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     

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.     

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.     

The synthesis and characterization of copper(II)–<Emphasis Type="Italic">p</Emphasis>-aminosalicylate complexes with diamine ligands

The complexes were synthesized by the reaction between sodium salt of p-aminosalicylic acid (PAS) and Cu(II) for 1 and corresponding ethylenediamine (en) or its derivatives for 2–6. The complexes were characterized by using elemental analyses, FT-IR, UV–Vis, magnetic moment measurements, and thermal analyses techniques. In complex 1[Cu₂(PA)₄(H₂O)₂], two Cu(II) ions were found as bridged by four μ-O:O′ p-aminosalicylato (PA) ligands, forming a cage structure, and two aqua ligands to form dinuclear square-pyramidal geometry around Cu(II) ions. In the complexes 2–6, the PA (anionic form of p-aminosalicylic acid) coordinated to Cu(II) ions as monodentate manner by using its oxygen atom of deprotonated carboxylic acid and ethylenediamine derivatives coordinated to the Cu(II) ions in bidentate manner to form mononuclear octahedral complexes [Cu(PA)₂(L)₂] (L = ethylendiamine, N,N-dimethylethylendiamine, N,N′-dimethylethylendiamine, N,N,N′,N′-tetramethylethylendiamine, and 1,3-propanediamine, for complexes 2, 3, 4, 5, and 6, respectively). In all the complexes OH and NH₂ groups of PA ligands were not coordinated to metals.     

Swelling of <Emphasis Type="Italic">N</Emphasis>-vinylcaprolactam-dodecyl methacrylate gel in {heptane + toluene} mixtures

A copolymer gel has been synthesized from N-vinylcaprolactam and dodecyl methacrylate in ethanol using the free radical cross-linking polymerization method. Characterizations of the gel were performed by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermal gravimetric analysis (TGA) techniques. Swelling behavior of the gel was investigated in heptane, toluene, and their binary mixtures with different compositions. Swelling value in toluene is higher than that in heptane and swelling value increases with the increasing initial content of toluene in the binary mixture with heptane. The swelling values are correlated by the first- and second-order differential equations, and the best model correlating the experimental results is a second-order one. Diffusion coefficients have also been calculated for heptane and toluene at each concentration by power-law and first-order equations. While the diffusion mechanism of the gel in heptane is a Fickian one, the gel swelled in toluene exhibits a non-Fickian character. Diffusion mechanisms of the gels in binary mixtures are much more complicated. Because of the higher swelling degree in toluene compared to that in heptane, selectivity of the gel in different {heptane + toluene} mixtures with selectivity close to 1 has also been taken into consideration.     

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.     

Detection of Variation in Long-Term Micropropagated Mature Pistachio via DNA-Based Molecular Markers

Determination of genetic stability of in vitro-grown plantlets is needed for safe and large-scale production of mature trees. In this study, genetic variation of long-term micropropagated mature pistachio developed through direct shoot bud regeneration using apical buds (protocol A) and in vitro-derived leaves (protocol B) was assessed via DNA-based molecular markers. Randomly amplified polymorphic DNA (RAPD), inter-simple sequence repeat (ISSR), and amplified fragment length polymorphism (AFLP) were employed, and the obtained PIC values from RAPD (0.226), ISSR (0.220), and AFLP (0.241) showed that micropropagation of pistachio for different periods of time resulted in “reasonable polymorphism” among donor plant and its 18 clones. Mantel’s test showed a consistence polymorphism level between marker systems based on similarity matrices. In conclusion, this is the first study on occurrence of genetic variability in long-term micropropagated mature pistachio plantlets. The obtained results clearly indicated that different marker approaches used in this study are reliable for assessing tissue culture-induced variations in long-term cultured pistachio plantlets.     

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.     

Hubbing and routing in postal delivery systems

We consider the combined hubbing and routing problem in postal delivery systems and develop an iterative two-stage solution procedure for the problem. In the first stage, hub locations are determined and postal offices are multiply allocated to the hubs. The second stage gives the routes in hub regions that alter the distances between points used in the hub-location problem. The procedure then iterates between two stages by updating the distances used in hubbing in order to produce a route-compatible hub configuration. Computational experience is reported for the test problems taken from the literature. For a case study Turkish postal delivery system data are utilized. As the case study is applied on a road network, a final stage, seeking improvements based on special structures in the routed network, is appended to the two-stage solution procedure.