The Uzawa–HSS method for saddle-point problems

Based on the Hermitian and skew-Hermitian splitting iteration scheme, we propose a Uzawa-type iteration method for solving a class of saddle-point problems whose coefficient matrix has non-Hermitian positive definite (1, 1)-block. The convergence properties of this novel method are analyzed, which show that the Uzawa-type iteration method is convergent if the iteration parameters satisfy suitable restrictions.     

On the realization of double occurrence words

Let S be a double occurrence word, and let M_S be the word’s interlacement matrix, regarded as a matrix over . Gauss addressed the question of which double occurrence words are realizable by generic closed curves in the plane. We reformulate answers given by Rosenstiehl and by de Fraysseix and Ossona de Mendez to give new graph-theoretic and algebraic characterizations of realizable words. Our algebraic characterization is especially pleasing: S is realizable if and only if there exists a diagonal matrix D_S such that M_S+D_S is idempotent over .     

On the dimensions of the binary codes of a class of unitals

Let U_β be the special Buekenhout-Metz unital in PG(2,q²), formed by a union of q conics, where q=p^e is an odd prime power. It can be shown that the dimension of the binary code of the corresponding unital design U_β is less than or equal to q³+1−q. Baker and Wantz conjectured that equality holds. We prove that the aforementioned dimension is greater than or equal to .     

Ab initio periodic study of the conformational behavior of glycine helical homopeptides

Representative helicoidal conformations of polyglycine infinite chains have been investigated by using periodic boundary conditions, the B3LYP hybrid functional, and large basis sets, by means of the CRYSTAL code. The exploitation of the helix roto‐translational symmetry permits to optimize at a relatively low cost the structure of systems whose unit cell contains more than 300 atoms, much larger than the one investigated till now. In the present calculations, the helix symmetry is exploited at three levels. First, for the automatic generation of the structure. Second, for the calculation of the one‐ and two‐electron integrals that enter into the Fock matrix definition. Only the irreducible wedge of the Fock matrix is computed. Finally, for the diagonalization of the Fock matrix, where each irreducible representation is separately treated. The efficiency and accuracy of the computational scheme are documented, by considering cells containing up to 47 glycine residues. Results are compared with previous calculations and available experimental data. The role of hydrogen bonding in stabilizing polyglycine conformers is also addressed. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Local duality for equitable partitions of a Hamming space

The Hamming space Qn is the set of binary words of length n. A partition (C₁,C₂,…,Cr) of Qn with quotient matrix B=[bij]_r×r is equitable if for all i and j, any word in the cell Ci has exactly bij neighbors in the cell Cj. In this paper, we provide an explicit formula relating the local spectrum of cells in the face to that in the orthogonal face.     

New characterizations of EP, generalized normal and generalized Hermitian elements in rings

We present a number of new characterizations of EP elements in rings with involution in purely algebraic terms. Then, we study equivalent conditions for an element a in a ring with involution to satisfy aⁿa^∗ = a^∗aⁿ or aⁿ = (a^∗)ⁿ for arbitrary n ∈ N. For n = 1, we present some new characterizations of normal and Hermitian elements in rings with involution.     

‘Modified Hermitian and skew‐Hermitian splitting methods for non‐Hermitian positive‐definite linear systems’ [Numer. Linear Algebra Appl. 14 (2007) 217–235]

In this note, some errors in the article (Numer. Linear Algebra Appl. 2007; 14 :217–235) are pointed out and some correct results are presented. Copyright © 2011 John Wiley & Sons, Ltd.