Hudson equation

The equation of Hudson is still world-widely employed for the estimation of minimum or optimmn weight of armor block. Hudson equation is expressed by ... 

Mills, W.B., Dean, J.D., Porcella, D.B., Gherini, S.A., Hudson, R.J.M., Frick, W.E., Rupp, G.L., Bowie, G.L. (1982) Water Quality Assessment A Screening Procedure for Toxic and Conventional Pollutants. Part 1, U.S. EPA, EPA-600/6-82-004a. Mokbel, I., Rauzy, E., Loiseleur, H., Berro, C., Jose, J. (1995) Vapor pressures of 12 alkylcyclohexanes, cyclopentane, butylcyclo-pentane and frara -decahydronaphthalene down to 0.5 Pa. Experimental results, correlation and prediction by an equation of state. Fluid Phase Equil. 108, 103-120. 

Electronic relaxation is a crucial and difficult issue in the analysis of proton relaxivity data. The difficulty resides, on the one hand, in the lack of a theory valid in all real conditions, and, on the other hand, by the technical problems of independent and direct determination of electronic relaxation parameters. At low fields (below 0.1 T), electronic relaxation is fast and dominates the correlation time tc in Eq. (3), however, at high fields its contribution vanishes. The basic theory of electron spin relaxation of Gdm complexes, proposed by Hudson and Lewis, uses a transient ZFS as the main relaxation mechanism (100). For complexes of cubic symmetry Bloembergen and Morgan developed an approximate theory, which led to the equations generally... 

For undersaturated ([M] < Km) systems with relatively fast internalisation kinetics (kmt > k, ), the uptake of trace metals may be limited by their adsorption. Because the transfer of metal across the biological membrane is often quite slow, adsorption limitation would be predicted to occur for strong surface ligands (small values of k ) with a corresponding value of Km (cf. equations (35) and (36)) that imposes an upper limit on the ambient concentration of the metal that can be present in order to avoid saturation of the surface ligands. More importantly, as pointed out by Hudson and Morel [7], this condition also imposes a lower limit on the carrier concentration. Since the complexation rate is proportional to the metal concentration and the total number of carriers, for very low ambient metal concentrations, a large number of carriers are required if cellular requirements are to be satisfied. 

The second statement has to do with the notion that in the Eigen mechanism for proton transfer there must be intermediate ion pairs. The reference to the unpublished work of Kreevoy and Liang (3) reflects the impact of their studies on some of our own recent work surveyed below. In fact, there is an extensive published literature concerning phenol-amine complexes in which the existence of the intermediates in equation 2 has been established in different organic solvents. One of the oldest such papers is that of Bell and Barrow (11) going back to 1959. Others include Hudson and co-workers (12) in 1972, and Baba and co-workers (13) in 1969. 

Equations similar to those for mutarotation have been derived, expressing the relationship between the solubility behavior of the two forms of lactose and the equilibrium or rate constants (Hudson 1904). The constants derived by both mutarotation and solubility methods are in agreement. The solubility equations have been used to develop procedures for measuring a- and /3-lactose in dry milk (Roetman 1981). 

The forcing variable is the coolant temperature jc2c as in Sincic and Bailey (1977) and more recently in Mankin and Hudson (1984). In eq. (10) jti is a dimensionless reactant concentration while x2 is a dimensionless reactor temperature. These equations hold at the limit of infinite reaction activation energy. All models were thus chosen so that extensive simulation results existed in the literature, and they cover a wide range of lumped reactor types. 

The velocity of the reaction is greatly accelerated by acid or base. The rate is at a minimum for pyranose-pyranose interconversions in the pH range 2.5 to 6.5. Both acids and bases accelerate mutarotation rate, with bases being more effective. This was expressed by Hudson (1907) in the following equation ... 

In contrast, NIST Standard Reference Material SRM 1939 from Hudson River sediment in New York state had an EF of 0.7 for PCB 95 (Equation (4.4) on Chirasil-Dex) [70]. Similar nonracemic residues were reported for PCBs 95,136,149,174, and 183 in this SRM [106]. These sediments are heavily contaminated with PCBs from historical releases from the General Electric capacitor plant in Schenectady, New York. Microbially mediated biotransformation of PCBs has occurred in these sediments by both anaerobic reductive dechlorination [155] and aerobic oxygenase and dioxygenase activity [153]. A subsequent. 

This explains why Hudson, Bass, and Purcell (7) obtained two different solutions to a matrix by making different substitutions using the restrictive equations. Their presentation of the matrix used is not in its most expanded form but is contracted by application of the restrictive equations this makes it difficult to visualize the singularity problems. When their matrix is rewritten in the complete form, it becomes readily apparent that their Compounds 3 and 4 are involved in a singu-... 

Hudson et al. (67) describe two parameter-based methods for compound selection. The most descriptive compound (MDC) method is aimed at selecting compounds that represent the population as a whole. An information vector is accumulated from the ranked Euclidean distance of each compound in the data set to all others. The most descriptive compound is that with the largest information, which equates to the compound with the smallest overall distance to all other compounds. The next compound is chosen to give the greatest additional information and so on. The sphere-exclusion method used attempts to select compounds that most effectively cover the property space. A compound is selected, say the MDC, and all compounds are removed that are closer to it than a user-defined radius. The... 

Although the Birch reduction (alkali metals in liquid NH3) of the pyrrole ring is apparently unknown (c/. equation 8), the partial reduction of pyrroles to 2,5-dihydropyrroles using Zn/HCl has been of considerable utility. For example, pyrrole gives 2,5-dihydropynole as the major product upon treatment with Zn dust/20% aq. HCl (equation 9), and Lemal and McGregor observed that 2,5-dimethylpyrrole gives a mixture of trans- (78%) and c/5-2,5-dimethyl-2,5-dihydropyrrole (22%) under similar conditions (47% yield). In one of these studies, Hudson and Robertson demonstrated that 2,5-dihydropyrrole is not reduced to pyrrolidine under these reaction conditions. Using these same conditions, Schumacher and Hall reported the reduction of 2-benzylpyrrole to the 2,5-dihydro derivative (67%) in a synthesis of the antibiotic anisomycin. ... 

Table I summarizes the results obtained for 2-, 3-, and 4-CP degradation in the methanogenic cultures from the upper Hudson River based upon the stoichiometry in equation 10. The methane production in the background controls resulting from endogenous carbon in the sediment inoculum has been subtracted from these values. The results show that the measured values of methane produced agree very well with those calculated from the equation. Thus, they support the observation that each of the monochlorophenol isomers was mineralized to CH4 and C02.

A similar equation was first proposed by Hudson and McCoubrey and later by numerous researchers. Equation 16.69 is a general combining rule for the cross-energy parameter as a function of the molecular energy (e) and size (o) parameters. The exponent n is a characteristic of the potential function. The ionization potential term is often ignored. However, in some cases, as shown by Coutinho et al. for C02/alkanes, the ioiuzation term can be approximated using the co-volume parameters ... 

Ganapathisubramanian and Noyes (1982-4) constructed a model consisting of seven differential equations. The numerical solutions of these equations did not correlate with the horatian behavior observed by Hudson-Mankin (1981) in B-Z reaction in a flow reactor. 

Many linear polyenes exhibit anomalous fluorescence behaviour in the sense that the fluorescence rate constant kf calculated from the absorption spectrum (Equation 2.11) is much smaller than that determined by lifetime and quantum yield measurements (Equation 3.33). In 1972, Hudson and Kohler reported high-resolution absorption and emission spectra of all-trart.v-l, 8-diphenylocta-l, 3,5,7-tetraene at low temperature, which proved that the lowest excited singlet state Si was not that reached by the strongly allowed 7t,Jt transition (/ 1.5) that is predicted by MO theory and observed at 410nm.3" Rather, very weak (f 0.06), structured absorption that had been hidden under the tail of the jt,jt -absorption in solution spectra was detected at slightly longer wavelengths. 

In this equation, X represents an exchangeable site , which may actually be a site in a mineral or on a mineral surface. However, usually it is not known just how or where the ions are adsorbed, and X- is then simply a component representing a unit charge anywhere in or close to the solid phase (Dzombak and Hudson, 1995). In either case, though, some manipulation of the CEC allows us to assign a value Kx to the ratio... 

The term kH20 [H20] represents the contribution of the water molecules. Since [H20] varies only slightly from 55.6 M (moles per liter) in aqueous systems, it is usually included in the kHi0 term, as in Hudson s original equation. As will be discussed later (see p. 22), this term can be broken into two parts representing the acidic and basic characteristics of water. 

Hudson38 measured the temperature coefficient for the interconversions of a- and /3-lactose, and Lowry and Smith57 calculated activation energies from Hudson s data by means of the integrated Arrhenius equation ... 

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