Formulas for the Inverses of Toeplitz Matrices with Polynomially Singular Symbols

We consider large finite Toeplitz matrices with symbols of the form (1– cos )^p f() where p is a natural number and f is a sufficiently smooth positive function. By employing techniques based on the use of predictor polynomials, we derive exact and asymptotic formulas for the entries of the inverses of these matrices. We show in particular that asymptotically the inverse matrix mimics the Green kernel of a boundary value problem for the differential operator Submitted: June 20, 2003     

Some remarks on half-factorial orders

In questo articolo, si dimostra il legame fra la semi-fattorialità e la fattorialità debole nel contesto degli ordini algebrici. In particolare, si ottiene che un ordine semi-fattoriale ha il stesso numero di classi che su chiusura integrale.     

Triterpene Glycosides of Scheffleropsis angkae. IV. Structure of Glycosides L-C2 and L-I2

Two new triterpene glycosides of the -amyrin series, L-C ₂ and L-I ₂ , 27-hydroxyursolic acid 3-O--L-arabinopyranoside and its 28-O--L-rhamnopyranosyl-(14)-O--D-glucopyranosyl-(16)-O--D-glucopyranosyl ester, are isolated from leaves ofScheffleropsis angkae(Araliaceae). The structures of the glycosides are established using chemical methods and NMR techniques ( ¹ H, ¹³ C, ¹³ C-APT, COSY, TOCSY, HSQC, HMBC, and ROESY).     

Unification of lower-bound analyses of the lift-and-project rank of combinatorial optimization polyhedra

We present a unifying framework to establish a lower bound on the number of semidefinite-programming-based lift-and-project iterations (rank) for computing the convex hull of the feasible solutions of various combinatorial optimization problems. This framework is based on the maps which are commutative with the lift-and-project operators. Some special commutative maps were originally observed by Lovász and Schrijver and have been used usually implicitly in the previous lower-bound analyses. In this paper, we formalize the lift-and-project commutative maps and propose a general framework for lower-bound analysis, in which we can recapture many of the previous lower-bound results on the lift-and-project ranks.     

Module containment property for linear equations

A general module containment property is proved for almost periodic linear systems of differential equations, in both finite and infinite dimensions.     

Online scheduling with reassignment

This paper studies online scheduling problems with reassignment on two identical machines. We can reassign some jobs under certain rules after all the jobs have been assigned. Three different versions are studied and optimal algorithms are proposed.     

1D to 3D NMR study of microporous alumino‐phosphate AlPO4‐40

From one‐ to two‐ and three‐dimensional MAS NMR solid‐state experiments involving ³¹P and ²⁷Al, we show that the structure of microporous alumino‐phosphate AlPO₄‐40 contains at least four times more sites than expected, and we attribute two types of Al_IV sites. The newly described ²⁷Al‐³¹P MQ‐HMQC opens new possibilities of describing details of three‐dimensional bounded networks. Copyright © 2009 John Wiley & Sons, Ltd.