The Acid-Base/Deprotonation Equilibrium Can Be Studied with a MicroScale Thermophoresis (MST)

MicroScale thermophoresis (MST) is a rapidly developing bioanalytical technique used routinely for the examination of ligand-target affinity. It has never been used so far for the analysis of acid-base dissociation and the determination of pK_a constant. This work is the-proof-of-concept of this new idea. It demonstrates that the pK_a values obtained from the thermophoretic data are consistent with the reference methods. As a result, the analytical potential and utility of the MST technology can become even greater, especially if the new detection system of thermophoretic movement will be developed in the future. Even now, taking into account the necessity to use fluorescence, the proposed method may be useful in many respects.     

Influence of Substrate Surface Polarity on Epitaxial Layer Growth of CuInSe2 on GaAs

CuInSe₂ thin films with thicknesses of about 0.1 μm were deposited onto (III) B-oriented GaAs substrates by flash evaporation. At substrate temperatures T_sub = 695–820 K the films have the chalcopprite structure with some admixture of the cubic sphalerite phase. At T_sub > 820 K only the sphalerite phase was found All the films are partly polycrystalline. From the electrical properties it follows that the films are characterized by nearly complete compensation at T_sub = 695–820 K. At T_sub = 870 K the films are p-type conducting and show two acceptor states with ionization energies of about 8 meV and 105 meV.     

Detection of bacteria using antimicrobial polymer derived via ring-opening metathesis (romp) pathway

There is growing interest in the detection of bacteria in consumables, for example, in the food and water sectors. In this study, the aim was to produce a polymer-based bacteria biosensor via ROMP (ring opening metathesis polymerization). In the first part of the study, block and random copolymers were synthesized, and their biocidal activities were tested on the glass surface. Interdigitated electrode arrays coated with the polymers possessing the highest activity were used to screen the affinity towards different bacterial strains by monitoring impedance variations in real-time. The polymer-coated electrode could detect gram-positive and gram-negative bacteria strains at a concentration of 10⁷ cfu/mL. The results show that ROMP-based polymer offers bacterial detection and can be used in developing biosensor devices for efficiently detecting pathogenic bacteria.     

A tractable multi-leader multi-follower peak-load-pricing model with strategic interaction

While single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower games that can be applied, e.g., to model strategic booking decisions in the European entry-exit gas market. For this nontrivial class of games, we develop a solution algorithm that is able to compute the complete set of Nash equilibria instead of just individual solutions or a bigger set of stationary points. Additionally, we prove that for this class of games, the solution set is finite and provide examples for instances without any Nash equilibria in pure strategies. We apply the algorithm to a case study in which we compute strategic booking and nomination decisions in a model of the European entry-exit gas market system. Finally, we use our algorithm to provide a publicly available test library for the considered class of multi-leader multi-follower games. This library contains problem instances with different economic and mathematical properties so that other researchers in the field can test and benchmark newly developed methods for this challenging class of problems.

     

Integer solution of a set of bilinear equations

An efficient method for a design of transmultiplexer filters is suggested. The perfect reconstruction conditions lead to the bilinear equations for FIR filters coefficients. The method of solving these equations results from the presented theorem. Usefulness of the algorithm in fixed-point arithmetic is the crucial issue. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calderón–Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood–Paley–Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calderón–Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.     

The divisor problem for d 4 (n) in short intervals

In this paper we establish an asymptotic formula for the sum

A Grothendieck-type theorem for the space of totally measurable functions

Let Σ be a σ-algebra of subsets of a non-empty set Ω. Let X be a real Banach space and let X^* stand for the Banach dual of X. Let B(Σ, X) be the Banach space of Σ-totally measurable functions f: Ω → X, and let B(Σ, X)^* and B(Σ, X)^** denote the Banach dual and the Banach bidual of B(Σ, X) respectively. Let bvca(Σ, X^*) denote the Banach space of all countably additive vector measures ν: Σ → X^* of bounded variation. We prove a form of generalized Vitali-Hahn-Saks theorem saying that relative σ(bvca(Σ, X^*), B(Σ, X))-sequential compactness in bvca(Σ, X^*) implies uniform countable additivity. We derive that if X reflexive, then every relatively σ(B(Σ, X)^*, B(Σ, X))-sequentially compact subset of B(Σ, X)_c^~ (= the σ-order continuous dual of B(Σ, X)) is relatively σ(B(Σ, X)^*, B(Σ, X)^**)-sequentially compact. As a consequence, we obtain a Grothendieck type theorem saying that σ(B(Σ, X)^*, B(Σ, X))-convergent sequences in B(Σ, X)_c^~ are σ(B(Σ, X)^*, B(Σ, X)^**)-convergent.     

Potential operators associated with Jacobi and Fourier–Bessel expansions

We study potential operators (Riesz and Bessel potentials) associated with classical Jacobi and Fourier–Bessel expansions. We prove sharp estimates for the corresponding potential kernels. Then we characterize those 1≤p,q≤∞$1\le p,q\le \infty$, for which the potential operators are of strong type (p,q)$(p,q)$, of weak type (p,q)$(p,q)$ and of restricted weak type (p,q)$(p,q)$. These results may be thought of as analogues of the celebrated Hardy–Littlewood–Sobolev fractional integration theorem in the Jacobi and Fourier–Bessel settings. As an ingredient of our line of reasoning, we also obtain sharp estimates of the Poisson kernel related to Fourier–Bessel expansions.