Some Theoretical Problems

Unlike electrode reactions, the value of a in homogeneous proton transfer reactions smoothly varies over a wide range of free energies of the process[16]. This fact appears to us to be of considerable importance, since it indicates that a significant role is played by certain factors which are unknown as yet, but are typical of electrode processes and are manifested in an abrupt change in the value of a. 

Another important question which we have already touched upon in section 2.1 is the removal of hydrogen atoms formed as a result of a barrierless discharge. While considering the removal of hydrogen atoms from an electrode surface at high cathodic potentials, their ionization reaction is usually neglected, since the rate constant of 

In view of this, it is interesting to consider in greater detail the ways of removal of hydrogen in the case of a barrierless dis-charge[122,180,181]. 

In the steady state, the rate of production of hydrogen atoms (1) is equal to the sum of the rate of their removal in ionization reactions (2) and the rate of electrochemical desorption (3)  

Here ki are the respective rate constants (which in principle may depend on potential), 6 is the degree of coverage of the electrode surface by adsorbed hydrogen, Xh+ is the molar fraction of hydrogen ions in the double layer, and (1 - Xj +) is the corresponding value for water molecules (we ignore the presence of other ions, since it does not affect the final results). We assume here that electrochemical desorption in this case occurs in the reaction of a hydrogen atom with a hydronium ion. 

---

The extensive possibilities of the practical application of synthesis, and the study of the properties of ion-ex-change resins have aroused widespread interest in chemistry. This chapter discusses some theoretical problems with cationic resins as catalysts in hydrolysis reactions. New types of cationic resins have been examined and some important generalizations on ion-exchange reactions have been formulated. 

Two earlier reviews were published on high temperature cells and batteries based on molten salt and solid electrolytes. The first one (69) describes the Li/Cl2 cells, particularly the LiA.l/LiCl-KCl/Cl2 cell with gaseous CI2. Li cells with chalcogenides as cathode materials are mentioned, as well as some details of construction. This review, and the 26 references attached to it, reflects the state of the Li molten salt batteries to the end of 1970 (69). The second review (70), prepared two years later is more comprehensive. It discusses in detail some theoretical problems, the thermodynamics and rate processes in electrochemical cells, and presents tables and... 

E.J. Brandas, Some theoretical problems in chemistry and physics, Int. J. Quant. Chem. 106 (2006) 2836-2839. 

Using surface complexation models is another way to quantitatively describe the ion-exchanges processes. Surface complexation models also apply the law of mass action, combined with surface electric work (Table 1.7). However, there are some theoretical problems with the calculations, namely, that the equations of intrinsic stability use concentrations instead of activities, without discussing... 

T.Seiyama, M.Ehashira, M.lwamoto, in Some Theoretical Problems of Catalysis eds T.Kwan, G.K. Boreskov, K.Tamaru. Univ. Of Tokyo Press, Tokyo 1973, p.35... 

Steele, J. H., Notes on Some Theoretical Problems in Production Ecology,... 

Finally, many interesting practical problems remain to be studied for which an electrostatic approach may be helpful. Some theoretical problems remain unresolved, as mentioned in Barber (1980) and Kinraide (1994). One problem is... 

Frederick Macaulay, Some Theoretical Problems Suggested by tbe Movement of Interest Rates, Bond Yields, and Stock Prices in the U.S. Since 1856 (New York National Bureau of Economic Research, 1938). 

In spite of its importance, research into sulpholipid metabolism has been sporadic and neither the routes for synthesis nor for degradation have been elucidated. Most experiments on synthesis have centred on the so-called sulphoglycolytic pathway for which some theoretical problems exist [3,4]. Another possible route for the formation of sulphonic acids involves the addition of sulphite to double bonds. A facile chemical synthesis of sulphoquinovose uses this method and there is some experimental evidence for the involvement of sulphite in sulpholipid synthesis [see S]. Accordingly, we began work on sulpholipid synthesis with this possible reaction strongly in our minds. 

Yet, some theoretical problems are left to be discussed to seek for the ultimate and idealistic features as a nonadiabatic-transition theory Although a trajectory thus hopping plural times converges to run on an adiabatic potential surface asymptotically, the off-diagonal density matrix element Pij t) does not vanish practically, as in the original SET. This is ascribed to an incomplete treatment of the nuclear-electronic entanglement. This issue, often referred to as the problem of decoherence, is originated from the nuclear wavepacket bifurcation due to different slopes of potential surfaces, which will be discussed more precisely below. 

Successful separations of many complex mixtures by HPLC gradient elution have demonstrated the utility of this technique (1-5). In contrast to HPLC, gradient development in TLC has been applied relatively rarely, owing to the rather complex devices required for the generation of reproducible gradients and lack of a simple theory of gradient development. Niederwieser and Honegger (6,7) have systematized many experimental results and outlined some theoretical problems. 

There are some theoretical developments and practical implementations of methods, allowing to solve 3D reconstruction problem. They differ on their technical characteristics, scheme of data collecting and processing, qualitative results of the obtained images. 

There are some theoretical complications discussed in Refs. 91 and 92. Experimental complications include adsorption of solvent or of film on the electrode [93,94] the effect may be used to detect atmospheric contaminants. The atmosphere around the electrode may be flushed with dry nitrogen to avoid condensation problems [87]. 

For this purpose, a short overview will be given concerning some theoretical properties of the QCMD model (Sec. 2), This will allow for a suitable classification of the application problems. In the course of the following discussion, we will introduce two different classes of integration techniques ... 

The mechanism of TFL can be summarized to the ordered him lubrication, concluded from previous researches. It should be noted that the property and mechanism of TFL are not fully understood to date, and there remains a wide blank area to be covered between experiments and theoretical predictions and it leaves a far cry to achieve predictive ability. Some key problems associated with theoretical modeling which need to be addressed are ... 

Over the years an abundance of outlier tests have been proposed that have some theoretical rationale at their roots. ° Such tests have to be carefully adjusted to the problem at hand because otherwise one would either not detect true outliers (false negatives) in every case, or then throw out up to 50% of the good measurements as well (false positivesj. o Robust methods have been put forward to overcome this. Three tests will be described ... 

The purpose of this chapter is to review ultrafast, time-resolved X-ray diffraction from liquids. Both experimental and theoretical problems will be treated. The stmcture of the chapter is as follows. Section II describes the principles of a time-resolved X-ray experiment and details some of its characteristics. Basic elements of the theory are discussed briefly in Sections III-V. Finally, Section VI presents recent achievements in this domain. The related field of time-resolved X-ray spectroscopy, although very promising, wiU not be discussed. 

Abstract After some historical remarks we discuss different criteria of dynamical stability of stars and the properties of the critical states where the loss of dynamical stability leads to a collapse with formation of a neutron star or a black hole. At the end some observational and theoretical problems related to quark stars are discussed. 

In this review I first make a historical excursus into the problem, mentioning the results of the key works. Several criteria of stability are discussed, with the main focus on the static criteria, and the energetic method, which permits to obtain conclusions about the stability (sometimes approximate) in a most simple way. Critical states of compact stars at the boundary of the dynamic stability are considered, at which the star is becoming unstable in the process of energy losses, and a collapse begins leading to formation of a neutron star or a black hole. Physical processes leading to a loss of stability are discussed. At the end some observations and theoretical problems connected with quark stars are considered. 

This paper may be regarded as a sequel to my second book on Cationic Polymerisation [1]. I have aimed here at providing a fairly detailed discussion of some theoretical aspects of the subject which is still (or perhaps now more than ever before) in Dainton s words rudis indigestaque moles (a crude and ill-digested, i.e., confused, mass) [2], I also intend to discuss specifically some of the problems raised by Mayo and Morton in their article Ionic Polymerization in the book Unsolved Problems in Polymer Science [3]. 

To a certain extent a similar statement could be made about research on the chemistry of mineral-water interfaces. Some theoretical models (2,3) developed to date have focused primarily on their ability to fit data collected from one experimental technique, namely potentiometric titration. While these models have done much to improve our understanding of the oxide-water interface, we do not have a complete picture of the interfacial region at present. Although potentiometric titrations can still provide new insights, failure to utilize other techniques may result in the problem mentioned in Forni s statement above. 

---