On nonlinear boundary value problems in the discrete setting

ABSTRACT

Results appearing in this paper can be used to establish the solvability of nonlinear discrete time systems subject to generalized nonlinear boundary conditions. Two separate sets of results are established, each of which can be used to establish existence of solutions to problems for which previous related work proves inconclusive. The first set of results imposes conditions on the sizes of nonlinearities, while the second framework requires geometric properties of the nonlinearity in the dynamics.     

The temperature dependent amide I band of crystalline acetanilide

The temperature dependent anomalous peak in the amide I band of crystalline acetanilide is thought to be due to self-trapped states. On the contrary, according to the present model, the anomalous peak comes from the fraction of ACN molecules strongly hydrogen-bonded to a neighboring ACN molecule, and its intensity decreases because, on average, this fraction decreases as temperature increases. This model provides, for the first time, an integrated and theoretically consistent view of the temperature dependence of the full amide I band and a qualitative explanation of some of the features of nonlinear pump–probe experiments.     

Crystal structure of a spirophosphonium compound,C24H18ClN2P,CH3OH

10,10-(5H,5H)-spirobiphenophosphazinium chloride is one of the few examples of a spirophosphonium salt reported in the literature. This compound crystallized in space groupP2₁/c witha = 12·293(7),b = 13·279(8),c = 17·56(1) Å, = 130·43(3) ° andZ = 4. The finalR index was 0·057. The results of the X-ray analysis indicated that this phosphorus heterocycle may indeed possess aromatic character. This contention was supported in solution by a³¹ P nmr study.Taken in part from the thesis submitted by R. N. Jenkins for the Ph.D. degree, August 1972.     

Preparation, separation, and characterization of ruthenium(II) thiocyanate linkage isomers

The reaction of [(p-cym)Ru(bpy)Cl](+) (p-cym = eta(6)-p-cymene; bpy = 2,2'-bipyridine) with SCN(-) gives a mixture of the linkage isomers [(p-cym)Ru(bpy)(SCN)](+) and [(p-cym)Ru(bpy)(NCS)](+). The linkage isomers were efficiently separated by column chromatography on Hg(NO3)2-coated Al2O3. Both isomers were fully characterized by elemental analysis, (1)H NMR and IR spectroscopy, and X-ray crystallography. The equilibrium constant for the conversion of the S-bound to the N-bound isomer was determined to be 0.29(4) in methanol-d4 and 0.74(7) in acetone-d6, respectively, at 50 degrees C. Kinetic data for the linkage isomerization reaction are also reported.     

Ho2(Co,Si)17化合物的结构与磁晶各向异性

用三弧Czochralski法和真空电弧熔炼法制备了Ho2Co17-xSix化合物.通过X射线衍射和磁性测量手段研究了化合物的结构与内禀磁性.重点讨论了磁晶各向异性和自旋重取向转变.实验结果表明,Ho2Co17为Th2Ni17型六角结构,在0.5≤x≤3的化合物均为Th2Zn17型菱方结构,能够获得单相2:17型化合物的最大Si含量是x=3.在x≤2的浓度范围,化合物的易磁化方向垂直于c轴.随Si含量增加,化合物的居里温度和Co原子平均磁矩单调减少.根据Ho2Co17-xSix化合物的居里温度和自旋重取向温度,获得了磁相图.根据热磁曲线,确定了温度补偿点.在Ho2Co17化合物中观察到了在1005 K发生自旋重取向转变.     

79Kr高自旋超形变的观测

通过５５Ｍｎ（３０Ｓｉ,αｐｎ）反应布居了７９Ｋｒ的高自旋态．用ＧＡＳＰ阵列配以由４０个ΔＥ×ＥＳｉ（Ａｕ）望远镜所组成的带电粒子球实现γγγ－带电粒子符合测量．观测到由相对强度为（２．７±０．３）％的８条级联γ跃迁所组成的７９Ｋｒ高自旋超形变转动带．除了在转动频率ω＞０．９５ＭｅＶ处急剧下降外,该带的动力学转动惯量近乎常数（22ñ2／ＭｅＶ）并被解释为具有四极形变参数β２＝０．５１以及本征侵入组态为π５０ν５１． High-spinstates in 79Kr were populated via the fusion evaporation reaction 55Mn (30Si,αpn)at 130 MeV.Promptγ γγ charged particle coincidences were measured by using the GASP array in conjunction with the ΔE×E Si(Au) charged particle ball.Asu perdeformed band consisting of 8 γ ray transitions with an intensity of (2.7±0.3)% has been indentified in 79Kr.The dynamic moment of inertia for the band is nearly constant at approxately 22ñ2/MeV below arotational frequency of 0.95 MeV...     

运用密度泛函活性理论的信息论方法研究苯并富烯衍生物的芳香性

文献中已有越来越多的芳香性体系被发现,同时也有越来越多的芳香性指标被提出来,但是如何解释芳香化合物稳定性的起源以及理解芳香性的本质仍然是当今理论化学中一个悬而未决的难题。运用我们新近提出的密度泛函活性理论信息论方法,不久前我们曾对一系列富烯衍生物进行了系统研究并得到了一个全新的认识。本文进一步探讨苯并富烯衍生物的芳香性行为,目的在于考察一个或多个苯环与富烯连接之后其芳香性发生变化的情况。运用香农熵,费舍尔信息,Ghosh-Berkowitz-Parr熵,Onicescu信息能,信息增益,以及相对Rényi熵六个信息量,和四种芳香指标,ASE,HOMA,FLU和NICS,我们系统地研究了信息量和芳香性指标在单、双、三苯并富烯衍生物中的相关性。我们发现,不管是否有苯环与富烯相连,芳香指标和信息量的交叉相关性都是一样的。这表明,虽然苯环本身具有芳香性,但苯环与富烯相连并不能改变富烯的芳香性与反芳香性本质。苯并富烯衍生物与富烯衍生物的芳香性和反芳香性一致。苯并富烯衍生物的芳香性和反芳香性完全取决于富烯本身的芳香性和反芳香性。这些结果为认识和理解复杂体系芳香性和反芳香性起源和本质将提供有益的启示。     

蒙药新-Ⅱ中微量硒的测定

采用硒 -硫氰酸钾 -罗丹明 B-明胶 - OP体系分光光度法测定蒙药新 - 中微量硒。其含量为 6 .6—7.3μg· g-1 ,回收率为 94 %— 95 %。     

Simplified categorization of outdoor activities for male and female U.S. indoor workers-a feasibility study to improve assessment of ultraviolet radiation exposures in epidemiologic study questionnaires

Skin cancer studies depend on questionnaires to estimate exposure to ultraviolet light and subsequent risk but are limited by recall bias. We investigate the feasibility of developing a short checklist of categories comprising outdoor activities that can improve sun exposure questionnaires for use in epidemiologic studies. We recruited 124 working and retired U.S. radiologic technologists (52% women). Each subject was instructed to complete a daily activity diary, listing main indoor and outdoor activities between 9:00 A.M. and 5:00 P.M. during a 7 day period. A total of 4697 entries were associated with 1408 h (21.1%) of the total 6944 h spent outdoors. We were able to classify the activities into seven main activity categories: driving, yard work, home-maintenance, walking or performing errands, water activities, other recreational or sports activities and leisure activities or relaxing outside. These activities accounted for more than 94% of time spent outdoors both for working and retired men and women. Our data document the feasibility and guidance for developing a short checklist of outdoor activities for use in epidemiologic questionnaires for estimating sunlight exposures of working and retired indoor workers.     

An environmental model for the interactions of industry with two competing agricultural resources

In this paper we model the interactive dynamics between normal agriculture, auxiliary agriculture, industry and the ecosphere using a system of ordinary non-linear differential equations. We study the long-term effects of each of these assets on each other. Mathematical analyses of the model equations with regard to invariance of non-negativity, dissipativity of solutions, and local and global analyses of the system’s equilibria are carried out. We establish conditions for the existence of a positive interior equilibrium using the theory of uniform persistence.