含各向异性左手材料的一维Thue-Mores准周期结构的反射带隙

采用传输矩阵法,研究了由各向同性右手材料和各向异性左手材料组成的Thue-Morse准周期结构的反射带隙,分析了入射角、偏振和晶格比例缩放因子对反射带隙的影响.结果表明该结构存在一个全方向反射带隙,该带隙的宽度由TE模的低频带边缘和TM模的高频带边缘决定.当在该结构中插入一层缺陷时,在全方向带隙中出现一条缺陷模.对TE模,缺陷模的位置受入射角的影响很弱,而对TM模,缺陷模的位置随入射角的增大,向高频方向移动.     

确定性矩阵可分离压缩成像

针对可分离压缩传感使用的可分离随机正交矩阵在处理大尺度图像等高维信号感知时难度太大或成本过高的问题,引入确定性测量矩阵,提出确定性矩阵可分离压缩传感,可将如托普利兹矩阵及循环矩阵等具有确定性结构的矩阵作为可分离压缩传感的左、右可分离矩阵.该方案可以降低独立元素的数目,从而显著降低前端物理实现的难度与成本.数值模拟实验分别评估了该方法在不同采样率及不同图像尺寸下的压缩重建性能,结果表明该方法在独立元素非常少的情形下得到与原随机正交矩阵相近的重建质量,证明了其可行性.     

Dual-modality and dual-energy gamma ray densitometry of petroleum products using an artificial neural network

The prediction of volume fractions in order to measure the multiphase flow rate is a very important issue and is the key parameter of multi-phase flow meters (MPFMs). Currently, the gamma ray attenuation technique is known as one of the most precise methods for obtaining volume fractions. The gamma ray attenuation technique is based on the mass attenuation coefficient, which is sensitive to density changes; density is sensitive in turn to temperature and pressure fluctuations. Therefore, MPFM efficiency depends strongly on environmental conditions. The conventional solution to this problem is the periodical recalibration of MPFMs, which is a demanding task. In this study, a method based on dual-modality densitometry and artificial intelligence (AI) is presented, which offers the advantage of the measurement of the oil–gas–water volume fractions independent of density changes. For this purpose, several experiments were carried out and used to validate simulated dual modality densitometry results. The reference density point was established at a temperature of 20 °C and pressure of 1 bar. To cover the full range of likely density fluctuations, four additional density sets were defined (at changes of ±4% and ±8% from the reference point). An annular regime with different percentages of oil, gas and water at different densities was simulated. Four features were extracted from the transmission and scattered detectors and were applied to the artificial neural network (ANN) as inputs. The input parameters included the ²⁴¹Am full energy peak, ¹³⁷Cs Compton edge, ¹³⁷Cs full energy peak and total scattered count, and the outputs were the oil and air percentages. A multi-layer perceptron (MLP) neural network was used to predict the volume fraction independent of the oil and water density changes. The obtained results show that the proposed ANN model achieved good agreement with the real data, with an estimated root mean square error (RMSE) of less than 3.     

Iterative approximation of fixed points of Prešić operators on partial metric spaces

We study the convergence of the Pre?i? type k‐step iterative method for a class of operators satisfying Pre?i? type contractive conditions on the setting of partial metric spaces. Some examples are presented to illustrate our obtained results. As applications of the presented convergence theorems, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.     

Exponential moments of first passage times and related quantities for Lévy processes

For a Lévy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval , the sojourn time in the interval , and the last exit time from . Moreover, whenever these quantities are finite, we derive their respective asymptotic behavior as .     

Limit circle invariance for two differential systems on time scales

In this paper we consider two linear differential systems on a time scale. Both systems depend linearly on a complex spectral parameter λ. We prove that if all solutions of these two systems are square integrable with respect to a given weight matrix for one value λ₀, then this property is preserved for all complex values λ. This result extends and improves the corresponding continuous time statement, which was derived by Walker (1975) for two non‐hermitian linear Hamiltonian systems, to appropriate differential systems on arbitrary time scales. The result is new even in the purely discrete case, or in the scalar time scale case, as well as when both time scale systems coincide. The latter case also generalizes a limit circle invariance criterion for symplectic systems on time scales, which was recently derived by the authors.     

The Green function for the mixed problem for the linear Stokes system in domains in the plane

We construct the Green function for the mixed boundary value problem for the linear Stokes system in a two‐dimensional Lipschitz domain.     

Nash equilibrium strategies for a defined contribution pension management

This paper studies the time-consistent investment strategy for a defined contribution (DC) pension plan under the mean–variance criterion. Since the time horizon of a pension fund management problem is relatively long, two background risks are taken into account: the inflation risk and the salary risk. Meanwhile, there are a risk-free asset, a stock and an inflation-indexed bond available in the financial market. The extended Hamilton–Jacobi–Bellman (HJB for short) equation of the equilibrium value function and the verification theorem corresponding to our problem are presented. The closed-form time-consistent investment strategy and the equilibrium efficient frontier are obtained by stochastic control technique. The effects of the inflation and stochastic income on the equilibrium strategy and the equilibrium efficient frontier are illustrated by mathematical and numerical analysis. Finally, we compare in detail the time-consistent results in our paper with the pre-commitment one and find the distinct properties of these two results.     

Extended Gerber–Shiu functions in a risk model with interest

We consider a compound Poisson risk model with interest. The Gerber–Shiu discounted penalty function is modified with an additional penalty for reaching a level above the initial capital. We show that the problem can be split into two independent problems; an original Gerber–Shiu function and a first passage problem. We also consider the case of negative interest. Finally, we apply the results to a model considered by Embrechts and Schmidli (1994).