On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

Continuous time collocation methods for Volterra-Fredholm integral equations

Summary Integral equations of mixed Volterra-Fredholm type arise in various physical and biological problems. In the present paper we study continuous time collocation, time discretization and their global and discrete convergence properties.     

A local characterization of the johnson scheme

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod. Partial support provided by NSF (USA), SERC (UK), ZWO (NL).     

Observation of p(1×1)-type rows on TiO2(110)-p(1×2) surface by scanning tunneling microscope (STM)

The TiO₂(110) surfaces were observed by a Scanning Tunneling Microscope (STM). We found two types of bright p(1×1)-type rows on the p(1×2) surface. One p(1×1)-type formed independently and corresponds to the bridging oxygen rows. The second p(1×1)-type appeared in a bright grouping, forming narrow rows, and corresponds to the five-fold titanium rows. The above results suggest the following two conclusions. First, the density of state (DOS) on the bridging oxygen rows becomes higher than that on the five-fold titanium atom rows when a bridging oxygen row exists independently on the p(1×2) surface. Second, the bright rows on a TiO₂(110)-p(1×1) surface correspond to the five-fold titanium atom rows. The results further show the validity of DOS calculations on the TiO₂(110)-p(1×1) surface by Diebold et al. [Phys. Rev. Lett. 77 (1996) 1322]. The difference of width for Ti₂O₃ unit rows on the p(1×2) and p(1×3) surfaces in STM images are also discussed.     

Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Congruences,equational theories and lattice representations

We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.To László Fuchs on the occasion of his 70th birthday     

Disordered charge distributions and dielectric loss in extra dense flint glasses

The complex permittivities of some extra dense flint glasses (EDF glasses) have been studied. The dielectric features of the samples are dominated by their PbO content. Both refractive indices and dielectric losses exhibit a close relation to the concentration of Pb ions. The latter are located either at sites of the network atoms or filling the potential minima interstitially. They can be identified by their different relaxation mechanisms. The dispersion in the submillimeter wave and FIR area is characterized by a very broad distribution of comparably sharp resonant states. Thermal lens — or hysteresis effects can be excluded.     

A remark on partial linear spaces of girth 5 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces.     

含嘧啶环的双冠醚(Ⅳ)

前文已报道由啶环桥联两个苯并冠醚的双冠醚的合成与性质。由于嘧啶环的刚性较大,能把两个冠醚单元固定在有效地协同作用位置,因此以它们作中性载体的离子选择性电极具有较好的选择性。为了进一步研究这类双冠醚的性质,我们合成了四种嘧啶环桥联两个脂肪族冠醚的双冠醚,并经元素分析、IR、′HNMR鉴定。