KT-nearfields of rank 2

Summary Nearfields of rank 2 over their kernel which are not Dickson nearfields have recently been constructed by H. Zassenhaus. Here it is shown that KT-nearfields of rank 2 over their kernels and of characteristic 2 are necessarily Dickson nearfields which are coupled to quadratic field extensions and their Dickson group is isomorphic to ₂. Using results of Gröger one obtains all KT-nearfields of rank 2 over the field of rational numbers.     

Quadratically constrained least squares and quadratic problems

Summary We consider the following problem: Compute a vectorx such that Ax–b₂=min, subject to the constraint x₂=. A new approach to this problem based on Gauss quadrature is given. The method is especially well suited when the dimensions ofA are large and the matrix is sparse.It is also possible to extend this technique to a constrained quadratic form: For a symmetric matrixA we consider the minimization ofx ^T A x–2b ^T x subject to the constraint x₂=.Some numerical examples are given.This work was in part supported by the National Science Foundation under Grant DCR-8412314 and by the National Institute of Standards and Technology under Grant 60NANB9D0908.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

Functional inequality characterizing nonnegative concave functions in (0, ∞) k

Summary In the present note we prove that every functionf: (0, ) [0, ) satisfying the inequalityaf(s) + bf(t) f(as + bt), s, t > 0, for somea andb such that 0 <a < 1 <a + b must be of the formf(t) = f(1)t, (t > 0). This improves our recent result in [2], where the inequality is assumed to hold for alls, t 0, and gives a positive answer to the question raised there.An analogue for functions of several real variables of the above result characterizes concave functions. Conjugate functions and some relations to Hölder's and Minkowski's inequalities are mentioned.     

Bootstrap,wild bootstrap,and asymptotic normality

Summary We show for an i.i.d. sample that bootstrap estimates consistently the distribution of a linear statistic if and only if the normal approximation with estimated variance works. An asymptotic approach is used where everything may depend onn. The result is extended to the case of independent, but not necessarily identically distributed random variables. Furthermore it is shown that wild bootstrap works under the same conditions as bootstrap.This work has been supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 Stochastische Mathematische Modelle     

Problème inverse de la théorie du potentiel logarithmique pour les lemniscates

The paper is related to the question of uniqueness in the inverse logarithmic potential problem. This question is to find the conditions on which two domains D ₁ and D ₂ producing the same external potential must coincide. Assuming the general hypothesis of regularity and an additional condition of connectivity of (D₁D₂)_c, we prove a theorem of uniqueness in the case when one of the domains is a lemniscate. The main tool is one lemma for Cauchy's potential due to M. Sakai. We give a simple proof of its extension to Newtonian potential.

     

Factorial regular representation of groups in complete graphs

A necessary and sufficient condition for the group of isomorphisms involved in a factorization of a complete graph into isomorphic factors is established.     

Conditional solubility versus pO2− of cerium(III) oxide in molten equimolar NaCl+KCl at 727°C

Reactions between cerium trichloride and oxide ions were studied in NaCl+KCl (1/1) at 1000°K, by potentiometry with a calcia-stabilized zirconia membrane electrode. Titration curves clearly demonstrated the existence of soluble cerium oxychloride (CeO⁺) and precipitated cerium oxide (Ce₂O₃), with respective dissociation constants 10^?11 and 10^?30 (molality scale). The corresponding conditional solubility diagram {log S (Ce^III)=f(pO^2?)} is presented and discussed.     

Ein Neues,tricyclisches schwefelreiches Phosphan

A New Tricyclic Sulfur-rich Phosphane From the products of the reaction of P₄S₃ with tert-Butyliodide the compound (t-Bu(S)P)₂P₄S₃ was isolated in low yield. The compound is stable and has a structure related to the hydrocarbon brexane. By reaction with triphenylphosphin the compounds (t-BuP)(t-Bu(S)P)P₄S₃ and (t-BuP)₂P₄S₃ were obtained. The ³¹P-nmr spectra of all compounds were solved and used to determine the structure of the molecules. A complete set of ³¹P-nmr data is given.     

Synthesis of PNIPAAm-g-P4VP Microgel as Draw Agent in Forward Osmosis by RAFT Polymerization and Reverse Suspension Polymerization to Improve Water Flux

Microgels have unique and versatile properties allowing their use in forward osmosis areas as a draw agent. In this contribution, poly(4-vinylpyridine) (P4VP) was synthesized via RAFT polymerization and then grafted to a poly(N-Isopropylacrylamide) (PNIPAAm) crosslinking network by reverse suspension polymerization. P4VP was successfully obtained by the quasiliving polymerization with the result of nuclear magnetic resonance and gel permeation chromatography characterization. The particle size and particle size distribution of the PNIPAAm-g-P4VP microgels containing 0, 5, 10, 15 and 20 wt% P4VP were measured by means of a laser particle size analyzer. It was found that all the microgels were of micrometer scale and the particle size was increased with the P4VP load. Inter/intra-molecular-specific interactions, i.e., hydrogen bond interactions were then investigated by Fourier infrared spectroscopy. In addition, the water flux measurements showed that all the PNIPAAm-g-P4VP microgels can draw water more effectively than a blank PNIPAAm microgel. For the copolymer microgel incorporating 20 wt% P4VP, the water flux was measured to be 7.48 L∙m⁻²∙h⁻¹.