Random walks on the hexagon

This paper gives several examples of how flow graphs can be used to determine the probability distribution of certain random variables. All the examples deal with random walks on the hexagon. Ideas for further such examples are listed at the end of the paper.     

A nonsymmetric matrix with integer eigenvalues

A nonsymmetric N?×?N matrix with elements as certain simple functions of N distinct real or complex numbers r ₁, r ₂, …, r_N is presented. The matrix is special due to its eigenvalues???the consecutive integers 0,1,2, …, N?1. Theorems are given establishing explicit expressions of the right and left eigenvectors and formulas for recursive calculation of the right eigenvectors. A special case of the matrix has appeared in sampling theory where its right eigenvectors, if properly normalized, give the inclusion probabilities of the conditional Poisson sampling design.     

Transition Metal-Free Synthesis of meta-Bromo- and meta-Trifluoromethylanilines from Cyclopentanones by a Cascade Reaction

Anilines are key constituents in biologically active compounds and often obtained from transition metal-catalyzed coupling of an aryl halide with an amine. In this work, we report a transition metal-free method for the synthesis of meta-bromo- and meta-trifluoromethylanilines starting from 3-tribromomethylcyclopentanone or 3-(2-bromo-2-chloro-1,1,1-trifluoroethyl)cyclopentanone, respectively. The scope of the transformation is shown by application of primary, secondary and aromatic amines. The reaction proceeds in acceptable to high yields (20–81 %), and allows for the synthesis of anilines with substitution patterns otherwise difficult to access.     

[4+3] Cycloaddition of Donor–Acceptor Cyclopropanes with Amphiphilic Benzodithioloimine as Surrogate for ortho‐Bisthioquinone

Donor–acceptor cyclopropanes were reacted with amphiphilic benzodithioloimine to give seven‐membered heterocycles with two sulfur atoms. Formally, this transformation can be regarded as a [4+3] cycloaddition reaction of the three‐membered ring and ortho‐bisthioquinone. The benzodithioloimine serves as a surrogate for this highly reactive diene. The structure of the products was confirmed by X‐ray crystallography. Broad signals in ¹³C NMR studies suggest that several conformers, slowly interconverting on the NMR timescale, are present at room temperature.     

A high-frequency apparatus for chromatographic recording and for titration

Summary A high-frequency device, using the Q-meter principle, has been tested. It is compared with a simple crystal oscillator. It was found that the stability is increased about 100 times. The new device can find application in chromatographic recording and for monitoring purposes. A titration cell with a defined cell-constant is also described.

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Zusammenfassung Ein Hochfrequenzgerät nach dem Q-Meter-Prinzip wurde getestet und mit einem einfachen Kristalloszillator verglichen. Die Stabilität des ersteren ist etwa 100fach größer. Das neue Gerät kann zur chromatographischen Registrierung und für Zwecke der Betriebsüberwachung verwendet werden. Eine Titrationszelle mit definierter Zellkonstante wurde gleichfalls beschrieben.

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Résumé On a mis à l'essai un dispositif haute-fréquence mettant en application le principe du compteur-Q. On le compare avec un oscillateur simple à cristal. On a trouvé que la stabilité est augmentée d'environ cent fois. Le nouveau dispositif peut trouver une application dans l'enregistrement chromatographique et pour des usages de contrôle. On décrit également une cuve de titrage avec une constante de cellule définie.

     

Amorphous drug nanosuspensions. 1. Inhibition of Ostwald ripening

Amorphous drug nanosuspensions are prone to particle growth due to Ostwald ripening. By incorporating a second component of extremely low aqueous solubility, Ostwald ripening can be inhibited. These studies indicate that to inhibit ripening, the drug/inhibitor mixture (in the particles) must form a single phase. The drug/inhibitor mixture can be characterized by the interaction parameter chi using the Bragg-Williams theory, in which single phase mixtures are obtained for chi < 2. The chi parameter can be calculated from the (crystalline) solubility of the drug in the inhibitor, provided the inhibitor is a liquid, and the melting entropy and temperature of the drug.     

Gels of hydrophobically modified hydroxyethyl cellulose cross-linked by amylose. Competition with cyclodextrin

Previous work has shown that amylose (AM) can cross-link hydrophobically modified polymers by inclusion complexation, whereby thermoreversible cold-setting gels are formed. In this work, the competition between AM and cyclodextrin (CD) for the formation of inclusion complexes with hydrophobically modified hydroxyethyl cellulose (HMHEC) is investigated. A detailed study of viscosity, NMR self-diffusion, and chemical shifts of the two-component mixture, CD and HMHEC, was performed. The results imply that 2:1 (CD:polymer hydrophobe) complexes may be formed. The three-component mixtures, HMHEC/AM/CD, were investigated by rheology, NMR self-diffusion, and intensities of the NMR resonance peaks. The CD molecules competed efficiently with the AM molecules, as seen by a decreased storage modulus, an increased self-diffusion of AM and HMHEC, and increased NMR intensities of the HMHEC hydrophobes, as the concentration of CD increased in the solution. A high concentration of CD is needed in the mixtures to inhibit all interactions between HMHEC and AM, and it was shown that there still is an effect of AM at excess CD concentration in the mixtures.