Aggregate expression

Fig. 49A-C (on page 70) Phenotype of PSA-NCAM+ cells in SVZa. A Double-staining for BrdU andPSA-NCAM in postischemic day-4 anterior SVZa. A large BrdU+ cluster is negative for PSA-NCAM (arrowheads). Nevertheless, some of the cells of an adjacent PSA-NCAM+ aggregate express BrdU (arrows the framed area is magnified in the lower panel). B Double-staining for PSA-NCAM and/3III-tubulin in postischemic day-23 anterior SVZa. Note almost complete colabeling. C Double-staining for PSA-NCAM and Nestin in postischemic day-9 caudate SVZa. Double-labeled cells are depicted by arrows. Asterisk, anterior horn of lateral ventricle. Scale bars = 100 pm (A, B) 50 pm (C)...

These findings have wider implications for the study of inhomogeneous but still laminar flows. Namely, any macroscopically measured flow parameter can only be an aggregate expression of the wide spatial variations within the flow field, resulting from inhomogeneities in molecular strain. Conversely, molecular behavior cannot be extracted from macroscopic flow measurements alone, without local probing of the morphology of both strain and flow fields. 

Note the use of parenthesis around the logical function. Without these around the And operation the expression will be incorrectly evaluated. Both these expressions contain strings of characters enclosed in double quotes that are used to represent bit patterns. These examples illustrate binary representations but octal and hexadecimal formats may also be used (see Box 5.5). Using the concatenation operator to construct array expressions is only one approach. It is also possible to use aggregate expressions that take the form ... 

An aggregate expression constructs an array from scalar t5 es. A string expression may use objects of a composite type or explicitly specify the value to be stored in the array The common way to express a binary value is to use a siring literal viz. ... 

The ability of oil droplets to aggregate, expressed as the initial coalescence efficiency (ainit), describes the initial fraction of encounters between oil droplets necessary to set off partial coalescence. 

This expression can be generalized to two-dimensional aggregates (disclike micelles) and to spherical micelles, where... 

It is assumed that irreversible aggregation occurs on contact. The rate of coagulation is expressed as the aggregation flux J of particles towards a central particle. Using a steady-state approximation, the diffusive flux is derived to be... 

In slow coagulation, particles have to diffuse over an energy barrier (see the previous section) in order to aggregate. As a result, not all Brownian particle encounters result in aggregation. This is expressed using the stability ratio IV, defined as... 

Altliough tire tlieories of colloid stability and aggregation kinetics were developed several decades ago, tire actual stmcture of aggregates has only been studied more recently. To describe tire stmcture, we start witli tire relationship between tire size of an aggregate (linear dimension), expressed as its radius of gyration and its mass m ... 

The methods involved in the production of proteins in microbes are those of gene expression. Several plasmids for expression of proteins having affinity tails at the C- or N-terminus of the protein have been developed. These tails are usefiil in the isolation of recombinant proteins. Most of these vectors are commercially available along with the reagents that are necessary for protein purification. A majority of recombinant proteins that have been attempted have been produced in E. Coli (1). In most cases these recombinant proteins formed aggregates resulting in the formation of inclusion bodies. These inclusion bodies must be denatured and refolded to obtain active protein, and the affinity tails are usefiil in the purification of the protein. Some of the methods described herein involve identification of functional domains in proteins (see also Protein engineering). 

The term solubility thus denotes the extent to which different substances, in whatever state of aggregation, are miscible in each other. The constituent of the resulting solution present in large excess is known as the solvent, the other constituent being the solute. The power of a solvent is usually expressed as the mass of solute that can be dissolved in a given mass of pure solvent at one specified temperature. The solution s temperature coefficient of solubility is another important factor and determines the crystal yield if the coefficient is positive then an increase in temperature will increase solute solubility and so solution saturation. An ideal solution is one in which interactions between solute and solvent molecules are identical with that between the solute molecules and the solvent molecules themselves. A truly ideal solution, however, is unlikely to exist so the concept is only used as a reference condition. 

The popuiation baiance provides the mathematicai framework incorporating expressions for the various crystai formation, aggregation and disruption mechanisms to predict the finai particie size distribution. Note, however, that wiiiie particies are commoniy characterized by a iinear dimension the aggregation and particie disruption terms aiso require conservation of particie voiume. It was shown in Chapter 2 that the popuiation baiance accounts for the number of particies at each size in a continuous distribution. The quantity conserved is thus the number (popuiation) density and may be thought of as an extension of the more famiiiar mass baiance. The popuiation baiance is given by (Randoiph and Larson, i988)... 

Smoluehowski also presented a simple theory of aggregation kineties assuming eollisions of perfeet eolleetion effieieney to prediet spherieal partiele size distributions in a uniform liquid shear field of eonstant veloeity gradient. The aggregation kernel is then expressed as... 

As early as 1916, Smoluehowski showed that aggregation of spherieal partieles in a laminar shear field ean be expressed as... 

The significance of this novel attempt lies in the inclusion of both the additional particle co-ordinate and in a mechanism of particle disruption by primary particle attrition in the population balance. This formulation permits prediction of secondary particle characteristics, e.g. specific surface area expressed as surface area per unit volume or mass of crystal solid (i.e. m /m or m /kg). It can also account for the formation of bimodal particle size distributions, as are observed in many precipitation processes, for which special forms of size-dependent aggregation kernels have been proposed previously. 

Aggregated time in service (10 hr) The calendar and/or operating time considered for the data denominator development, expressed in terms of 1 million hours (standby or running). 

The ionization eonstant should be a function of the intrinsic heterolytic ability (e.g., intrinsic acidity if the solute is an acid HX) and the ionizing power of the solvents, whereas the dissoeiation constant should be primarily determined by the dissociating power of the solvent. Therefore, Ad is expeeted to be under the eontrol of e, the dieleetrie eonstant. As a consequenee, ion pairs are not deteetable in high-e solvents like water, which is why the terms ionization constant and dissociation constant are often used interchangeably. In low-e solvents, however, dissociation constants are very small and ion pairs (and higher aggregates) become important species. For example, in ethylene chloride (e = 10.23), the dissociation constants of substituted phenyltrimethylammonium perchlorate salts are of the order 10 . Overall dissociation constants, expressed as pArx = — log Arx, for some substanees in aeetie acid (e = 6.19) are perchloric acid, 4.87 sulfuric acid, 7.24 sodium acetate, 6.68 sodium perchlorate, 5.48. Aeid-base equilibria in aeetie acid have been earefully studied beeause of the analytical importance of this solvent in titrimetry. 

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