Theory in Brief

Gel filtration is a size-exclusion chromatography mode, whereby proteins and peptides are resolved according to their hydrodynamic volumes. The most simple and widely accepted approach to describe the retention in size-exclusion chromatography (SEC) is by considering a selective permeation of macromolecules into the pores of the packing on the basis of their molecular size (more precisely, hydrodynamic volume) (see Fig. 1). It is possible to distinguish three cases  

Case A large molecules cannot penetrate into the packing pores and will be eluted with an elution volume (Vg) corresponding to the interparticle volume of the column (Vq)  

Case C intermediate sized molecules can partially penetrate the V, and will be eluted with an elution volume between Vq and V,. The elution volume increases with decreasing hydrodynamic volume of the biopolymer. 

It is important to underline that the calibration curve is vahd only for proteins of the same shape, e.g. globular proteins. It has in fact been proven that the radius of gyration of a spherical polymer is less than that of a linear polymer of the same molecular weight. 

Rosen eld36 showed that the rotatory strength a transition,assumed to be between states 0 and n, is the imaginary part of the scalar product the electric dipole and magnetic dipole transition moments for the transition  

The quantities, e, m, x and p- are the charge, mass, position, and momentum of the j th electron, respectively Zje, M/, ft/ and P , are the charge, mass, position, and momentum of the Zth nucleus, respectively and c is the speed light. The transition may be between electronic states, typically the ground state and an electronically excited state, or it may be between different vibrational levels of the ground state. The theoretical description of electronic CD and VCD37.38 therefore reduces to the task of evaluating the transition moments by q. [2] in a computationally viable manner. Because the inherent complexities involved, reasonably reliable evaluation of transition moments has only been available relatively recently for small molecules. 

Approximate models include the coupled oscillator (CO), the fixed partial charge (FPC),i7 i - o the charge flow (CF), the ring current, the 

A number of approximate VCD models are based on electronic structure calculations. The LMO modeH is a more accurate molecular orbital (MO) approach in evaluation of VCD intensities and has been implemented at the ab initio level. The nuclear and the electronic contributions to the dipole transition moments are treated completely separately in this model. The expressions of nuclear contributions are derived with full nuclear charges. For the expression of the electronic contributions, the BO approximation is invoked after the electronic part of the magnetic dipole operator is modified in such a way that the BO difficulty is avoided. Nonvanishing electronic contributions to the magnetic transition moments are thus obtained, which come from the displacements of the centroids of the localized MOs during vibrations. 

Exact a priori formulations for VCD intensities are obtained by adding high-order corrections to the BO wavefunctions. Nafie and Freedman,22 and to a certain extent also Craig and Thirunamachandran,2 have developed the 

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The above results show that the APB undergoes a roughening transition at T j 1490 K, which is below the bulk first-order transition, and this transition is in agreement with the Kosterlitz-Thouless theory. In brief, the APB is flat below T j and, above T j, it develops transverse fluctuations and wanders through the lattice. 

The issue of no-armamre reinforcement of materials and also the high interest of growing industry for them has naturally attracted a lot of work to the field of elastomer reinforcement. The theories, and some qualitative models (or just lucid proposals), trying to explain the phenomenon can be sorted in several classes [2-8]. Moreover, some classes can be divided into groups of theories. In brief, we can describe it with three classes ... 

The overview provided above covers the classical perspective on crystallization and particularly nucleation. A rapidly growing body of work shows that this view is not complete. The alternative model for nucleation is often termed the two-step nucleation theory. In brief, this model sng-gests that nucleation is a multistep process where the first step involves phase separation via the formation of liquid or amorphous nanoparticles. This is then followed by crystallization within this particle. The activation energy for each of these steps is relatively small, and it is expected that the overall process would be faster when compared with a single-step (classical) process with the same overall activation energy. Experimental and theoretical evidence supports this mechanism, and it has been suggested that the nucleation process is likely to proceed in this way in most, if not all, cases. ... 

In the presence of some fomi of relaxation the equations of motion must be supplemented by a temi involving a relaxation superoperator—superoperator because it maps one operator into another operator. The literature on the correct fomi of such a superoperator is large, contradictory and incomplete. In brief, the extant theories can be divided into two kinds, those without memory relaxation (Markovian) Tp and those with memory... 

The theory has certain practical limitations. It is useful for o/w (od-in-water) emulsions but for w/o (water-in-oil) systems DLVO theory must be appHed with extreme caution (16). The essential use of the DLVO theory for emulsion technology Hes in its abdity to relate the stabdity of an o/w emulsion to the salt content of the continuous phase. In brief, the theory says that electric double-layer repulsion will stabdize an emulsion, when the electrolyte concentration in the continuous phase is less than a certain value. 

Chapter 3 of Volume 1 discusses many of the basic properties of gas and methods presented for calculating them. Chapter 6 of Volume 1 contains a brief discussion of heat transfer and an equation to estimate the heat required to change the temperature of a liquid. This chapter discusses heat transfer theory in more detail. The concepts discussed in this chapter can be used to predict more accurately the required heat duty for oil treating, as well as to size heat exchangers for oil and water. 

In this short review, a brief overview of the underlying principles of TDDFT has been presented. The formal aspects for TDDFT in the presence of scalar potentials with periodic time dependence as well as TD electric and magnetic fields with arbitrary time dependence are discussed. This formalism is suitable for treatment of interaction with radiation in atomic and molecular systems. The Kohn-Sham-like TD equations are derived, and it is shown that the basic picture of the original Kohn-Sham theory in terms of a fictitious system of noninteracting particles is retained and a suitable expression for the effective potential is derived. 

A particular question of interest is whether the DNA torsional motions observed on the nanosecond time scale are overdamped, as predicted by simple Langevin theory, and as observed for Brownian motions on longer time scales, or instead are underdamped, so that damped oscillations appear in the observed correlation functions. A related question is whether the solvent water around the DNA exhibits a normal constant viscosity on the nanosecond time scale, or instead begins to exhibit viscoelastic behavior with a time-, or frequency-, dependent complex viscosity. In brief, are the predictions for... 

In this article, a brief discussion will be given on the relevance of continuum theory in explaining the rate of electron transfer and the activation of species in solution we will concentrate in particular on molecular and quantum mechanical models of ET reactions at the electrode/electrolyte interface that are needed to replace those based on the continuum approach. ... 

The approach that is used to identify a regulatory mechanism in any biochemical process is discussed in Chapter 3. In brief, the approach is (i) identify the regulatory enzymes or processes (ii) study the properties of the enzymes or processes (iii) on the basis of the properties, formulate a theory of regulation (iv) test the theory. 

Most chemical reaction engineering textbooks contain material on residence time distribution theory. Levenspiel [17] and Hill [18] present particularly useful introductions as do refs. 9 and 16. The proceedings of a recent summer school [19] contains a brief overview of the field [8] as well as papers describing many specific applications of RTD theory in chemical engineering contexts. Nauman s comprehensive invited review cited earlier [4] is an extremely thorough and yet highly readable contribution to the literature. The book by Nauman and Buffham [20], will no doubt fill a most important gap in the literature on mixing in continuous flow systems. 

The Epilogue contains some thoughts as to how psychopharmacology has influenced modem psychiatry and psychology in practice and theory. This brief chapter also contains an account of the controversy about extending prescription authority to non-medical psychotherapists. 

If the view that there can be a multiple self is carried to its extreme conclusion, it is more naturally labelled a no-self theory. In the history of thought this view is associated especially with Hume a more sophisticated and elaborate version is found in Buddhism.20 Two Neo-Buddhist theories have recently been proposed by Serge-Christophe Kolm (1982) and by Derek Parfit (1984). I shall present a brief summary of Kolm s view, to provide a context for the chapter from his book, excerpted below.21... 

Let us now briefly outline the structure of this review. The next section contains information concerning the fundamentals of the electrochemistry of semiconductors. Part III considers the theory of processes based on the effect of photoexcitation of the electron ensemble in a semiconductor, and Parts IV and V deal with the phenomena of photocorrosion and light-sensitive etching caused by those processes. Photoexcitation of reactants in a solution and the related photosensitization of semiconductors are the subjects of Part VI. Finally, Part VII considers in brief some important photoelectrochemical phenomena, such as photoelectron emission, electrogenerated luminescence, and electroreflection. Thus, our main objective is to reveal various photo-electrochemical effects occurring in semiconductors and to establish relationships among them. 

It is well known that optical activity is induced for achiral species in the presence of chiral species, giving rise to ICD for the absorption band(s) of the achiral species. In the introduction Section, a historical summary is described in brief. The theory of ICD has been developed by Tinoco, Jr.46), Mason 47), and Schipper 48). 

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