小学数学课堂教学中的思维训练——以“2、5、3的倍数的特征”为例

小学高年级数学教学,要注意通过合适的问题,引导学生进行深入的思考,领悟内在原理,得到必要的数学思维训练。“2、5、3的倍数的特征”的教学,不能只引导学生通过观察分析、归纳概括来发现规律、得到结论,还要通过问题链引导学生进一步搞清楚结论的内在原理,把握十进位值制记数法这一本质,体会数位分解这一思想方法。

Study on fast calibration of a ULA's gain and phase error

Array calibration is important in engineering practice. In this paper, fast calibration methods for a ULA's gain and phase errors both in far and near fields are proposed. In the far field, using a single sound source without exact orientation, this method horizontally rotates the array exactly once, performs eigen value decomposition for the covariance matrix of received data, then computes the gain and phase error according to the formulas. In the near field, using the same single sound source, it is necessary to rotate the array horizontally at most three times, build equations according to geometric relations, then solve them. Using the formula proposed in this paper, spherical waves are modified into plane waves. Then eigen values decomposition is performed. These two calibration methods were shown to be valid by simulation and are fast, accurate and easy to use. Finally, an analysis of factors influencing estimation precision is given.

Reflection full-waveform inversion using a modified phase misfit function

Reflection full-waveform inversion （RFWI） updates the low- and high- wavenumber components, and yields more accurate initial models compared with conventional full-waveform inversion （FWI）. However, there is strong nonlinearity in conventional RFWI because of the lack of low-frequency data and the complexity of the amplitude. The separation of phase and amplitude information makes RFWI more linear. Traditional phase-calculation methods face severe phase wrapping. To solve this problem, we propose a modified phase-calculation method that uses the phase-envelope data to obtain the pseudo phase information. Then, we establish a pseudophase-information-based objective function for RFWI, with the corresponding source and gradient terms. Numerical tests verify that the proposed calculation method using the phase-envelope data guarantees the stability and accuracy of the phase information and the convergence of the objective function. The application on a portion of the Sigsbee2A model and comparison with inversion results of the improved RFWI and conventional FWI methods verify that the pseudophase-based RFWI produces a highly accurate and efficient velocity model. Moreover, the proposed method is robust to noise and high frequency.

Super number roots and factorizations for a kind of polynomial

It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.

A dynamic problem on the edges of a mode Ι crack subjected to moving unit-step loads

By the theory of complex functions, a dynamic problem on the edges of a mode I crack subjected to moving unit-step loads are investigated. The Riemann-Hilbert problem is easily formulated by the ways of self-similar functions. The analytical solution obtained is rather simple and concise. After the solution was utilized by superposition theorem, the relevant solution on the case of arbitrary loading can be obtained.

Some Results on Position Restriction Scheduling Problems

In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj = 1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.

Design and Implementation of Image Encryption Method by Using Chaotic Mapping Based on Multi-layer Parameter Disturbance

Bit-plane decomposition makes images obtain a number of layers. According to the amount of data information, images are encrypted, and the paper proposes image encryption method with Chaotic Mapping based on multi-layer parameter disturbance. The advantage of multi-layer parameter disturbance is that it not only scrambles pixel location of images, but also changes pixel values of images. Bit-plane decomposition can increase the space of key. And using chaotic sequence generated by chaotic system with different complexities to encrypt layers with different information content can save operation time. The simulation experiments show that using chaotic mapping in image encryption method based on multi-layer parameter disturbance can cover plaintext effectively and safely, which makes it achieve ideal encryption effect.

Composition Operators from α-Bloch Spaces into Q_K Type Spaces

Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ: Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK(p,q) and QK,0(p,q) spaces are discussed, where 0 < α < ∞.