and x‐ray sources (Al/Mg Twin and Al Mono). In the energy range 200–1500 eV a transmission function T(E) = a₀ + b₁E (where a₀, b₁ and b₂ are variable parameters) was found to give an appropriate approximation for eight tested spectrometer settings, implementing the largest changes in the case of pass energy variations. Determination and application of the transmission functions were integrated in the XPS analysis software (UNIFIT 2004) and tested by means of an Ni90Cr10 alloy. The results demonstrate the practicability of the SSA and QPA methods, giving decreased errors of <8% in comparison with errors up to 38% obtained using Wagner's sensitivity factors. Copyright © 2005 John Wiley & Sons, Ltd.     

Copolymer of Di (methacryloyloxymethyl) naphthalene and divinylbenzene as a column packing for high-performance liquid chromatography

Summary A new porous polyaromatic ester packing was synthetized for high performance liquid chromatography. The relationship between retention and chain length of the members of homologous series of alkylbenzenes, N-alkylanilines, alkylarylethers, alkylbenzoates and alkylarylketones on this new stationary phase using different eluents was investigated. Using the alkylarylketone scale the retention indices of the homologues and test compounds were calculated. The results were compared with those obtained for poly (styrene-divinylbenzene) polymers. For both types of packing the first members of each homologous series gave non-linear behaviour. The methylene group index increments are different for the studied homologous series; thus there is no simple additivity of the retention indices. The efficiency of the porous polymeric columns is a function of the capacity factor of the solute and the organic component of the eluent.