Factorized-Sparse-Approximate-Inverse Preconditionings of Linear Systems with Unsymmetric Matrices

The paper considers the application of factorized-sparse-approximate-inverse (FSAI) preconditionings to linear algebraic systems with nonsingular unsymmetric coefficient matrices. Special attention is paid to methods for optimizing the sparsity pattern of such preconditioners. It is numerically demonstrated that the efficiency of FSAI preconditionings can be substantially improved by applying the so-called postfiltering and prefiltering in order to sparsify preconditioning matrices. Bibliography: 20 titles.     

Selective photorefractive scattering in LiNbO<Subscript>3</Subscript>:Rh crystals

Photorefractive scattering occurs in rhodium-doped lithium niobate crystals irradiated by coherent light. The photorefractive scattering has both wide-angle and selective components. The results of experimental investigation of selective photorefractive scattering in LiNbO₃:Rh crystals and calculation of the spatial structure of scattering are reported. The selective scattering is regarded as a kind of a frequency-degenerate fourwave vector interaction.     

Synthesis of broadband interference filters: II. Suppression of high reflection bands of the fourth,fifth, and sixth orders

The spectral properties of multilayer interference systems formed by multiple replication of the symmetric ternary period ABCBA are investigated. The problem of synthesis of structures with suppression of adjacent bands of high reflection of the fourth, fifth, and sixth orders among their spectral characteristics is solved. It is shown that there are only six variants of selection of the optical thicknesses of layers in a period. When the high reflection bands of the fourth, fifth, and sixth orders are suppressed, the high reflection band of the first order remains in only four cases. The values of refractive indices of layers for which the problem hasa solution are found. The refractive indices of layers in all six cases are described by different relations determining the dependence of the refractive index of one of the components on arbitrarily selected refractive indices of the other two components.     

用于机械振动实时监测的光纤光栅有源传感装置

把一对中心反射波长分别为1562.11nm和1562.71nm的光纤光栅粘贴在均质、等厚、等腰三角形悬臂梁上下表面作为环形腔光纤激光器端镜，当机械振动激励自由端时，通过观测激光输出脉冲，地施加于自由端的机械振动的频率进行了实时监测；观察两光栅波长漂移量差值的变化，可在0～6.1mm的范围内判断所测振动的振幅。低于100Hz时，实验结果与实际值基本吻合。     

An Efficient Numerical Model for Planar Spiral Inductor On-Chip

In this paper, a very useful numerical technique has been developed for analyzing the transient characteristics of a planar-spiral inductor on-chip. A locally conformal technique and an alternating-direction implicit scheme are applied to the finite-difference time-domain method. A formulation for solving three dimensional Maxwell’s equations is proposed. Using the proposed method, various parameters of the planar-spiral inductors have been analyzed and an equivalent circuit, which includes frequency-independent circuit elements, has been introduced. Highly computational efficiency is implemented. Numerical results show excellent agreement with the measured data over a wide frequency range.     

Patterns—a fundamental idea of mathematical thinking and learning

Taking advantage of patterns is typical of our everyday experience as well as our mathematical thinking and learning. For example a working day or a morning at school displays a certain structure, which can be described in terms of patterns. On the one hand regular structures give us the feeling of permanence and enable us to make predictions. On the other hand they also provide a chance to be creative and to vary common procedures. School students usually encounter patterns in math classes either as number patterns or geometric patterns. There are also patterns that teachers can find in analyzing the errors students make during their calculations (error patterns) as well as patterns that are inherent to mathematical problems. One could even go so far as to say that identifying and describing patterns is elementary for mathematics (cf. Devlin 2003). Practising good interacting with patterns supports not only the active learning of mathematics but also a deeper understanding of the world in general. Patterns can be explored, identified, extended, reproduced, compared, varied, represented, described and created. This paper provides some examples of pattern utilization and detailed analyses thereof. These ideas serve as “hooks” to encourage the good use of patterns to facilitate active learning processes in mathematics.     

Dielectric investigations of associate formation process in thin nitrobenzene interlayers formed between metal substrates

Studies of thickness and temperature dependencies of the dielectric susceptibility of nitrobenzene interlayers formed on conductive substrates were carried out. The obtained data were processed under the assumption of the existence of dimers (with opposite directions of molecular dipole moments) in orientationally ordered wall-adjacent layers. The results were treated on the basis of Lifshits theory.     

The thermodynamic properties of Ln2BaO4 (Ln = Sm, Dy, Ho)

The thermodynamic properties of the Ln₂BaO₄ phases (Ln = Dy, Ho, Sm) were studied by the electromotive force method with a fluoride electrolyte (890–1180 K), solution calorimetry in 1.07 N hydrochloric acid at 298.15 K, and differential scanning calorimetry (298–860 K). The experimental data were jointly processed, and the thermodynamic functions of the compounds over the temperature range 298–1200 K were calculated.     

Thermal conductivity of crystalline chrysotile asbestos

The thermal conductivity of crystalline chrysotile asbestos made up of hollow tubular Mg₃Si₂O₅(OH)₄ filaments is measured in the range 5–300 K. The paper discusses the possibility of using this material in studies of the thermal conductivity of thin filaments of metals and semiconductors incorporated into the channels of crystalline chrysotile asbestos tubes.     

Effect of ion impinging on the microstructure and field emission of carbon nanotubes

Effects of ion impinging on the microstructure and field electron emission properties of screen-printed carbon nanotube films were investigated. We observed that the plasma treatment modified the microstructure of CNTs along with the remarkable increase of emission site density. With the prolongation of ion impinging time, the emission current falls down first, and then rises up to higher than that of the untreated films. It is proposed that the change of emission characteristics is due to the different emission mechanisms. After the treatment, electrons are emitted predominantly from the nano-nodes on the tube wall instead from the nanotube tips.