Dispersion relation of excitation mode in spin-polarized Fermi gas

We study the dispersion relation of the excitation mode in a spin-polarized Fermi gas.In the frame of the imaginarytime finite temperature field theory,the polarization tensor is calculated by taking the random phase approximation.The population imbalance effects on the dispersion relation of the excitation mode and the spin-spin correlation susceptibility are investigated.The numerical results in terms of the imbalance ratio indicate the polarization effects on the dispersion relation and susceptibility χ.     

On jet-convex functions and their tensor products

In this article, we introduce necessary and sufficient conditions for the tensor product of two convex functions to be convex. For our analysis we introduce the notions of true convexity, jet-convexity, true jet-convexity as well as true log-convexity. The links between jet-convex and log-convex functions are elaborated. As an algebraic tool, we introduce the jet product of two symmetric matrices and study some of its properties. We illustrate our results by an application from global optimization, where a convex underestimator for the tensor product of two functions is constructed as the tensor product of convex underestimators of the single functions.     

Extraction of hydroxyaromatic compounds in river water by liquid-liquid-liquid microextraction with automated movement of the acceptor and the donor phase

Liquid-liquid-liquid microextraction with automated movement of the acceptor and the donor phase technique is described for the extraction of six hydroxyaromatic compounds in river water using a disposable and ready to use hollow fiber. Separation and quantitative analyses were performed using LC with UV detection at 254 nm. Analytes were extracted from the acidified sample solution (donor phase) into the organic solvent impregnated in the pores of the hollow fiber and then back extracted into the alkaline solution (acceptor phase) inside the lumen of the hollow fiber. The fiber was held by a conventional 10 microL LC syringe. The acceptor phase was sandwitched between the plunger and a small volume of the organic solvent (microcap). The acceptor solution was repeatedly moved in and out of the hollow fiber using a syringe pump. This movement provides a fresh acceptor phase to come in contact with the organic phase and thus enhancing extraction kinetics thereby leading to the improvement in enrichment of the analytes. The microcap separates the acceptor phase and the donor phase in addition to being partially responsible for mass transfer of the analytes from the donor solution to the acceptor solution. Under stirring, a fresh donor phase will enter through the open end of the fiber that will also contribute to the mass transfer. Various parameters affecting the extraction efficiency viz type of organic solvent, extraction time, stirring speed, effect of sodium chloride, and concentration of donor and acceptor phases were studied. RSD (3.9-5.6%), correlation coefficient (0.995-0.997), detection limit (2.0-51.2 ng/mL), enrichment factor (339-630), relative recovery (93.2-97.9%), and absolute recovery (33.9-63.0%) have also been investigated. The developed method was applied for the analysis of river water.     

Greybody factor for a scalar field coupling to Einstein's tensor

We study the greybody factor and Hawking radiation for a scalar field coupling to Einstein's tensor in the background of Reissner–Nordström black hole in the low-energy approximation. We find that the presence of the coupling terms modifies the standard results in the greybody factor and Hawking radiation. Our results show that both the absorption probability and Hawking radiation increase with the coupling constant. Moreover, we also find that for the stronger coupling, the charge of black hole enhances the absorption probability and Hawking radiation of the scalar field, which is different from those of ones without coupling to Einstein's tensor in the black hole spacetime.     

Efficient anisotropic filtering of diffusion tensor images

To improve the accuracy of structural and architectural characterization of living tissue with diffusion tensor imaging, an efficient smoothing algorithm is presented for reducing noise in diffusion tensor images. The algorithm is based on anisotropic diffusion filtering, which allows both image detail preservation and noise reduction. However, traditional numerical schemes for anisotropic filtering have the drawback of inefficiency and inaccuracy due to their poor stability and first order time accuracy. To address this, an unconditionally stable and second order time accuracy semi-implicit Craig-Sneyd scheme is adapted in our anisotropic filtering. By using large step size, unconditional stability allows this scheme to take much fewer iterations and thus less computation time than the explicit scheme to achieve a certain degree of smoothing. Second-order time accuracy makes the algorithm reduce noise more effectively than a first order scheme with the same total iteration time. Both the efficiency and effectiveness are quantitatively evaluated based on synthetic and in vivo human brain diffusion tensor images, and these tests demonstrate that our algorithm is an efficient and effective tool for denoising diffusion tensor images.