Experimental investigation on large deflection response of a frame impacted by a moving body

This paper reports on the experimental investigation of the dynamic large deflection response of a portal frame impacted at its midspan by a body moving at a certain speed. Both the deflection and velocity vs. time curves of the midspan and the dynamic history of a number of desired locations were recorded during the process of response. On the basis of the test data, the momentum and kinetic energy conversion between the frame and the moving body in the impact process are realized, and the occurrence and expansion of plastic regions are described. Investigation results show that the initial collision is approximately ideally inelastic, and that the elastic deformation plays a considerable role in the response though the input energy is much larger than the maximum elastic energy capacity of the beam member; therefore, in a general impact, the energy ratio should not be regarded as a sufficient criterion for a rigid—plastic solution. The ratios of the impulse transferred to and the energy absorbed by the frame in the initial collision to that carried by the moving body before impact is only related to the ratiobetween the equivalent mass of the frame paticipating in the initial collision and the mass of the impacting body, having nothing to do with the impacting velocity to a certain extent.     

New Aspects of Cyclodextrin Chemistry Induced by Outside Type Complex Formation; Asymmetric Reduction of Indol-3-Pyruvic Acid with NaBH4 in Aqueous Solution

Asymmetric reduction of indol-3-pyruvic acid (IPA) with NaBH₄ in aqueous solution in the presence of various cyclodextrins (α-, β-, γ-, mono-6-amino-6-deoxy-β- and di-6^ABamino-6^AB-deoxy-β-cyclodextrin) was investigated. From the NMR and circular dichroism spectral studies, the conformation of the CyD–substrate complexes is suggested; the part of carboxylic group stay in the cavity of α-CyD, whole of IPA in β-CyD, two molecules in a γ-CyD cavity, and IPA(s) is/are on the rim of the cavity of mono-6-amino-6-deoxy-β- and di-6^ABamino-6^AB-deoxy-β-CyD (AβCyD, DAβCyD) with electrostatic interaction between amino group and carboxylic group. This conformational difference provides in the difference in the optical selectivity of reduction.     

Splitless injection of up to hundreds of microliters of liquid samples in capillary GC: Part II,experimental results

Sample evaporation in splitless injection of large volumes is rapid: depending on the experiment, results indicate that 200 μl of hexane, for instance, evaporates in 2–10 s, producing vapor at a rate of many hundreds of milliliters per minute. A 60 × 4 mm packed bed of 20–35 mesh Tenax TA enabled injection of 200 μl volumes of all solvents tested, and even 1 ml injections were possible provided they were performed over a period of 30 s. Retention of volatile sample components depends on the sample solvent, the injection volume, and the injection speed, but only little on the injector temperature. Losses of n-tridecane varied from hardly 15 % (when dissolved in pentane) to ca 60 % (ethyl acetate); losses of n-heptadecane were usually below 20 %. The column temperature during injection should be at least ca 20–30°C above the standard solvent boiling point.     

大型液相色谱分离过程FAD－SMT数学模型及其数值解

提出大型液相色谱分离过程ＦＡＤ－ＳＭＴ数学模型，把色谱分离连续性方程转变为对流扩散方程和常微分方程组，并提出模型的数值方法，分析了数值解的稳定条件和收敛条件以及空间和时间步长的选取。实验结果表明，ＦＡＤ－ＳＭＴ数学模型计算的液相色谱分离葡萄糖、果糖和分离甘露醇、山梨醇理论与实验流出曲线相吻合。灵敏度分析结果表明：相平衡常数比轴向扩散系数和总传质系数对色谱分离有较大的影响。     

Enthalpic determinations of aliphatic ester-solvent systems with correlations

Calorimetric measurements were carried out on ester-solvent systems where the esters were H(CH₂)_xCOO(CH₂)_yH, with x and y varying from 1 to 5, and the solvents were n-hexane and 1,2-dichloroethane. Calculation of the enthalpies of cavity formation enabled the enthalpies of interaction to be determined. Both enthalpies correlated with number of carbon atoms N, equal to x+y in the esters, giving for 1,2-dichloroethane

Range-Renewal Processes: SLLNs and Power Laws*

Given n samples(viewed as an n-tuple) of a γ-regular discrete distribution π,in this article the authors concern with the weighted and unweighted graphs induced by the n samples. They first prove a series of SLLN results(of Dvoretzky-Erd¨os’ type). Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1 + γ. They also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distribu...     

The existence of minimal large positive solutions for a class of nonlinear cooperative systems

In this paper we establish the existence of the minimal large positive solution for a general class of nonlinear cooperative systems including the simplest prototype of García-Melián et al. (2016). Precisely, based on the existence of a large positive supersolution, we can infer the existence of the minimal large positive solution. Moreover, we also give some sufficient easily computable conditions for the existence of a large positive supersolution. Our results generalize, very substantially, some of the findings of García-Melián et al. (2016) adopting a rather novel methodology.     

Large deviations for martingales with some applications

Let(X _i ) be a martingale difference sequence. LetY be a standard normal random variable. We investigate the rate of uniform convergence

Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.