The 1-width of (0,1)-matrices having constant row sum 3

In this note we establish upper bounds for the 1-width of an m × n matrix of 0's and 1's having three 1's in every row and having a constant number, c, of 1's in every column. When c = 3, this upper bound is $\text{n}\text{2}$ and when c = 4 this estimate is $\text{5n}\text{9}$. In these cases the upper bound is best possible, in the sense that for every possible size there exist matrices with this maximal 1-width. The technique of proof is also used to improve the known bound for the 1-width of (0, 1)-matrices with constant line sum 4.     

Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations

For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -point boundary conditions. These relationships are investigated as well.

     

Defining topological features of membrane proteins by nanoelectrospray ionisation mass spectrometry

The D‐galactose‐H⁺ symport protein, GalP, of Escherichia coli is the bacterial homologue of the human glucose transport protein, GLUT1. Here we demonstrate that mass spectrometry can be used to map modification by covalently bound reagents, and also to detect structural changes in the GalP protein that occur upon substrate binding. The small thiol‐group‐specific reagent N‐ethylmaleimide (NEM) was used to modify the cysteine residues in GalP(His)₆ both alone and in the presence of D‐glucose, a known substrate. Employing a mixture of proteolysis and thermal degradation methods, the three cysteine residues were found to undergo sequential reactions with NEM, with Cys374 being modified first, followed by Cys389 and finally Cys19, thus indicating their different accessibilities within the three‐dimensional structure of the protein. Prior binding of the substrate D‐glucose to the protein protected Cys19 and Cys374 against NEM modification, but not Cys389. Cys374 had been expected to be shielded by D‐glucose binding while Cys389 had been expected to be unaffected, consistent with their proposed respective locations in the vicinity of, and distant from, the sugar binding site. However, the inaccessibility of Cys19 was unexpected and suggests a structural change in the protein promoted by D‐glucose binding which changes the proximity of Cys19 with respect to the D‐glucose‐binding site. Copyright © 2010 John Wiley & Sons, Ltd.     

Computer-aided spillway design using the boundary element method and non-linear programming

The general context of this paper is to support the design of spillways by a direct mathematical approach instead of trial-and-error methods. First, a two-dimensional model is formulated to determine the free surface and the discharge for a stationary, incompressible, homogeneous, non-viscous and irrotational flow over a fixed spillway. The flow satisfies the Laplace equation and the Bernoulli equation (potential flow). An important feature of the model is that it can be extended to design the spillway structure when the spillway is not fixed but the pressure on the spillway is described by a cavitation criterion. Next, the continuous model is discretized by the boundary element method (BEM). We use a non-linear programming algorithm to calculate the pressures and the shape of the spillway. A computer-aided design package is developed on a PC using the equations describing the free surface, the BEM and standard optimization techniques. The input and output of the model are realized using graphical routines. Finally, we discuss the convergence and the computation time of the algorithms.     

Stoichiometrically controlled direct solid-state synthesis of C60H2

The direct solid-state synthesis of C₆₀H₂ has been demonstrated by controlling the amount of hydrogen introduced into the reaction with C₆₀. Palladium hydride has been used as the source of hydrogen. The main product 1,2-C₆₀ is the isomer predicted to have the lowest energy of the possible 23 isomers; in addition, small amounts of the thermodynamically most stable isomer of C₆₀H₄, 1,2,3,4-C₆₀H₄, have also been obtained.     

Closed queueing networks with batch services

In this paper we study queueing networks which allow multiple changes at a given time. The model has a natural application to discrete-time queueing networks but describes also queueing networks in continuous time. It is shown that product-form results which are known to hold when there are single changes at a given instant remain valid when multiple changes are allowed.     

Radiative and non-radiative decays from the excited state of Ti3+ ions in oxide crystals

The fluorescence spectra of Ti³⁺ in Y₃Al₅O₁₂ (YAG), Al₂O₃ (sapphire), YAlO₃ (YAP) observed at 10 K are composed of zero-phonon lines accompanied by the broad vibronic sidebands. The temperature dependence of the fluorescence lifetime and of the total intensity of the broadband measured in YAG and Al₂O₃ indicate that the radiative decay times from the excited states are nearly constant in the range 10–300 K. This demonstrates that the broadband radiative emissions in Ti³⁺:YAG and Ti³⁺:Al₂O₃ are due to magnetic dipole transitions or to electric dipole transitions induced by static odd-parity distortion, respectively. The decrease of the fluorescence lifetime with increasing temperature in Ti³⁺:YAG and Ti³⁺:Al₂O₃ is due to non-radiative decay from the excited state which occurs through phonon-assisted tunnelling between the excited and ground states. The radiative decay of Ti³⁺:YAP is enhanced with increasing temperature, indicating that radiative decay rate contains a term associated with odd-parity phonons. Nevertheless, a non-radiative decay rate of 3.6 × 10⁴ s^–1 observed in the temperature range 10–300 K is due to excited state absorption, which depopulates the excited state and quenches the fluorescence at the laser wavelength.