Theoretical study of the in-plane components of the 13C shielding tensors in condensed aromatic hydrocarbons

The Pople model for chemical shielding is applied to calculate the in-plane components of the ¹³C shielding tensors of condensed aromatic hydrocarbons. The wave functions are evaluated using the MNDO method and the calculated results are supported by the very good agreement with the experimental results in the few cases in which experimental information is available.The relationship found between the calculated bond orders and the in-plane components of the ¹³C shielding tensors suggest that the experimental study of the ¹³C shielding tensors in these compounds may provide a powerful technique for studying aromaticity. The in-plane components are found to be directly affected by the degree of delocalization of the -electrons in the adjacent bonds. Rules are given for estimating the orientation of the two in-plane components of the shielding tensor.     

Bondesson's functions in reliability theory

Bondesson's functions in reliability theory are shown to be related to a recursive sequence of probability distributions. These are the ‘higher-order’ versions of the mean remaining lifetime in an equilibrium renewal process. Based on these functions, classes of distribution functions can be defined. This paper will investigate these classes and place Bondesson's work in the content of the other work done in reliability theory. Connections are made with the decreasing variance residual lifetime class and stochastic ordering. Copyright © 1999 John Wiley & Sons, Ltd.     

A construction of a perfect set of Euler tours of K2k + I

In this article we define a perfect set of Euler tours of K_2k + I, I a 1-factor of K_2k, to be a set of Euler tours of K_2k + I that partition the 2-paths of K_2k, with the added condition that if ab ∈ I, then each Euler tour contains either the digon a b a or b a b. We prove for all k > 1 that K_2k + I has a perfect set of Euler tours, and, as a corollary, that L(K_2k) has a Hamilton decomposition. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 183–211, 1998     

Finiteness of Higher K -Groups of Orders and Group Rings

In this paper, we prove that if R is the ring of integers in a number field F, A any R-order in a semisimple F-algebra, then K_2n(A), G_2n(A) are finite groups for all positive integers n. Hence, even dimensional higher K- and G-groups of integral grouprings of finite groups are finite. We also show that in odd dimensions, SK_n of integral and p-adic integral grouprings of finite p-groups are also finite p-groups (Received: August 2005)     

Newton's method and Schwarzian derivatives

We discuss Newton's method with respect to obtaining convergence to a fixed point with orders of convergence greater than 2. We identify the role played by the Schwarzian derivative in controlling the convergence of Newton's map to a super stable fixed point.     

A conjecture of Abe-Iiyori and the Ree groups ~2F_4(q),Ⅱ

In this paper the author has solved a problem of Abe and liyori for the finite simple groups 2F4(q) and 2F4(2)'.     

Run orders and quantitative factors in asymmetrical designs

Results on run orders leading to trend-free symmetrical factorial designs are extended to the asymmetrical case, using the character theory of abelian groups. The tools developed apply equally to the construction of designs for quantitative treatment factors with eight or more regularly spaced levels. Abelian group theory can also be used to find minimum-cost run orders for asymmetrical designs, with a cost based on the number of changes of levels between successive runs.     

例外型Chevalley群G_2(q)的h函数值

设G是有限群,πe(G)表示G中元素的阶的集合,h(πe(G))表示满足πe(H)=πe(G)条件的有限群H的同构类类数,本文证明了例外型Chevalley群G2(q)的h函数值为1或∞.     

Quasirecognition of One Class of Finite Simple Groups by the Set of Element Orders

We prove that a finite group, having the same set of element orders as a finite simple group L and the prime graph with at least three connected components, possesses a (unique) nonabelian composition factor which is isomorphic to L, unless L is isomorphic to the alternating group of degree 6.     

Traces of Eichler—Brandt matrices and type numbers of quaternion orders

LetA be a totally definite quaternion algebra over a totally real algebraic number fieldF andM be the ring of algebraic integers ofF. For anyM-orderG ofA we derive formulas for the massm(G) and the type numbert(G) of G and for the trace of the Eichler-Brandt matrixB(G, J) ofG and any integral idealJ ofM in terms of genus invariants ofG and of invariants ofF andJ. Applications to class numbers of quaternion orders and of ternary quadratic forms are indicated.