Conservative, defined

The quantity sf is a result of the normalization constraint, while, sy 1 are the Lagrange multipliers associated with the charge-current conservation defined by Equation 8.17. On the other hand, if Equation 8.18 is divided by Rk we can reexpress the corresponding equation as... 

Capacity presentation in wt% is very useful from technological point of view, because it gives direct information on how much of hydrogen can be stored in a material. Regardless of the units, there are several ways to express hydrogen capacity. The reversible capacity is conservatively defined as the plateau... 

The stability of finely dispersed suspension is determined on the optical density. The time of the suspension optical density conservation defines the stability of suspension. The activity of suspension is found on the bands intensity changes by means of IR and Raman spectra. The intensity increasing testify to transfer of NS surface energy vibration part on the molecules of medium or composition. The line speading in spectra testify to the growth of electron action of nanocomposites with medium molecules. Last fact is confirmed by x-ray photoelectron investigations. 

The polymer motion is governed by the equations of mass and momentum conservation, defined for each layer, combined to a constitutive relationship. Let p and v denote the pressure and the velocity vector in the flow domain respectively. The velocity v and the pressure p are unknowns that obey the Navier-Stokes equations, i.e. the mass (1) and momentum (2) conservation equation. The momentum equation expresses a balance of the several forces involved surface force, gravity, fluid stresses, and inertia ... 

These expressions are inserted in the conservation equations, and the boundary conditions provide a set of relationships defining the U and V coefficients [125-129]. 

We hope that by now the reader has it finnly in mind that the way molecular symmetry is defined and used is based on energy invariance and not on considerations of the geometry of molecular equilibrium structures. Synnnetry defined in this way leads to the idea of consenntion. For example, the total angular momentum of an isolated molecule m field-free space is a conserved quantity (like the total energy) since there are no tenns in the Hamiltonian that can mix states having different values of F. This point is discussed fiirther in section Al.4.3.1 and section Al.4.3.2. 

Flere the subscripts and/refer to the initial and final states of the system and the work is defined as the work perfomied on the system (the opposite sign convention—with as work done by the system on the surroundings—is also in connnon use). Note that a cyclic process (one in which the system is returned to its initial state) is not introduced as will be seen later, a cyclic adiabatic process is possible only if every step is reversible. Equation (A2.1.9), i.e. the mtroduction of t/ as a state fiinction, is an expression of the law of conservation of energy. 

The treatment of such order-disorder phenomena was initiated by Gorsky (1928) and generalized by Bragg and Williams (1934) [5], For simplicity we restrict the discussion to the synnnetrical situation where there are equal amounts of each component (x = 1/2). The lattice is divided into two superlattices a and p, like those in the figure, and a degree of order s is defined such that the mole fraction of component B on superlattice p is (1 +. s)/4 while that on superlattice a is (1 -. s)/4. Conservation conditions then yield the mole fraction of A on the two superlattices... 

The first tenn is tire dipole force, sometimes called tire trapping force, Fj, because it is a conservative force and can be integrated to define a trapping potential for tire atom ... 

The probability for a particular electron collision process to occur is expressed in tenns of the corresponding electron-impact cross section n which is a function of the energy of the colliding electron. All inelastic electron collision processes have a minimum energy (tlireshold) below which the process cannot occur for reasons of energy conservation. In plasmas, the electrons are not mono-energetic, but have an energy or velocity distribution,/(v). In those cases, it is often convenient to define a rate coefficient /cfor each two-body collision process ... 

One property of the exact trajectory for a conservative system is that the total energy is a constant of the motion. [12] Finite difference integrators provide approximate solutions to the equations of motion and for trajectories generated numerically the total energy is not strictly conserved. The exact trajectory will move on a constant energy surface in the 61V dimensional phase space of the system defined by. 

A mapping is said to be symplectic or canonical if it preserves the differential form dp A dq which defines the symplectic structure in the phase space. Differential forms provide a geometric interpretation of symplectic-ness in terms of conservation of areas which follows from Liouville s theorem [14]. In one-degree-of-freedom example symplecticness is the preservation of oriented area. An example is the harmonic oscillator where the t-flow is just a rigid rotation and the area is preserved. The area-preserving character of the solution operator holds only for Hamiltonian systems. In more then one-degree-of-freedom examples the preservation of area is symplecticness rather than preservation of volume [5]. 

If we know the moles of A and the number of reaction units associated with A and B, then we can calculate the moles of B. Note that a conservation of reaction units, as defined by equation 2.3, can only be applied between two species. There are five important principles involving a conservation of reaction units mass, charge, protons, electron pairs, and electrons. 

For different types of collections, this balance is differently defined. For example paper conservation treatments commonly undertaken in the museum conservation laboratory would be impractical in a Hbrary archive having a far greater collection size. The use of treatments for mass paper quantities would be unacceptable in the art museum. Documents in archives and books in Hbraries serve a different goal from art objects in a museum. Their use value Hes primarily in their information rather than in an intrinsic esthetic value. Whereas optimal preservation of that information value requires preservation of the object itself, a copy or even a completely different format could serve the same purpose. 

Direct and Indirect Energy Gap. The radiative recombination rate is dramatically affected by the nature of the energy gap, E, of the semiconductor. The energy gap is defined as the difference in energy between the minimum of the conduction band and the maximum of the valence band in momentum, k, space. Eor almost all semiconductors, the maximum of the valence band occurs where holes have zero momentum, k = 0. Direct semiconductors possess a conduction band minimum at the same location, k = O T point, where electrons also have zero momentum as shown in Eigure la. Thus radiative transitions that occur in direct semiconductors satisfy the law of conservation of momentum. 

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