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.     

Colorimetric and electrochemical Pb~(2+) detection by imine-bridged tetrathiafulvalene-pyridine derivatives

Imine-bridged TTF-π-pyridine derivatives, 2NTTF, 3NTTF and 4NTTF, were synthesized and the cation-binding study was performed. It is noted that with the addition of the micromolar concentration of Pb2+ to the solution, these compounds display remarkable changes in solution color, 1H NMR spectra and electrochemical properties. The nitrogen atom of the imine-bridge in 2NTTF not only serves as a π-conjugated spacer but also participates in the sensing and coordinating properties.     

Simple and efficient synthesis of 3,4-dihydro-2-pyridones via novel solid-supported aza-annulation

A diverse array of 3,4-dihydro-2-pyridones 13 were produced utilizing the unique properties of solid-supported reactions to both drive the reactions to completion and isolate the desired products. The pyridones were synthesized in high purity by a simple sequence of novel steps commencing from an acetophenone-functionalized resin. The para-substituted acetophenone 9 could be anchored to the resin through either a sulfonamide or a carboxamide linkage. The sulfonamide resin 9a, which gave the best results, was treated with several aryl aldehydes and ethoxide to give a variety of chalcones 10a-k in excellent yield (82-99%) upon TFA cleavage. Addition of either methyl or allyl malonate and DBU to 10a-k afforded smoothly the Michael adducts 11a-j (70-99%) which were subsequently cyclized in one step employing acetic acid as a catalyst and several diverse amines to give pure 3,4-dihydro-2-pyridones 13a-p in moderate to excellent yields (30-98%).     

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

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彩色负片印片颗粒指数的准确测定

分析了彩色负片印片颗粒指数σper实际测试中不同性能负片的测试特点和影响因素。印片颗粒指数的测试点应根据彩色负片的感光特性确定,为正常扩印时对应正片0．74中灰密度的负片密度点。影响印片颗粒指数值的两个主要因素是彩色相纸的反差修正系数α和彩色负片的覆盖力系数ECP;建立了α和ECP的实验求取方法,并通过对几种负片参量的实际测定,分析和说明了参量变化对印片颗粒指数数值的影响程度和应进行的修正。     

Er3+-Yb3+共掺磷酸盐玻璃(LGS-L)波导放大器设计

就作者自行研制的Er3 + Yb3 + 共掺磷酸盐玻璃 (LGS L) ,用重叠积分方法进行放大器设计。在Er3 + 、Yb3 + 掺杂浓度分别为 1.5 1× 10 2 6ions/m3 、19.1× 10 2 6ions/m3 的情况下可获得 2 .6dB/cm的增益 ;Er3 + 掺杂浓度为2× 10 2 6ions/m3 时 ,在 4cm的器件上可获得超过 15dB的增益。此外 ,讨论了信号光和抽运光光场强度的横向分布与Er3 + 、Yb3 + 横向掺杂浓度分布之间的重叠对放大器增益的影响 ,放大器的最佳长度 ,以及在 980nm抽运下 ,Yb3 + 、Er3 + 掺杂浓度比对放大器增益的影响。     

远红外契伦柯夫FEL的动力学理论

契伦柯夫自由电子激光可以产生远红外相干受激辐射。本文建立了契伦柯夫自由电子激光的动力学理论并详细研究了初始信号频率,电子束电压和束—介质膜间隙对器件性能的影响。与自由电子激光,回旋自谐振脉塞比较,指出了短波契伦柯夫自由电子激光的几个显著特点。     

Radiative melting of a horizontal clear ice layer

In this paper the horizontal layer of clear ice sticking to the substrate is melted by comparatively short wave radiation similar to solar radiation for the purpose of removing ice from the surface of the material subject to atmospheric icing. The radiating source used for melting is 300 wattages halogen lamps whose color temperature is 3200K at 100 voltages. From the present investigation, a typical phenomenon of backmelting is observed clearly and it can be found that the predicted results including the melting rate of upper and lower layers which are melted by radiant energy impinged on or penetrated the ice layer are in good agreement with the experimental results.

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Aufschmelzen einer waagerechten Klareisschicht durch Strahlung

Zusammenfassung Eine waagerechte Klareisschicht, die auf einer Unterlage aufgefroren war, wurde durch kurzwellige Strahlung, Ähnlich der Sonnenstrahlung, zum Schmelzen gebracht, um die Entfernung von Eis nach atmosphÄrischer Vereisung zu untersuchen. Die Strahlungsquelle war eine 300 Watt-Halogenlampe mit einer Farbtemperatur von 3200 Kelvin bei 100 Volt. Als typische Erscheinung wurde ein Rückseiten-Schmelzen gefunden, im übrigen sind die vorausberechneten Schmelzraten an der Ober- und der Unterseite durch aufgenommene oder durchgelassene Strahlungsenergie in guter übereinstimmung mit den Messungen.

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Nomenclature a_v monochromatic absorption coefficient - A transmission (= q _r ⁺ {h_i}/q_ro) - c_p specific heat - E_bv monochromatic emissive power - h_D mass transfer coefficient - h_i initial thickness of ice layer - h_m thickness of substrate - L_i latent heat of melting - L_w latent heat of evaporation or condensation - heat flux absorbed at surface of substrate - q_r0 radiant heat flux impinged onto ice or free surface - q _r ⁺ {y} forward radiant heat flux - q _r ^– {y} backward radiant heat flux - S₁ thickness of upper melt layer - S₂ thickness of lower melt layer - S'₂ distance from free surface to bottom surface of ice layer - t time - T temperature - T₁ temperature of air-water or air-ice interface - T₂ temperature of substrate surface - T₃ temperature of back side surface of substrate - T_b temperature of radiating source - T_i temperature in ice layer - T_w1 temperature in upper melt layer - T_w2 temperature in lower melt layer - T environmental temperature - W_w saturated vapor concentration at free surface - W_t8 vapor concentration at environment - y distance from free or ice surface - y grid size of water or ice - y_m grid size of substrate Greek symbols heat transfer coefficient - spectral absorptivity - _t total absorptivity - _i thermal diffusivity of ice - _m thermal diffusivity of substrate - _w thermal diffusivity of water - _i thermal conductivity of ice - _m thermal conductivity of substrate - _w thermal conductivity of water - wavelength - _av densitiy of air-vapor mixture - _i density of ice - Stefan-Boltzman constant     

EFFECT OF POLYETHYLENEIMINE ON THE PROPERTIES OF CONCENTRATED SUSPENSIONS OF TITANIUM DIOXIDE MICROBEADS

The effect of polyethyleneimine (PEI) concentration on the properties of titanium dioxide (TiO2) suspensions is studied with or without the addition of an electrolyte (barium acetate). Measurements of the apparent viscosity and the stability of TiO2 suspensions showed that PEI is an effective dispersant for TiO2 particles in suspension in the absence of an electrolyte, not only reducing the viscosity of the suspension but also increasing its stability. In the presence of an electrolyte, however, small quantities of polyethyleneimine could neither disperse the TiO2 particles nor de-crease the viscosity of the TiO2 suspensions; only PEI concentrations beyond saturation adsorption could perceptively improve the stabilitv of TiO2 suspensions.