The number of strictly increasing mappings of fences

Let X and Y be fences of size n and m, respectively and n, m be either both even or both odd integers (i.e., |m-n| is an even integer). Let \(r = \left\lfloor {{{(n - 1)} \mathord{\left/ {\vphantom {{(n - 1)} 2}} \right. \kern-0em} 2}} \right\rfloor\) . If 1<n<-m then there are \(a_{n,m} = (m + 1)2^{n - 2} - 2(n - 1)(\begin{array}{*{20}c} {n - 2} \\ r \\ \end{array} )\) of strictly increasing mappings of X to Y. If 1<-m<-n<-2m and s=1/2(n?m) then there are a _n,m+b _n,m+c _n of such mappings, where $$\begin{gathered} b_{n,m} = 8\sum\limits_{i = 0}^{s - 2} {\left( {\begin{array}{*{20}c} {m + 2i + 1} \\ l \\ \end{array} } \right)4^{s - 2 - 1} } \hfill \\ {\text{ }}c_n = \left\{ \begin{gathered} \left( {\begin{array}{*{20}c} {n - 1} \\ {s - 1} \\ \end{array} } \right){\text{ if both }}n,m{\text{ are even;}} \hfill \\ {\text{ 0 if both }}n,m{\text{ are odd}}{\text{.}} \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} $$      

Counting the number of isotone selfmappings of crowns

Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is . The number of all order-preserving selfmappings of a 2n-element crown is

Beitrag zur aufeinanderfolgenden thermochemischen Bestimmung von SiO2 und Al2O3 Aus flusssaurer lösung

Zusammenfassung Die vorliegende Arbeit gibt eingangs einen Überblick von Publikationen, die sich mit der thermochemischen Bestimmung von SiO₂ und Al₂O₃ aus flußsaurer Lösung befassen. Davon ausgehend werden Versuche beschrieben und Ergebnisse diskutiert, die mit konstanten Einwaagen von 700 mg SiO₂ und etwa 100 mg Al₂O₃ aus flußsaurer Lösung und verschiedenen Kombinationen von Injektionsreagenzien erhalten wurden und die auf die Belange der Analyse von gefällten Natriumaluminiumsilicaten abgestimmt waren. Die vorgenommenen Untersuchungen führen zu den Schluß, daß Al₂O₃ und SiO₂ in Natriumaluminiumsilicaten aus flußsaurer Lösung mit der Injektionsreagenskombination SrCl₂KCl bestimmt werden sollten.

---

The first part of the paper gives a review of the literature dealing with thermochemical determinations of SiO₂ and Al₂O₃ in hydrofluoric acid solution. The results of experiments with constant samples weights of 700 mg SiO₂ and about 100 mg Al₂O₃ in hydrofluoric acid solution with differently combined injection reagents are discussed. The determinations were based on the analysis of precipitated sodium aluminium silicates.The investigations revealed that combined SrCl₂/KCl solution should be used as injection reagent for determination of the Al₂O₃ and SiO₂ contents of sodium aluminium silicates in hydrofluoric acid.

---

, . , (700 ) ( 100 ) , . . , SrCl₂-KCl .

     

Surface melting description

The surface melting is regarded in terms of the order parameter profiles which characterise phases extended inside a whole sample. The characterisation of the phase is, however, due to the order parameter behavior at the surface. The phase really observed is predicted by means of the thermodynamic conditions; thus, the surface melting phase is in competition to the softening modes at the surface. The presented idea is based on the discussion concerning the possible results of the leading theories, a modified van der Waals approach and an Ising type model for pseudospins. The experimental evidence is reviewed and interpreted.     

Infrared Spectra of the Halothane–Trimethylamine Complex in Liquefied Krypton

Optics and Spectroscopy - The IR absorption spectra of solutions of mixtures of halothane (C2HBrClF3) and trimethylamine ((CD3)3N) in liquefied krypton were obtained and analyzed. Bands assigned to...     

A novel method for the synthesis of 1-aryltetrahydroisoquinolines

Carbenium ions generated from substituted benzhydryls using acid catalysis undergo smooth intramolecular trapping by pendant sulfonamide groups to provide excellent yields of 1-aryltetrahydroisoquinolines.     

Thermal stability and conductivity of hot-pressed Si3N4–graphene composites

This study concerns new Si₃N₄–graphene composites manufactured using the hot-pressing method. Because of future applications of silicon nitride for cutting tools or specific parts of various devices having contact with high temperatures there is a need to find a ceramic composite material with good mechanical and especially thermal properties. Excellent thermal properties in the major directions are characteristic of graphene. In this study, the graphene phase is added to the silicon nitride phase in a quantity of up to 10 mass%, and the materials are sintered under uniaxial pressure. The mixture of AlN and Y₂O₃ is added as sintering activator to the composite matrix. The studies focus on thermal stability of produced composites in argon and air conditions up to the temperature of 1,000 °C. The research also concerns the influence of applied uniaxial pressure during the sintering process on the orientation of graphene nanoparticles in the Si₃N₄ matrix. The study also presents research on anisotropy of thermal diffusivity and following thermal conductivity of ceramic matrix composites versus the increasing graphene quantity. Most of the presented results have not been published in the literature yet.     

A note on the Flesaker-Hughston model of the term structure of interest rates

A term structure model proposed by Flesaker and Hughston (1996a,b) is analysed within the general framework of arbitrage-free term structure modelling. Basic valuation formulae for caps and swaptions are presented.