On the use of immersed boundary methods for shock/obstacle interactions

This paper describes the implementation of immersed boundary method using the direct-forcing concept to investigate complex shock–obstacle interactions. An interpolation algorithm is developed for more stable boundary conditions with easier implementation procedure. The values of the fluid variables at the embedded ghost-cells are obtained using a local quadratic scheme which involves the neighboring fluid nodes. Detailed discussions of the method are presented on the interpolation of flow variables, direct-forcing of ghost cells, resolution of immersed-boundary points and internal treatment. The method is then applied to a high-order WENO scheme to simulate the complex fluid–solid interactions. The developed solver is first validated against the theoretical solutions of supersonic flow past triangular prism and circular cylinder. Simulated results for test cases with moving shocks are further compared with the previous experimental results of literature in terms of triple-point trajectory and vortex evolution. Excellent agreement is obtained showing the accuracy and the capability of the proposed method for solving complex strong-shock/obstacle interactions for both stationary and moving shock waves.     

On hypersurfaces in a Riemannian vector bundle with prescribed Gaussian curvature and convexity

Let M be a compact Riemannian manifold, E a Riemannian vector bundle on M and the unit subbundle of E. We prove that there is no radial graph on with a strictly positive Gaussian curvature and that the Gaussian curvature of a convex radial graph must be identically equal to zero. Moreover, by solving on a nonlinear degenerate equation of Monge-Ampère type, we prove the existence of radial graphs having simultaneously a Gaussian curvature identically equal to zero and a prescribed strictly positive vertical Gaussian curvature.Mathematics Subject Classification (2000):35J60, 53C55, 58G30     

Studies on the Reduction of the Nitro Group in 4-Nitroindazoles by Anhydrous SnCl2 in Different Alcohols

The bakers' yeast reduction of a number of alkyl levulinates occurs in good to moderate yields to give the corresponding (S) alcohols in > 98% ee. The (S) alcohol la has been converted to synthetically useful (S)- or (R)-4- methylbutyro-lactone and (S)-(+)-l,4-pentanediol in good yields.     

A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI VARIATIONAL INEQUALITIES

The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.     

Synthesis and in vitro cytotoxicity studies of novel triazolo[4,3-b]pyridazinones

New triazolo[4,3-b]pyridazinones were synthesized and evaluated for their potential in vitro cytotoxic antitumor properties. The compounds were prepared by 1,3-dipolar cycloaddition of pyridazin-3-ones with N-aryl-C-ethoxycarbonylnitrile imines, generated in situ from ethylhydrazono-á-bromoglyoxylates. The peri- and regioselectivity of the reaction were ascertained by ¹H and ¹³C NMR spectroscopy of the cycloadducts.     

A version of Wiener’s and Lévy’s theorems

We obtain weighted algebra analogues of the classical theorems of N. Weiner and P. Lévy on absolutely convergent Fourier series      

A self-adaptive descent LQP alternating direction method for the structured variational inequalities

Numerical Algorithms - In this paper, by combining the logarithmic-quadratic proximal (LQP) method and alternating direction method, we proposed an LQP alternating direction method for solving...     

Results of Vidav-Palmer Type in m-Convex Algebras

Using the notion of a normal cone, we give results of Vidav-Palmer type in terms of hermitian, quasi-hermitian and uniformly quasi-hermitian elements. Consequences are also given.     

Microporous membranes obtained from polypropylene blends with superior permeability properties

A blend of two polypropylene resins, different in molecular structure, one with linear chains and the other with long chain branches, was investigated to develop microporous membranes through melt extrusion (cast film process) followed by film stretching. The branched component significantly affected the row‐nucleated lamellar crystalline structure in the precursor films. The arrangement and orientation of the crystalline and amorphous phases were examined by wide angle X‐ray diffraction and Fourier transform infrared spectroscopy methods. It was found that blending of a small amount of a long chain branched polypropylene improved the orientation of the both crystalline and amorphous phases in the precursor films. Annealing, followed by cold and hot stretching were consequently employed to generate and enlarge pores in the films as a result of lamellae separation. SEM micrographs of the surface of the membranes obtained from the blend revealed elongated thin fibrils and a large number of lamellae. The lamellae thickness for the blend was much shorter in comparison to that of the linear PP precursor film. The permeability of the samples to water vapor and N₂ was significantly enhanced (more than twice) for the blend system. The porosity of the blend membrane showed a significant improvement with a value of 53% compared to 41% for the linear PP membrane. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 148–157, 2008