Test Functions, Schur–Agler Classes and Transfer-Function Realizations: The Matrix-Valued Setting

Given a collection of test functions, one defines the associated Schur–Agler class as the intersection of the contractive multipliers over the collection of all positive kernels for which each test function is a contractive multiplier. We indicate extensions of this framework to the case where the test functions, kernel functions, and Schur–Agler-class functions are allowed to be matrix- or operator-valued. We illustrate the general theory with two examples: (1) the matrix-valued Schur class over a finitely-connected planar domain and (2) the matrix-valued version of the constrained Hardy algebra (bounded analytic functions on the unit disk with derivative at the origin constrained to have zero value). Emphasis is on examples where the matrix-valued version is not obtained as a simple tensoring with ${{\mathbb C}^{N}}$ of the scalar-valued version.     

Chloroform sorption in nanoporous crystalline and amorphous phases of syndiotactic polystyrene

The transport of chloroform in films of atactic polystyrene and of semicrystalline syndiotactic polystyrene in its nanoporous form (δ‐form) has been investigated by gravimetric analysis. Experimental tests have been performed at 35, 49, and 56 °C and at several vapor pressures ranging from 0.5 to 100 Torr. Nonequilibrium lattice fluid prediction of the amorphous sorption behavior was used to enucleate the sorption contribution of the crystalline nanoporous phase from semicrystalline samples. Sorption behavior of the crystalline phase has been interpreted on the basis of Langmuir equation. Moreover, the chloroform sorption at low activities in the crystalline nanoporous phase has been predicted by using Grand Canonical Monte Carlo molecular simulations. Isosteric heats of sorption were also experimentally evaluated for the crystalline phase, and compared with the corresponding prediction of molecular simulation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 8–15, 2008     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Butylene copolyesters based on aldaric and terephthalic acids. Synthesis and characterization

The synthesis, characterization, and some properties of new copolyesters analogous to poly(butylene terephthalate) (PBT), based on L ‐arabinaric and galactaric acids, are described. These copolyesters were obtained by polycondensation reaction in the melt of mixtures of methyl 2,3,4‐tri‐O‐methyl‐L ‐arabinarate or methyl 2,3,4,5‐tetra‐O‐methyl‐galactarate and dimethyl terephthalate with 1,4‐butanediol. Their weight‐average molecular weights ranged between 10,000 and 34,000, with polydispersities ranging from 1.4 to 2.2. The composition of all the copolymers was analyzed by NMR, and was found to have a statistical microstructure. All these copolyesters were thermally stable, with degradation temperatures well above 300 °C. The melting temperature and crystallinity decreased in both series, and the glass transition temperature increased and decreased respectively, for the PBTGa and PBTAr series with increasing amounts of aldaric units in the copolyester chain. Only PBT‐derived copolyesters containing a maximum of 30% aldaric units showed discrete scattering characteristic of crystalline material. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1168–1177, 2009     

Extended gate field effect transistor using V2O5 xerogel sensing membrane by sol–gel method

Since the first use of glass electrode to the detection of pH, many efforts have been made to develop new techniques and methods. In this study, the pH sensing properties of an extended gate field effect transistor (EGFET) based on the vanadium pentoxide xerogel thin film is investigated. The vanadium pentoxide was prepared by a sol–gel route. The X-ray diffractogram indicates the presence of a lamellar structure of the vanadium pentoxide xerogel films. The film was investigated as a sensor in the pH range of 2–12 and the corresponding EGFET has a sensitivity of 58.1 mV/pH. This value suggests that the material is a promising candidate for applications as disposable biosensor.     

On Logarithmic Smoothing of the Maximum Function

We consider the maximum function f resulting from a finite number of smooth functions. The logarithmic barrier function of the epigraph of f gives rise to a smooth approximation g of f itself, where >0 denotes the approximation parameter. The one-parametric family g converges – relative to a compact subset – uniformly to the function f as tends to zero. Under nondegeneracy assumptions we show that the stationary points of g and f correspond to each other, and that their respective Morse indices coincide. The latter correspondence is obtained by establishing smooth curves x() of stationary points for g , where each x() converges to the corresponding stationary point of f as tends to zero. In case of a strongly unique local minimizer, we show that the nondegeneracy assumption may be relaxed in order to obtain a smooth curve x().     

Optimal Investment in a Levy Market

In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric Levy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the resulting models are incomplete and there are many equivalent martingale measures. However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios based in stocks and bonds, showing that the new assets are superfluous for certain martingale measures that depend on the utility function we use.     

Electron scattering on two-neutron halo nuclei: The case of He

The formalism to describe electron scattering reactions on two-neutron halo nuclei is developed. The halo nucleus is described as a three-body system (core +n + n), and the wave function is obtained by solving the Faddeev equations in coordinate space. We discuss elastic and quasielastic scattering using the impulse approximation to describe the reaction mechanism. We apply the method to investigate the case of electron scattering on ⁶He. Spectral functions, response functions, and differential cross sections are calculated for both neutron knockout and knockout by the electron.     

Conic Set-Valued Maps in Vector Optimization

The paper deals with the properties of a conic set-valued function defined on the set of all ideal points of vector programming problems. The results here about the continuity and derivability of this conic set-valued map, can be used to get information about the sensitivity of the problem and the stability of the order associated to every ideal point. Furthermore, it is proved that certain contingent cones are determined by the ideal conic set-valued map.