Formalization phase

It often requires 4-6 years of clinical testing to accumulate all required data. Testing in humans is begun after sufficient acute and subacute animal toxicity studies have been completed. Chronic safety testing in animals is usually done concurrently with clinical trials. In each of the three formal phases of clinical trials, volunteers or patients must be informed of the investigational status of the... 

For the treatment of a propagation scheme for Eqns. (37-40) a formal phase space is introduced... 

Generally, the first formal phase of the litigation process is for witnesses (fact and expert) to be deposed. They are questioned by attorneys of both sides, usually in a conference room setting. A judge is not present. Their deposition is videotaped for possible use in later stages of the trial. 

Formalization phase builds a formal model to facilitate the use and integration of knowledge in the application, with a structure that is understandable and computable by the machine. It... 

Keywords cognitive science, collaborative problem solving, design experiments, evolution phase, falsification, formalization phase, instructional cycle, joystick, mental model, microworlds, motivation, Newtonian mechanics, phenomenological problems, physics, scientific inquiry, scientific method, ThinkerTools, transfer phase, transfer test... 

Another reason why many ThinkerTools students are able to transfer what they have learned might be derived from the formalization phase of the instructional cycle. In this phase, students summarize what they have teamed into a simple, easy to remember principle that allows them to make precise predictions across a range of different contexts. In other words, they sununarize their knowledge into a form that is easy to remember, generally applicable, and powerhil. Thus their knowledge is in a form that enables it to be app ed across a range of different situations. 

Formal phase transition curves for different mechanisms of molecular interaction are shown in Fig. 2a. Since these mechanisms are independent, the curves after intersection continue to keep their course and divide the phase plane into four sections. The point D turns out to be not triple but quadruple. The area of existence of second intermediate state, second liquid L2, together with that of liquid, Li, appears on the phase plane. 

The application of formal phase-equilibrium thermodynamics leads to an expression for the depression of the melting temperature by low molecular weight diluent, when it is excluded from the crystalline phase. This expression is given by [6]... 

This portion of the chapter can be summarized by noting that there is a substantial body of evidence demonstrating that formal phase-equilibrium thermodynamics can be successfully applied to the fusion of homopolymers, copolymers, and polymer-diluent mixtures. This conclusion has many far-reaching consequences. It has also been found that the same principles of phase equilibrium can be applied to the analysis of the influence of hydrostratic pressure and various types of deformation on the process of fusion [11], However, equilibrium conditions are rarely obtained in crystalline polymer systems. Usually, one is dealing with a metastable state, in which the crystallization is not complete and the crystallite sizes are restricted. Consequently, the actual molecular stmcture and related morphology that is involved determines properties. Information that leads to an understanding of the structure in the crystalline state comes from studying the kinetics and mechanism of crystallization. This is the subject matter of the next section. 

The signal comparison function has been impieinented and tested during a steam generator tube inspection. A formal test in the real-life context was successfully done with a simple rule (parameters phase and amplitude) based on the central frequency for the distance signal. 

Campolieti G and Brumer P 1994 Semiclassical propagation phase indices and the initial-value formalism Phys. Rev. A 50 997... 

An Extended (Sufficiency) Criterion for the Vanishing of the Tensorial Field Observability of Molecular States in a Hamiltonian Formalism An Interpretation Lagrangeans in Phase-Modulus Formalism A. Background to the Nonrelativistic and Relativistic Cases Nonreladvistic Electron... 

Section VI shows the power of the modulus-phase formalism and is included in this chapter partly for methodological purposes. In this formalism, the equations of continuity and the Hamilton-Jacobi equations can be naturally derived in both the nonrelativistic and the relativistic (Dirac) theories of the electron. It is shown that in the four-component (spinor) theory of electrons, the two exha components in the spinor wave function will have only a minor effect on the topological phase, provided certain conditions are met (nearly nonrelativistic velocities and external fields that are not excessively large). 

The question of determination of the phase of a field (classical or quantal, as of a wave function) from the modulus (absolute value) of the field along a real parameter (for which alone experimental determination is possible) is known as the phase problem [28]. (True also in crystallography.) The reciprocal relations derived in Section III represent a formal scheme for the determination of phase given the modulus, and vice versa. The physical basis of these singular integral relations was described in [147] and in several companion articles in that volume a more recent account can be found in [148]. Thus, the reciprocal relations in the time domain provide, under certain conditions of analyticity, solutions to the phase problem. For electromagnetic fields, these were derived in [120,149,150] and reviewed in [28,148]. Matter or Schrodinger waves were... 

For the Fourier coefficients of the modulus and the phase we note that, because of the time-inversion invariance of the amplitude, the former is even in f and the latter is odd. Therefore the former is representable as a cosine series and the latter as a sine series. Formally,... 

Several years ago Baer proposed the use of a mahix A, that hansforms the adiabatic electronic set to a diabatic one [72], (For a special twofold set this was discussed in [286,287].) Computations performed with the diabatic set are much simpler than those with the adiabatic set. Subject to certain conditions, A is the solution of a set of first order partial diffei ential equations. A is unitary and has the form of a path-ordered phase factor, in which the phase can be formally written as... 

Experimental observation of topological phases is difficult, for one reason (among others) that the dynamic-phase part (which we have subtracted off in our formalism, but is present in any real situation) in general oscillates much faster than the topological phase and tends to dominate the amplitude behavior [306-312]. Several researches have addressed this difficulty, in particular, by neutron-interferornehic methods, which also can yield the open-path phase [123], though only under restricted conditions [313]. 

The phase-modulus formalism for nonrelativistic electrons was discussed at length by Holland [324], as follows. 

In writing the Lagrangean density of quantum mechanics in the modulus-phase representation, Eq. (140), one notices a striking similarity between this Lagrangean density and that of potential fluid dynamics (fluid dynamics without vorticity) as represented in the work of Seliger and Whitham [325]. We recall briefly some parts of their work that are relevant, and then discuss the connections with quantum mechanics. The connection between fluid dynamics and quantum mechanics of an electron was already discussed by Madelung [326] and in Holland s book [324]. However, the discussion by Madelung refers to the equations only and does not address the variational formalism which we discuss here. 

The Hemian-Kluk method has been developed further [153-155], and used in a number of applications [156-159]. Despite the formal accuracy of the approach, it has difficulties, especially if chaotic regions of phase space are present. It also needs many trajectories to converge, and the initial integration is time consuming for large systems. Despite these problems, the frozen Gaussian approximation is the basis of the spawning method that has been applied to... 

Type-n structures are formally the out-of-phase transition states between two type-I structures, even if there is no measurable banier. 

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