The laplace transform

Book Reviews

The laplace transformR. E. Bellman and R. S. Roth: World Scientific, Singapore, 1984     

The general nucleolus and the reduced game property

The nucleolus of a TU game is a solution concept whose main attraction is that it always resides in any nonempty -core. In this paper we generalize the nucleolus to an arbitrary pair (,F), where is a topological space andF is a finite set of real continuous functions whose domain is . For such pairs we also introduce the least core concept. We then characterize the nucleolus forclasses of such pairs by means of a set of axioms, one of which requires that it resides in the least core. It turns out that different classes require different axiomatic characterizations.One of the classes consists of TU-games in which several coalitions may be nonpermissible and, moreover, the space of imputations is required to be a certain generalized core. We call these gamestruncated games. For the class of truncated games, one of the axioms is a new kind ofreduced game property, in which consistency is achieved even if some coalitions leave the game, being promised the nucleolus payoffs. Finally, we extend Kohlberg's characterization of the nucleolus to the class of truncated games.     

On locally optimal nonparametric tests

Summary There is an abundancy of problems in which no parametric model realistically describes the situation and in which, accordingly, we have to resort to nonparametric methods. As the numerical problems connected with nonparametric tests are becoming less and less important, rank tests, permutation tests and the like are becoming more and more part of the standard armatory of applied statisticians. The lack of tabulated critical values, for instance, should no longer be a serious objection against the use of permutation tests in practice; cf. Edgington (1987).The rationale underlying permutation and rank tests has been outlined in quite a number of text books and papers; cf. Fraser (1957), Lehmann (1959), Hájek-Sidák (1967) or Witting (1970). Roughly speaking, permutation tests are constructibel if the data can be condensed by means of a sufficient and complete statistic allowing for the proper kind of conditioning. Rank tests arise if the underlying problem is invariant with respect to (w.r.t.) a large group of transformations which leads to a maximal invariant statistic consisting of (signed) ranks.Most practical nonparametric problems, however, are too complex to be tractable by just one of those approaches. Many of them, however, can be handled by a combination of both techniques. In this paper we outline the logic underlying that combined reduction method and apply it to construct locally most powerful tests. Moreover, we discuss what we label Hoeffding's transfer problem, i.e. the uniformity aspect of locally most powerful tests with respect to the starting point at the boundary. We are concentrating on the discussion of the nonparametric two-sample location and scale problem. Further important problems are mentioned in Section III.This is a written account of an invited lecture delivered by the third author on occasion of the 14th Symposium über Operations Research, Ulm, September 6–8, 1989.     

L.P.-games with sufficiently many players

L.P.-games aren-person cooperative games arising from a linear program as studied by Owen and Billera/Raanan. Employing a version of nondegeneracy of games developed by Weidner and the author, we show that methods from the Geometry of Numbers are the suitable tool in order to obtain lower bounds for the number of players of each type that ensure that the core and the competitive equilibrium coincide.     

Study of the thermal oxidation of polyolefines—II: Effect of layer thickness on the rate of oxidation in the melt phase

A study was made of the kinetics of oxygen absorption and isothermal weight change as a function of layer thickness for molten polyethylene at 157° under oxygen at 650 torr pressure. The effect of the rate of transport processes on the rate of thermal oxidation was found to be conversion dependent.Comparison of the experimental data on the effect of layer thickness on the maximum rate of oxygen absorption with the results of calculations (carried out assuming various overall reaction orders and applying literature data on permeability coefficient) suggests that, during degradation, the reaction rate is affected by the opposed transport processes of oxygen and the volatile decomposition products. The weight change, closely related to the transport process of volatile products, is diffusion-controlled over the whole range of thickness studied. At the same time, below a critical thickness (approx. 0·05 mm), even the maximum rate of oxygen consumption may be considered a function of only the kinetic parameters.     

Synthesis by the method of Merrifield of an actapeptide contained in lysozyme of hen egg-white (sequence Cys64--Gly71)

The solid-phase peptide synthesis of an octapeptide contained in hen egg-white lysozyme (sequence Cys (residue 64) to Gly (residue 71)) is reported. Each step of the synthesis was verified by amino acid analysis. Three main reaction products were obtained. The octapeptide (50% of the reaction products) was purified by two chromatographies on Dowex 50 × 2. The purified peptide was digested by an aminopeptidase and degradated by means of Edman' s method; this latter procedure has shown that the purified octapeptide still contained around 10% of a shorter peptide.     

Thermal investigation of PEG 4000 — oxazepam binary system

A thermal study using DSC and Hot Stage Microscopy (HSM) was carried out to investigate the interaction in solid state of the binary system PEG 4000 — oxazepam, and to establish their phase diagram. The eutectic composition, which melting occurs at lower temperature as compared with the pure components, has been determined. The results obtained by DSC and HSM have indicated that PEG 4000 — oxazepam mixtures displays no obvious incompatibilities, and that the system shows a typical eutectic behaviour. However because of the closeness of the melting of PEG 4000 to the eutectic temperature, it was difficult to determine precisely the eutectic composition and temperature on the basis of DSC measurements alone. The use of heats of fusion corresponding to physical mixtures allowed an estimation of the eutectic composition at 6% w/w oxazepam. Additional information of temperature (57.6C) and composition (5–10% w/w oxazepam) of the eutectic was obtained by HSM using the contact method. This low melting temperature in this range of compositions offers advantages in terms of drug stability and easy manufacture.