Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

带风险指数的金融均衡的存在性定理及其结构特征(下)

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、虚资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Duffie，D＆W．Shfer（1985）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下会随机风险因素的情形，也适用于商品空间为无限维的情形，除此之外，还给出了怎样判别资产结构是否属于T类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均市分配不确定性的反却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

A new method for the quantitative analysis of organochlorine pesticides and polychlorinated biphenyls

A simple method is described for the quantitative determination of organochlorine pesticides and polychlorinated biphenyls (PCB's) in water at the sub-ppb level. A micro gas-phase extractor advantageously replaces other preconcentration and purification techniques. The extract is analyzed by capillary gas chromatography without further enrichment. The recovery at the ppb level was nearly 100% for organochlorine pesticides and more than 80% for PCB's. The complete procedure including sample preparation, steam distillation-extraction, and capillary gas chromatographic analysis is carried out in less than four hours.     

Cardinality enrichment of flexible cross correlation (FCC) code for SAC-OCDMA system by alleviation interference scheme (AIS)

In this paper, we propose an alleviation interference scheme (AIS) for spectral amplitude coding (SAC) – optical code division multiple access (OCDMA) coding system approaches. The AIS SAC-OCDMA systems is demonstrated by utilizing the new flexible cross correlation (FCC) code. The FCC code has advantages, such as flexibility in-phase cross-correlation at any given number of users and weights, as well as effectively reduces the impacts of phase-induced intensity noise (PIIN) and has the multiple-access interference (MAI) cancelation property. The results indicated good performance whereas the FCC (W = 4, K = 150) AIS SAC-OCDMA coding system offers 66%, 172%, 650% and 900% percentage of cardinality enrichments as a contrast to DCS (W = 4, K = 90), MDW (W = 4, K = 55), MFH (W = 4, K = 20) and Hadamard (W = 8, K = 15) codes, respectively. Finally, the FCC AIS SAC-OCDMA coding system has low effective receive power Psr = −21 dBm which is expected to be more significant for future SAC-OCDMA coding systems without requiring any amplification at the receiving plant.     

Time-like proton form factor measurement with P(-)ANDA

The electromagnetic probe is an excellent tool to investigate the structure of the nucleon. The nearly 4π detector PANDA, will allow to make a precise determination of the electromagnetic form factors of the proton in the time-like region with unprecedented precision. In the one-photon exchange approximation, the center of mass unpolarized differential cross section of the reaction pp → e~+e~- is a linear combination of the squared moduli of the electric G_E and magnetic G_M proton form factors. The precise measurement of the angular distribution over almost full angular range then directly gives these quantities. At present only two experiments have provided the ratio R = |G_E|/|G_M| but with large statistical uncertainties. It is shown that with strict PID cuts and a kinematic fit, the dominant background, (p)p→π~+π~-, can be supressed to much less than 1% of the signal, without affecting the extraction of the ratio R. PANDA will therefore offer a unique opportunity to measure the ratio with a precision ranging from <1% at low q~2 up to 30 % for q~2 =14 (GeV/c)~2.     

Calcium isotope fractionation in liquid chromatography with crown ether resin in methanol medium

Breakthrough mode liquid chromatography was employed to investigate calcium (Ca) isotope fractionation in methanol medium. Highly porous silica beads, the inner pores of which were embedded with a benzo-18-crown-6 ether resin, were used as column packing material. Enrichment of heavier isotopes of Ca was observed in the frontal part of the respective Ca chromatograms. The values of the isotope fractionation coefficient (?) were in the order of 10^?3 at 25 °C. Use of methanol as solvent has little advantage over the aqueous system as far as the values of ? are concerned. However, a substantial improvement was observed concerning the adsorption capacity of the crown ether resin for Ca ions. Molecular orbital calculations supported the present isotopic results in a qualitative fashion.     

Phase signatures in laser-assisted electron-atom collisions

We study electron-atom scattering in the presence of a laser field with elliptic polarization. We discuss the dependence of the differential cross sections for the cases of circular and linear polarizations as a function of scattering angle. Interesting typical signatures of the phase between the two components of the circular polarization of the laser field appear in the differential cross section.     

A Thomas-Fermi type picture and the electromagnetic structure of the nucleon

Using a Thomas-Fermi type picture of the nucleon as a dense system of quarks and antiquarks, we give a rationale for the ‘dipole’ nature, scaling and other characteristics of the nucleon electromagnetic form factors. Similar considerations are then given for the electromagnetic structure of the pion.     

Analysis of two neutron (proton) transfer reaction data in the Zr-region

The spectroscopic amplitudes, form factors, angular distributions and total cross-sections for two nucleon transfer reactions in Zr-region in the zero range distorted wave Born approximation are calculated using consistent set of shell model wave functions. A single normalisation factor gives a good fit to all the two neutron transfer reaction data whereas the corresponding fit for the two-proton transfer reaction data is less satisfactory.