Alternative approach for Siegel's lemma

In this article, we present an alternative approach to show a generalization of Siegel's lemma which is an essential tool in Diophantine problems. Our main statement contains the so-called analytic Siegel's lemma as well as the Bombieri-Vaaler lemma. Our proof avoids relying on the ordinary geometry of numbers

Rate of Solution of Solid Particles Followed by Chemical Reaction in Agitation Vessel

In this paper, the authors deal with the dissolution of acid anhydride in water followed by the hydrolysis reaction. Classification may be made of the types of reaction taking place depending upon the relative rates of diffusion and hydrolysis of the acid anhydride. (1) Diffusion resistance is controlling and the overall rate of reaction depends only on the rate of solution. In this case the higher the agitator speed, the larger the rate of solution. (2) Diffusion resistance and the chemical resistance to hydrolysis are comparable in magnitude. In this case the overall rate of reaction depends not only on the agitator speed, but also on the rate of hydrolysis. (3) Chemical resistance to hydrolysis is controlling and the overall rate of reaction is independent of the agitator speed. The authors derived the generalized rate equation and demonstrated the three types of reaction by the hydrolysis reaction of phthalic acid anhydride and benzoic acid anhydride suspended in water under agitation. The authors propose the idea of “the degree of transitional saturation” and “the agitation coefficient for heterogeneous reaction”. The latter is useful for the determination of the available agitation intensity for heterogeneous liquid phase reactions

Effect of Liquid- and Gas-Mixing on the Rate of Mass Transfer between Two Phases in Crosscurrent Flow

The theoretical correlations have been derived by the authors for the concentration gradients in the froth layer on a sieve or bubble-cap plate, based on the assumption that the flow velocities of the gas and liquid in each direction are constant throughout the froth layer. The degree of liquid- and gas-mixing was experessed by the backmixing diffusion. Point efficiency varies with change in the number of transfer units and with the degree of gas-mixing. The liquid-mixing has no effect on the point efficiency. Plate efficiency is affected by both the liquid- and gas-mixing. The effect of the liquid-mixing is more marked than that of gas-mixing

Involvement and Possible Role of Eosinophils in Asthma Exacerbation

Eosinophils are involved in the development of asthma exacerbation. Recent studies have suggested that sputum and blood eosinophil counts are important factors for predicting asthma exacerbation. In severe eosinophilic asthma, anti-interleukin (IL)-5 monoclonal antibody decreases blood eosinophil count and asthma exacerbation frequency. However, even in the absence of IL-5, eosinophilic airway inflammation can be sufficiently maintained by the T helper (Th) 2 network, which comprises a cascade of vascular cell adhesion molecule-1/CC chemokines/eosinophil growth factors, including granulocyte-macrophage colony-stimulating factor (GM-CSF). Periostin, an extracellular matrix protein and a biomarker of the Th2 immune response in asthma, directly activates eosinophils in vitro. A major cause of asthma exacerbation is viral infection, especially rhinovirus (RV) infection. The expression of intercellular adhesion molecule (ICAM)-1, a cellular receptor for the majority of RVs, on epithelial cells is increased after RV infection, and adhesion of eosinophils to ICAM-1 can upregulate the functions of eosinophils. The expressions of cysteinyl leukotrienes (cysLTs) and CXCL10 are upregulated in virus-induced asthma. CysLTs can directly provoke eosinophilic infiltration in vivo and activate eosinophils in vitro. Furthermore, eosinophils express the CXC chemokine receptor 3, and CXCL10 activates eosinophils in vitro. Both eosinophils and neutrophils contribute to the development of severe asthma or asthma exacerbation. IL-8, which is an important chemoattractant for neutrophils, is upregulated in some cases of severe asthma. Lipopolysaccharide (LPS), which induces IL-8 from epithelial cells, is also increased in the lower airways of corticosteroid-resistant asthma. IL-8 or LPS-stimulated neutrophils increase the transbasement membrane migration of eosinophils, even in the absence of chemoattractants for eosinophils. Therefore, eosinophils are likely to contribute to the development of asthma exacerbation through several mechanisms, including activation by Th2 cytokines, such as IL-5 or GM-CSF or by virus infection-related proteins, such as CXCL10, and interaction with other cells, such as neutrophils

Mass Transfer in Agitated Liquid-Solid Systems

The authors performed experiments on the solution of solid particles in agitated liquids in a series of geometrically similar agitators. A great variety of solid particles, including several kinds of spherical crystals, whose particle size, shape and density varied over a wide range were used as the solid samples. Pure water, dilute hydrogen chloride and aqueous solutions of gelatine, polyvinyl alcohol, sucrose and glycerine of various concentrations were used as the liquids. Several methods for determining the rate of solution of solid particles were considered, and the analysis of the data was performed in terms of the mass transfer coefficient. As for the experimental results on the agitation process, it was found that the physical properties of the solid particles, i.e., the difference in density between the liquid and the solid, the size and shape of the particles, as well as the viscosity and the density of the liquid were important factors controlling the rate of mass transfer. Between the agitator speeds of Nf and Nₐ all the data were correlated by the following dimensionless equations. For solid particles with an unknown surface shape factor, and for solid particles with a known surface shape factor, where These equations represent the general correlation of the variables involved in determining the magnitude of the rate of mass transfer in agitated liquid-solid systems, and are used to estimate the mass transfer rate for any liquid-solid combination in a series of geometrically similar vessels and impellers

Micro-Mixing in a Continuous Flow Reactor : Coalescence and Redispersion Models

For the fluid mixing which occurs in a continuous flow reactor, two different mechanisms must be considered. The one is macro-mixing resulting from the difference in residence time of outflowing fluid and the other is micro-mixing caused by the mass exchange between fluid elements. In this paper new models for the micro-mixing are presented as follows : The incoming fluid is broken up into discrete fragments of equal volume which are small enough compared to the reactor size. A fragment of fluid comes into contact and coalescence with another l/tc times per unit time on an average, and is immediately rebroken into two fragments of equal volume. The concentration in the fragments becomes uniform at the instant of coalescence. From the above assumptions, the basic design equations are derived, and for the ideal perfect macro-mixing reactor, the effect of micro-mixing on the conversion of zero, first, and second order reactions is considered. In the case of first order reactions the micro-mixing has no effect on the conversion. In the case of reactions of zero and second order, the conversion is caluculated by equations (24), (36) and (30), (38), respectively. And the validity of these equations for second order reaction is discussed using a reaction which takes place in liquid droplets dispersed in an inert phase

Characteristics of the elderly in high - resolution computed tomography lung densitometry

To determine the characteristics of the elderly in high - resolution computed tomography (HRCT) lung densitometry, mean lung density (MLD) and relative area of the lungs showing attenuation values less than -950 HU (RA(950)) on HRCT were evaluated in nonsmoking control subjects (n = 80) and patients with asthma (n = 80) in relation to their age and pulmonary function. MLD was significantly decreased, and RAW was significantly increased with increasing age in both asthmatics and controls. The MLD values were significantly lower in asthmatics compared with controls in subjects aged between 60 and 69 years and over age 70. RAgsov alues were significantly higher in asthmatics compared with controls in subjects aged between 50 and 59 years, between 60 and 69, and over 70. % FEV(1) and FEV(1) / FVC were significantly decreased in elderly asthmatic patients over 70 years of age compared with the values in those under 49. Percent residual volume (% RV) was significantly larger in patients over 70 years of age than in those between 50 and 59, and under 49 years. RAW was significantly larger in patients with steroid-dependent intractable asthma (SDIA) between 50 and 59 years of age, and between 60 and 69 compared with RA 950 in those without SDIA. However, RAW did not differ significantly between SDIA and non-SDIA in patients over age 70. The results suggested that in % LAA of the lungs on HRCT was significantly increased in the elderly subjects with and without asthma, and it was significantly higher in the elderly asthmatics than the elderly controls.高齢者の病態的特徴を明らかにするために，健常者80例および非喫煙喘息患者80例を対象として，平均肺CT値（MLD）ならびに高分解能CT（HRCT）による－950HU以下の肺low attenuation area（RA950）を評価し，年齢及び肺機能との関連を検討した。　 1．健常者，喘息患者いずれにおいても年齢とともにMLDは有意に減少し，RA(950)は有意に増加した。MLDは，60－69歳と70歳以上の年 齢層において，健常者に比して喘息患者で有意に低値を示した。RA(950)。は，50－59歳・60－69歳・70歳以上の年齢層において，健常者に比して喘息患者で有意に高値を示した。　 2．喘息患者において，1秒量（% FEV(1)）および1秒（FEV(1)/ FVC）は，49歳以下の年齢層に比して70歳以上の年齢層で有意に低値を示した。一方，残気量（% RV）は，50－59歳ならびに49歳以下の年齢層に比して70歳以上の年齢層で有意に高値を示した。 3．50－59歳および60－69歳の年齢層では，RA(950)は，ステロイド依存性重症難治性喘息（SDIA）患者において非SDIA患者に比して有意に高値を示した。しかし，70歳以上の年齢層では両者に有意の差は認められなかった。これらの結果より，HRCT上の肺low attenuation areaは高齢者において有意に増加すること，さらに嘱息患者の方が健常者に比してより高値を示すことが示唆された