Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data

The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption on the initial temperature, there exists a global unique solution. No smallness conditions are imposed on the data. The global existence issues for infinite energy initial velocity, and for the Bénard system are also discussed.     

The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains

We study the regularity of the Navier-Stokes equations in arbitrary Lipschitz domains.     

The numerical simulation of a typical fluid-structure interaction problem

To determine the dynamic response of a structure under the influence of the fluid flow one must solve a coupled computational fluid dynamics (CFD) and computational structural dynamics (CSD) mathematical problem. This paper presents the comparison of two methods for the calculation of the fluid-structure interaction. The first one is of explicit-implicit type and uses a staggered time advancement of the fluid and structure problems. The second uses a fully implicit discretization in the physical time of the fluid-structure equations and an explicit advancement in the dual-time. The physical fluid-structure problem is accompanied by the equations of the mesh motion, which are written as for a pseudo-structural system with its own dynamics. Representative numerical results are presented for the two degrees of freedom tipical section in unsteady transonic flow. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coherent neural oscillations induced by weak synaptic noise

Nonlinear Dynamics - We analyze the effect of synaptic noise on the dynamics of the FitzHugh–Nagumo (FHN) neuron model. In our deterministic parameter regime, a limit cycle solution cannot...     

The nanotechnology patent thicket revisited

Despite all predictions and promises, nanotechnology still seems to be more of an emerging science than a fully fledged revolution. More often than not, the patent system is blamed for this, supposedly tangling up nanotechnology in an impenetrable thicket of exclusionary rights instead of setting it free. Drawing on methods of complex network analysis, we provide empirical evidence suggesting that, at least in Europe, there is actually no patent thicket present in nanotechnology. Yet, the situation appears to be different in the USA.     

The Gel’fand Problem for the Biharmonic Operator

We study stable and finite Morse index solutions of the equation ${\Delta^2 u = {e}^{u}}$ . If the equation is posed in ${\mathbb{R}^N}$ , we classify radial stable solutions. We then construct nonradial stable solutions and we prove that, unlike the corresponding second order problem, no Liouville-type theorem holds, unless additional information is available on the asymptotics of solutions at infinity. Thanks to this analysis, we prove that stable solutions of the equation on a smoothly bounded domain (supplemented with Navier boundary conditions) are smooth if and only if ${N \leqq 12}$ . We find an upper bound for the Hausdorff dimension of their singular set in higher dimensions and conclude with an a priori estimate for solutions of bounded Morse index, provided they are controlled in a suitable Morrey norm.     

Are signal intensity and homogeneity useful parameters for distinguishing between benign and malignant soft tissue masses on MR images?: Objective evaluation by means of texture analysis

Objectives

To objectively identify possible differences in the signal characteristics of benign and malignant soft tissue masses (STM) on magnetic resonance (MR) images by means of texture analysis and to determine the value of these differences for computer-assisted lesion classification.

Method

Fifty-eight patients with histologically proven STM (benign, n=30; malignant, n=28) were included. STM texture was analyzed on routine T1-weighted, T2-weighted and short tau inversion recovery (STIR) images obtained with heterogeneous acquisition protocols. Fisher coefficients (F) and the probability of classification error and average correlation coefficients (POE+ACC) were calculated to identify the most discriminative texture features for separation of benign and malignant STM. F>1 indicated adequate discriminative power of texture features. Based on the texture features, computer-assisted classification of the STM by means of k-nearest-neighbor (k-NN) and artificial neural network (ANN) classification was performed, and accuracy, sensitivity and specificity were calculated.

Results

Discriminative power was only adequate for two texture features, derived from the gray-level histogram of the STIR images (first and 10th gray-level percentiles). Accordingly, the best results of STM classification were achieved using texture information from STIR images, with an accuracy of 75.0% (sensitivity, 71.4%; specificity, 78.3%) for the k-NN classifier, and an accuracy of 90.5% (sensitivity, 91.1%; specificity, 90.0%) for the ANN classifier.

Conclusion

Texture analysis revealed only small differences in the signal characteristics of benign and malignant STM on routine MR images. Computer-assisted pattern recognition algorithms may aid in the characterization of STM, but more data is necessary to confirm their clinical value.     

Phenylethylene glycol-derived LpxC inhibitors with diverse Zn2+-binding groups

The Zn²⁺-dependent bacterial deacetylase LpxC is a promising target for the development of novel antibiotics. Most of the known LpxC inhibitors carry a hydroxamate moiety as Zn²⁺-binding group. However, hydroxamic acids generally exhibit poor pharmacokinetic properties. (S)-N-Hydroxy-2-{2-hydroxy-1-[4-(phenylethynyl)phenyl]ethoxy}acetamide (3) is a known phenylethylene glycol derivative potently inhibiting LpxC with a K_i of 66?nM. In vitro experiments have confirmed in silico predictions that the hydroxamate moiety of 3 is indeed metabolically labile. In this study, several strategies were explored to replace the hydroxamate moiety by other Zn²⁺-binding groups while maintaining target activity. In total, 15 phenylethylene glycol derivatives with diverse Zn²⁺-binding groups like carboxylate, hydrazide, carboxamide, sulfonamide, vicinal diol, thiol, thioester, and hydroxypyridinone moieties were prepared in divergent syntheses. However, their biological evaluation revealed that the replacement of the hydroxamate moiety of 3 by any of the investigated Zn²⁺-binding groups is detrimental for LpxC inhibitory and antibacterial activity.     

Construction of a bipotential for a multivalued constitutive law

Bipotentials are non smooth mechanics tools, which allows modelling various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). We answer the following question: given a graph M representing a material behaviour, is there a bipotential b for which M is the set of (x, y) such that b (x, y) = 〈x, y 〉? We state a simple necessary and sufficient condition for the existence of b. If it is fulfilled, we construct the bipotential. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)