Factor evolution

Paulus, H. F. and Gack, C. (1990). Pollinators as prepollinating isolation factors evolution and speciation in Ophrys (Orchidaceae). Israel Journal of Botany 39 43-79. 

To analyze this phenomenon further, 2D numerical simulations of (49) and (50) were performed using a central finite difference approximation of the spatial derivatives and a fourth order Runge-Kutta integration of the resulting ordinary differential equations in time. Details of the simulation technique can be found in [114, 119]. The material parameters of the polymer blend PDMS/PEMS were used and the spatial scale = (K/ b )ll2 and time scale r = 2/D were established from the experimental measurements of the structure factor evolution under a homogeneous temperature quench. 

The first term representsJhe factorized evolution in terms of exciton amplitude (B+B) = (B+) (B). G is the irreducible (unfactorized) part of the Green function. The response function will be expressed in terms of G rather than G(p). 

The effect of the reaction temperature, poisoning and sintering rates as well as the Reynolds number on the effectiveness factor evolution have been investigated. 

Isaacs, H.V., Andreazzoli, M., Slack, J.M. 1999. Anteroposterior patterning by mutual repression of orthodenticle and caudal-type transcription factors. Evolution and Development 1, 143-152. 

In a previous work (1), we established that the damage factor evolution is independent of load level and number of cycles to failure, provided the tests duration remains short enough (pure fatigue tests). Under these conditions, the damage factor gains continuously increasing values that depend only on the cycle ratio to failure (Fig.2) ... 

Kulikov, V.l. and Muzya, G.l. (1997) Ether lipids and platelet-activating factor evolution and cellular fimction. Biochemistry, 62,1103—1108. 

The formation volume factor for water (B, reservoir volume per stock tank volume), is close to unity (typically between 1.00 and 1.07 rb/stb, depending on amount of dissolved gas, and reservoir conditions), and is greater than unity due to the thermal contraction and evolution of gas from reservoir to stock tank conditions. 

So long as the field is on, these populations continue to change however, once the external field is turned off, these populations remain constant (discounting relaxation processes, which will be introduced below). Yet the amplitudes in the states i and i / do continue to change with time, due to the accumulation of time-dependent phase factors during the field-free evolution. We can obtain a convenient separation of the time-dependent and the time-mdependent quantities by defining a density matrix, p. For the case of the wavefiinction ), p is given as the outer product of v i) with itself. 

It is only during an evolution (perhaps between sampling points in an FID) that these totals need be divided amongst the various lines in the spectmni. Therefore, one of the factors in the transition probability represents the conversion from preparation to evolution the other factor represents the conversion back from evolution to detection. 

For bound state systems, eigenfunctions of the nuclear Hamiltonian can be found by diagonalization of the Hamiltonian matiix in Eq. (11). These functions are the possible nuclear states of the system, that is, the vibrational states. If these states are used as a basis set, the wave function after excitation is a superposition of these vibrational states, with expansion coefficients given by the Frank-Condon overlaps. In this picture, the dynamics in Figure 4 can be described by the time evolution of these expansion coefficients, a simple phase factor. The periodic motion in coordinate space is thus related to a discrete spectrum in energy space. 

Many factors other than current influence the rate of machining. These involve electrolyte type, rate of electrolyte flow, and other process conditions. For example, nickel machines at 100% current efficiency, defined as the percentage ratio of the experimental to theoretical rates of metal removal, at low current densities, eg, 25 A/cm. If the current density is increased to 250 A/cm the efficiency is reduced typically to 85—90%, by the onset of other reactions at the anode. Oxygen gas evolution becomes increasingly preferred as the current density is increased. 

Time constraints ate an important factor in selecting nmr experiments. There are four parameters that affect the amount of instmment time requited for an experiment, A preparation delay of 1—3 times should be used. Too short a delay results in artifacts showing up in the 2-D spectmm whereas too long a delay wastes instmment time. The number of evolution times can be adjusted. This affects the F resolution. The acquisition time or number of data points in can be adjusted. This affects resolution in F. EinaHy, the number of scans per EID can be altered. This determines the SNR for the 2-D matrix. In general, a lower SNR is acceptable for 2-D than for 1-D studies. 

When a battery produces current, the sites of current production are not uniformly distributed on the electrodes (45). The nonuniform current distribution lowers the expected performance from a battery system, and causes excessive heat evolution and low utilization of active materials. Two types of current distribution, primary and secondary, can be distinguished. The primary distribution is related to the current production based on the geometric surface area of the battery constmction. Secondary current distribution is related to current production sites inside the porous electrode itself. Most practical battery constmctions have nonuniform current distribution across the surface of the electrodes. This primary current distribution is governed by geometric factors such as height (or length) of the electrodes, the distance between the electrodes, the resistance of the anode and cathode stmctures by the resistance of the electrolyte and by the polarization resistance or hinderance of the electrode reaction processes. 

Small particles are required, to provide a large surface-area-to-mass ratio and for the solid to remain in suspension. Surface absorption of air (oxygen) by the solid, or tlie evolution of combustible gas or vapour on heating, may be a predisposing factor. The presence of moisture reduces the tendency to ignite it also favours agglomeration to produce larger particles. An increase in the proportion of inert solid in particles tends to reduce combustibility. 

To describe an arbitrary nonequilibrium evolution of the adsorbate we need the whole hierarchy, or at least a suitably truncated subset. We can close the hierarchy at the level of 2-site correlators by a factorization of higher correlators with 1-site overlap [58,59]... 

In the PPF, the first factor Pi describes the statistical average of non-correlated spin fiip events over entire lattice points, and the second factor P2 is the conventional thermal activation factor. Hence, the product of P and P2 corresponds to the Boltzmann factor in the free energy and gives the probability that on<= of the paths specified by a set of path variables occurs. The third factor P3 characterizes the PPM. One may see the similarity with the configurational entropy term of the CVM (see eq.(5)), which gives the multiplicity, i.e. the number of equivalent states. In a similar sense, P can be viewed as the number of equivalent paths, i.e. the degrees of freedom of the microscopic evolution from one state to another. As was pointed out in the Introduction section, mathematical representation of P3 depends on the mechanism of elementary kinetics. It is noted that eqs.(8)-(10) are valid only for a spin kinetics. 

Figure 4-419 illustrates the concept of corrosion process under concentration polarization control. Considering hydrogen evolution at the cathode, reduction rate of hydrogen ions is dependent on the rate of diffusion of hydrogen ions to the metal surface. Concentration polarization therefore is a controlling factor when reducible species are in low concentrations (e.g., dilute acids). 

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