Path integrals over the group manifolds

Particle motion in the SU(2) manifold is quantized by path integrals. It is shown that the Poschl-Teller, Wood-Saxon, and Rosen-Morse potentials are solved by relating their propagators to the path integrations over the SU(2) manifold. Examples with some other groups are mentioned.     

Particle production in a class of anisotropic cosmologies

Scalar particle production is studied in a class of anisotropic spacetimes which are the exact solutions of Einstein equations with a perfect stiff fluid. Massless field creations are also discussed.     

Die Sechseck-n-Waben in der Ebene,welche von n Kreisbüscheln erzeugt werden

In this paper, the problem of determining the pencils of circles which form a hexagonal n-web in E₂, is completely solved. It is well-known that n pencils of circles orthogonal to a fixed circle form a hexagonal n-web. Therefore, the main problem is the determination of all circle pencils which form a hexagonal n-web and which do not cut a fixed circle orthogonally. In this connection the following results have been obtained: The number of hexagonal 4-webs is six, whereas the number of hexagonal 5-webs is two.Finally, after having proved that the number of hexagonal 6-webs is one, it is shown that, for n7, there exist no circle pencils forming a hexagonal n-web without being orthogonal to a fixed circle.     

Pure uterine lipoma

Lipomatous tumors of the uterus are unusual, benign neoplasms seen in postmenopausal women. Although many of the mixed-type cases such as lipoleiomyoma and fibrolipoma have been reported, pure uterine lipomas are extremely rare. In the literature, a few cases with pure uterine lipoma have been reported. We first present the advanced magnetic resonance findings of pure uterine lipoma, followed by those of ultrasonography (US) and computed tomography (CT). We markedly detected lipid peaks on the magnetic resonance spectroscopy (MRS) and the apparent diffusion coefficient value to be 0.00 due to chemical-shift effects with diffusion-weighted imaging (DWI). Although pelvic lipomatous tumors can be diagnosed with US and CT, in some cases, further workup may be required to localize the lesion. MRI may yield more valuable data for differential diagnosis. MRS and DWI findings provide additional clues on the nature of the lesion.     

奇异摄动初值问题的一致收敛有限差分法

通过一阶和二阶导数讨论了带小参数的线性二阶常微分方程的初值问题.在均匀网格上得出了带常数拟合因子的指数型拟合差分格式,给出了离散最大模意义上的一阶一致收敛性.文中给出了数值结果.     

An unusual case of acute disseminated encephalomyelitis confined to brainstem

Acute disseminated encephalomyelitis (ADEM) is an immune-mediated demyelinating disorder usually encountered in children or adolescents and characterized by multifocal neurological deficits of rapid onset. Typical target areas of demyelination include the corona radiata, centrum semiovale, periventricular white matter, cerebellar peduncles and brainstem. Involvement of deep gray matter nuclei is also frequent. We report a 6-year-old boy with ADEM who had only brainstem involvement. Serial magnetic resonance images representing the stage of disease and response to steroid treatment are presented.     

A parameter-uniform numerical method for a Sobolev problem with initial layer

The present study is concerned with the numerical solution, using finite difference method of a one-dimensional initial-boundary value problem for a linear Sobolev or pseudo-parabolic equation with initial jump. In order to obtain an efficient method, to provide good approximations with independence of the perturbation parameter, we have developed a numerical method which combines a finite difference spatial discretization on uniform mesh and the implicit rule on Shishkin mesh(S-mesh) for the time variable. The fully discrete scheme is shown to be convergent of order two in space and of order one expect for a logarithmic factor in time, uniformly in the singular perturbation parameter. Some numerical results confirming the expected behavior of the method are shown.      

SERS-based sandwich immunoassay using antibody coated magnetic nanoparticles for Escherichia coli enumeration

A method combining immunomagnetic separation (IMS) and surface-enhanced Raman scattering (SERS) was developed to enumerate Escherichia coli (E. coli). Gold-coated magnetic spherical nanoparticles were prepared by immobilizing biotin-labeled anti-E. coli antibodies onto avidin-coated magnetic nanoparticles and used in the separation and concentration of the E. coli cells. Raman labels have been constructed using rod shaped gold nanoparticles coated with 5,5-dithiobis-(2-nitrobenzoic acid) (DTNB) and subsequently with a molecular recognizer. Then DTNB-labeled gold nanorods were interacted with gold-coated magnetic spherical nanoparticle-antibody-E. coli complex. The capture efficiency and calibration graphs were obtained and examined in different E. coli concentrations (10(1)-10(7) cfu mL(-1)). The correlation between the concentration of bacteria and SERS signal was found to be linear within the range of 10(1)-10(4) cfu mL(-1) (R(2) = 0.992). The limit of detection (LOD) and limit of quantification (LOQ) values of the developed method were found to be 8 and 24 cfu mL(-1), respectively. The selectivity of the developed immunoassay was examined with Enterobacter aerogenes, Enterobacter dissolvens, and Salmonella enteriditis which did not produce any significant response. The ability of the immunoassay to detect E. coli in real water samples was also investigated and the results were compared with the experimental results from plate-counting methods. There was no significant difference between the methods that were compared (p > 0.05). This method is rapid and sensitive to target organisms with a total analysis time of less than 70 min.     

Solution of the path integral for the H-atom

The Green's function of the H-atom is calculated by a simple reduction of Feynman's path integral to gaussian form.