Oxidative cyclization and fragmentation of steroidal alcohols induced by ceric ammonium nitrate

Oxidative cyclizations of steroidal alcohols (1a–1d) using ceric ammonium nitrate (CAN) in aqueous acetonitrile or aqueous acetic acid gave the corresponding cyclic ethers (2a–2d), whereas the tertiary alcohol (4) gave secosteroid (5).     

15N and 13C NMR chemical shifts of 6‐(fluoro,chloro, bromo,and iodo)purine 2′‐deoxynucleosides: measurements and calculations

The ¹⁵N and ¹³C chemical shifts of 6‐(fluoro, chloro, bromo, and iodo)purine 2′‐deoxynucleoside derivatives in deuterated chloroform were measured. The ¹⁵N chemical shifts were determined by the ¹H? ¹⁵N HMBC method, and complete ¹⁵N chemical‐shift assignments were made with the aid of density functional theory (DFT) calculations. Inclusion of solvation effects significantly improved the precision of the calculations of ¹⁵N chemical shifts. Halogen‐substitution effects on the ¹⁵N and ¹³C chemical shifts of purine rings are discussed in the context of DFT results. The experimental coupling constants for ¹⁹F interacting with ¹⁵N and ¹³C of the 6‐fluoropurine 2‐deoxynuleoside are compared with those from DFT calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

The irredundant ramsey number s(3, 7)

The irredundant Ramsey number s(m, n) is the smallest p such that for every graph G with p vertices, either G contains an n-element irredundant set or its complement G contains an m-element irredundant set. Cockayne, Hattingh, and Mynhardt have given a computer-assisted proof that s(3, 7) = 18. The purpose of this paper is to give a self-contained proof of this result. © 1995 John Wiley & Sons, Inc.     

Light-assisted synthesis of metal oxide hierarchical structures and their catalytic applications

Short reaction times and morphology control in the synthesis of inorganic materials under nonthermal conditions remain a challenge. Herein we report a rapid, self-templating, and nonthermal method based on ultraviolet light to prepare metal oxide hierarchical structures. With this method, the morphology of the metal oxides was controlled readily without using templates.     

Ramsey linear families and generalized subdivided graphs

The following results are obtained. (i) Let p, d, and k be fixed positive integers, and let G be a graph whose vertex set can be partitioned into parts V₁, V₂,…, V_a such that for each i at most d vertices in V₁ … V_i have neighbors in V_i+1 and r(K_k, V_i) p | V(G) |, where V_i denotes the subgraph of G induced by V_i. Then there exists a number c depending only on p, d, and k such that r(K_k, G)c | V(G) |. (ii) Let d be a positive integer and let G be a graph in which there is an independent set I V(G) such that each component of G−I has at most d vertices and at most two neighbors in I. Then r(G,G)c | V(G) |, where c is a number depending only on d. As a special case, r(G, G) 6 | V(G) | for a graph G in which all vertices of degree at least three are independent. The constant 6 cannot be replaced by one less than 4.