Open questions

The questions are clustered under two headlines ( Catalyst Systems and Kinetic and Mechanistic Aspects ) and are compiled in an arbitrary order. 

It is not clear whether Nd-carboxylates are reduced by aluminum alkyls to the respective alcohols prior to the formation of the active catalyst. It has to 

In the activation of halide-based Nd-precursors the halide is not reduced by aluminum alkyls. Therefore, the generation of the active Nd-species should be possible with a very small or even the molar equivalent of an aluminum alkyl. The consumption of aluminum alkyl will somewhat depend on the donor present in the NdCl3 system. To our opinion systematic studies lack in this respect. 

There is evidence that heterogeneous or micro-heterogeneous Nd systems lead to higher levels of gel than homogeneous systems. Most certainly, there are other factors which contribute to gel formation. In this context it has to be clarified which factors trigger gel formation and what is the quantitative contribution of catalyst heterogeneity. 

With many Nd catalyst systems multimodal or at least bimodal MMDs are obtained. From this observation it is concluded that there are several active species. A particularly highly active species which causes high molar masses at low monomer conversions is present at the start of the polymerization. Once the initial induction period is over and consistent kinetics are observed, often this species is no longer active. The fate of the species is not clear. Does this species die off after the initial high activity or is it transformed to a species which exhibits a significantly lower activity Is the early species heterogeneous and the normal species homogeneous  

In this brief final chapter we collect in one place the main questions that remain unanswered concerning the models explored in this work. We proceed more or less in the order of the chapters. In many cases, the open problems mentioned here have already been identified and discussed in the discussion section of the corresponding chapter, so the reader may wish to check there as well. 

As noted in the discussion section of Chapter 2, there remains a gap in our knowledge of the basic chemostat model in the case of differing removal rates for the competitors. The principal open problem is to extend the result of [Hsul], described in Section 4 of Chapter 2, to general monotone uptake functions. It would also be desirable to include the class of not necessarily monotone uptake functions identified in [BWol], The recent work [WLu] represents a major step in this direction. 

In Chapter 3, two limit cycles played a prominent role. The first occurred in the planar system, representing oscillations in the simple food chain. Neither the stability nor the uniqueness of the limit cycle was established. Kuang [Kl] shows that the limit cycle is unique and asymptotically stable - for parameter values near where the rest point loses stability - by examining the Hopf bifurcation from the rest point. For other values of parameters, the uniqueness and stability questions remain open. 

Limit cycles also appear in Chapter 4, but no bifurcation theorems were used (although the Hopf bifurcation theorem could have been used). Uniqueness of these cycles is a question of major interest and importance. To more accurately model the chemostat as it is used in commercial production, the plasmid model discussed in Chapter 10 should be combined with the inhibitor model of Chapter 4. More specifically, consider two organisms - differing only by the presence or absence of a plasmid that confers immunity to the inhibitor - competing in a chemostat (equation (4.2) of Chapter 9 modified for the presence of the inhibitor). The techniques of analysis used in Chapter 4 do not apply, since the system is not competitive in the mathematical sense. Yet an understanding of this system would be very important. 

The model in Chapter 4 had only one competitor taking up the inhibitor, but this is only a first approximation. One could justify this assumption only by showing that nothing changes if the system is modified to allow for uptake by both competitors. However, such modification complicates the analysis. Finally, could it be that a threshold amount needs to be consumed before the inhibitor is effective Adding thresholds to the model would be an interesting modeling task. 

Finally, we turn to a series of topics which are important for a detailed understanding of charge transport in DNA, but so far have not been treated at a sufficiently comprehensive level. 

Construction of an asymptotic solution to the stationary concentration polarization problem of 5.3, uniformly valid for all voltages (see [16]). 

Application of the uniform asymptotics above to the study of nonstationary effects occurring at high concentration polarization, such as the anomalous rectification in 5.4. 

4) Why does DH in doped a-Si H depend on the sign of the majority carrier A hole trapped on a covalent bond removes one electron 

5) Does the above model for hydrogen motion apply to other amorphous semiconductors, such as a-Si H, a-Ge H, a-SixGe x-. H, a-SixCi-x Experimental determinations of whether the conclusions for a-Si H apply to these other amorphous alloys would greatly advance our understanding of these materials and would likely improve their technological usefulness. 

(1985). Tetrahedrally Bonded Amorphous Semiconductors, ed. by D. Adler and H. Fritzsche. Plenum Press, New York, 129. 

Abeles, B., Wronski, C.R. Stephens, R.B., and Brooks, B. (1980b). Solar Cells 2, 227. 

(1956). The Mathematics of Diffusion. Clarendon Press, Oxford. 

Cell extracts of Pyrococcus contain low activities of fructose-1,6-bisphosphate aldolase [295] and NAD(P)-dependent glyceraldehyde-3-phosphate dehydrogenase [301, 308a], which probably have anabolic functions (see ref [308b]). Glyceraldehyde-3-phosphate dehydrogenase has been purified from Pyrococcus woesei [308a] (see Chapter 7 by Hensel in this volume). 

Afzelius, B.A. (1985). The immotile-cilia syndrome a microtubule-associated defect. CRC Crit. Rev. Biochem. 19, 63-87. 

Aitken, J. (1991). Do sperm find eggs attractive Nature 351, 19-20. 

Aitken, R.J., Sutton, M., Warner, P. and Richardson, D.W. (1985). Relationship between the movement characteristics of human spermatozoa and their ability to penetrate cervical mucus and zona-free hamster oocytes, f. Reprod. Fertil. 73, 441-449. 

Aitken, R.J. (1990). Motility parameters and fertility, in Controls of Sperm Motility Biological and Clinical Aspects (C. Gagnon, ed.), pp. 285-302. CRC Press, Boca Raton, FL. 

Al-Anzi, B. and Chandler, D.E. (1998). A sperm chemoattractant is released from Xenopus egg jelly during spawning. Dev. Biol. 198, 366-375. 

Why is the linear pathway of the x33y task so long. What happens during this time A linear progression is not very plausible. What alternative courses are imaginable  

Why do fractional multiples of elementary time arise in FPM26f58 It is the occurrence of these fractional values that impair the NESTLE results of the various elementary times. Are these peaks created by chance or do they convey some unknown meaning  

What are the evidences that indicate the occurence of minimal linear pathway in all pathways of a task. Perhaps longer reaction times posses longer linear pathways The equations of median pathways propose that these pathways contain the the minimal linear pathway (common linear pathway principle). 

What are the elementary times of the middle finger The x22y tasks contain approximately 100 trials where the middle finger presses the response key. Can these results be used to compute the elementary times of the two middle fingers Is there a difference to the elementary times of the index fingers  

Do women have more symmetrical elementary times than men (H32A)  

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Because of the general difficulty encountered in generating reliable potentials energy surfaces and estimating reasonable friction kernels, it still remains an open question whether by analysis of experimental rate constants one can decide whether non-Markovian bath effects or other influences cause a particular solvent or pressure dependence of reaction rate coefficients in condensed phase. From that point of view, a purely... 

Strategies for aehieving intra- and intennoleeular seleetivity are the subjeet of a very aetive field of eurrent researeh with many open questions. Under the label eoherent eontrol it ineludes approaehes that exploit the eoherenee properties of laser radiation to eontrol ehemieal reaetions. Figure B2.5.18 suimnarizes the different sehemes of intra- and intennoleeular seleetivity. 

In spite of the three methods of estimating magnitude estimates and not exact formulas. 

The Vinland Map, supposed evidence of the Viking discovery of America long before Columbus, was proclaimed a forgery after the detection in the ink of titanium white, a modem pigment (see Pigments, inorganic) (13). Subsequendy, however, after another analytical study, the interpretation of the eadiet results has been questioned, and the matter of authenticity of this unique document stiU remains an open question (14,15). 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

Thirty percent of the tumor-derived mutations are in L3, which contains the single most frequently mutated residue, Arg 248. Clearly the interaction between DNA and the specific side chain of an arginine residue inside the minor groove is of crucial importance for the proper function of p53. It is an open question whether this interaction is needed for the recognition of specific DNA sequences, or is required for the proper distortion of the DNA structure, or a combination of both. Other residues that are frequently mutated in this region participate in interactions with loop L2 and stabilize the structures of loops L2 and L3. Mutations of these residues presumably destabilize the structure so that efficient DNA binding can no longer take place. 

An elegant NMR experiment by the group of Lynn Jelinski at Cornell University has established that at least part of the microcrystals is built up from the polyalanine repeats in the protein chains. These experiments, which were made on C-enriched proteins produced by feeding the spiders C-labeled alanine, showed that there were two populations of alanine side chains, one ordered and oriented perpendicular to the fiber axis and a second less ordered. Jelinski s interpretation is that parts of the polyalanine sequences are incorporated as p strands in the microcrystals with an orientation parallel to the fiber axis. Whether or not the Gly-Gly-X repeats also form P strands in the microcrystals remains an open question. 

The specification and the proposal should be reviewed in depth. Options and their cost should be covered. Completeness is important because it is now time for the vendor to commit to any remaining items. If there was a single vendor in the lead, then, once the open questions are resolved, it would be safe to place the order. If, at the meeting, all questions were settled in a satisfactory manner, it can be quite good psychologically to place the order on the spot. 

Based on a general knowledge of base-catalyzed reactions of carbonyl compounds, a reasonable sequence of steps can be written, but the relative rates of the steps is an open question. Furthermore, it is known that reactions of this type are generally reversible so that the potential reversibility of each step must be taken into account. A completely... 

Thus one may eonelude that the observed behavior resembles qualitatively spinodal deeomposition in the bulk, although the power laws deserib-ing droplet growth are presumably different. However, these late stages when a deseription with power laws and universal exponents apply have probably not yet been reaehed. It is also an open question to what extent the negleet of hydrodynamie interaetions would be adequate in these late... 

Transport numbers for several non-haloaluminate ionic liquids generated from ionic liquid self-diffusion coefficients are listed in Table 3.6-7. The interesting, and still open, question is whether the NMR-generated transport numbers provide the same measure of the fraction of current carried by an ion as the electrochemically... 

Wliich forces have dominated in the recently observed warming of the climate is still an open question. The last landmark report of the United Nations Intergovernmental Panel on Climate Change (IPPC) concludes ... 

KdV equation (equation 3.45), the nature of any deeper mathematical connection, if there is one, remains an intriguing open question,... 

The much more difficult task of finding how often a given state transition graph appears when one samples all possible topologies (or how the Q sets are individually weighted), remains an open question. 

Turbulence is generally understood to refer to a state of spatiotemporal chaos that is to say, a state in which chaos exists on all spatial and temporal scales. If the reader is unsatisfied with this description, it is perhaps because one of the many important open questions is how to rigorously define such a state. Much of our current understanding actually comes from hints obtained through the study of simpler dynamical systems, such as ordinary differential equations and discrete mappings (see chapter 4), which exhibit only temporal chaosJ The assumption has been that, at least for scenarios in which the velocity field fluctuates chaotically in time but remains relatively smooth in space, the underlying mechanisms for the onset of chaos in the simpler systems and the onset of the temporal turbulence in fluids are fundamentally the same. 

There is another class of problems, known as noudeterministic polynomial time or class NP - problems, which may not iicco.ssarily be solvable in polynomial time, but the actual solutions to which may be tested for correctness in polynomial time. The problem of finding a size-iV preimage for a linear CA, for example, is a class NP problem. While it is obvious that P C NP, whether P yf NP remains an open question. 

It is also quite an open question whether the second law is applicable to living organisms the fineness of the cell-structure, and the comparatively enormous—almost microscopically visible —molecules of the colloidal substances occurring in the latter, make it not impossible that there are processes going on there which are quite outside the consideration of thermodynamics. 

This open question is symbolized by the unusual type of equilibrium arrows used in Scheme 11-2. 

To what extent the above suggests that the sulfoxide sulfur of thiirene oxides is more nucleophilic than that of thiirane oxides remains an open question. 

The skills of questioning are widely covered elsewhere and therefore not dealt with in detail here. The most common distinction is between open and closed questions. Closed questions provoke only very short, sometimes one-word responses - for example, have you had a nice day or are you intending to write this e-mail . Open questions are types of questions that encourage fairly elaborate responses. The onus is on the respondent. Open questions tend to start with words such as how, why and what. Since this is the type that is mainly used by mentors, the different kinds of open questions are looked at more closely in Table 5.1 (Parsloe and Wray, 2000). 

Despite the fact that EDSS have been successfully used to solve complex enviromnental problems, it seems clear that more research is needed in this area. From our experience during last years, we have identified the still open questions in the development and application of EDSS. It can be foreseen that the research bottlenecks for EDSS for water scarcity and integrated water resources management should be focused on the following issues ... 

Nevertheless, despite all these remarkable achievements, some open questions still remain. Among them is the influence of the molecular transport properties, in particular Lewis number effects, on the structure of turbulent premixed flames. Additional work is also needed to quantify the flame-generated turbulence phenomena and its relationship with the Darrieus-Landau instability. Another question is what are exactly the conditions for turbulent scalar transport to occur in a coimter-gradient mode Finally, is it realistic to expect that a turbulent premixed flame reaches an asymptotic steady-state of propagation, and if so, is it possible, in the future, to devise an experiment demonstrating it ... 

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