Decimal logarithm

Extensive tabulations of Antoine parameters are available for many chemicals of importance to engineers, chemists, and environmental scientists (9,19,20). Caution is in order when using tabulated Antoine constants because several forms of the correlating equation are found in the Hterature. In particular, there are variations in the sign before the second term, the units of temperature, and the use of natural or decimal logarithms of the vapor pressure. 

Note that the lipophilicity parameter log P is defined as a decimal logarithm. The parabolic equation is only non-linear in the variable log P, but is linear in the coefficients. Hence, it can be solved by multiple linear regression (see Section 10.8). The bilinear equation, however, is non-linear in both the variable P and the coefficients, and can only be solved by means of non-linear regression techniques (see Chapter 11). It is approximately linear with a positive slope (/ ,) for small values of log P, while it is also approximately linear with a negative slope b + b for large values of log P. The term bilinear is used in this context to indicate that the QSAR model can be resolved into two linear relations for small and for large values of P, respectively. This definition differs from the one which has been introduced in the context of principal components analysis in Chapter 17. 

An alternative graphical solution makes use of the biphasic exponential nature of the plasma concentration function ineq. (39.16). At larger time values, when the effect of absorption has decayed, the function behaves approximately as monoexponential. Under these conditions, and after replotting the concentration data on a (decimal) logarithmic scale, one obtains a straight line for the later part of the curve (Fig. 39.8a). This line represents the P-phase of the plasma concentration and is denoted by C ... 

Decimal Logarithms of the Formation Constants of Beryllium Complexes with Ligands Containing Phosehonato Groups 4... 

Figure 2. Dependence of value for hydrosilylation reaction rate constants on decimal logarithm of determinant of pseudo-ANB-matrices in the series of a,co-oligodiorganodihydridesiloxanes (table 1). 

A confluent monolayer of Madin-Darby canine kidney (MDCK) cells was grown in 96-well plates. Serial tenfold dilutions in minimal essential medium were prepared from the aliquots of allantoic fluid taken from the irradiated specimen. These dilutions were applied to MDCK cells and incubated for 48 h at 36 °C in 5% C02. The cells were then washed two times for 5 min with phosphate buffered saline (PBS) and incubated for 1 h with 100 pi of 0.5 mg/ml solution of 3-(4,5-dimethyl-thiazolyl-2) 2,5-diphenyltetrazolium bromide (MTT, ICN Biochemicals Inc., Aurora, Ohio). After lh, the colored deposit was dissolved in 100 pi DMSO, and optical density in the wells was measured on plate reader Victor 1420 (Perkin Elmer, Finland). Based on the data obtained, the infectious titer of the vims was determined as a decimal logarithm of reciprocal to the dilution of the specimen causing destruction of 50% of cells. The inhibiting action of irradiation was evaluated by decreasing the vims titer. 

S.Red. Cl =Sulphite Reducing Clostridia—Clostridium welchii =Decimal logarithms of counts... 

Equation (5.12) is the Nemst equation for the variation of M/M potential E with concentration Converting the natural logarithm into a decimal logarithm... 

The pKs value correlates to the negative decimal logarithm of the product of solubility. 

The denaturation of GFPuv in buffer solutions at various pH values was measured by the loss of fluorescence intensity and expressed in the decimal logarithm of the decrease in native GFPuv concentration vs the time of exposure at constant temperature (Fig. 1). To estimate D-values at constant heating temperatures and pH values (Table 1), the interval of GFPuv concentrations considered was between 3.5 (acetate, pH 5.18) and... 

Snyder used decimal logarithms instead of natural ones, causing a difference of a factor of 2.3 between the value given here and the literature data [331]. 

The decimal logarithm of the transmission coefficient is called absorption A = log(l/T), or A = log(l/T ) for the corrected transmission. The latter quantity can be measured directly in a double-beam spectrophotometer (by use of the corresponding system for the second beam) or by a memorization of the reference spectrum and its subtraction from the curve measured for the system under study of the single-beam device. 

Because of the wide range of partitioning coefficient values, in most cases the decimal logarithm of K i, is used, and it is denoted as LogP ... 

Lipophilicity is frequently used in QSAR analysis and expressed as the partition coefficient P (or by its decimal logarithm, log P) between a nonaqueous and aqueous phase. Another parameter, which takes into account the equilibrium of an ionizable compound at a stated pH value, is the distribution coefficient (Z>), which depends on the P of the single species and on the pAT values of the chosen compound. P and D have been evaluated for different N-substituted l,2-benzisothiazol-3-one derivatives using the partition between -octanol and water. Selected data are reported in Table 9 <1996FES493, 2002EJM553>. 

The specific activity (Ci) is expressed as K, (first-order rate constant calculated in decimal logarithms) per ml of protein N per ml of reaction mixture and is determined at a substrate concentration of 0.05 M a-N-benzoyl-L-argininamide at pH 5.5 and 39°C in the presence of 0.005 M cysteine and 0.001 M EDTA. 

Converting the natural logarithm into decimal logarithm, Eq. (7) yields... 

Expressed as first-order rate constant (in decimal logarithms) per mg. of enzyme N per cubic centimeter. 

Fig. 3 Dependence of the decimal logarithm of irreducible correlator tun = rnlw) -on distance n along polymer chain for macromolecules of equimolar composition at the values of parameters (Eq. 20) h = 70, h = 0.01. Curves are presented for macromolecules whose length is Z = 2 x lO (1) 6 x lO (2) 12 x lO (3). Thin lines represent asymptotic expressions at n n. Volume fraction of monomeric units in the globule is = 0.9...

The energy of the optical wave that propagates along axis z is proportional to the square of the amplitude of its electric vector. It is equal to /g at the entrance of the medium defined by z = 0, and to / at the output of the medium defined by z = /. In a classical absorption set-up, also called the transmission set-up, which is used in the great majority of experiments and is displayed in Figure 5.AI, the measured quantity is the absorbance A equal to the decimal logarithm of the ratio of these two energies (also called intensities). With the help of eq. (5.A6), we may write... 

Converted into decimal logarithms from the authors data for natural logarithms. ... 

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