Open problem

There are numerous open problems concerning the behavior of the algorithms discussed in this article. Among the most important ones are  

SAWs with nearest-neighbor attraction (— theta point). The transition of polymer conformation from the high-temperature (good-solvent) regime to the theta point to the collapsed regime is well modeled by the self-avoid- 

Branched polymers. In recent years much attention has been devoted to the theoretical and experimental study of branched polymers, whose behavior is quite different from that of linear or ring polymers. The simplest case is that of branched polymers with fixed topology, such as star or comb polymers. Many of the algorithms for linear polymers can be adapted to this case, although both the ergodicity and the efficiency are nontrivial problems. See Ref. 40, Section 2.4.3 for some references, and see Refs 169-172, 174, 176 for recent work using the pivot algorithm. 

Fisher, in Critical Phenomena (Stellenbosch 1982), Lecture Notes in Physics 186, edited by F. J. W. Hahne (Springer-Verlag, Berlin-Heidelberg-New York, 1983), pp. 1-139. 

DeGennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979). 

Stability of the described solution branches (the middle branch with negative differential resistance is expected to be unstable). 

Effects of space charges (finite e). It is expected that the inclusion of space charges will eliminate current saturation (limiting currents) at the lower and middle branches. These branches are instead expected to meet at another turning point, due to punch through (in this purely electro-diffusional formulation without source terms).5 

Uniqueness of electro-diffusional steady states is expected and should be proved for one-dimensional systems with less than three alterations of sign N. 

The possibility should be considered of generalizing the present treatment with N(x) piecewise constant to the case of arbitrary sign varying N(x). 

The precise nature of bifurcation at IV4 = N r (likewise, for other Ni, i = 1,2,3). It is expected that at JV4 = Nf the lower and middle limiting current branches fuse and annihilate each other, leaving an inflection point at the voltage-current curve for N4 N .  

Give general characterisations of the properties of conservativity, sub-and superconservativity. The equivalent conditions should have chemical meanings, properties that are easier to check than the original ones. 

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In the next section we describe the basic models that have been used in simulations so far and summarize the Monte Carlo and molecular dynamics techniques that are used. Some principal results from the scaling analysis of EP are given in Sec. 3, and in Sec. 4 we focus on simulational results concerning various aspects of static properties the MWD of EP, the conformational properties of the chain molecules, and their behavior in constrained geometries. The fifth section concentrates on the specific properties of relaxation towards equilibrium in GM and LP as well as on the first numerical simulations of transport properties in such systems. The final section then concludes with summary and outlook on open problems. 

Table 3.7 list,s the critical density and type of process for several von Neumann and Moore neighborhood rules. In the first and fourth columns, the rules are defined by the fractions (m/n), which specify a threshold of rn cr = 1 sites out of a total of n possible votes. The table entries for are taken from published results [vich84j using the CAM-6 hardware simulator [marg87] whether some or all of these values can be determined analytically remains an open problem. 

The relationships between thermodynamic entropy and Shannon s information-theoretic entropy and between physics and computation have been explored and hotly debated ever since. It is now well known, for example, that computers can, in principle, provide an arbitrary amount of reliable computation per kT of dissipated energy ([benu73], [fredkin82] see also the discussion in section 6.4). Whether a dissipationless computer can be built in practice, remains an open problem. We must also remember that computers are themselves physical (and therefore, ultimately, quantum) devices, so that any exploration of the limitations of computation will be inextricably linked with the fundamental limitations imposed by the laws of physics. 

Margolus (margfiOb] generalizes Feynman s formalism - which applies to strictly serial computation - to describe deterministic parallel quantum computation in one dimension. Each row in Margolus model is a tape of a Turing Machine, and adjacent Turing Machines can communicate when their tapes arc located at the same coordinate. Extension of the formalism to more than one dimension remains an open problem. 

From the comparison of the achievements and open problems new perspectives are emerging. In particular, the results collected in these pages demonstrate that the synergic use of different and complementary spectroscopic... 

The Driven Henon-Heiles System V. Outlook Open Problems... 

For similar motivations, there are limited incentives to develop an alternative SCR process for stationary sources based on methane (CH4-SCR) or other HCs, or based on NTP technologies, if not for specific, better applications. The situation is instead quite different for mobile sources, and in particular for diesel engine emissions. The catalytic removal of NO under lean conditions, e.g. when 02 during the combustion is in excess with respect to the stoichiometric one (diesel and lean-burn engines, natural gas or LPG-powered engines), is still a relevant target in catalysis research and an open problem to meet future exhaust emission regulations. 

B Phillip, H Dautzenber, KJ Linow, J Kotz, W Dawydoff. Polyelectrolyte complexes—Recent developments and open problems. Prog Polym Sci 14 91-172, 1989. 

The following Chapter will use the results and conclusions from the analysis performed in this Chapter, to derive some final conclusions and recommendations. Moreover, the posed research questions from Chapter 1 will be addressed and some open problems will be stated, to improve the current way in which companies manage safety. 

Contents Open Problems of the Present-Day Theoretical Chemistry. - On the Structure of Scientific Theories. - Pioneer Quantum Mechanics and its Interpretation. - Beyond Pioneer Quantum Mechanics. - A Framework for Theoretical Chemistry. - Reductionism, Holism and Complementarity. - Bibliography and Author Index. - Index. 

This review has no final conclusions. The whole matter of P.E. spectra of volatile metal compounds is still under investigation the results obtained until now yield only a partial picture, and there are several fundamental problems still open, so generalized conclusions are not warranted at the present stage of research. However, some points regarding the significance of the P.E. spectroscopic technique in coordination chemistry are already self-evident. We shall try to identify open problems, lines of future research, and precautions to be taken both in the experimental research and in the interpretive work, at least in the form and to the extent suggested by the present partial stage of the development of research in this field. 

Cejka, ]. Centi, G. Perez-Pariente,). Roth, W. J., Zeolite-based materials for novel catalytic applications Opportunities, perspectives and open problems. Catal. Today 2012,179 2-15. 

The dynamics of controlled systems is an open problem that has recently attracted the attention of scientific community [13]. In fact, oscillatory behavior in chemical systems is an interesting topic (which has been typically studied in autocatalytic reactions, e.g., the Lotka system see [44] and references therein). Dynamics of controlled systems can be explained in terms of interconnections. Indeed, by analogy with control systems, autocatalytic chemical systems can be described as examples of chemical feedback [44]. 

The advances in isolation methods made possible a clarification of the chemistry of cannabis. In 1963, our group reisolated CBD and reported its correct structure and stereochemistry. A year later we finally succeeded in isolating pure A -tetrahydrocannabinol (A -THC), elucidated its structure, obtained a crystalline derivative and achieved a partial synthesis from CBD. Several years later, a minor psychotomimetically active constituent, A -THC, was isolated from marijuana. Whether this THC isomer is a natural compound, or an artifact formed during the drying of the plant, remains an open problem. 

The general shape of a macromolecule is sometimes referred to as macroconformation—in contrast to microconformation, which concerns the succession of torsion angles about a limited number of consecutive bonds. The random coil, rigid rod, and rigid helix represent examples of macroconformations. The same term is used to specify the molecular shape in semicrystalline polymers, one of the most important and still open problems in the field of polymer morphology. 

In this section we will briefly discuss some open problems. The metala-logy principle leads to new chemical relationships of preparative importance. The concept of isolobal fragments (the metal with all ligands except the combined ir-systems), developed by R. Hoffmann and coworkers will be extremely helpful from the theoretical standpoint. On the other hand this empirical principle raises some questions, the answering of which will acquire preparative relevance. 

A major limitation of the dissipative mechanisms involving multiplicative noise —and by extension the iGLE and WiGLE models— is that they involve equilibrium changes only in the strength of the response with respect to the instantaneous friction kernel. They do not involve a change in the response time of the solvent at equilibrium limits. Presumably the response time also changes in some systems, and the inclusion of this variation is a necessary component of the minimal class of models for nonstationary stochastic dynamics. Plow this should be included, however, is an open problem which awaits an answer. 

Problem solving is an important and integral part of physical chemistry in addition to the concepts, principles and methods. There is a vast range of problems closed problems, with one answer open problems, which can have more than one answer and for which data may not be supplied problems that can be solved by pencil-and-paper or by the computer problems that need experiment in order to be solved and real-life problems versus scientific problems or even thought problems. A thorough classification of problem types has been made by Johnstone (107). 

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