A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

Semi-preparative liquid-chromatographic separation of all four stereoisomers of α-bisabolol on tribenzoylcellulose

Summary A semi-preparative low-pressure liquid-chromatographic procedure using tribenzoylcellulose has been developed for the separation and isolation of the four -bisabolol stereoisomers. Stereochemical assignments were made by HPLC-polarimeter coupling and by using the authentical isomers. This method can be applied to the quality control of chamomile preparations, as it allows the detection of adulterations resulting from admixtures of synthetic -bisabolol. In addition, the isolation of all four -bisabolol stereoisomers from commercially available synthetic -bisabolol has been made possible.     

Asymptotic expansions in the integral and local limit theorems in banach spaces with applications to ω-statistics

LetB be a real separable Banach space and letX,X ₁,X ₂,...∈B denote a sequence of independent identically distributed random variables taking values inB. DenoteS _n =n ^?1/2(X ₁+...X _n ). Let π:B→R be a polynomial. We consider (truncated) Edgeworth expansions and other asymptotic expansions for the distribution function of the r.v. π(S _n ) with uniform and nonuniform bounds for the remainder terms. Expansions for the density of π(S _n ) and its higher order derivatives are derived as well. As an application of the general results we get expansions in the integral and local limit theorems for ω-statistics $$\omega _n^p (q)\mathop { = n^{{p \mathord{\left/ {\vphantom {p 2}} \right. \kern-\nulldelimiterspace} 2}} }\limits^\Delta \smallint _{(0,1)} \{ F_n (x) - x\} ^p q(x)dx$$ and investigate smoothness properties of their distribution functions. Herep≥2 is an even number,q: [0, 1]→[0, ∞] is a measurable weight function, andF _n denotes the empirical distribution function. Roughly speaking, we show that in order to get an asymptotic expansion with remainder termO(n ^?α), α<p/2, for the distribution function of the ω-statistic, it is sufficient thatq is nontrivial, i.e., mes{t∈(0, 1):q(t)≠0}>0. Expansions of arbitrary length are available provided the weight functionq is absolutely continuous and positive on an nonempty subinterval of (0, 1). Similar results hold for the density of the distribution function and its derivatives providedq satisfies certain very mild smoothness condition and is bounded away from zero. The last condition is essential since the distribution function of the ω-statistic has no density whenq is vanishing on an nonempty subinterval of (0, 1).     

Mitteilungen aus dem Institut für Radiumforschung

Zusammenfassung Es wurde mit Hilfe des schon früher beschriebenen Quarzapparates Thoriumbromid aus reinem Thoroxyd dargestellt, das nach zwei verschiedenen Methoden gereinigt war und auf Grund spektroskopischer Untersuchung als absolut rein und frei von seltenen Erden angesehen werden mu\te.Das geschmolzene Thorbromid wurde nach zwei Methoden analysiert und dabei die beiden VerhÄltnisse ThBr₄4 Ag und ThBr₄4 AgBr bestimmt.Zwei unabhÄngige Serien von 12, respektive 15 Analysen gaben die folgenden Resultate:Serie I. 54·45867g Thorbromid verbrauchten 42·58666g Silber und gaben 74·13448g Silberbromid, entsprechend einem Atomgewicht des Thoriums Th=232·15±0·016.Serie II. 74·30630g Thorbromid verbrauchten 58·11096g Silber und gaben 101·15848g Silberbromid, woraus sich das Atomgewicht Th=232·12±0·014 berechnet.Als Mittel dieser beiden Werte ergibt sich Th=232·135.Da aber die Analysenserie aus den oben besprochenen, uns triftig erscheinenden Gründen als die zuverlÄssigere angesehen werden mu\, glauben wir, da\ der aus ihr resultierende WertTh=232·12 als das derzeit wahrscheinlichste Atomgewicht des Thoriums anzusehen ist, wenn Ag=107·880 angenommen wird. Aus dem in 27 Bestimmungen gefundenen VerhÄltnis von angewandtem Silber zu gefundenem Silberbromid, AgAgBr= 0·574453, ergibt sich dann das Atomgewicht des Broms zu Br=79·916 in vollster übereinstimmung mit der von Baxter seinerzeit gefundenen Zahl.     

Versuche zur Herstellung eines «Bis(triasterans)» und Synthese des heterocyclischen (Tricyclo[4.4.1.01,6]undeca-3,8-dien-11,11-dimethyl)sulfits

Tentative Synthesis of ‘Bis(triasterane)’ and Synthesis of the Heterocyclic (Tricyclo[4.4.1.0^1,6]undeca-3,8-diene-11,11-dimethyl)sulfite The synthesis of the bis(triasterane) ( 1 ) has been tried; the reaction of ‘isotetraline’ (1,4,5,8-Tetrahydronaphthalene; 2 ) with diazomalonate yielded the tricyclic systems 5 and 6 , and not 4 . Hydrolysis of 5 gave the monocarboxylic acid 7 , and not the dicarboxylic acid 9 . The latter could be obtained from the dibromoderivative 8 , but 9 couldn't be converted to the acyl chloride 10 . The reduction of 9 with LiAlH₄ yielded the crystalline diol 11 , which was cyclized with SOCl₂ to the heterocycle 12 . The spectral data of the new compounds 5, 6, 7, 11 and 12 are reported and discussed.     

Über einige neue Bispirane

We have obtained four new bispirane systems in which both spiroatoms are vicinal atoms in cyclopropane or cyclobutane rings and in which the heterocyclic component has the basic structure of 1,4-dioxep-2-ene. We have shown that from two possibilities (bispiran, propellan) the general reaction leads only to a bispiran system. To the bispiran2 exhibiting the highest hyperchromism we ascribed the bispirocoplanar conformation (Fig. 1).

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Mit 3 Abbildungen     

4-Aryldihydropyridines,a New Class of Highly Active Calcium Antagonists

The aryldihydropyridines first prepared by Hantzsch almost 100 years ago have recently been found to be highly effective calcium antagonists with suitable pharmacological profiles. An illustrative example is dimethyl-l,4-dihydro-2,6-dimethyl-4-(o-nitrophenyl)pyridine-3,5-dicarboxylate (Nifedipine) which is already employed therapeutically. This substance lowers the frequency of attack of angina pectoris and reduces blood pressure. The discovery of the therapeutic activity of this class of substances initiated renewed investigation of the Hantzsch condensation and the synthesis of numerous 4-aryldihydropyridines and related compounds. Qualitative and quantitative structure/activity relationships of these substances can be deduced from their biological data.     

Identification of amber and imitations by near infrared reflection spectroscopy

Imitations of amber have been prepared since a long time, but the number of imitations is increasing since modern polymers are available. At present, many imitations are based on a few synthetic polymers and even experts have some problems in distinguishing between real and falsed amber without destruction of the material. IR-Spectroscopy or pyrolysis combined with gas chromatography/mass spectrometry are very efficient methods in identifying amber and imitations but these methods need a sample preparation. By means of near infrared reflection spectroscopy it is possible to identify amber and imitations without any sample preparation in a short time. Optimization of the method and the application are discussed.     

Theoretical and experimental study of the adsorption on radioactive gases on continuous flow columns

A bimolecular reaction model was used to describe the adsorption process in continuous flow columns filled with solid adsorbents. The analytical solution of the model for low gas concentrations and a cascade-type numerical method for higher gas concentrations were developed. An air flow apparatus using activated carbon as adsorbent and methyl-iodide labelled with¹²⁵I as adsorbate was constructed for measuring breakthrough- and accumulation curves.