Pythagorean euclidean four point properties

Characterizations of real inner product spaces among a class of metric spaces have been obtained based on homogeneity of metric pythagorean orthogonality, a metrization of the concept of pythagorean orthogonality as defined in normed linear spaces. In the present paper a considerable weakening of this hypothesis is shown to characterize real inner product spaces among complete, convex, externally convex metric spaces, generalizing a result of Kapoor and Prasad [9], and providing a connection with the many characterizations of such spaces using euclidean four point properties.     

Molecular weight dependence of diblock copolymer segregation at a polymer/polymer interface

Utilizing forward recoil spectrometry (FRES), we have determined the segregation isotherm which describes the interfacial excess z_i^* of diblock copolymers of poly (d₈-styrene-b-2-vinylpyridine) (dPS-PVP) at the interface between the homopolymers PS and PVP as a function of ?_∞, the volume fraction of diblock copolymer remaining in the host homopolymer. All the samples were analyzed after annealing at temperatures and times sufficient to achieve equilibrium segregation. The effect of the degree of polymerization of both the diblock copolymers and the host homopolymers on the segregation isotherm is investigated. When the degree of polymerization of the homopolymer is much larger than that of the diblock copolymer, the normalized interfacial excess (z_i^*/R_g), where R_g is the radius of gyration of an isolated block copolymer chain, is a universal function of that portion of the block copolymer chemical potential due to chain stretching. The existence of such a universal function is predicted by theory and its form is in good agreement with self-consistent mean field calculations. Using these results, one can predict important aspects of the block copolymer segregation (e.g., the saturation interfacial excess) without recourse to the time-consuming numerical calculations. © 1994 John Wiley & Sons, Inc.     

Crystallographic report: Bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The centrosymmetric structure of {Cd[S₂CN(CH₂Ph)₂]₂}₂ features both bridging and chelating dithiocarbamate ligands so that a square pyramidal S₅ coordination geometry results. Copyright © 2004 John Wiley & Sons, Ltd.     

Modeling elastic shells immersed in fluid

We describe a numerical method to simulate an elastic shell immersed in a viscous incompressible fluid. The method is developed as an extension of the immersed boundary method using shell equations based on the Kirchhoff‐Love and the planar stress hypotheses. A detailed derivation of the shell equations used in the numerical method is presented. This derivation, as well as the numerical method, uses techniques of differential geometry. Our main motivation for developing this method is its use in constructing a comprehensive, three‐dimensional computational model of the cochlea (the inner ear). The central object of study within the cochlea is the basilar membrane, which is immersed in fluid and whose elastic properties rather resemble those of a shell. We apply the method to a specific example, which is a prototype of a piece of the basilar membrane, and study the convergence of the method in this case. Some typical features of cochlear mechanics are already captured in this simple model. In particular, numerical experiments have shown a traveling wave propagating from the base to the apex of the model shell in response to external excitation in the fluid. © 2004 Wiley Periodicals, Inc.     

Do the Experimental Violations of Bell Inequalities Require a Non-Local Interpretation of Quantum Mechanics？

Since the data show that Bell inequalities are violated experimentally, we must conclude that any hidden variable theory （which correctly predicts experimental data ） will be non-local. But, to conclude that the experimental violations of Bell inequalities show quantum mechanics to be non-local is unjustified. Specifically, the key assumptions required to obtain a Bell inequality are （ 1 ） locality and （2） the assignment of meaningful （ non- negative） probabilities to seemingly physical correlations （Bell expresses these correlations via ＂ hidden variables＂ ）. Since the Bell inequality is violated by experiment, at least one of these assumptions is wrong. The widespread conclusion that locality must be relinquished is valid only if we retain the previously mentioned correlations （ ＂hidden variables＂ ）. We will demonstrate that the latter are not physical observables - they are not elements of physical reality.     

Encapsulation of ZnS:Mn2+ nanocrystals with diblock copolymers

The encapsulation of the nanocrystalline manganese‐doped zinc sulfide (ZnS:Mn) in poly(styrene‐b‐2vinylpyridine) (PS‐PVP) diblock copolymers is reported. Below the critical micelle concentration in the absence of nanocrystals (NCs), inverse micelles of PS‐PVP were induced by adding ZnS:Mn NCs, the presence of which was confirmed by scanning force microscope and dynamic light scattering. In toluene, a PS‐selective solvent, the less‐soluble PVP blocks preferentially surround the ligand‐coated ZnS:Mn NCs. For PS‐PVP encapsulated ZnS:Mn NCs, the ratio of blue emission to orange emission of ZnS:Mn NCs is dependent on both the concentration of PS‐PVP and the solvent quality. The pyridine of PVP blocks form complexes with the Zn atoms via the nitrogen lone pair and thus the sulfur vacancies are passivated. As a result, the defect‐related blue emission is selectively quenched even when the micelles are not formed. As the concentration of PS‐PVP encapsulating the ZnS:Mn NCs increases, the intensity of blue emission decreases. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3227–3233, 2006