Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines

In this paper we propose some improvements to a recent decomposition technique for the large quadratic program arising in training support vector machines. As standard decomposition approaches, the technique we consider is based on the idea to optimize, at each iteration, a subset of the variables through the solution of a quadratic programming subproblem. The innovative features of this approach consist in using a very effective gradient projection method for the inner subproblems and a special rule for selecting the variables to be optimized at each step. These features allow to obtain promising performance by decomposing the problem into few large subproblems instead of many small subproblems as usually done by other decomposition schemes. We improve this technique by introducing a new inner solver and a simple strategy for reducing the computational cost of each iteration. We evaluate the effectiveness of these improvements by solving large-scale benchmark problems and by comparison with a widely used decomposition package.     

在一个新步长规则下梯度投影算法的全局收敛性

考虑约束最优化问题：minx∈Ωf(x)其中:f:R^n→R是连续可微函数，Ω是一闭凸集。本文研究了解决此问题的梯度投影方法，在步长的选取时采用了一种新的策略，在较弱的条件下，证明了梯度投影响方法的全局收敛性。     

Shear banding in strained semicrystalline polyamide 6 films as revealed by atomic force microscopy: Role of the amorphous phase

Atomic force microscopy (AFM) has been used to visualize the plastic deformation mechanisms that are responsible for the yielding of semicrystalline polymers of low degree of crystallinity (<50%). Indeed, AFM, if operated in suitable conditions, is able to image both the amorphous and the crystalline phases. Polyamide 6 films have been drawn at temperatures T < 160 °C. Postmortem AFM observations show that, at yield, shear bands nucleate and propagate in the amorphous phase. They cross the crystalline lamellae and run over the whole surface of the sample. By crossing the lamellae, they form nanoblocks of uniform size. Neither the size of the nanoblocks nor the angle between the tensile axis and the shear bands can be explained in terms of crystal plasticity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 687–701, 2004     

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.     

Using the gradients of temperature and internal parameters in Continuum ThermodynamicsIntroduction des gradients de température et de paramètres internes en Thermodynamique des Milieux Continus

In this paper, the possibility of using the gradients of the temperature and of the internal parameters as additional state variables in Continuum Thermodynamics is considered. The expressions of the two principles are discussed and Clausius–Duhem inequality is derived under an appropriate statement of the internal entropy production. Several formulations are proposed and compared to existing results in the literature. To cite this article: P. Ireman, Q.S. Nguyen, C. R. Mecanique 332 (2004).     

Fabricating tunable nanoparticle density gradients with the contact printing based approach

Recently, the generation of spatial gradient nanoparticle assemblies has attracted much attention. Such assemblies can be intriguing templates for building novel molecular architectures, and be employed as a combinatorial tool for quick determination of interaction selectivity for nanoparticles. In this communication, we report on convenient contact printing based techniques for generating lateral gradients containing nanoparticles with tunable geometry, scale and steepness. In the first method, octadecyltrichlorosilane (OTS) gradient surfaces were generated via the contact printing approach, and then spaces un-occupied by OTS molecules were back-filled with an amine-terminated silane, which allows the grafting of nanoparticles that were surface functionalized with carboxylic acid. By varying the size and geometry of the stamp, different geometrical gradients were generated. In addition, by changing the stamping procedures, either well-defined stepwise gradients or continuous gradients can be achieved. Furthermore, the contact printing based technique can be utilized in combination with diffusion of the aminosilane molecules to directly create its gradient, and consequently a nanoparticle density gradient.     

Capacity factors and peak widths in the gradient elution reversed phase separation of high molar mass polystyrenes

Summary A simplex method for determining the constantsS andk _o from the equation lnk’=lnk _o−S ϕ (was developed and applied to the reversed phase separation of high molar mass polystyrenes using gradients of any curvature. Experimental retention times described using the equation had a standard deviation of 1.1%. The inclusion of a quadratic term in the equation was found to be unwarranted. BothS and lnk _o varied linearly with ln molar mass. The logarithm of peak width of an eluting polystyrene peak was found to be a linear function of the mobile phase composition at elution. The slope was equal toS.