1H one- and two-dimensional five-pulse ESEEM investigations on a radiation center in betaine phosphite single crystals

1D and 2D five-pulse ESEEM experiments on a PO ₃ ^2? center in γ-irradiated betaine phosphite are presented to study the protons bound to the radical in more detail. The ESEEM results are in accordance with previous ENDOR investigations. From the 2D fivepulse ESEEM experiments the¹H ENDOR assignment in the ferroelectric ordered state of betaine phosphite could be completed. Additionally, the occurrence of ordered proton states in the disordered paraelectric high-temperature phase and of disordered proton states in the ordered ferroelectric low-temperature phase as well could be observed due to the enhanced resolution of the 2D method.     

Operators with singular continuous spectrum,VII. Examples with borderline time decay

We construct one-dimensional potentialsV(x) so that if onL ²(), thenH has purely singular spectrum; but for a dense setD, D implies that |,e ^-itH |C |t|^-1/2 ln(|t|) for t>2. This implies the spectral measures have Hausdorff dimension one and also, following an idea of Malozemov-Molchanov, provides counterexamples to the direct extension of the theorem of Simon-Spencer on one-dimensional infinity high barriers.This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

Infinite products of finite simple groups

We classify the sequences of finite simple nonabelian groups such that has uncountable cofinality.

     

Structures of two ketals derived from a pentacyclic cage diketone

The structure of a compound derived from a symmetrical cage diketone in which one of the ketone C=O groups has been converted into a ketal is reported. An investigation into reasons for the selective functionalization resulted in the isolation of acis, cisoid, cis linear triquinane derivative in which both ketones are converted to ketals that share a transannular oxygen atom. Crystal data:2, monoclinic,P2₁/c,a=7.6298(9),b=7.673(3),c=22.125(3)Å,=97.59(1)°,V=1283.9(5)ų, andR=0.048 (1001 reflections);4, triclinic,P¯1,a=7.3864(9),b=9.6362(9),c=10.3889(9)Å,=75.749(6),=76.300(8), =83.100(8)°,V=694.8(4)ų, andR=0.088 (1284 reflections).