Efficient frontiers

Efficient frontiers also invariably place Treasury bills as the risk-free asset. T-bills may be risk-free from a creditworthiness point of view, bnt it is not tenable that a three-month nominal asset is a risk-free instrn-ment for someone with, say, a 30-year savings horizon. If you are investing for 30 years, over which time you are interested in your prospective real returns, then a 30-year linker (to be held to maturity) is your riskfree asset, almost by definition. 100% invested in that bond becomes the lowest risk portfolio on yonr frontier. Efficient frontier analysis starts to lose its impact once this premise is accepted, not least because you do not have a large data sample of consecutive, nonoverlapping 30-year periods (for any asset) to produce robust analysis. ... 

This analysis confirms that the effect of cyclic constraints is not purely steric but also has an electronic component. Another aspect of this dichotomy is shown in Fig. 11 which illustrates the decrease in the energy gap between the frontier in-plane rc-MOs. The decrease in the C1-C6 distance destabilizes the occupied MO where the interaction between the end orbitals is antibonding and, at the same time, stabilizes the empty MO where the 7i -orbitals overlap constructively. As a result, the efficiency of the photochemical Bergman cyclization should increase and, indeed, the most efficient photo-Bergman cyclizations reported in the literature involve cyclic enediynes.43 Again, the analogy with interrupted [2 + 2] photocycloaddition is instructive. 

Carboxymethyl glycoside lactones are easily prepared by diverse routes and react readily with nucleophilic species. Their reaction with amines, a simple addition which does not require any intermediate activation, is very general, and many examples of new pseudo-glycoconjugates prepared by this method are described. Moreover, 1,2-bisfunctionalized carbohydrate systems are efficiently constructed by reaction of the free OH on position 2 obtained after the opening of the lactone ring. Applications at the frontier of materials and biology have been envisaged and further studies in these fields will be reported in the near future. 

The reactivity and selectivity of the Diels-Alder reaction can be understood in terms of Frontier Molecular Orbital (FMO) theory which evolved during studies of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffmann58 and, independently, by Fukui59. FMO theory explains the driving force of a reaction between two compounds by the efficiency with which the molecular orbitals of the two partners overlap. This orbital interaction is maximized when their energy separation is small. FMO theory further states that the two most important interacting orbitals are the Highest Occupied... 

An enormous amount of work has been done in this wide field and a number of excellent reviews on different aspects of sulfur electrochemistry has been published [1-7], so here we confine our attention to some principal reactions and interesting apphcations of both anodic and cathodic activation of sulfur-containing molecules. Compared to other chalco-genides, sulfur has frontier orbitals that have volume, symmetry, and energy more suitable for efficient interaction with adjacent carbon atoms. The ionization of molecular sulfur requires about 10 eV. Conjugation of the pz orbitals of sulfur with a 7T-system lowers the ionization potential by ca. 2 eV. For this reason, compounds of divalent sulfur undergo oxidation rather easily often giving rise to cation radicals or dications. The stability of this species is in line with the... 

Electron-transfer-induced FQ is the most practical and efficient mechanism of signal transduction for the detection of explosives. This is because explosives, especially 2,4,6-trinitrotoluene (TNT), are often highly electron-deficient molecules that readily accept electrons from excited fluorophores. In addition, explosive devices that contain TNT also usually contain a synthetic by-product, 2,4-dinitrotoluene (DNT), which is also highly electron deficient. A basic frontier molecular orbital-based mechanism for electron transfer FQ is illustrated in Figure 3. 

The model is subject to the same set of constraints as the deterministic model, with 0i as the risk trade-off parameter (or simply termed the risk factor) associated with risk reduction for the expected profit. 0j is varied over the entire range of (0, oo) to generate a set of feasible decisions that have maximum return for a given level of risk, which is equivalent to the efficient frontier portfolios for investment applications. 

Tables 6.3-6.5 show the computational results for Risk Model II over a range of values of risk parameter 02 with respect to different recourse penalty costs, for three representative cases of 0 = 1E — 10, IE — 7, and 1.55E — 5, respectively. An example of the detailed results is presented in Table 6.6 for 02 = 50 of the first case. Figure 6.2 illustrates the corresponding efficient frontier plot for Risk Model II while Figure 6.3 provides the plot of the expected profit for different levels of risk.

Figure 6.2 Risk Model II efficient frontier plot.

From Table 6.7 and the corresponding efficient frontier plot in Figure 6.4, similar trends to Risk Model II (and also the expected value models) are observed in which decreasing values of 0 correspond to higher expected profit until a certain constant profit value is attained ( 81 770). The converse is also true in which a constant profit of 59330 is reached in the initially declining expected profit for increasing values of 0i. 

Figure 6.4 Risk Model III efficient frontier plot.

In order to understand the effect of each term on the overall objective function of the system, different values of 0i and 02 are evaluated to construct the efficient frontier of expected cost versus risk measured by standard deviation. This will be demonstrated in the illustrative case studies. 

Further optimization of the formation of fullerenes in combustion lead to the development of efficient pilot plants [53-56], Currently, 400 kg of fullerenes per year (Mitsubishi s Frontier Carbon Corporation) are obtained by these methods. 

Smart materials are extremely efficient, performing a variety of jobs that would otherwise require researchers and engineers to spend a lot of time and money to develop and design a number of different substances. Materials capable of multitasking are one of the most interesting and promising frontiers of chemistry and materials science. This chapter describes research on a variety of materials and systems that exhibit some degree of responsiveness to their environment. 

Finding or producing a clean source of hydrogen is just one of the difficulties fuel cell researchers face. The previous sections of this chapter have discussed why fuel cells are desirable and how they have proven their reliability in the Apollo missions and elsewhere, but numerous problems remain to be solved before this frontier of science can develop cost-effective devices and achieve the promise of a clean, efficient energy source. 

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