Cliques in dense inhomogeneous random graphs

The theory of dense graph limits comes with a natural sampling process which yields an inhomogeneous variant of the Erd?s–Rényi random graph. Here we study the clique number of these random graphs. We establish the concentration of the clique number of for each fixed n , and give examples of graphons for which exhibits wild long‐term behavior. Our main result is an asymptotic formula which gives the almost sure clique number of these random graphs. We obtain a similar result for the bipartite version of the problem. We also make an observation that might be of independent interest: Every graphon avoiding a fixed graph is countably‐partite. © The Authors Random Structures & Algorithms Published byWiley Periodicals, Inc. Random Struct. Alg., 2016 © 2017 The Authors Random Structures & Algorithms Published by Wiley Periodicals, Inc. Random Struct. Alg., 51, 275–314, 2017     

Radiation chemistry of poly(propylene oxide)

Atactic, isotactic, and optically active poly(propylene oxides), PPOx, were irradiated with both γ-rays and electron beams. Up to a dose of 37 Mrad no change could be detected in the optical activity. G values for hydrogen evolution decreased as compared to polypropylene in about the same ratio as G(H₂) of polyoxymethylene decreased as compared to polyethylene. G values for crosslinking and scission, estimated by means of gelation theories of Saito and Inokuti, were found to be greater for isotactic than for atactic PPOx. The behavior of transient infrared and ultraviolet absorption bands is discussed. Intrinsic viscosity data indicate a rapid initial chain degradation whereas CO gas and OH group production is linear with dose. Evidence for the conversion of one type of free radical to another on heating an irradiated sample from 77°K to room temperature is based on the behavior of transient infrared and ultraviolet absorption bands.     

Optimal control of discrete systems involving delays

For a class of discrete systems with delays and additional state-dependent constraints, a maximum principle is derived. The existing general results in the field of discrete optimal control theory make it possible to deal with this class of optimization problems in a straight-forward way. The formulation of the results presented is fairly general and includes a number of cases when the constraints are specified in more detail.     

Die Anwendung von Silikagel in der anorganischen Analyse. Trennung und Bestimmung kleiner Zirkonium-Mengen

Zusammenfassung Die Bedingungen der quantitativen Sorption von Zirkonium an einer Silikagelsäule wurden untersucht. Die Vollständigkeit der Sorption wurde in Abhängigkeit vom ph, der Durchflußgeschwindigkeit und dem Volumen der Waschflüssigkeit untersucht. In 1- bis 1,2-n HCl oder HNO₃ ist die Sorption sehr selektiv, Zirkonium kann von einer Reihe von Begleitelementen getrennt werden. Der Einfluß einiger Anionen auf die Vollständigkeit der Zirkoniumelution aus der Säule wurde untersucht. Nach einer statischen Methode wurde die Kapazität des verwendeten Silikagels bestimmt. Die erzielten Ergebnisse wurden zur Bestimmung kleiner Zirkoniummengen in mineralischen Rohstoffen verwendet.

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Summary The conditions for quantitative Sorption of zirconium on a silica gel column were studied. The completeness of the sorption was studied in relation to ph, the rate of flow, and the volume of the wash liquid. The sorption is very selective in 1–1.2N HCl or HNO₃. Zirconium may be separated from a number of accompanying elements. The influence of several anions on the completeness of the zirconium elution from the column was investigated. The capacity of the silica gel employed was determined by a statistical method. The results obtained were employed for determining-small quantities of zirconium in mineral raw materials.

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Résumé On a étudié les conditions de sorption quantitative du zirconium sur colonne de silicagel. On a examiné l'influence du ph, de la vitesse d'écoulement et du volume de liquide de lavage sur la sorption. Celle-ci se montre très sélective dans l'acide chlorhydrique 1 à 1,2N ou dans l'acide nitrique et le zirconium peut être séparé d'avec une série d'éléments qui l'accompagnent. On a étudié l'influence de quelques anions sur l'élution du zirconium de la colonne. On a déterminé la capacité du silicagel employé d'après une méthode statistique. On a utilisé les résultats obtenus pour doser de petites quantités de zirconium dans les matières premières minérales.

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Herrn Prof. Dr. Ing.M. Jureek zum 60. Geburtstag gewidmet.     

Affinities of insoluble hexacyanoferrates(II) for alkali metals and ammonium

The affinities of insoluble ferrocyanides of bivalent manganese, iron and cadmium for sodium potassium, rubidium, caesium and ammonium have been studied. It has been found that the affinities of the univalent cations for the ferrocyanides generally increase in the usual order Na<K<NH₄<Rb<Cs. Comparing the results with those previously obtained, the affinity towards formation of double ferrocyanides with univalent cations generally follows the order Cd ∼ Mn >Co>Fe(II)>Ni>Zn>Cu>Fe(III). The precipitation isotherms of the systems are presented and the relationship between the affinities and some other properties of the transition metal ferrocyanides is discussed.     

Optimal control existence results for general discrete systems

General existence theorems for discrete optimal control problems are derived. It is assumed that dynamical equations of the system, as well as all control and state constraints, depend on the finite history of the system. All results are formulated in a general way in regular topological spaces. To prove such theorems, some basic concepts and results of the theory of the so-called multivalued mappings are necessary which are briefly summarized. The imposed assumptions are general enough to be of practical interest. The reported results thus include and generalize all known cases which are met in the discrete optimal control theory. Practical importance of the obtained results is illustrated on the so-called multiproduct inventory problem which is treated in the detail. Using the derived results we are able to show that under usual assumptions the inventory problem has an optimal solution.     

Phase composition of ceramic-based alkali-activated polymers: combination of X-ray diffraction and thermal analysis

Journal of Thermal Analysis and Calorimetry - Thermal properties and fire propagation performance were studied for the new and aged electrical wires. Two fine electrical wires were tested using the...     

Changes in structure and composition of gypsum paste at elevated temperatures

Journal of Thermal Analysis and Calorimetry - The structure and composition of the gypsum at elevated temperatures were studied by means of scanning electron microscopy, X-ray diffraction (XRD) and...