Formality, level

The K-matrix method is essentially a configuration interaction (Cl) performed at a fixed energy lying in the continuum upon a basis of "unperturbed funetions that (at the formal level) includes both diserete and eontinuous subsets. It turns the Schrodinger equation into a system of integral equations for the K-matrix elements, which is then transformed into a linear system by a quadrature upon afinite L basis set. 

To date, analyses of the Phycomyces light responses have remained at a rather formal level whereas the ultimate goal must be a detailed description of the chemical steps in reception, transmission and reaction to the stimulus of light. The first of these steps is excitation of the photoreceptor by light and it is therefore not unexpected that many attemps have been made to identify and isolate this compound. In spite of much effort during the past years, not only wi th Phycomyces, the blue light photo-... 

Summing over all pairs of segments in the solution we strictly speaking rim into problems with the tf-function interaction, which could be avoided by using a potential of finite range (cf. Sect. 2.2). Furthermore the constant Uq in principle differs from the definition (5.25). We here ignore all such complications, which do not affect the essential features of the derivation. We rather argue on a purely formal level. 

We shall present in this contribution to the Annals a survey of some recent advancements in the description of the properties of molecules in solution obtained by using a continuum representation of the solvent [1], The exposition will be kept at a relatively low formal level, our intention being to give a contribution not addressed to specialists in the field. In this introduction, we will report some comments to make the understanding of the approach easier. 

The next formal level of closure is at the level of the dynamical equations for the turbulent stresses, which we shall call mean Reynolds-stress closures (MRS). There have only been a few experimental calculations at this level, and such closures are not yet tools for practical analysis. 

To calculate the scaling functions we now follow the flow up to some fixed surface chosen far from the critical manifold, such that i/ C- The resulting macroscopic Hamiltonian allows for a perturbative treatment, all critical effects being absorbed into the renormalization of the couplings. On the purely formal level the precise choice of tliis manifold where the scaling... 

Semi-formal representations can be used as an intermediate step for the generation of a model with the intended level of detail and formalization First, the operations are specified by chemists or process experts on a conceptual, semi-formal level, and subsequently formalized and refined. Since such semi-formal representations are currently missing, inadequate workarounds like spreadsheets or informal documents are often used in industrial practice. 

This set F(K,a) is a formal level set of the electronic density p(K,r) for the threshold level a. Whereas electrons are negatively charged, the density of electrons is either positive or zero, and a negative charge means a positive value for the density function... 

This statement implies that not only the Coulomb interaction is included in Er and Exc but also the (retarded) Breit interaction. It thus points at the fact that a consistent and complete discussion of many-electron systems and consequently of RDFT must start from quantum electrodynamics (QED). RDFT necessruily has to reflect the various features of QED, both on the formal level and in the derivation of explicit functionals. The most important differences to the noiu-elativistic situation arise from the presence of infinite zero point energies and ultraviolet divergencies. In addition, finite vacuum corrections (vacuum polarization, Casimir energy) show up in both fundamental quantities of RDFT, the four current and the total energy. These issues have to be dealt with by a suitable renormalization procedure which ultimately relies on the renormalization of the vacuum Greens functions of QED. The first attempt to take... 

On the formal level, the offshore safety regulations comprise (1) statutes and (2) decrees and regulations issued pursuant to each of the statutes (or pursuant to several of them in combination). 

The paper is organized as follows. In section 2 we explain the main assumptions on a semi-formal level. Section 3 defines amodel for the Go-failure. An appropriate probabilistic specification is provided in section 4. A system failure including a Go-Failure is analyzed in 5. The example of a Go-If failure will he addresses in sections 6 and 7. 

According to Gaden (1955, 1959), four types of product accumulation can be distinguished on the formal level based on the quantitative relationship... 

We can always anticipate the idea of a completed generic truth. The generic being of a truth is never presented. A truth is uncompletable. But what we can know, on a formal level, is that a truth will always have taken place as a generic infinity. This allows the possible fictioning of the effects of such a truth having-taken-place. That is, the subject can... 

The formal level of the presentation is directed primarily toward the first- and second-year graduate student in engineering science although it is expected that students in physics will also find it useful. Considerable pains have been taken to provide a textbook which could also be used in a first course on reactor analysis. The introductory sections of each of the principal chapters have been organized and written with this thought in mind. In these sections the treatment is initiated with the aid of elementary mathematical models and emphasis is placed on a discussion of the principal physical concepts to be developed. The more sophisticated mathematical considerations and the development of the broader theory are left in each case to later sections. Thus it is expected that this work will serve as an elementary text which can also be used in an intermediate course by simply including the complete treatment. 

Finally, we would like to elaborate the proposed protocol of the high-friction map, eqn (13.17). Its construction is based purely on the thermodynamic consideration, eqn (13.15), validated by the central limit theorem. Therefore it may offer a general rule to obtain the Smoluchowski limit to any phase-space dynamics under study. The protocol proposed in this chapter is based on the fact that the map is universal at formal level and is therefore obtainable with thermodynamic consideration. It means the Smoluchowski dynamics can be taken care of by the related Fokker-Planck equation, upon the universal map being carried out. It is worth pointing out that the resultant diffusion operator in eqn (13.18) clearly originates from only the Hamiltonian part of the... 

OOP on the formalism level defining kinematic and kinetic methods for the objects introduced on the system level,... 

Since there are already objects in multibody systems, OOP on the system level has always been done. Recent investigations consequently use object-oriented models for the database to store the system information [11]. Using OOP on the formalism level is more difficult and a current field of research [9], [10]. OOP on the linear algebra level is quite common, there are already commercial packages available. There are several methods to do OOP on the scalar level ... 

---