Conductance Study of Binding of Some Rb+ and Cs+ Ions by Macrocyclic Polyethers in Acetonitrile Solution

A conductance study of the interaction between Rb+ and Cs+ ions and18-crown-6 (18C6), dicyclohexyl-18-crown-6 (DC18C6), dibenzo-18-crown-6 (DB18C6),dibenzo-24-crown-8 (DB24C8), and dibenzo-30-crown-10 (DB30C10) inacetonitrile solution has been carried out at various temperatures. The formationconstants of the resulting 1:1 complexes were determined from the molarconductance-mole ratio data and found to vary in the orderDC18C6 > 18C6 > DB30C10 > DB18C6 DB24C8for Rb+ ion andDC18C6 > 18C6 > DB30C10 DB24C8 > DB18C6for Cs+ ion. The enthalpy and entropy of complexation were determined fromthe temperature dependence of the formation constants. The complexes with the18-crowns are both enthalpy and entropy stabilized while, in the case of largecrown ethers, the corresponding complexes are enthalpy stabilized but entropydestabilized.     

Matrix summability and a generalized Gibbs phenomenon

Letf be a real-valued function sequence {f _k } that converges to on a deleted neighborhoodD of . If there is a subsequence {f _k(j) } and a number sequencex such that lim _j x _j = and either lim _j f _k(j) (x _j )>lim sup _x (x) or lim _j f _k(j) (x _j ) x (x), thenf is said to display theGibbs phenomenon at . IfA is a (real) summability matrix, thenAf is a function sequence given by(Af) _n (x)= _k=0 a _n,k f _k (x). IfAf displays the Gibbs phenomenon wheneverf does, thenA is said to beGP-preserving. By replacingf _k (x) withf _k (x _j )F _k,j , the Gibbs phenomenon is viewed as a property of the matrixF, andGP-preserving matrices are determined by properties of the matrix productAF. The general results give explicit conditions on the entries {a _n,k } that are necessary and/or sufficient forA to beGP-preserving. For example: if(x)0 thenF displaysGP iff lim _k,j F _k,j 0, and ifA isGP-preserving then lim _n,k A _n,k 0. IfA is a triangular matrix that is stronger than convergence, thenA is notGP-preserving. The general results are used to study the preservation of the Gibbs phenomenon by matrix methods of Nörlund, Hausdorff, and others.     

On algebraic Riccati equations associated with M-matrices

We consider the algebraic Riccati equation for which the four coefficient matrices form an M-matrix K. When K is a nonsingular M-matrix or an irreducible singular M-matrix, the Riccati equation is known to have a minimal nonnegative solution and several efficient methods are available to find this solution. In this paper we are mainly interested in the case where K is a reducible singular M-matrix. Under a regularity assumption on the M-matrix K, we show that the Riccati equation still has a minimal nonnegative solution. We also study the properties of this particular solution and explain how the solution can be found by existing methods.     

Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold $\overline{M}$. We first assume the pull back Weitzenböck operator of $\overline{M}$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of $\overline{M}$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when $\overline{M}$ is the space form.     

Contributions to the Optimization of a Caprolactam Production Plant by Radiotracer Techniques

Residence time spectra and material distributions in an operating caprolactam production plant were measured by means of sodium 24, bromine 82 and technetium 99m. The results of the tracerexperiments contributed to an optimization of the plant.     

Enhanced electronic and nonlinear optical responses of C24N24 cavernous nitride fullerene by decoration with first row transition metals; A computational investigation

The electronic (energy gap and work function) as well as electrical properties (dipole moment, polarizability, and first hyperpolarizabilities) of the first-row transition metals decorated C₂₄N₂₄ cavernous nitride fullerene were explored using DFT calculations. The transition metals are decorated at N4 cavity of C₂₄N₂₄ fullerene. According to our spin polarized computations, the most stable spin state monotonically increases to sextet for Mn@C₂₄N₂₄ and thereafter dropped off gradually to singlet state for Zn@C₂₄N₂₄ system. The findings demonstrate that transition metals can remarkably decrease the HOMO-LUMO energy gap and work function values up to 63% and 21% of bare C₂₄N₂₄, respectively. As can be seen, when the Sc and Ti metals are located above the N4 cavity of fullerene, systems of enhanced static hyperpolarizabilities (β₀) are delivered. These findings might provide an effective strategy to design high performance eletcro-optical materials based on carbon- nitride fullerene.     

Zur Anreicherung der stabilen Isotope des Schwefels durch Fest-Flüissig-Austausch unter Verwendung von Ionenaustauschern

An verschiedenen Systemen chemischer Verbindungen wurden Versuche zur Anreicherung des stabilen Isotopes ³⁴S unter Verwendung der Ionenaustauscher Wofatit L 150, SBW und SBK nach den Methoden der Frontalchromatographie und der Bandenverdrāngungschromatographie ausgeführt. Beim Isotopenaustauschsystem Hydrogensulfit (am Ionenaustauscher)/Schwefeldioxid (in wäβriger Lösung) wurden Verfahrensweise und Betriebsparameter hinsichtlich des Anreicherungsgrades optimiert. Mit Hilfe einer einfachen Methode gelang es, aus den Versuchsergebnissen Werle für den elementaren Trennfaktor und die Trennstufenhöhe zu berechnen.     

Beiträge der Radiotracertechnik zur Rationalisierung einer großtechnischen Anlage zur Caprolactamproduktion

This paper reviews ways in which radioactive tracer techniques can he used to improve the efficiency of a caprolactam production plant, Residence time spectra and material distributions in different parts of the plant were measured by application of sodium 24, bromine 82 and technetium 99m. The investigations led to improved cumeneoxidators and gave useful informations on the catalytic decomposition of the phenolic tar and the hydrogenation process of phenol. It could he shown that the construction of the lactam extractor must he varied and the results of the tracerexperiments made in the distillation unit contributed to a higher quality of the final product.     

On the γ-filtration of oriented cohomology of complete spin-flags

We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihilator of the torsion part of the γ-filtration. Moreover, if the formal group law determined by the oriented cohomology theory is congruent to the additive formal group law modulo 2, then at degree 2 and 3, we show that the γ-filtration of complete spin-flags is torsion free.     

Modification of the Solution Behavior of Pd12L24 Metal–Organic Nanocages via PEGylation

The dilute solutions behaviors of Pd₁₂L₂₄ metal–organic nanocage and its two PEGylated derivatives are explored. The basic nanocages can self‐assemble into vesicle‐like blackberry structures in polar solvents via counterion‐mediated attraction, whereas the PEGylated nanocages always stay as discrete ions under the same conditions, demonstrating that the PEGylation can improve the stability of the single nanocages. In addition, larger nanocages are found to self‐assemble in less polar solvents.