Abstract:
Diabetic retinopathy (DR) is a common cause of blindness. Although many studies have indicated an association between homocysteine and DR, the results so far have been equivocal. Amongst the many determinants of homocysteine, B-vitamin status was shown to be a major confounding factor, yet very little is known about its relationship to DR. In the present study, we, therefore, investigated the status of B-vitamins and homocysteine in DR. A cross-sectional case–control study was conducted with 100 normal control (CN) subjects and 300 subjects with type-2 diabetes (T2D). Of the 300 subjects with T2D, 200 had retinopathy (DR) and 100 did not (DNR). After a complete ophthalmic examination including fundus fluorescein angiography, the clinical profile and the blood levels of all B-vitamins and homocysteine were analyzed. While mean plasma homocysteine levels were found to be higher in T2D patients compared with CN subjects, homocysteine levels were particularly high in the DR group. There were no group differences in the blood levels of vitamins B1 and B2. Although the plasma vitamin-B6 and folic acid levels were significantly lower in the DNR and DR groups compared with the CN group, there were no significant differences between the diabetes groups. Interestingly, plasma vitamin-B12 levels were found to be significantly lower in the diabetes groups compared with the CN group; further, the levels were significantly lower in the DR group compared with the DNR group. Higher homocysteine levels were significantly associated with lower vitamin-B12 and folic acid but not with other B-vitamins. Additionally, hyperhomocysteinemia and vitamin-B12 deficiency did not seem to be related to subjects' age, body mass index, or duration of diabetes. These results thus suggest a possible association between vitamin-B12 deficiency and hyperhomocysteinemia in DR. Further, the data indicate that vitamin-B12 deficiency could be an independent risk factor for DR.

Abstract:
La_{0.75}Sr_{0.25}Cr_{0.5}Mn_{0.5}O_{3}-δ (LSCM) perovskite nanoparticles for use as anode material in intermediate temperature solid oxide fuel cells (IT-SOFCs) were synthesized using 3,3’,3”- nitrilotripropionic acid (NTP), citric acid and oxalic acid as carriers via a combustion method. The influence of the carrier on phase and morphology of the obtained pristine products was characterized using X-ray diffraction (XRD), thermal gravimetric analysis (TGA), and scanning electron microscopy (SEM). XRD results showed, that the LSCM had rhombohedral symmetry with R-3c space group; a single phase LSCM perovskite formed after calcination of fired gel at 1200°C for 7 h. Scanning electron microscopy analysis of the pristine powders showed spherical shape and particle sizes in the range of 50 – 500 nm.

Abstract:
In plane Couette flow, the incompressible fluid between two plane parallel walls is driven by the motion of those walls. The laminar solution, in which the streamwise velocity varies linearly in the wall-normal direction, is known to be linearly stable at all Reynolds numbers ($Re$). Yet, in both experiments and computations, turbulence is observed for $Re \gtrsim 360$. In this article, we show that for certain {\it threshold} perturbations of the laminar flow, the flow approaches either steady or traveling wave solutions. These solutions exhibit some aspects of turbulence but are not fully turbulent even at $Re=4000$. However, these solutions are linearly unstable and flows that evolve along their unstable directions become fully turbulent. The solution approached by a threshold perturbation could depend upon the nature of the perturbation. Surprisingly, the positive eigenvalue that corresponds to one family of solutions decreases in magnitude with increasing $Re$, with the rate of decrease given by $Re^{\alpha}$ with $\alpha \approx -0.46$.

Abstract:
We report the computation of a family of traveling wave solutions of pipe flow up to $Re=75000$. As in all lower-branch solutions, streaks and rolls feature prominently in these solutions. For large $Re$, these solutions develop a critical layer away from the wall. Although the solutions are linearly unstable, the two unstable eigenvalues approach 0 as $Re\to\infty$ at rates given by $Re^{-0.41}$ and $Re^{-0.87}$ -- surprisingly, the solutions become more stable as the flow becomes less viscous. The formation of the critical layer and other aspects of the $Re\to\infty$ limit could be universal to lower-branch solutions of shear flows. We give implementation details of the GMRES-hookstep and Arnoldi iterations used for computing these solutions and their spectra, while pointing out the new aspects of our method.

Abstract:
The phenomenon of bursting, in which streaks in turbulent boundary layers oscillate and then eject low speed fluid away from the wall, has been studied experimentally, theoretically, and computationally for more than 50 years because of its importance to the three-dimensional structure of turbulent boundary layers. We produce five new three-dimensional solutions of turbulent plane Couette flow, one of which is periodic while four others are relative periodic. Each of these five solutions demonstrates the break-up and re-formation of near-wall coherent structures. Four of our solutions are periodic but with drifts in the streamwise direction. More surprisingly, two of our solutions are periodic but with drifts in the spanwise direction, a possibility that does not seem to have been considered in the literature. We argue that a considerable part of the streakiness observed experimentally in the near-wall region could be due to spanwise drifts that accompany the break-up and re-formation of coherent structures. We also compute a new periodic solution of plane Couette flow that could be related to transition to turbulence.

Abstract:
The Kleiser-Schumann algorithm has been widely used for the direct numerical simulation of turbulence in rectangular geometries. At the heart of the algorithm is the solution of linear systems which are tridiagonal except for one row. This note shows how to solve the Kleiser-Schumann problem using perfectly triangular matrices. An advantage is the ability to use functions in the LAPACK library. The method is used to simulate turbulence in channel flow at $Re=80,000$ (and $Re_{\tau}=2400$) using $10^{9}$ grid points. An assessment of the length of time necessary to eliminate transient effects in the initial state is included.

Abstract:
In this note, we identify a natural class of subsets of affine Weyl groups whose Poincare series are rational functions. This class includes the sets of minimal coset representatives of reflection subgroups. As an application, we construct a generalization of the classical length-descent generating function, and prove its rationality.

Abstract:
We give an elementary combinatorial proof of a special case of a result due to Bazlov and Ion concerning the Fourier coefficients of the Cherednik kernel. This can be used to give yet another proof of the classical fact that for a complex simple Lie algebra, the partition formed by its exponents is dual to that formed by the numbers of positive roots at each height.

Abstract:
We show that the rank 10 hyperbolic Kac-Moody algebra $E_{10}$ contains every simply laced hyperbolic Kac-Moody algebra as a Lie subalgebra. Our method is based on an extension of earlier work of Feingold and Nicolai.

Abstract:
The Chebyshev points are commonly used for spectral differentiation in non-periodic domains. The rounding error in the Chebyshev approximation to the $n$-the derivative increases at a rate greater than $n^{2m}$ for the $m$-th derivative. The mapping technique of Kosloff and Tal-Ezer (\emph{J. Comp. Physics}, vol. 104 (1993), p. 457-469) ameliorates this increase in rounding error. We show that the argument used to justify the choice of the mapping parameter is substantially incomplete. We analyze rounding error as well as discretization error and give a more complete argument for the choice of the mapping parameter. If the discrete cosine transform is used to compute derivatives, we show that a different choice of the mapping parameter yields greater accuracy.