Smooth Solution of the Compressible Navier–Stokes Equations in an Unbounded Domain with Inflow Boundary Condition

The barotropic compressible Navier–Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution (u, p) of the system (1.1) in the Sobolev spaceH^{k + 3} × H^{k + 2}provided that the derivatives of the data of the problem are sufficiently small, wherek ≥ 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a linearized form of (1.1).     

A comparison of CCS tandem overload controls

In this paper we analyse issues associated with overloads in tandem switching systems in Common Channel Signalling (CCS) networks. In particular, we examine the need for, and effectiveness of, Automatic Congestion Control (ACC), a CCS mechanism which allows a congested switching system to inform adjacent CCS nodes of its level of overload, and subsequently controls the rate at which traffic is sent to the congested node. We demonstrate the critical need for end-offices and tandem switching systems to implement some form of ACC if network performance is to be maintained during congestion, especially in tandem exchanges. In addition, we find that the presently defined ACC should be expanded to allow more levels of congestion to be reported to adjacent nodes, so that a more effective, finer grained control is produced.     

On c‐Bhaskar Rao designs with block size 4

Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λ_min=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λ_min≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009     

Asymptotic packing via a branching process

It is shown that under certain side conditions the natural random greedy algorithm almost always provides an asymptotically optimal packing of disjoint hyperedges from a hypergraph H.     

One-pot synthesis of polysubstituted indoles from aliphatic nitro compounds under mild conditions

Polysubstituted indoles can be prepared directly from functionalized nitroalkanes under very mildly acidic conditions in a simple, one-pot, two-stage procedure.     

Model-based automated extraction of microtubules from electron tomography volume.

We propose a model-based automated approach to extracting microtubules from noisy electron tomography volume. Our approach consists of volume enhancement, microtubule localization, and boundary segmentation to exploit the unique geometric and photometric properties of microtubules. The enhancement starts with an anisotropic invariant wavelet transform to enhance the microtubules globally, followed by a three-dimensional (3-D) tube-enhancing filter based on Weingarten matrix to further accentuate the tubular structures locally. The enhancement ends with a modified coherence-enhancing diffusion to complete the interruptions along the microtubules. The microtubules are then localized with a centerline extraction algorithm adapted for tubular objects. To perform segmentation, we novelly modify and extend active shape model method. We first use 3-D local surface enhancement to characterize the microtubule boundary and improve shape searching by relating the boundary strength with the weight matrix of the searching error. We then integrate the active shape model with Kalman filtering to utilize the longitudinal smoothness along the microtubules. The segmentation improved in this way is robust against missing boundaries and outliers that are often present in the tomography volume. Experimental results demonstrate that our automated method produces results close to those by manual process and uses only a fraction of the time of the latter.     

Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices).     

Fabrication of material-independent morphology gradients for high-throughput applications

Gradient surfaces allow rapid, high-throughput investigations and systematic studies in many disparate fields, including biology, tribology and adhesion. We describe a novel method for the fabrication of material-independent morphology gradients, involving a two-step process of particle erosion followed by a chemical polishing procedure that preferentially removes features with a small radius of curvature as a function of time. Gradients are fabricated on aluminium surfaces, but they may be readily transferred to other materials via a replication technique, which allows for the production of identical roughness gradient samples with any chosen surface chemistry. The gradients have been characterized by means of scanning electron microscopy and optical profilometry. Standard roughness parameters (Ra, Rq, Rz, Sm and Sk) were calculated from optical profilometry data. The roughness has also been assessed over different wavelength windows by means of a fast Fourier transformation approach.