Graphs with a Small Number of Nonnegative Eigenvalues

In this paper, by means of computer checking, all simple graphs with at most two nonnegative eigenvalues, and all minimal simple graphs with exactly two (respectively, three) nonnegative eigenvalues are determined. Received: April 5, 1996 / Revised: May 2, 1997     

Ab initio calcuation of ideal strength for cubic crystals under three-axial tension

Ab initio calculation of ideal strength of cubic crystals under three-axial tension was performed using the LMTO-ASA method. Computed values are in a good agreement with those obtained previously by means of semi-empirical polynomial approach. The values of equilibrium lattice parameter obtained in the framework of ab initio method are well comparable with the experimental data whereas a less satisfactory agreement was achieved in the case of bulk moduli.     

Subtotally positive and Monge matrices

A real matrix is called k-subtotally positive if the determinants of all its submatrices of order at most k are positive. We show that for an m × n matrix, only mn inequalities determine such class for every k, 1 ? k ? min(m,n). Spectral properties of square k-subtotally positive matrices are studied. Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated. Since totally positive matrices are 2-subtotally positive as well, the presented necessary conditions for this completion problem are also necessary conditions for totally positive matrices.     

Structure build‐up at rest in polymer nanocomposites: Flow reversal experiments

Evolution of the microstructure as well as the shear stress and the normal stress difference of polymer/layered silicate nanocomposites prepared by melt mixing of poly[butylene succinate‐co‐adipate] and organically modified montmorillonite are investigated in transient forward and reverse start‐up shear flows at different clay loading and different shear rates. Special attention is paid to the structure build‐up at rest and to the amplitude of the overshoots observed during the reverse start‐up test in the shear stress and the normal stress difference. The model that we have developed previously is used to suggest an explanation for the observed phenomena. The model is able to capture observed behavior of the shear stress in both forward and reverse start‐up flows. It fails, however, to predict experimentally observed overshoot in the normal stress difference. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1728–1741, 2009     

Toeplitz Operators and Group Representations

Toeplitz operators on the Bergman space of the unit disc can be written as integrals of the symbol against an invariant operator field of rank-one projections. We consider a generalization of the Toeplitz calculus obtained upon taking more general invariant operator fields, and also allowing more general domains than the disc; such calculi were recently introduced and studied by Arazy and Upmeier, but also turn up as localization operators in time-frequency analysis (witnessed by recent articles by Wong and others) and in representation theory and mathematical physics. In particular, we establish basic properties like boundedness or Schatten class membership of the resulting operators. A further generalization to the setting when there is no group action present is also discussed, and the various settings in which similar operator calculi appear are briefly surveyed.     

Nil-extensions of unions of groups induced by identities

This paper is a continuation of [11]. Here we study all identities which induce decompositions into nil-extensions of a union of groups and identities which induce various special types of these decompositions. Supported by Grant 0401A of SF Servia through Math. Inst. SANU.     

Productive Coreflective Classes in Top

If sequential cardinals do not exist then every topological space is generated from a converging sequence by using finite products, disjoint sums and quotients. The author acknowledges the support of the grants MSM 0021620839 and GAČR 201/06/0933 of Czech Republic.     

Switching of chirality from racemic to homochiral state in new liquid crystalline monomers with bent-core molecules

The synthesis and physical properties of bent-shaped molecules with ester linkages and methoxy substitution on a non-central ring are presented. Terminal chains of most mesogens contain a group with double bond, which promotes polymerization. In all the compounds studied a B₂ phase just below the isotropic phase has been found. Polarization current profiles indicate that this phase is antiferroelectric, and dielectric spectroscopy data with a pronounced high frequency mode support this fact. For several compound chirality switching from racemic to the homochiral state was seen after application of a low frequency a.c. field. Another phase, which could be assigned to the B₇ family, appears below the B₂ phase on cooling.     

The Mixed Norm Spaces of Polyharmonic Functions

Let be a bounded domain with C ² boundary. And let H _k be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H _k for which the mixed-norm ||·|| _{p, q, ϕ} <∞. The main result of the paper is the norm equivalence: