{\boldsymbol(}\boldsymbol{\mathcal{Z}}_{\bf 1}, \boldsymbol{\mathcal{Z}}_{\bf 2}{\boldsymbol)}-Complete Partially Ordered Sets and Their Representations by \boldsymbol{\mathcal{Q}}-Spaces

The present paper proposes a general theory for $\left( \mathcal{Z}_{1}, \mathcal{Z}_{2}\right) $ -complete partially ordered sets (alias $\mathcal{Z} _{1}$ -join complete and $\mathcal{Z}_{2}$ -meet complete partially ordered sets) and their Stone-like representations. It is shown that for suitably chosen subset selections $\mathcal{Z}_{i}$ (i?=?1,...,4) and $\mathcal{Q} =\left( \mathcal{Z}_{1},\mathcal{Z}_{2},\mathcal{Z}_{3},\mathcal{Z} _{4}\right) $ , the category $\mathcal{Q}$ P of $\left( \mathcal{Z}_{1},\mathcal{Z}_{2}\right) $ -complete partially ordered sets and $\left( \mathcal{Z}_{3},\mathcal{Z}_{4}\right) $ -continuous (alias $\mathcal{ Z}_{3}$ -join preserving and $\mathcal{Z}_{4}$ -meet preserving) functions forms a useful categorical framework for various order-theoretical constructs, and has a close connection with the category $\mathcal{Q}$ S of $\mathcal{Q}$ -spaces which are generalizations of topological spaces involving subset selections. In particular, this connection turns into a dual equivalence between the full subcategory $ \mathcal{Q}$ P _s of $\mathcal{Q}$ P of all $\mathcal{Q}$ -spatial objects and the full subcategory $\mathcal{Q}$ S _s of $\mathcal{Q}$ S of all $\mathcal{Q}$ -sober objects. Here $\mathcal{Q}$ -spatiality and $\mathcal{Q}$ -sobriety extend usual notions of spatiality of locales and sobriety of topological spaces to the present approach, and their relations to $\mathcal{Z}$ -compact generation and $\mathcal{Z}$ -sobriety have also been pointed out in this paper.     

A unified three point approximating subdivision scheme

In this paper,we propose a three point approximating subdivision scheme,with three shape parameters,that unifies three different existing three point approximating schemes.Some sufficient conditions for subdivision curve C0 to C3 continuity and convergence of the scheme for generating tensor product surfaces for certain ranges of parameters by using Laurent polynomial method are discussed.The systems of curve and surface design based on our scheme have been developed successfully in garment CAD especially for clothes modelling.     

一些随机重合点定理

本文引入了一种满足更一般的收缩不等式的多重函数类,并证明了属于该类的可测多重函数对的一些随机重合点定理。     

Reaction of electron rich heterocycles with electrophiles. Formylation of indoles via thiomethylation

The formylation of indoles 1 by dithiocarbenium-ions 2 is discussed. The reaction proceeds to thioacetals 4 under mild conditions. Longer reaction times yield bisindolylmonomethylcyanines 5–6 . Generally, the reaction is inhibited by the presence of electron-withdrawing groups at the pyrrol nucleus of indole 1 , e.g. an acetyl group.     

Dye and its removal from aqueous solution by adsorption: A review

In this review article the authors presented up to-date development on the application of adsorption in the removal of dyes from aqueous solution. This review article provides extensive literature information about dyes, its classification and toxicity, various treatment methods, and dye adsorption characteristics by various adsorbents. One of the objectives of this review article is to organise the scattered available information on various aspects on a wide range of potentially effective adsorbents in the removal of dyes. Therefore, an extensive list of various adsorbents such as natural materials, waste materials from industry, agricultural by-products, and biomass based activated carbon in the removal of various dyes has been compiled here. Dye bearing waste treatment by adsorption using low cost alternative adsorbent is a demanding area as it has double benefits i.e. water treatment and waste management. Further, activated carbon from biomass has the advantage of offering an effected low cost replacement for non-renewable coal based granular activated carbon provided that they have similar or better adsorption on efficiency. The effectiveness of various adsorbents under different physico-chemical process parameters and their comparative adsorption capacity towards dye adsorption has also been presented. This review paper also includes the affective adsorption factors of dye such as solution pH, initial dye concentration, adsorbent dosage, and temperature. The applicability of various adsorption kinetic models and isotherm models for dye removal by wide range of adsorbents is also reported here. Conclusions have been drawn from the literature reviewed and few suggestions for future research are proposed.     

Cytotoxic effect,enzyme inhibition,and in silico studies of some novel N-substituted sulfonyl amides incorporating 1,3,4-oxadiazol structural motif

Molecular Diversity - The acetylcholinesterase and carbonic anhydrase inhibitors (AChEIs and hCAIs) remain key therapeutic agents for many bioactivities such as anti-Alzheimer and antiobesity...     

DNS of backward‐facing step flow with fully turbulent inflow

Direct numerical simulation (DNS) has been performed to study the channel flow over a backward‐facing step at a Reynolds number Re_b=5600 based on the step height h and the inflow bulk velocity U_b. A dynamic method has been used in order to generate realistic turbulent inflow conditions. The results upstream of the step compared well with the fully developed channel flow. Downstream of the step our results show excellent agreement with experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

Influence of Macro-pores on DNAPL Migration in Double-Porosity Soil Using Light Transmission Visualization Method

Double porosity is a substantial microstructure characteristic in a wide range of geomaterials. It is a natural phenomenon that can be found in many types of soil, and it can result from biological, chemical or mechanical damage. In this paper, the influence of macro-pores on dense non-aqueous phase liquid (DNAPL) migration in double-porosity medium was investigated using light transmission visualization technique. Three experiments were carried out in two-dimensional flow chambers filled with a double-porosity medium composed of a mixture of local sand and sintered kaolin clay spheres arranged in a periodic manner. In each experiment, a different volumetric fraction of macro-pores and micropores was used. Tetrachloroethylene (PCE) was used to simulate DNAPL, and it was dyed using Oil-Red-O for better visualization. A predetermined amount of PCE was injected into the flow chambers and this amount was re-calculated using image analysis. A very strong correlation was found between the PCE amount injected and the amount calculated from image analysis in each experiment. The experiment was repeated by filling the flow chamber with silica sand to represent single-porosity medium. The results show that the macro-pores have a considerable effect on the PCE migration in double-porosity soil as the PCE movement was the fastest in the third experiment which contained the largest macro-pores volume. The accuracy of the method was validated using statistical analysis. The results show a slight difference between the means of the three experiments, indicating that the method is viable for monitoring NAPL migration in double-porosity medium under different volumetric fractions of macro-pores and micropores.