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.     

Measurement of spin-dependent total cross-section differenceΔσ T in neutron-proton scattering at 16 MeV

A new measurement ofΔσ _T for polarized neutrons transmitted through a polarized proton target at 16.2 MeV has been made. A polarized neutron beam was produced with the³H(d, n)⁴ He reaction; proton polarization over 90% was achieved in a frozen spin target of 20 cm³ volume. The measurement yields the valueΔσ _T=(?126±21±14) mb. The result of a simple phase shift analysis for the³ S ₁?³ D ₁ mixing parameter ε₁ is presented and compared with the theoretical potential model predictions.     

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.     

Anwendung von Silicagel in der anorganischen Analyse. Abtrennung des Thoriums von Zirkonium

Zusammenfassung Die Sorption des Thoriums und Zirkoniums an Silicagel aus ÄDTA und Weinsäure wurde verfolgt. Bei ph 7 in Gegenwart von Weinsäure durchläuft das Zirkonium die Silicagelkolonne, während Th(IV) quantitativ sorbiert wird. Diese Tatsache wurde zur Trennung des Thoriums von Zirkonium im Konzentrationsverhältnis 1200 angewandt. Da Zr(IV) aus 0,5-n HCl quantitativ sorbiert wird, woraus die Th(IV)-sorption praktisch gleich Null ist, kann auf diese Weise Zr(IV) von einem beträchtlichen Überschuß an Th(IV) getrennt werden. Die Trennung ist noch im Verhältnis 11000 quantitativ.

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Summary The sorption of thorium and zirconium on silica gel from EDTA and tartaric acid was followed. At ph 7 and in the presence of tartaric acid, the zirconium passes through the silica gel column, whereas Th(IV) is sorbed quantitatively. This finding was employed for the separation of thorium from zirconium in a concentration ratio of 1200. Because Zr(IV) is quantitatively sorbed from 0.5N HCl, while the sorption of Th(IV) is practically zero from this medium, Zr(IV) can be separated from a considerable excess of Th(IV) in this way. The separation is still quantitative at a ratio of 11000.

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Résumé On a suivi l'adsorption du thorium et du zirconium sur silicagel à partir d'EDTA et d'acide tartrique. A pn 7, en présence d'acide tartrique, le zirconium traverse la colonne de silicagel, alors que le thorium-IV est adsorbé quantitativement. On a mis à profit cet état de fait pour séparer le thorium du zirconium pour des concentrations dans le rapport 1200. Comme le zirconium-IV est adsorbé quantitativement à partir d'HCl 0,5N, tandis que l'adsorption du thorium-IV est alors pratiquement nulle, on peut séparer de cette manière le zirconium-IV d'un excès important de thorium-IV. La séparation est encore quantitative pour le rapport 11000.

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

Sorption of the peroxocomplex of titanium on silica gel and its analytical use

Summary Sorption of the titanium peroxocomplex on silica gel was studied in dependence on the pH and on the presence of various complexing substances, especially tartaric and citric acids. The distribution coefficients for the titanium peroxocomplex and for some other components were determined. Optimum conditions were established for the separation of small amounts of titanium from a number of accompanying cations and anions on a column and under static conditions.     

Synthesis,characterization and screening of biological activity of Zn(II), Fe(II) and Mn(II) complexes with trithiocyanuric acid

New Zn(II), Fe(II) and Mn(II) complexes with a combination of nitrogen-donor ligands and trithiocyanuric acid (ttcH₃) were prepared and characterized by elemental analysis, IR and UV–Vis spectroscopies. The antitumor activity of the prepared complexes, together with already known Ni(II) species, were assayed in vitro against G-361 (human malignant melanoma), HOS (human osteogenic sarcoma), K-562 (human chronic myelogenous leukaemia) and MCF-7 (human breast adenocarcinoma) tumor cell lines. The IC₅₀ values of the Fe(II) and Mn(II) compounds turned out to be lower than those of cisplatin and oxaliplatin. The antimicrobial activities were evaluated by MIC against bacteria (Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Enterococcus faecalis). The molecular structure of [Zn(taa)(ttcH)] · H₂O (taa = tris(2-aminoethyl)amine) was determined by X-ray diffraction. The central atom is pentacoordinated by four N atoms of taa and one N atom of the ttcH dianion.     

New methods in synthesis of acetylcholinesterase reactivators and evaluation of their potency to reactivate cyclosarin-inhibited AChE

Nine potential AChE reactivators were synthesized using modification of currently known synthetic pathways. Their potency to reactivate AChE inhibited by cyclosarin nerve agent was tested in vitro. According to the previous results, 1,4-bis(2-hydroxyiminomethylpyridinium)butane dibromide seems to be the most potent AChE reactivator. The reactivation potency of these compounds depends on structural factors such as presence of quaternary nitrogens, length of the linking chain between both pyridinium rings, and position of the oxime moiety at the pyridinium ring.