Refraction holodiagrams and Snell's law

The refraction holodiagram RHD is analyzed here with respect to the law of refraction. Particularly, we study the surface that exactly conjugates by refraction a virtual point source with a real image or conversely. By using the total optical path as a parameter we build a diagram that consists in a family of Descartes ovals of the apple type that contains the Pascal's limaçon as a particular extreme case and the spherical surface with the Weierstrass points as another. These representations permit the straightforward application of Fermat's principle in the case of arbitrary refracting surfaces and show the shape of generalized Fresnel's zones in the intersections with any surface. Snell's law is applied to rays incident on the apple type surfaces to find out the conditions for exact conjugation. Sensitivity to optical path variations is also discussed. The RHD curves family can be represented in a Cartesian way where the ovals appear as equally spaced straight lines.     

Determination of flutter derivatives via a neural network approach

A neural-network-based method is offered to determine the flutter derivatives of section models under smooth and turbulent flows. The approach uses the observed dynamic responses to train an appropriate neural network. Subsequently, the modal parameters of the model for different mean velocities of wind flow are directly estimated using weight matrices in the neural network. The flutter derivatives can then be determined accurately. The validity of the present method is verified through numerical studies. Finally, the procedure is employed to process experimental data from an inverted-U-type section model, obtained from wind tunnel tests.     

两个回归函数相等的Bootstrap检验

两个回归参数相等性检验一直是统计界感兴趣的问题之一．在这篇文章中，四个检验统计量被用于度量两曲线的差异，在原假设下统计量的分布采用向量数据的重复抽样来逼近，并给出了—些模拟结果．     

Marking Games and the Oriented Game Chromatic Number of Partial <Emphasis Type="Italic">k</Emphasis>-Trees

 Nešetřil and Sopena introduced the concept of oriented game chromatic number. They asked whether the oriented game chromatic number of partial k-trees was bounded. Here we answer their question positively. Received: January 12, 2001 Final version received: February 25, 2002     

Self-Interactions of Strands and Sheets

Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness.     

Temperature-dependent magnetic moment in the MnAs-CrAs system

Magnetic susceptibilities have been measured for the mixed compounds Mn_1−xCr_xAs (0≤x≤1) and the compound MnP in the temperature region up to 1400 K. The _X¹_g vs. T curves of Mn_1−xCr_xAs follow the Curie-Weiss law only in the temperature region where the crystal structure is of the B8₁ type. Some important problems are pointed out from the data.     

Optical corrosion meter

In a previous study, a mathematical model relating surface and bulk behaviours of metals in aqueous solution has been developed. The model was established based on principles of holographic interferometry for measuring microsurface dissolution, i.e. mass loss, and on those of electrochemistry for measuring the bulk electronic current, i.e. corrosion current. In the present work, an optical corrosion meter was built based on the above model. The corrosion meter consists of an electrochemical cell in which the sample is immersed in aqueous solution. Furthermore, the corrosion meter has a holographic camera with a thermoplastic film for in situ processing of holograms in order to obtain real-time holographic interferoms of the sample in the electrochemical cell. Results of the present work indicate that optical holography is a very useful technique for measuring the corrosion current density of different alloys in aqueous solutions. As a result, the corrosion current density of aluminium, stainless steel, and low-carbon steel in 1 M KCl, 1 M NaCl, and 1 M NaOH solutions were obtained. A comparison between the corrosion data of samples showed that the corrosion current density of the stainless steel in 1 M NaCl is nearly three-folds higher than that of the aluminium in 1 M KCl and the low-carbon steel in 1 M NaOH.     

New critical dimensions forq-deformed bosonic string

Applying the mass shell condition forq-deformed open and closed strings, new critical space-time dimensions are derived. Supported by the Algerian Ministry of High Education and Research under contract N^oD2501/17/01/93. Permanent address.     

The gas dynamics of current-limiting devices during immobility time

The aim of this paper is to extend our knowledge about the gas-dynamic processes in arcs during immobility time. For this purpose, the conservation equations in a magnetohydrodynamic approximation were coupled with the thermochemical and Maxwell equations. Special features arc the introduction of dissociation and ionization of nitrogen and oxygen, and the simultaneous calculation of the distributions of current density and magnetic induction in the arc. Numerical calculations were performed with a reduced two-dimensional (2-D) time-dependent model. Results of the calculations were compared with measurements. The development in time of the measured and calculated are voltage and arc chamber pressure show very good agreement. The pumping effect of the double vortex in the arc region was confirmed by optical measurements. It is concluded that the three-layer model is a good representation for the main physical features during the immobility time, and that the presence of highly conducting gas in the downstream region of the arc is essential for its downstream movement