A modification of Armijo's step-size rule for negative curvature

Armijo's step-size procedure for function minimization is modified to include second derivative information. Accumulation points using this procedure are shown to be stationary points with positive semi-definite Hessian matrices.This research was supported by the United States Army Research Office.     

X-ray diffraction measurements on PE 2000 between 10 K and 300

Summary It was possible to obtain film exposures of the WAXS-diagram (2 50°) of a PE-fraction in the temperature range from 10 K to 300 K by using a special low temperature Guinier-chamber. The crystallographica-,b-andc-axis has been calculated from the positions of all reflexions. The different behaviour of their expansion coefficients can be explained by activation of rotational- and torsional-vibrations. If we take the number of net planes as constant and consider a temperature-independent part resulting from paracrystalline disorder (built up during crystallization), we can describe the linear increasing of the integral widths of the reflexions with decreasing temperature (10 ... 100%) with building up of inherent stresses inside the crystals.

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Zusammenfassung Eine spezielle Tieftemperatur-Guinier-Kammer ermöglichte es, Filmaufnahmen der Röntgenweitwinkelstreukurve (2 50°) einer hochkristallinen Polyäthylen-Fraktion im Bereich von ca. 10 K bis 300 K zu erhalten. Das unterschiedliche Temperaturverhalten der Ausdehnungskoeffizienten der kristallographischena-,b- undc-Achse, berechnet aus der Lage aller auswertbaren Reflexe, kann durch Anregung von Torsions- und Rotationsschwingungen erklärt werden. Unter der Annahme konstanter Kristallitgrößen sowie eines temperaturunabhängigen parakristallinen Gitterstörungsanteils (hervorgerufen durch Defekteinbau bei der Kristallisation), kann die starke Zunahme der integralen Breiten der Reflexe (bis ca. 100%) zu tiefen Temperaturen auf Eigenspannungen in den Kristalliten zurückgeführt werden.

     

Effects on the Thermal Properties and Bioactivity of Substitution of CaO by M2O3 (M=La, Y, Al) in Wollastonite Glass

The effects on the thermal properties and bioactivity of the substitution of CaO by La₂O₃, Y₂O₃ and Al₂O₃ in a glass of composition CaO·SiO₂ were studied and compared. The trivalent metal oxides were all effective in raising the glass transformation and softening temperatures when they replaced CaO in the glass of composition CaO·SiO₂. The experimental results suggest that Al₂O₃ plays the role of a glass-former, while La₂O₃ and Y₂O₃ behave as glass-modifiers. The tendency to devitrify appears to be the lower, the farther the glass composition is from those of the crystalline phases, owing to the need for diffusion over longer distances, the greater the composition difference. The substitution with the trivalent metal oxides is detrimental to the bioactivity, which is preserved only in the event of very small degrees of substitution. The most negative role appears to be played by Al₂O₃. This revised version was published online in July 2006 with corrections to the Cover Date.     

A semi-oriented radial measure for measuring the efficiency of decision making units with negative data,using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.     

A curvilinear method based on minimal-memory BFGS updates

We present a new matrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids the storage and the factorization of any matrix. We propose a modification of the L-BFGS method in which no information is kept from old iterations, so that memory requirements are minimal. The proposed algorithm incorporates a curvilinear path and a linesearch procedure, which combines two search directions; a memoryless quasi-Newton direction and a direction of negative curvature. Results of numerical experiments for large scale problems are also presented.     

一种新型左手材料的设计和特性研究

通过对左手材料的理论分析,设计了一种宽频带左手材料结构单元.该结构单元由一个矩形闭合环和十字型结构构成的谐振器和金属线组合而成.这种新结构中的谐振器实现负磁导率,金属线实现负介电常量,经过合理的设计,可以在某一频段内使得磁导率和介电常量同时为负,即具有负的有效折射率和正的波阻抗.数值仿真结果表明:在其工作频段内存在一个通带并且在17.6～29.0 GHz频率范围内折射率实部为负,而虚部接近于零;同时在该频率范围内波阻抗实部大于零,从而说明了该左手材料具有左手特性.除此之外,相对左手带宽达到48.9％,远远优于传统的左手材料.     

Negative viscosity due to magnetic properties of a non-dilute suspension composed of ferromagnetic rod-like particles with magnetic moment normal to the particle axis

The negative viscosity of a colloidal dispersion composed of ferromagnetic rod-like particles, which have a magnetic moment normal to the particle axis, have been investigated. A simple shear flow problem has been treated to clarify the particle orientational distribution and rheological properties of such a semi-dense dispersion, under circumstances of an external magnetic field applied in the direction normal to the shear plane of a simple shear flow. The results obtained here are summarized as follows. For the cases of a very strong magnetic field and magnetic interactions between particles, the magnetic moment of the rod-like particles is significantly restricted in the magnetic field direction, so that the particle approximately aligns in the shear flow direction. Also, the particle can easily rotate around the axis of the cluster almost freely even in a simple shear flow. Characteristic orientational properties of the particle cause negative viscosity, as in the previous study for a dilute dispersion. However, magnetic particle-particle interactions have a function to make such negative viscosity decrease.