Homogeneity of time

These principles may be regarded as the foundations of science." The homogeneity of time allows the expectation that repeating experiments will give the same results. The homogeneity of space makes it possible to compare the results of the same experiments carried out in two different laboratories. Finally, the isotropy of space allows one to reject any suspicion that a different orientation of our laboratory bench changes the result. 

Its total energy remains invariant (because of the homogeneity of time). 

Given the Lagrangian for a system of interacting particles, a number of fundamental system properties can be deduced. Among these properties are the basic conservation laws " which can be deduced invoking the principle of homogeneity of time and space for closed systems that do not interact with any external forces. 

Bornemann, F. A. Homogenization in Time of Singularly Perturbed Conservative Mechanical Systems. Manuscript (1997) 146pp... 

Digester Control For control purposes at constant sulfidity and alkah charge, the deligniftcation rate is treated as a homogeneous reaction, which is first order with respect to the lignin, % remaining in the wood, —dL jdt = kL. The influence of time, t, and temperature, T (Kelvin), has been incorporated into one term, called the JT-factor (33). 

The particle size distribution of Rhovanil Extra Pure vanillin shows a less narrow profile than other standard mesh grades available on the market. The product shows an improved mixabiUty in blending operations, allowing shorter blending time of compounds or food mixes, and better homogeneity of vanillin content, especially in low content vanillin blends. 

Nucleation The mechanism of crystal nucleation from solution has been studied by many scientists, and recent work suggests that—in commercial crystallization equipment, at least—the nucleation rate is the sum of contributions by (1) homogeneous nucleation and (2) nucleation due to contaci between crystals and a) other crystals, h) the walls of the container, and (c) the pump impeller. If is the net number of new crystals formed in a unit volume of solution per unit of time. 

Spin-spin relaxation is the steady decay of transverse magnetisation (phase coherence of nuclear spins) produced by the NMR excitation where there is perfect homogeneity of the magnetic field. It is evident in the shape of the FID (/fee induction decay), as the exponential decay to zero of the transverse magnetisation produced in the pulsed NMR experiment. The Fourier transformation of the FID signal (time domain) gives the FT NMR spectrum (frequency domain, Fig. 1.7). 

Generally, at any moment of time the concentration of components within a vapor cloud is highly nonhomogeneous and fluctuates considerably. The degree of homogeneity of a fuel-air mixture largely determines whether the fuel-air mixture is able to maintain a detonative combustion process. This factor is a primary determinant of possible blast effects produced by a vapor cloud explosion upon ignition. It is, therefore, important to understand the basic mechanism of turbulent dispersion. 

First, let us consider batch mixing processes, as exemplified by ordinaiy laboratory practice in solution kinetics. A portion of one solution (say, of the substrate) is added by pipet to a second solution (containing the reagent) in a flask, the flask is shaken to achieve homogeneity, and then samples are withdrawn at known times for analysis, or the solution is subjected to continuous observation as a function of time, for example, by spectrophotometry. For reactions on a time scale (measured by the half-life) of hours or even several minutes, the time consumed in these operations is a negligible portion of the reaction time, but as the half-life of the reaction decreases, it becomes necessary to consider these preliminary steps. Let us distinguish three stages ... 

For a continuous SMB process, the specific identified amount or batch produced is defined by unit of time in such a way that ensures a homogeneous material and quality within specified limits. In the case of a continuous SMB production run a batch is defined by the amount produced in a fixed time interval. A time limitation during manufacturing using SMB is established by the same fixed time interval as the batch. The duration of the production phase is thus established, which does not affect the quality of the drug substance [66]. 

Acetone powder (1.5 g) was extracted 4 times with 0.1 M sodium borate buffer (pH 7.6) at 4°C, homogenizing each time with a glass grinder equipped with a Teflon pestle. The first extraction was carried out with 80 ml of the buffer, followed by 3 times with 70 ml each of the buffer. Each homogenate was centrifuged at 16,000 g for 5 min. All supernatants were combined. 

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