On stratifiable locally convex spaces

In the present paper we prove several results on the stratifiability of locally convex spaces. In particular, we show that a free locally convex sum of an arbitrary set of stratifiable LCS is a stratifiable LCS, and that all locally convex F'-spaces whose bounded subsets are metrizable are stratifiable. Moreover, we prove that a strict inductive limit of metrizable LCS is stratifiable and establish the stratifiability of many important general and specific spaces used in functional analysis. We also construct some examples that clarify the relationship between the stratifiability and other properties.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Support vector machine classification for large data sets via minimum enclosing ball clustering

Support vector machine (SVM) is a powerful technique for data classification. Despite of its good theoretic foundations and high classification accuracy, normal SVM is not suitable for classification of large data sets, because the training complexity of SVM is highly dependent on the size of data set. This paper presents a novel SVM classification approach for large data sets by using minimum enclosing ball clustering. After the training data are partitioned by the proposed clustering method, the centers of the clusters are used for the first time SVM classification. Then we use the clusters whose centers are support vectors or those clusters which have different classes to perform the second time SVM classification. In this stage most data are removed. Several experimental results show that the approach proposed in this paper has good classification accuracy compared with classic SVM while the training is significantly faster than several other SVM classifiers.

Effect of pH, temperature, and moisture on the formation of volatile compounds in glycine/glucose model systems

Mixtures of glycine, glucose, and starch were extrusion cooked using sodium hydroxide at 0, 3, and 6 g/L of extruder water feed, 18% moisture, and 120, 150, and 180 degreesC target die temperatures, giving extrudates with pH values of 5.6, 6.8, and 7.4. Freeze-dried equimolar solutions of glucose and glycine were heated either dry or after equilibration to similar to 13% moisture at 180 degreesC in a reaction-tube system designed to mimic the heating profile in an extruder. Volatile compounds were isolated onto Tenax and analyzed by gas chromatography-mass spectrometry. For the extrudates, total yields of volatiles increased with decreasing pH at 180 degreesC, reached a maximum at pH 6.S at 150 degreesC, and increased with increasing pH at 120 degreesC. Amounts increased with temperature at all pH values. Pyrazines were the most abundant class for all sets of conditions (54-79% of total volatiles). Pyrroles, ketones, furans, oxazoles, and pyridines were also identified. Yields of volatiles from the reaction-tube samples increased by > 60% in the moist system. Levels of individual classes also increased in the presence of moisture, except pyrazines, which decreased similar to3.5-fold. Twenty-one of the compounds were common to the reaction-tube samples and the extrudates.

Microcolumn studies of dye adsorption onto manganese oxides modified diatomite

The method described here cannot fully replace the analysis of large columns by small test columns (microcolumns). The procedure, however, is suitable for speeding up the determination of adsorption parameters of dye onto the adsorbent and for speeding up the initial screening of a large adsorbent collection that can be tedious if a several adsorbents and adsorption conditions must be tested. The performance of methylene blue (MB), a basic dye, Cibacron reactive black (RB) and Cibacron reactive yellow (RY) was predicted in this way and the influence of initial dye concentration and other adsorption conditions on the adsorption behaviour were demonstrated.

Reduced-size polarized basis sets for calculations of molecular electric properties. III. Second-row atoms

Reduced-size polarized (ZmPolX) basis sets are developed for the second-row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced-size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.

Turbulent diffusion and mixing in interstellar dark clouds with adsorption onto grains

This paper reports the results of models of dark cloud chemistry incorporating a depth dependent density distribution with diffusive mixing and adsorption onto grains. The model is based on the approach taken by Xie et al. (1995), with the addition of grain accretion effects. Without diffusion, the central regions of the cloud freeze out in less than 10(7) years. Freeze-out time is dependent on density, so the diffuse outer region of the cloud remains abundant in gas for about an order of magnitude longer. We find that fairly small amounts of diffusive mixing can delay freeze-out at the centre of the model cloud for a time up to an order of magnitude greater than without diffusion, due to material diffusing inward from the edges of the cloud. The gas-phase lifetime of the cloud core can thus be increased by up to an order of magnitude or more by this process. We have run three different grain models with various diffusion coefficients to investigate the effects of changing the sticking parameters.

Adsorption of methylene blue onto activated carbon produced from steam activated bituminous coal: A study of equilibrium adsorption isotherm.

Chemical Engineering Journal, 124 (2006) 103.

Adsorption of basic dyes from aqueous solution onto activated carbons

The aim of this research is to compare the adsorption capacity of different types of activated carbons produced by steam activation in small laboratory scale and large industrial scale processes. Equilibrium behaviour of the activated carbons was investigated by performing batch adsorption experiments using bottle-point method. Basic dyes (methylene blue (MB), basic red (BR) and basic yellow (BY)) were used as adsorbates and the maximum adsorptive capacity was determined. Adsorption isotherm models, Langmuir, Freundlich and Redlich-Peterson were used to simulate the equilibrium data at different experimental parameters (pH and adsorbent particle size). It was found that PAC2 (activated carbon produced from New Zealand coal using steam activation) has the highest adsorptive capacity towards MB dye (588 mg/g) followed by F400 (476 mg/g) and PAC 1 (380 mg/g). BR and BY showed higher adsorptive affinity towards PAC2 and F400 than MB. Under comparable conditions, adsorption capacity of basic dyes, MB, BR and BY onto PAC 1, PAC2 and F400 increased in the order: MB <BR <BY. Redlich-Peterson model was found to describe the experimental data over the entire range of concentration under investigation. All the systems show favourable adsorption of the basic dyes with 0 <R-L <I (C) 2007 Elsevier B.V. All rights reserved.

The convex variable step-size (CVSS) algorithm

This letter introduces the convex variable step-size (CVSS) algorithm. The convexity of the resulting cost function is guaranteed. Simulations presented show that with the proposed algorithm, we obtain similar results, as with the VSS algorithm in initial convergence, while there are potential performance gains when abrupt changes occur.