Factorization property

In deriving Eqs. (454) and (455), we have explicitly used the factorization property of pf>aB for large separations the double prime in Eq. (455) indicates an irreducibility condition similar to the one used in Eq. (430), except that the words on its left have to be replaced by "on its right in the definition after Eq. (432). 

The most simple model for the dielectric properties of foods is called the distributive model. Here, the dielectric properties of each constituent of the food are added together according to their fractional make-up of the total product. The model assumes that the various constituents of the food are distributed uniformly throughout the product. For example, Figure 3 shows the total dielectric loss factor for a 0.5 molar aqueous solution of water at two temperatures. Note that the total loss factor, e"t is the sum of the ionic and polar contributions, e"c and e" An example of loss factor properties of mustard, ketchup, mayonnaise and water is shown in Figure 8. A comparison of food constituents important in determining dielectric properties is shown in Table 2, (USDA1963). 

Abstract. A comparative investigation of C6o fiillerene solubility and donor force of alkyl derivatives of benzene has been performed. Based on the found correlation, which was determined by current methods, between C6o solubility and donor force of solvents, it has been concluded that the process of Cgo dissolution in aromatic hydrocarbons is a process of intermolecular interaction combined with charge-transfer and formation of complexes of the donor-acceptor type. The agreement between a series of physical and chemical phenomena (factors, properties) observed in studies of C60 solubility and a number of existing criteria which allow the phenomena to be interpreted as a manifestation of the charge-transfer interaction substantiates our conclusion. 

Section IX is devoted to the important task of revealing the physical reason of the breakdown of the equivalence between density and trajectory perspective in the non-Poisson case. First of all, in Section IX.A, we show that several theoretical approaches to the generalized fluctuation-dissipation process rest implicitly on the assumption that the higher-order correlation functions of a dichotomous noise are factorized. In Section IX.B we show that the non-Poisson condition violates this factorization property, thereby explaining the departure of the density from the trajectory approach in the non-Poisson case. 

Tig>alliiYB,PandeyS, ShuklaSD. Anti-platdet activating factor property ofRubiaoordifolia Linn. bidianJ Bqier Biol 1993 31 533-535... 

Aqueous emulsions of styrene, methyl methacrylate, methyl acrylate, and ethyl acrylate were polymerized with y-radiation from a Co source in the presence of sodium dodecyl sulfate or sodium laurate. The continuous measurement of conversion and reaction rate was carried out dilato-metrically. The acrylates polymerized fastest and the over-all polymerization rate increased as follows styrene < methyl methacrylate < ethyl acrylate methyl acrylate. The effects of radiation dose, temperature, and original monomer and emulsifier concentrations were studied with respect to the following factors properties of polymer dispersions, number and size of polymer particles, viscometrically determined molecular weights, monomer-water ratio, and kinetic constants. 

Hikkel, I., Lucau-Danila, A., Delaveau, T., Marc, P., Devaux, F., and Jacq, C. (2003) A general strategy to uncover transcription factor properties identifies a new regulator of drug resistance in yeast. The Journal of Biological Chemistry, 278, 11427-11432. 

The subscript c indicates that only connected diagrams have to be included because the contributions due to disconnected graphs can be eliminated using the factorization property (Goldstone 1957)... 

Assuming the particles undergo Brownian motion, the velocity is by definition an isotropic random variable described by a real Gaussian process of zero mean. Hence all the odd-ordered velocity correlation functions are zero, and the factorization property for a real Gaussian process can be used to determine the even ordered velocity correlations in terms of the second order velocity correlation function. Noting in particular that... 

Tripathi, Y.B., S. Pandey, and S.D. Shukla. 1993. Anti-platelet activating factor property of Rubia cordfolia Linn. Indian. Exp. Biol. 31(6) 533-535. 

A general unitary transformation of the spin orbital basis, which conserves the factorization property (aja o -as) = 7sr7 r 7 r 7s r indepen-... 

Before determining A and B let us derive (1.8) in a way that does not presume the factorization property (1.5). Consider collisions in a dilute... 

When a product is needed for a specific application, it has to meet several requirements, sometimes termed constraints , which can be divided into three categories geometric constraints, property constraints, and economic constraints [2]. Geometric constraints involve the shape and dimensions of products and may be dictated by aesthetic, functional, and other factors. Property constraints are associated with material characteristics and environments (loads, chemicals, and others). Economic constraints correspond to the cost limits and they are closely related to the volume of production. 

Generalizations to various powers of Jn can easily be found by elementary means [11,14,22], Incidentally we note an interesting factorization property of the columns of B to be further discussed below. 

The discovery of ferrimagnetism in yttrium iron garnet has attracted attention to the use of these materials for microwave device applications. To date garnets are the most useful materials in the microwave industry because of their magnetization, linewidth, Curie temperature and g-factor properties. With the advent of solid-state lasers, yttrium aluminum garnet was soon found to be an excellent laser host material for room temperature and high power applications. 

These equations are precise, but for rapid estimation Fig. 17-11 is recommended, especially becaus- , of the somewhat indeterminate value of the fouling factors. Properties are read at the average fluid temperature. The film coefficients (Fig. 17-11) are based on inside area and must be multiplied by the proper area ratios to convert them to coefficients based on outside area. Finally, if the temperature drop across the film is very large or if the oil is very viscous, the coefficients should be multiplied by... 

Only when the film resistance is large or the oil is very viscous need the coefficients be multiplied by the viscosity gradient factor Properties are taken at the average fluid temperature. 

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