Periodic,multiplicative number-theoretical functions

D. Leitmann andD. Wolke [3] proved that multiplicative functions, which are restrictions of continuous, periodic functionsF: with irrational period, are constant equal to 0 or 1. In this note a simpler proof for this result is given.     

A comparison of two approaches to the optimal positioning of a new product in an attribute space

This paper is concerned with the optimal positioning of a new product in an attribute space. A deterministic optimization model that relies on the axiom of choice is compared with the model byShocker/Srinivasan [1974] that incorporates a probabilistic measure of choice. Investigating the assumptions and the construction of both models, it is shown that the probability function byShocker/Srinivasan is based on a controversial assumption and incorporates a parameter that has not been given an economic explanation. Furthermore, both models are applied to complex configurations. It is demonstrated that the optimal positions for the new product resulting from the model byShocker/Srinivasan depend heavily on the parameter just mentioned and may run contrary to plausible consequences of the axiom of choice.

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Zusammenfassung Für die optimale Gestaltung neuer Produkte, d.h. ihrer Positionierung in einem Raum von Produkteigenschaften, wird ein Modell angeboten, das auf einer deterministischen Kaufentscheidung beruht, ein anderes, das eine stochastische Kaufentscheidung unterstellt. Es wird gezeigt, daß der zuletzt genannte Modelltyp stark von der Spezifikation eines ökonomisch bisher nicht erklärten Parameters abhängt und z.T. Konsequenzen aufweist, die dem Wahlaxiom zuwider laufen, auf das das erstgenannte Modell aufbaut. Durch einen Vergleich auch komplexer Konfigurationen von Käuferbeurteilungen neuer Produkte wird gezeigt, welche Gestaltungsentscheidungen auf der Grundlage der beiden Modelle zur Optimierung einer Zielfunktion zu treffen sind.

     

On the Fourier transformation on spaces of (p,q)-multipliers

LetG denote a locally compact abelian topological group. The aim of the present paper is to prove an “intermediate” result between two well-known results ofL. Hörmander andG. I. Gaudry concerning the structure of the spaces ?_G?μ?t ^p,q (G).     

V-positivity,poverses and the economic global unicity theorems of Gale and Nikaido

Summary Strong theorems concerning globally unique solutions to nonlinear inequalities have been obtained byGale andNikaido via P-matrix characterizations of theJacobians of the mappings involved. We introduce two new concepts here: v-positivity and the poverse. These permit us to state and prove significant generalizations of the theorems just mentioned and, equally important, provide access to preliminary results concerning linear inequalities by the powerful direct techniques of linear programming theory.

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Zusammenfassung Gale undNikaido haben starke Sätze über globale, eindeutige Lösungen nichtlinearer Ungleichungen erhalten für den Fall, daß dieJacobi- Matrix der auftretenden Abbildung eineP-Matrix ist. Darauf aufbauend werden zwei neue Konzepte vorgestellt: v-positivity und die poverse. Diese erlauben es, Verallgemeinerungen der erwähnten Sätze aufzustellen und zu beweisen und, was von gleicher Bedeutung ist, die Verbindung zu früheren Ergebnissen über lineare Ungleichungen durch die wirkungsvollen direkten Verfahren der Theorie der Linearen Optimierung herzustellen.

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This Research was partly supported by Project No. NR 047-021, ONR Contracts NO 0014-67-A-0126-0008 and NO 0014-67-A-0126-0009 with the Center for Cybernetic Studies, The University of Texas.     

Isolation of a carbon nanohoop with M(o)bius topology

Carbon nanohoop,a class of constrained molecular architecture consisting of linked arene units,has attracted considerable interest from both experimental and th...     

Symplectic perturbation series methodology for non-conservative linear Hamiltonian system with damping

In this paper,the symplectic perturbation series methodology of the non-conservative linear Hamiltonian system is presented for the structural dynamic response ...     

Catalyst-and additive-free selective sulfonylation/cyclization of 1,6-enynes with arylazo sulfones leading to sulfonylated γ-butyrolactams

A convenient and regioselective sulfonylation/cyclization of 1,6-enynes with arylazo sulfones has been developed to access a series of sulfonylated γ-butyrolactams.The present reaction could be efficiently conducted under catalyst-and additive-free conditions,in which C-S and C-C bonds were selectively constructed in one-pot procedure.     

Phenothiazine-based covalent organic frameworks with low exciton binding energies for photocatalysis

Designing delocalized excitons with low binding energy (E_b) in organic semiconductors is urgently required for efficient photochemistry because the excitons in most organic materials are localized with a high E_b of >300 meV. In this work, we report the achievement of a low E_b of ∼50 meV by constructing phenothiazine-based covalent organic frameworks (COFs) with inherent crystallinity, porosity, chemical robustness, and feasibility of bandgap engineering. The low E_b facilitates effective exciton dissociation and thus promotes photocatalysis by using these COFs. As a demonstration, we subject these COFs to photocatalytic polymerization to synthesize polymers with remarkably high molecular weight without any requirement of the metal catalyst. Our results can facilitate the rational design of porous materials with low E_b for efficient photocatalysis.

We report the construction of phenothiazine-based covalent organic frameworks, which exhibited diverse structures, the feasibility of bandgap engineering, and unprecedented ultralow exciton binding energy of ∼50 meV for photocatalytic polymerization.     

Effect of Different Processing Methods on the Chemical Constituents of Scrophulariae Radix as Revealed by 2D NMR-Based Metabolomics

Scrophulariae Radix (SR) is one of the oldest and most frequently used Chinese herbs for oriental medicine in China. Before clinical use, the SR should be processed using different methods after harvest, such as steaming, “sweating”, and traditional fire-drying. In order to investigate the difference in chemical constituents using different processing methods, the two-dimensional (2D) ¹H-¹³C heteronuclear single quantum correlation (¹H-¹³C HSQC)-based metabolomics approach was applied to extensively characterize the difference in the chemical components in the extracts of SR processed using different processing methods. In total, 20 compounds were identified as potential chemical markers that changed significantly with different steaming durations. Seven compounds can be used as potential chemical markers to differentiate processing by sweating, hot-air drying, and steaming for 4 h. These findings could elucidate the change of chemical constituents of the processed SR and provide a guide for the processing. In addition, our protocol may represent a general approach to characterizing chemical compounds of traditional Chinese medicine (TCM) and therefore might be considered as a promising approach to exploring the scientific basis of traditional processing of TCM.     

Preparation of nano-hydroxyapatite/poly(<Emphasis Type="SmallCaps">l</Emphasis>-lactide) biocomposite microspheres

Nano-hydroxyapatite (HA)/poly(l-lactide) (PLLA) composite microspheres with relatively uniform size distribution were prepared by a solid-in-oil-in-water (s/o/w) emusion solvent evaporation method. The encapsulation of the HA nanopaticles in microshperes was significantly improved by grafting PLLA on the surface of the HA nanoparticles (p-HA) during emulsion process. This procedure gave a possibility to obtain p-HA/PLLA composite microspheres with uniform morphology and the encapsulated p-HA nanoparticle loading reached up to 40 wt% (33 wt% of pure HA) in the p-HA/PLLA composite microspheres. The microstructure of composite microspheres from core-shell to single phase changed with the variation of p-HA to PLLA ratios. p-HA/PLLA composite microspheres with the diameter range of 2–3 μm were obtained. The entrapment efficiency of p-HA in microspheres could high up to 90 wt% and that of HA was only 13 wt%. Surface and bulk characterizations of the composite microspheres were performed by measurements such as wide angle X-ray diffraction (WAXD), thermal gravimetric analysis (TGA), environmental scanning electron microscope (ESEM) and transmission electron microscopy (TEM).