Preface

<正>These two special issues of Acta Mathematica Scientia are dedicated to ProfessorJames Glimm on the occasion of his seventy-fifth birthday.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Thermally induced alkylation of diamond

We present an approach for the thermally activated formation of alkene-derived self-assembled monolayers on oxygen-terminated single and polycrystalline diamond surfaces. Chemical modification of the oxygen and hydrogen plasma-treated samples was achieved by heating in 1-octadecene. The resulting layers were characterized using X-ray photoelectron spectroscopy, thermal desorption spectroscopy, atomic force microscopy, Fourier transform infrared spectroscopy, and water contact angle measurements. This investigation reveals that alkenes selectively attach to the oxygen-terminated sites via covalent C-O-C bonds. The hydrophilic oxygen-terminated diamond is rendered strongly hydrophobic following this reaction. The nature of the process limits the organic layer growth to a single monolayer, and FTIR measurements reveal that such monolayers are dense and well ordered. In contrast, hydrogen-terminated diamond sites remain unaffected by this process. This method is thus complementary to the UV-initiated reaction of alkenes with diamond, which exhibits the opposite reactivity contrast. Thermal alkylation increases the range of available diamond functionalization strategies and provides a means of straightforwardly forming single organic layers in order to engineer the surface properties of diamond.     

Modification of tricine–SDS–PAGE for online and offline analysis of phosphoproteins by ICP-MS

This study describes a modification to tricine sodium dodecyl sulphate polyacrylamide gel electrophoresis to make it more effective for the separation of low molecular mass proteins and for coupling with inductively coupled plasma mass spectrometry (ICP-MS). The modified method employs low-percentage polyacrylamide gels (7–10%) (w/v) and low reagent concentrations that provide efficient separations, good quantitation and low matrix levels that are compatible with ICP-MS. Using phosphopeptides as a model system, and offline analysis, we obtained recoveries of 73% (w/v) in a 9% gel compared with 55% in a conventional 16% gel. Online coupling was achieved by modification of a standard commercially available gel electroelution apparatus and casting of the gel into a 7.3-cm-long tube. Online separation of a digest of β-casein was demonstrated with recovery of the mono- and tetraphosphopeptides, which were identified by comparison with peptide standards. A mass balance study with the standards yielded recoveries of 95% for tetraphosphopeptides and 48% for monophosphopeptides. The factors affecting the separations and recoveries are discussed in detail. The detection limits for 10-μL samples of the mono- and tetraphosphopeptides were 0.7 μM (7 pmol) and 0.2 μM (2 pmol) respectively.     

The Analytic Hierarchy Process and its Application to an Information Technology Decision

This paper describes how the analytic hierarchy process was applied to a decision concerning the selection of a computer operating system. Various practical issues and problems which arose whilst using the process are discussed. The method was found to be a useful aid for identifying the criteria upon which a decision depends. It also revealed useful data about the concerns and preferences of decision-makers. Some problems were, however, encountered when assessing the importance of an intangible factor relative to a tangible factor. Also, it was difficult to interpret the options' final scores because the method does not provide an indication of statistical significance.     

Capital Investment — An Optimal Control Perspective

Many managers appear to have a mental model of how investment decisions should be carried out. This paper attempts to identify some of the characteristics of such a mental model by constructing an optimal control model of the process of authorizing an investment project. The key activities in the model are design, support generation and authorization. It is assumed that the effort that can be expended on each is limited. The objective function is the net present value of the cash flows associated with the project. The solution to the model is readily interpreted qualitatively. For viable projects, four different patterns of decision-making are found, each of which is optimum under appropriate circumstances. It is argued that in many actual investment decisions it should be possible for managers to approximate reasonably closely the optimal behaviour, and that therefore the optimal control model may shed light on managers' mental model.     

Correlations for pairs of closed geodesics

In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.     

Chaos,transport and mesh convergence for fluid mixing

Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids （as considered here）, this interface is defined as a 50% mass concentration isosurface. For shock wave induced （Richtmyer-Meshkov） instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.     

On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action

Let be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring (associated to and the Frobenius homomorphism , in the indeterminate ) that is both -torsion and Artinian over .

     

Contact angle dependence of the resonant frequency of sessile water droplets

The resonant vibrations of small (microliter) sessile water droplets supported on solid substrates were monitored using a simple optical detection technique. A small puff of air was used to apply an impulse to the droplets and their time dependent oscillations were monitored by passing a laser beam through the droplet and measuring the variations of the intensity of the scattered light using a simple photodiode arrangement. The resulting time dependent intensity changes were then Fourier transformed to obtain information about the vibrational frequencies of the droplets. The resonant frequencies of droplets with masses in the range 0.005-0.03 g were obtained on surfaces with water contact angles ranging from 12 ± 4° to 160 ± 5°. The contact angle dependence of the resonant frequency of the droplets was found to be in good agreement with a simple theory which considers standing wave states along the meridian profile length of the droplets.