1. Preliminaries. Let X be the class of compact 1 connected semisimple Lie groups; 3C'C3C is the following set of groups, Sp(w), SU(w), Spin(w), G2, F*, EQ, E7, Es, U*(X) the weakly complex bordism of X [ l ] and A the ring U*(pt) = Z[Fi , F2, • • • ]. A is the weakly complex bordism ring defined by Milnor. The generators F,are weakly complex manifolds of dim 2i. The bordism class of a weakly c...

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

The Banach space E has the weakly compact approximation property (W.A.P. for short) if there is a constant C < ∞ so that for any weakly compact set D ⊂ E and ε > 0 there is a weakly compact operator V : E → E satisfying supx∈D ‖x − V x‖ < ε and ‖V ‖ ≤ C. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type ...

In this paper we present experimental data on the frequency domain response of a superconducting-quantum-interference-device ring (a Josephson weak link enclosed by a thick superconducting ring) coupled to a radio frequency tank circuit resonator. We show that with the ring weakly hysteretic the resonance line shape of this coupled system can display opposed fold bifurcations that appear to tou...

Previous spectroscopic studies on the phycocyanobilin-containing peptide beta-2T from Synechococcus sp. 6301 C-phycocyanin and the phycoerythrobilin-containing peptide beta-2TP from Porphyridium cruentum B-phycoerythrin indicated a different single thioether mode of attachment, postulated to be through the D-ring of the tetrapyrrole, in contrast to the A-ring linkage established for the other s...

The title compound, C(15)H(17)N(3), was prepared by reaction of benzoyl-pyridine and hexahydropyrimidine. The 1,3-diazinane ring adopts a chair conformation with one N-H group axial and the other equatorial. The axial N-H group participates in very weak hydrogen bonding to the lone pair of electrons of the N atom with the equatorial H atom producing a very weakly hydrogen-bonded dimer. The pyri...

Describing the subgroup structure of a non-commutative division ring is subject an intensive study in theory rings particular, and skew linear groups general. This still so far to be complete. In present paper, we this problem for weakly locally finite rings. Such constitute large class which strictly contains

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of $WAG2$-absorbing submodule. A number results concerning these classes submodules their homogeneous components are given.&#x0D; $N=\bigoplus _{h\in G}N_{h}$ submodule $h\in G.$ We say that $N_{h}$ is $h$-$WAG2$-absorbing $R_{e}$-module $M_{h}$ if $N_{h}\neq ...

A uniformly recurrent pseudoword is an element of a free profinite semigroup in which every finite factor appears in every sufficiently long finite factor. An alternative characterization is as a pseudoword which is a factor of all its infinite factors, that is one which lies in a J -class with only finite words strictly J -above it. Such a J -class is regular and therefore it has an associated...

It is proved that if an uncountable cardinal κ has ineffable subset of weakly compact cardinals, then a cardinal, and Ramsey (Rowbottom, Jónsson, or subtle) J\'onsson, cardinal.