The Jacobian and the Ginzburg-Landau energy

We study the Ginzburg-Landau functional for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional. Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001     

Asymptotic expansions for Markov processes with lévy generators

This paper considers a deterministic flow inn-dimensional space, perturbed by a Markov jump process with small variance. Asymptotic expansions are obtained for certain functionals of Feynman—Kac type, in powers of a small parameter representing a noise intensity. The methods are analytical rather than probabilistic.The research of the first author was partly supported by AFOSR under Contract No. 91-0116-0, by ONR under Contract No. N0014-83-K-0542, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR. The second author's research was partly supported by NSF under Contract No. DMS-8702537, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR.     

Lot Streaming in a Two-stage Flow Shop with Set-up,Processing and Removal Times Separated

This paper considers the job (lot) scheduling problem for two-stage flow shops in which the movement of transfer batches (sublots) from the first stage to the next are allowed. Set-up, processing and removal times are considered as separable and independent of the order in which jobs are processed at any of two stages. An optimal transfer batch sizing and scheduling algorithm which has an objective of minimizing the maximum flow time (makespan) is developed and demonstrated by a numerical example.     

Random walks generated by affine mappings

This article is concerned with Markov chains on ^m constructed by randomly choosing an affine map at each stage, and then making the transition from the current point to its image under this map. The distribution of the random affine map can depend on the current point (i.e., state of the chain). Sufficient conditions are given under which this chain is ergodic.     

The Conductance- and Capacitance-Frequency Characteristics of the Rectifying Junctions Formed by Sublimation of Organic Pyronine-B on p-Type Silicon

The rectifying junction characteristics of the organic compound pyronine-B film on a p-type Si substrate has been studied. The pyronine-B has been sublimed on the top of p-Si surface. The barrier height and ideality factor values of 0.79±0.04 and 1.13±0.06 eV for this structure have been obtained from the forward bias current-voltage (I-V) characteristics. From the low capacitance-frequency (C-f) characteristics as well as conductance-frequency (G-f) characteristics, the energy distribution of the interface states and their relaxation time have been determined in the energy range of (0.53−E_v)-(0.79−E_v) eV taking into account the forward bias I-V data. The interface state density N_ss ranges from 4.93×10¹⁰ cm⁻² eV⁻¹ in (0.79−E_v) eV to 3.67×10¹³ cm⁻² eV⁻¹ in (0.53−E_v) eV. Furthermore, the relaxation ranges from 3.80×10⁻³ s in (0.53−E_v) eV to 4.21×10⁻⁴ s in (0.79−E_v) eV. It has been seen that the interface state density has an exponential rise with bias from the midgap towards the top of the valence band. The relaxation time shows a slow exponential rise with bias from the top of the valence band towards the midgap.     

Competitive adsorption and desorption of a bi-solute mixture: effect of activated carbon type

This study aims to clarify the effects of carbon activation type and physical form on the extent of adsorption capacity and desorption capacity of a bi-solute mixture of phenol and 2-chlorophenol (2-CP). For this purpose, two different PACs; thermally activated Norit SA4 and chemically activated Norit CA1, and their granular countertypes with similar physical characteristics, thermally activated Norit PKDA and chemically activated Norit CAgran, were used. The thermally activated carbons were better adsorbers for phenol and 2-CP compared with chemically activated carbons, but adsorption was more reversible in the latter case. 2-CP was adsorbed preferentially by each type of activated carbon, but adsorption of phenol was strongly suppressed in the presence of 2-CP. The simplified ideal adsorbed solution (SIAS) model underestimated the 2-CP loadings and overestimated the phenol loadings. However, the improved and modified forms of the SIAS model could better predict the competitive adsorption. The type of carbon activation was decisive in the application of these models. For each activated carbon type, phenol was desorbed more readily in the bi-solute case, but desorption of 2-CP was less compared with single-solute. This was attributed to higher energies of 2-CP adsorption.     

Kinetic determination of trace levels of selenium(IV) and total selenium by Nile Blue A/hydrogen peroxide method

A kinetic method for the determination of selenium(IV) traces is proposed, based on its inhibitory action on the oxidation of Nile Blue A by hydrogen peroxide in phosphate buffer (pH 10.5). A linear dependence was established between the rate of the proposed indicator reaction and selenium concentration in the range 9.5 × 10^–2-1.58 ng cm^–3. The experimental conditions of maximal selenium effect were established. Selenium, determined by the tangent method, was determined at concentrations over the range 0.22–1.26 ng cm^–3, with relative standard deviations up to 4.5%. The reaction rate was followed spectrophotometrically. The effect of foreign ions on the accuracy of this method was also investigated. The method was applied to the determination of selenium in pharmaceutical preparations and wheat flour.     

A boundary-value problem for Hamilton-Jacobi equations in hilbert spaces

We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.The work of P. Cannarsa was partially supported by the Italian National Project Equazioni Differenziali e Calcolo delle Variazioni. H. M. Soner's work was supported by National Science Foundation Grant DMS-90-02249.