Chromatographic terminal band lengths

A terminal band length is defined here as the length of a dispersed solute band as it emerges from the chromatographic column. The number of terminal band lengths per column can be used in the same way that the number of theoretical plates per column is used to measure and compare chromatographic efficiencies, but with greater insight since the proposed unit of measure is an easily visualized, real entity. In addition, the height equivalent to a theoretical plate (HETP) can be regarded as a ratio of the terminal band lenght to sixteen times the number of equivalent terminal band lengths that could be contained in tandem in the column. This concept offers another approach to understanding the meaning of the term, HETP. The terminal band length of a series of homologues is constant and independent of retention time above a certain solute molecular size and column capacity ratio. Within those conditions the correlation between the recorded peak width and retention time during isothermal analysis occurs primarily as a result of change in solute velocity.     

Vibration analysis of rectangular plates coupled with fluid

The approach developed in this paper applies to vibration analysis of rectangular plates coupled with fluid. This case is representative of certain key components of complex structures used in industries such as aerospace, nuclear and naval. The plates can be totally submerged in fluid or floating on its free surface. The mathematical model for the structure is developed using a combination of the finite element method and Sanders’ shell theory. The in-plane and out-of-plane displacement components are modelled using bilinear polynomials and exponential functions, respectively. The mass and stiffness matrices are then determined by exact analytical integration. The velocity potential and Bernoulli’s equation are adopted to express the fluid pressure acting on the structure. The product of the pressure expression and the developed structural shape function is integrated over the structure-fluid interface to assess the virtual added mass due to the fluid. Variation of fluid level is considered in the calculation of the natural frequencies. The results are in close agreement with both experimental results and theoretical results using other analytical approaches.     

Calculation of simply supported circular plates in the statement of the problem of contact interaction in a package of two plates

The possibility of applying the mechanicomathematical model of bending of a package of transversely isotropic plates to approximate calculations of thick plates is investigated. Within the frame work of this model, the problem of axisymmetric bending of a package of two identical plates with simply supported edges is considered. The conditions of rigid contact are given between the plates. Based on the analytical result obtained, the unknown distribution of stresses and displacements across the thickness of the plate is approximated by the distribution of corresponding parameters in the package of two plates. For an isotropic body, the results of numerical calculations are compared with those given by the 3D theory of elasticity. In the case of a transversely isotropic body, a comparison with the results found by the refined bending model of plates (taking into account the transverse compression and shear) and the Timoshenko model is carried out. The accuracy to which the boundary conditions in every model are satisfied is analyzed. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 603–616, September–October, 2007.     

The extent to which triangular sub-patterns explain minimum rank

For any zero-nonzero pattern of a matrix, the minimum possible rank is at least the size of a sub-pattern that is permutation equivalent to a triangular pattern with nonzero diagonal. For certain numbers of rows and columns, the minimum rank of a pattern is k only when there is a k-by-k such triangle. Here, we complete the determination of such sizes by showing that an m-by-n pattern of minimum rank k must contain a k-triangle for m=5, k=4; m=6, k=5; and m=6, k=4. A table is given showing whether or not this happens for all m, n, k. In the process, a Schur complement approach to minimum rank is described and used, and simple ways to recognize the presence of triangles of sizes less than 7 are given.     

Identifying the elastic moduli of composite plates by using high-order theories. 2. Theoretical-experimental approach

The identification of elastic properties of laminated composite plates from measured eigenfrequencies has been performed. The elastic moduli of the laminates were determined by using a multilevel modeling and a two-step identification procedure. At the first step, based on a genetic algorithm, the Young’s and shear moduli were found, but at the second one, by minimizing an error function, the values of transverse moduli were refined. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 207–216, March–April, 2008.     

Finding upper-triangular representations for phase-type distributions with 3 distinct real poles

In this paper we seek particular representations for absolutely continuous Phase-type distributions with 3 distinct real poles. First, we define subsets of these Phase-type distributions given the 3 distinct poles. One subset contains distributions that have upper triangular PH representation of order n, but do not have a triangular one of PH order n−1. This is done by using the invariant polytope approach. For any distribution in our subsets we give an invariant polytope containing the corresponding distribution by finding the vertices of the polytope. Second, we propose a method that actually constructs the generator matrix of the required PH representation from the invariant polytope. Consequently, our method constructs an upper triangular PH representation that has minimal order among the upper triangular PH representations given the probability density function of a PH distribution.     

Preparation of a super‐long two column chromatography system and its application in separating glycosylated puerarin

Separation of Puerarin‐7‐O‐glucoside from its precursor, puerarin, using a common chromatography column packed with AB‐8 macroporous resin was unsuccessful. Therefore, in this study a 8 m super‐long flexible reinforced PVC column was externally added to the common column in order to improve the chromatography efficiency by increasing the number of theoretical plates. Both the PVC and common columns were separately packed with AB‐8 macroporous resin slurry. The packed PVC column was coiled after washing and stored until use. The microbial transformation mixture with puerarin‐7‐O‐glucoside and puerarin (250 mL) was loaded onto the common column, followed by washing with 2000 mL H₂O. After attaching the coiled external PVC column to the common column, a linear gradient of 10–30% ethanol was applied to elute the target compound. Two peaks appeared: peak I contained puerarin‐7‐O‐glucoside at 97.9% purity and 88.1% recovery rate, and peak II was puerarin at 98.7% purity and 87.0% recovery rate. The use of the coiled external flexible reinforced PVC column avoided spatial restriction for long columns, which made it much more convenient for column packing and chromatography operations. Furthermore, this method eliminated the resin blockage problem caused by stationary water pressure in a rigid vertical long column. Using an external super‐long column, the PVC tube was connected with the common column only during elution, which avoided delay in time period during sample loading and column washes associated with the use of long external columns. Copyright © 2009 John Wiley & Sons, Ltd.     

Discrete strip-concave functions, Gelfand-Tsetlin patterns, and related polyhedra

Discrete strip-concave functions considered in this paper are, in fact, equivalent to an extension of Gelfand-Tsetlin patterns to the case when the pattern has a not necessarily triangular but convex configuration. They arise by releasing one of the three types of rhombus inequalities for discrete concave functions (or “hives”) on a “convex part” of a triangular grid. The paper is devoted to a combinatorial study of certain polyhedra related to such functions or patterns, and results on faces, integer points and volumes of these polyhedra are presented. Also some relationships and applications are discussed.In particular, we characterize, in terms of valid inequalities, the polyhedral cone formed by the boundary values of discrete strip-concave functions on a grid having trapezoidal configuration. As a consequence of this result, necessary and sufficient conditions on a pair of vectors to be the shape and content of a semi-standard skew Young tableau are obtained.     

The application of heat conduction microcalorimetry to study the metabolism and pharmaceutical modulation of cultured mammalian cells

The heat produced by animal cells in culture can be used as the primary indicator of the kinetics of their metabolism because the scalar flux of it is a function of the metabolic flux. The validity of the relationship between heat and metabolism was demonstrated theoretically through the concept of thermal advancement and in experiments by the use of continuous cultures. This validation permitted the application of heat flux as a probe of the metabolic state of cells in culture. It consisted of an on-line heat conduction microcalorimeter that measures the instantaneous heat flow and dividing the smoothed signal with one obtained simultaneously using a dielectric spectrometer that records the change in capacitance as an estimate of the amount of viable biomass. In this mini-review, it is shown with Chinese hamster ovary cells (CHO320) genetically engineered to produce interferon-γ (IFN-γ) that heat flux is an early signal of deteriorating metabolism in cultures that produce considerable amounts of toxic lactate under fully aerobic conditions. The early detection favours the use of heat flux as the control variable in fed-batch cultures. This is a particularly useful finding in the context of the pharmaceutical industry because it will help to ensure the high fidelity of the cytokines, antibodies and vaccines produced in large-scale cultures. The monotonic relationship between the fluxes for heat and metabolism means that the enthalpy balance method can be employed to test the validity of the growth reaction for cells in culture. This showed that the crucial ratio between the substrates, glucose and glutamine, in the culture medium was incorrect at 5.5:1 instead of about 3:1, depending on the phase of the culture. Together with other changes to the medium composition, an improved formulation was made that ensured faster cell growth and greater specific rate (flux) of IFN-γ constitutive secretion while decreasing glucose utilisation and, most importantly, halving the excretion of lactate, that is toxic to the cells and harmful to the fidelity of their secondary products. Indirect calorimetry (oxygen uptake rate, OUR) is often favoured over the direct technique, but the former only measures aerobic metabolism. The environmental conditions in cultures favours lactate production even under fully aerobic conditions. Developments in measuring OUR mean that the stationary liquid phase balance can be used successfully to make the calorimetric:respirometric (CR) ratio a valuable tool in optimising cell culture to grow cells that synthesise the maximum amounts of the high fidelity secondary products.

Besides the value of heat flux in improving the cultures of animal cells producing heterologous products, three different techniques are examined that should be valuable in the testing the many compounds that are produced on a speculative basis as potential drugs. They are: (i) a thin-film thermopile transducer as an immunosensor; (ii) infra-red imaging of cells cultured in multi-well microtitre plates and (iii) integrated circuit (IC) calorimetry for small samples and low detection limit. One or more of these methods could well find favour with industry in the near future.     

层合析参固支边界条件下的不稳定后屈曲分析

为了深入地研究复合材料层板所独具的后屈曲特性,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组,并运用广义傅立叶级数法对其进行求解。重点分析了非对称层板在固支边界条件下的稳定性问题,发现层板在此条件下有可能存在非对称的失稳临界点和不稳定的后屈曲路径,进而构造了简化的物理模型进行解释,指出后屈曲的非对称性是由于结构关于Z轴不对称,而不稳定性是由于固支边界条件阻碍了前屈曲的发生。