On the homotopy fixed point problem for free loop spaces and other function complexes

Let G be a finite group, let X and Y be finite G-complexes, and suppose that for each K G, Y ^K is dim(X ^K)-connected and simple. G acts on the function complex F(X, Y) by conjugation of maps. We give a complete analysis of the homotopy fixed point set of the space F(X, Y). As a corollary, we are able to analyze at a prime p, the homotopy fixed point set of the circle action on X, where X denotes the free loop space of X, and X is a simply connected finite complex.Supported in part by NSF DMS 86-02430.To A. Grothendieck on the occasion of his sixtieth birthday     

Computing the maximal canonical form for trees in polynomial time

Known algorithms computing a canonical form for trees in linear time use specialized canonical forms for trees and no canonical forms defined for all graphs. For a graph \(G=(V,E)\) the maximal canonical form is obtained by relabelling the vertices with \(1,\ldots ,|V|\) in a way that the binary number with \(|V|^2\) bits that is the result of concatenating the rows of the adjacency matrix is maximal. This maximal canonical form is not only defined for all graphs but even plays a special role among the canonical forms for graphs due to some nesting properties allowing orderly algorithms. We give an \(O(|V|^2)\) algorithm to compute the maximal canonical form of a tree.     

The -PIP and integrability of a single function

Two examples are given that answer in the negative the following question asked by E. M. Bator: If is bounded and weakly measurable and for each in there is a bounded sequence in such that a.e., does it follow that is Pettis integrable?

     

On the possibility of improving the integral evaluation section in ab initio Hartree–Fock calculations on large molecules

A modified integral package for evaluation of two-electron integrals over Gaussian basis functions is described. Modifications are implemented in the MOLECULE program system and are especially suited for the study of large molecules and molecular complexes.     

Water sorption properties of carbonized layers produced by controlled B<Superscript>+</Superscript> bombardment of thin polyimide and polysulfone films

Thin polyimide (PI) and polyethersulfone (PES) films are widely used as functional layers for microelectronic sensors. Ion implantation modifies the layer structure and morphology of these polymers and hence results in new mechanical and optical properties. However, ion-modified layers also show a change in sensitivity to moisture uptake under specific conditions. This is important for developing humidity sensors. Therefore, the water sorption ability of such modified polymer layers is studied by spectroscopic ellipsometry under definite relative humidity conditions (1–95%). Swelling data were obtained by fitting procedures based on changes of effective layer thickness and optical constants due to water uptake. Irradiation doses from 0.5 to 5×10¹⁵ B⁺ cm^–2 at an energy of 180 keV were used for polymer modification. At irradiation doses from 0.5 to 0.7×10¹⁵ B⁺ cm^–2, the maximum out-of-plane swelling is reached. At higher doses >2×10¹⁵ B⁺ cm^–2, the swelling decreases and corresponds to values of the pure polymer layers. The wetting properties of the layer surfaces determined by contact angle measurements are important to explain this behavior.     

A tetrameric copper(I) alkoxide with a π-tethered ligand: 2-allyl-6-methylphenoxocopper(I)

The complex 2-allyl-6-methylphenoxocopper(I) has been prepared by reaction between mesitylcopper(I) and 2-allyl-6-methylphenol. Crystallographic studies show that the compound is tetrameric with a distorted cubane-type copper(I)-oxygen core, and with additional π-coordination of the ligand to copper through the alkene functionality (ν(CC)=1520 cm⁻¹). The ligands thus act both as chelates and as bridges between adjacent copper(I) centres. Copper(I) exhibits trigonal pyramidal coordination geometry with CuC distances to the CC group of 1.976(9) and 2.017(11) Å and CuO distances of 1.973(6), 2.021(6) and 2.577(6) Å, respectively.     

Decarboxylation in the synthesis of 4‐alkyl‐, 4‐alkenyl‐ and 4‐acylpyrimidines

Decarboxylation of allylic esters of 4‐carboxypyrimidines in toluene at 111 °C in the presence of a Pd(0) catalyst, gives a mixture of a 4‐alkenylpyrimidine and a pyrimidine unsubstituted in the 4‐position. If the decarboxylation is carried out in the presence of benzaldehyde, then benzaldehyde is added to the 4‐position. Decarboxylation of 4‐carboxypyrimidines in the presence of different electrophiles, results in incorporation of the electrophile into the 4‐position together with a pyrimidine unsubstituted in the 4‐position. Use of microwave irradiation enhances the rate of the decarboxylations.     

Ground-state dipole polarizability of lithium hydride. Accurate SCF and CAS SCF calculations

Accurate calculations of the dipole polarizability tensor of lithium hydride are performed using the finite-field perturbation approach in the SCF and CAS SCF method. The SCF results (α_? = 22.1, α_⊥ = 25.4 au) are expected to be very close to the HF values. The CAS SCF calculations predict a positive correlation contribution, giving α_? = 26.3 and α_⊥ = 29.3 au.