A general theory of surrogate dual and perturbational extended surrogate dual optimization problems

For the optimization problem (P) α = inf h(G), where G ≠ Ø is a subset of a locally convex space $\text{F}\text{and}\text{h: F →}\text{R}\text{?}$, we introduce and study two general concepts of dual problems, encompassing the classical surrogate dual problem. The first one involves only a family of surrogate constraints sets Δ_{G, Φ} ? F (Φ ∈ W), where W ? R^X, X being a locally convex space. The second one uses a perturbation functional $\text{?: F × X →}\text{R}\text{?}$ and a family of sets $\text{}\text{?}\text{gD}{}_{\mathrm{(F,x0),\Phi }}\text{? F × X (Φ ∈ W)}$, where W ? R^X. We give duality theorems, introduce Lagrangians, and show some relations between these problems and the dual problems to (P) defined with the aid of a perturbation and a concept of conjugation of functionals.     

Structure and mechanical properties of talc‐filled blends of polypropylene and styrenic block copolymers

The structure–property relationships of isotactic polypropylene (iPP)/styrenic block copolymer blends filled with talc were examined by optical and scanning electron microscopy, wide‐angle X‐ray diffraction, and tensile‐ and impact strength measurements. The composites were analyzed as a function of the poly(styrene‐b‐ethylene‐co‐propylene) diblock copolymer (SEP) and the poly(styrene‐b‐butadiene‐b‐styrene) triblock copolymer (SBS) content in the range from 0 to 20 vol % as elastomeric components and with 12 vol % of aminosilane surface‐treated talc as a filler. Talc crystals incorporated in the iPP matrix accommodated mostly plane‐parallel to the surface of the samples and strongly affected the crystallization process of the iPP matrix. The SBS block copolymer disoriented plane‐parallel talc crystals more significantly than the SEP block copolymer. The mechanical properties depended on the final phase morphology of the investigated iPP blends and composites and supermolecular structure of the iPP matrix because of the interactivity between their components. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1255–1264, 2004     

Metal-support interactions in systems palladium deposited on oxidized tungsten surfaces

The morphology of the palladium (Pd) overlayers on oxidized tungsten (W) tips has been studied by Field Emission Microscopy (FEM). The effect of thermal treatment on the interaction of Pd with the support and chemisorption of CO on variously treated Pd-containing samples has been investigated. The results are discussed in relation to complementary macroscopic experiments by synchrotron radiation excited photoelectron spectroscopy (SRPES) and thermally programmed desorption (TPD) of carbon monoxide (CO) on a polycrystalline W foil. A distinct influence of support pre-oxidation on the Pd layer growth has been demonstrated. Two types of oxidized supports have been used: tungsten with oxygen pre-adsorbed at room temperature (RT) and then heated to 700 K (WO_x/W (RT) system) and tungsten oxidized at 1300 K (WO_x/W (1300 K) system) in situ. The surface of WO_x/W (1300 K) sample is fully oxidized in contrast to WO_x/W (RT), where the presence of un-oxidized patches has been demonstrated by SRPES measurements. A Pd layer grows on the WO_x/W (RT) surface mostly on the densely populated planes (1 1 0) and (2 1 1) of the W tip. Heating of this system up to 700 K results in disaggregation of the original Pd layer. Pd clusters on the tungsten tip oxidized at 1300 K are localized on the atomically rough (1 1 1) plane. The observed differences in CO adsorption on the aforementioned types of investigated samples can be attributed to differences in the chemical nature of their surfaces.     

Square-wave voltammetry of 4,4′-diisopropyl-2,2′-bithiazoline and its complex with copper(II)

(4S)-4′-diisopropyl-2,2′-bithiazoline (DPT) is an electroactive organic chiral compound giving two reduction responses in square-wave voltammograms at potentials about −0.2 and −0.4 V by forming a complex with mercury which deposits at the electrode surface. By the addition of copper(II) ion to the solution of DPT a third peak appears between them at about −0.3 V, which corresponds to the reduction of adsorbed Cu-DPT complex. Optimal pH for the investigation of those redox processes was found to be 2.8. By square-wave voltammetric measurements it was interpreted that these redox reactions were quasireversible with immobilized reactants. By plotting i_p/f vs. frequency a quasireversible maximum was obtained, and the apparent standard reaction rate constants were calculated: log (k_s)DPT=(0.91 ± 0.9) and 1 < k_s < 65_S⁻¹, log (k_s)_CuDPT= (0.35 ± 0.9) and 0.3 < k_s < 18 S⁻¹ in 0.55 M NaCl.     

Acidity of montmorillonite pillared by alumina, zirconia and chromia

Acidic properties of Al-, Zr- and Cr- pillared montmorillonites prepared from Jelšovy Potok bentonite (Central Slovakia) have been investigated using temperature-programmed desorption of ammonia. The number of acid sites varied with different interlayer cations from 0.06 to 0.23 mmol g⁻¹. The character of acid sites was similar in the case of Al- and Zr- forms. It is obvious that the chromium analogue contains fewer acid sites, nevertheless, they seem to be stronger compared to Al- and Zr- pillared montmorillonites.     

The anisotropy of fluorescence in ring units

The time dependence of the anisotropy of fluorescence after an impulsive excitation in the ring unit (resembling the B850 ring of the purple bacterium Rhodopseudomonas acidophila) is calculated. Fast fluctuations of the environment are simulated by dynamic disorder and slow fluctuations by static disorder. Both types of disorder are taken into account simultaneously. Without dynamic disorder modest degrees of static disorder are sufficient to cause the experimentally found initial drop of the anisotropy on a sub-100 fs time scale. Two different models of the spectral density J(ω) of phonons have been often used in the literature to describe influence of the bath. The spectral density J(ω) enters the non-Markovian dynamical equations for the one exciton density matrix (entering the time dependence of the anisotropy of fluorescence). The spectral density J(ω) with high-energy tail leads to faster anisotropy decay.     

A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral

In the context of aggregation, the Choquet integral arises as a natural generalization of the weighted arithmetic mean. In their seminal work on bi-capacities, Grabisch and Labreuche have recently proposed an extension of the Choquet integral adapted to the situation where the values to be aggregated lie on a bipolar scale. In such a framework, they have derived generalizations of the Shapley value and of the Shapley interaction index that can be used to apprehend the main behavioral characteristics of the aggregation. Founding our approach on the intuitive notion of weight of a criterion, we propose alternative definitions of importance and interaction indices that may be more easily interpretable and we study their properties.