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On the continuation for variational inequalities depending on an eigenvalue parameter

In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Multicyclic polyethers derived from 1,1,1‐tris(4‐hydroxyphenyl)ethane and 2,6‐dihalopyridines

Poly(pyridine ether)s were prepared in two ways: the polycondensation of silylated 1,1,1‐tris(4‐hydroxyphenyl)ethane (THPE) with 2,6‐difluoropyridine (method A) and the polycondensation of free THPE with 2,6‐dichloropyridine (method B). With method A, the THPE/difluoropyridine feed ratio was varied from 1.0:1.0 to 1.0:1.6. Cycles, bicycles, and multicycles were the main reaction products, and crosslinking was never observed. When ideal stoichiometry was used exclusively, multicycles free of functional groups were obtained. These multicycles were detectable in matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectra up to B₃₈C₇₆ with a mass of approximately 32,000 Da. With method B, the reaction conditions were varied at a fixed feed ratio to achieve an optimum for the preparation of multicyclic polyethers, but because of the lower reactivity of 2,6‐dichloropyridine, a quantitative conversion was not achieved. The reaction products were characterized with MALDI‐TOF mass spectrometry, viscosity measurements, and size exclusion chromatography. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5725–5735, 2004     

Thermal behavior of metallodendrimers possessing bis(terpyridinyl)Ru(II) connectivity and different surface functionality

A series of metallodendrimers, assembled by means of bis(terpyridinyl)Ru^(II) connectivity on poly(propylene imine) dendrimer scaffolds, with homogeneous or heterogeneous surfaces, were prepared. Differential scanning calorimetry and thermogravimetric analysis were used to determine their thermal behavior, glass‐transition temperatures, and the decomposition kinetics and temperatures; no synergy effects for these properties were observed for the heterogeneously surfaced constructs in contrast to the corresponding homogeneously coated materials, which exhibited different values depending on their surface functionalities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1487–1495, 2004     

Wide‐angle X‐ray diffraction and differential scanning calorimetry study of the crystallization of poly(ethylene naphthalate), poly(butylene naphthalate), and their copolymers

The crystallization behavior of a series of poly(ethylene‐co‐butylene naphthalate) (PEBN) random copolymers was studied. Wide‐angle X‐ray diffraction (WAXD) patterns showed that the crystallization of these copolymers could occur over the entire range of compositions. This resulted in the formation of poly(ethylene naphthalate) or poly(butylene naphthalate) crystals, depending on the composition of the copolymers. Sharp diffraction peaks were observed, except for 50/50 PEBN. Eutectic behavior was also observed. This showed isodimorphic cocrystallization of the PEBN copolymers. The variation of the enthalpy of fusion of the copolymers with the composition was estimated. The isothermal and nonisothermal crystallization kinetics were studied. The crystallization rates were found to decrease as the comonomer unit content increased. The tensile properties were also measured and were found to decrease as the butylene naphthalate content of the copolymers increased. For initially amorphous specimens, orientation was proved by WAXD patterns after drawing, but no crystalline reflections were observed. However, the fast crystallization of drawn specimens occurred when they were heated above the glass‐transition temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 843–860, 2004     

Differential scanning calorimetry and thermogravimetric analysis investigation of the thermal properties and degradation of some radiation‐grafted films and membranes

The influence of irradiation and grafting on the crystallinity of three base polymers has been investigated with differential scanning calorimetry. Grafting has the largest effect on the base polymer crystallinity and results in a reduction of the crystallinity. The thermal degradation of the base polymers and grafted films has been investigated with thermogravimetric analysis. The extent of the fluorination of the base polymer, the irradiation method, and the graft level all influence the thermal degradation and its activation energy. It is proposed that the variation of the chain lengths of the grafted polystyrene chains is actually a primary underlying factor responsible for the influence of these various parameters on the degradation process. The first results of a comparative thermal analysis of some fuel‐cell membranes are also presented, and the promise and shortcomings of this method are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2612–2624, 2004