Inverse function,Taylor's expansion and extended Schröder's processes

Based on the Taylor's expansion of an inverse function, we extend the Schröder's process to find and improve high-order fixed-point iteration functions (IFs) for solving a nonlinear equation. We illustrate the extended processes by using them to find better iterative methods to compute the nth root and the logarithm of a strictly positive real number. IFs for inverse trigonometric function evaluations are also considered.     

Measurement of 76Se and 78Se (γ, n) Cross Sections

The (γ, n) cross sections of Se isotopes (⁷⁶Se,⁷⁸Se) were measured to supply fundamental data for estimating the inverse reaction cross section, i.e., the ⁷⁹Se(n, γ)⁸⁰Se cross section. The enriched samples and a reference ¹⁹⁷Au sample were irradiated with laser-Compton scattering (LCS) γ-rays. The excitation function of each (γ, n) cross section was determined for the energy range from each near neutron separation energy to the threshold energy of (γ, 2n) reaction. The energy point corresponding to each cross section was deduced using the accurately determined energy distribution of LCS γ-rays. Systematic (γ, n) cross sections for Se isotopes including ⁸⁰Se were compared with those calculated by using a statistical model calculation code TALYS.     

A Guass–Newton-like method for inverse eigenvalue problems

In this paper, we propose a Guass–Newton-like method for finding least-square solutions to inverse eigenvalue problems. We show that the proposed method converges under some mild conditions. In particular, if the method converges to the exact solution, the convergence rate is at least quadratic in the root sense. Numerical examples are given to justify the theoretical result.     

Two-stage iterations based on composite splittings for rectangular linear systems

In this paper, we introduce a two-stage method to solve rectangular linear systems that exhibits faster convergence than typical stationary iterative methods. Under suitable conditions, we prove convergence of the new method. The number of outer iterations can be reduced by using a few significant number of inner iterations for efficient computations. Further, we perform a comparison analysis, and establish that a higher number of inner iterations ensures a smaller spectral radius of the global iteration matrix. We also discuss the uniqueness of a proper splitting, and illustrate different comparison theorems for different subclasses of proper splittings.     

An extended inner–outer factorisation algorithm based on the structure of a transfer function matrix inverse

In this paper, the structure feature of the inverse of a multi-input/multi-output square transfer function matrix is explored. Instead of complicated advanced mathematical tools, we only use basic results of complex analysis in the analysing procedure. By employing the Laurent expression, an elegant structure form of the expansion is obtained for the transfer function matrix inverse. This expansion form is the key of deriving an analytical solution to the inner–outer factorisation for both stable plants and unstable plants. Different from other computation algorithm, the obtained inner–outer factorisation is given in an analytical form. The solution is exact and without approximation. Numerical examples are provided to verify the correctness of the obtained results.     

Image‐based Continuous Displacement Measurements Using an Improved Spectral Approach

Digital Image Correlation algorithms capable of determining continuous displacement fields are receiving growing attention in the field of mechanical properties identification. In this paper, we develop an Improved Spectral Approach (ISA) to reconstruct continuous displacements based on their Fourier decomposition. This approach leads to a time and memory‐efficient algorithm, thanks to the fast Fourier transform. Moreover, the Fourier‐based decomposition enables accurate heterogeneous measurements. Improvements consist in increasing the accuracy and convergence rate as well as dealing with non‐periodic displacements and images. Furthermore, a theoretical framework is presented to quantify the noise sensitivity of the ISA from which useful information is retrieved. The approach is evaluated using synthetic images deformed by heterogeneous displacement fields. Comparisons show that the introduced modifications lead to lower uncertainties by one order of magnitude in the case of non‐periodic images and displacement field studied. Moreover, first‐order (SO1) and second‐order (SO2) subset‐based Digital Image Correlation algorithms are compared with the ISA. The comparisons herein reveal that the uncertainties of the ISA are 6–9 times smaller than those of the SO1 due to insufficiency of the first‐order shape function for the estimation of heterogeneous displacements, while being slightly smaller than those of the SO2. Moreover, as the image smoothness decreases, the uncertainties of the SO2 deviate from those of the ISA and the exact displacements. The presented approach shows great potentials for challenging applications such as strain measurements at microstructural levels.     

Efficient non-linear model based predictive control

For a large number of degrees of freedom and/or large dimension systems, non-linear model based predictive control algorithms based on dual mode control can become intractable. This paper proposes an alternative which deploys the closed-loop paradigm that has proved to be very effective for the case of linear time-varying or uncertain systems. The various attributes and computational advantages of the approach are shown to carry over to the non-linear case.     

Dieaway Measurements of Fast Neutrons in an Iron Assembly using Californium-252

The fast transient behavior of the fast neutron population in an iron assembly immediately following the burst was measured by changing the energy response of the neutron detector with use made of ²⁵²Cf as a randomly pulsed source.

Comparison between experiment and calculation proved that this type of transient experiment would be useful for evaluating the method of calculation adopted in solving space-time-dependent problems.     

CO2激光作用对直流TIG电弧温度的影响

在CO<,2>激光垂直穿过TIG电弧条件下,对激光作用电弧前、后的电弧等离子体局部光谱特征进行了分析,并采用波尔兹曼图法计算了电弧局部电子温度,研究了激光对电弧等离子体轴向温度分布影响的基本规律.结果表明,激光作用电弧后,电弧等离子体的光谱特征保持不变,但整体辐射强度增加;从激光作用位置到阳极区间的电弧温度升高,而靠近...