On a stochastic hyperbolic integro-differential equation

In this paper we study an initial-boundary-value problem for a hyperbolic integro-differential equation with random memory and a random noise. We establish the existence, uniqueness and exponential stability of solutions. Our method consists of finite-dimensional approximation and energy estimates.     

Numerical simulation on an interaction of a vortex street with an elliptical leading edge using an unstructured grid

An algorithm for a time accurate incompressible Navier–Stokes solver on an unstructured grid is presented. The algorithm uses a second order, three‐point, backward difference formula for the physical time marching. For each time step, a divergence free flow field is obtained based on an artificial compressibility method. An implicit method with a local time step is used to accelerate the convergence for the pseudotime iteration. To validate the code, an unsteady laminar flow over a circular cylinder at a Reynolds number of 200 is calculated. The results are compared with available experimental and numerical data and good agreements are achieved. Using the developed unsteady code, an interaction of a Karman vortex street with an elliptical leading edge is simulated. The incident Karman vortex street is generated by a circular cylinder located upstream. A clustering to the path of the vortices is achieved easily due to flexibility of an unstructured grid. Details of the interaction mechanism are analysed by investigating evolutions of vortices. Characteristics of the interactions are compared for large‐ and small‐scale vortex streets. Different patterns of the interaction are observed for those two vortex streets and the observation is in agreement with experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

A new joint model for longitudinal and survival data with a cure fraction

We develop a new joint cure rate model for longitudinal and survival data. The model allows for multiple longitudinal markers as well as a cure structure for the survival component based on the promotion time cure rate model, as described in Ibrahim et al. (Bayesian Survival Analysis, Springer, New York, 2001). Several characteristics and properties of the new model are discussed and examined. A real dataset from a melanoma clinical trial is given to demonstrate the methodology.     

Small zeros of quadratic forms with linear conditions

Given a quadratic form and M linear forms in N+1 variables with coefficients in a number field K, suppose that there exists a point in K^N+1 at which the quadratic form vanishes and all the linear forms do not. Then we show that there exists a point like this of relatively small height. This generalizes a result of D.W. Masser.     

A remark on the moduli field of a curve

We give a purely algebro-geometric proof of the fact that every nonsingular projective curve can be defined over a finite extension of its moduli field. This extends a result byWolfart [7] to curves over fields of arbitrary characteristic. Received: 30 November 2001     

Photo-orientation at liquid crystal—polymer interfaces

It is suggested that liquid crystal—polymer interfaces are coupled systems, in which the components mutually influence the orientational state of each other. The photo-orientation process at liquid crystal-polymer interfaces provides a striking example of such a coupling. Experiments show that the anisotropic structure generated by polarised light at a polymer surface is strongly affected by the phase of the liquid crystal covering the polymer. Photo-orientation is significantly more efficient when the liquid crystal is in the isotropic phase than when it exhibits orientational order. The observations are interpreted by assuming that in the smectic and nematic phases the liquid crystal stabilises to a large extent polymer chain-segments aligned parallel to the director, while it blocks the photo-induced formation of chain-segments in the perpendicular direction. Other situations, in which the coupling between the liquid crystal and the polymer can be important, are also discussed briefly.     

An isochore versal deformation theorem

We introduce a cohomological approach to isochore deformation problems. We use this formulation in order to prove an isochore versal deformation theorem for holomorphic function germs.     

Assignment of chemical shifts in benzohydroxamic acid and structure of its silylated derivatives by 15N enrichment

¹⁵N isotopic enrichment was necessary for the unequivocal assignment of the ¹H NMR lines to the protons in the NH–OH fragment of benzohydroxamic acid, BHXA, C₆H₅CONHOH, in dry dimethyl sulfoxide solutions. The assignment [δ(NH) = 11.21, δ(OH) = 9.01, ¹J(¹⁵N,¹H) = 102.2 Hz, ²J(¹⁵N,¹H) <1.5 Hz], which is opposite to that used by other authors, confirms the assignment extended to BHXA by Brown and co‐workers from the spectra of acetohydroxamic acid. The enrichment allowed also assignment of the ²⁹Si lines in the spectra of disilylated benzohydroxamic acid, (Z)‐tert‐butyldimethylsilyl N‐tert‐butyldimethylsilyloxybenzoimidate (2) and (Z)‐tert‐butyldiphenylsilyl N‐tert‐butyldiphenylsilyloxybenzoimidate (3), and confirmed structure of the monosilylated products, N‐tert‐butyldiphenylsilyloxybenzamide (4) and N‐tert‐butyldiphenylsilyloxy benzoimidic acid (5). Copyright © 2003 John Wiley & Sons, Ltd.     

NMR studies on a palladium(II) complex containing an incompletely coordinated facultative pentadentate Schiff base ligand

Palladium(II) dichloride reacts with 1,10‐bis(2‐pyrrolyl)‐2,5,9‐triaza‐1,9‐decadiene to give a [Pd(C₁₅H₂₀N₅)]Cl complex in which the ligand is four‐coordinated, leaving one pyrrole group dangling. By using COSY, gHSQC, gHMBC connectivities and NOE experiments it has been concluded that one linkage isomer exists in DMSO solution, in spite of the fact that different sets of N atoms of potentially pentadentate ligand might be involved in coordination, and that the three chelate rings in the complex cation are arranged in a sequence: five‐membered, six‐membered, five‐membered which is different from that (5–5–6) found by x‐ray studies on the related [Ni(C₁₅H₂₀N₅)]Cl compound. NMR studies allowed an unambiguous assignment of all ¹H and ¹³C NMR resonances for the complex. Results of x‐ray structural analysis of [Pd(C₁₅H₂₀N₅)](CH₃COO)H₂O supported the five‐membered, six‐membered, five‐membered ring sequence in the [Pd(C₁₅H₂₀N₅)]⁺ complex cation and show an E (trans) orientation of the dangling pyrrole group with respect to the metal center. Copyright © 2002 John Wiley & Sons, Ltd.