Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration

In this paper numerical approximation of history-dependent hemivariational inequalities with constraint is considered, and corresponding Céa’s type inequality is derived for error estimate. For a viscoelastic contact problem with normal penetration, an optimal order error estimate is obtained for the linear element method. A numerical experiment for the contact problem is reported which provides numerical evidence of the convergence order predicted by the theoretical analysis.     

An inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval

This paper is concerned with the inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval. Firstly, we give the definitions of generalized weight numbers for this operator which may have the multiple spectrum and then investigate the connections between the generalized weight numbers and other spectral characteristics. Secondly, we obtain the generalized spectral data, which consists of the generalized weight numbers and the spectrum. Then the operator is determined uniquely by the method of spectral mappings. Finally, we give an algorithm for reconstructing the potential function and the coefficients of the boundary conditions and the coefficients of the discontinuity conditions.     

New approach to identify the initial condition in degenerate hyperbolic equation

This paper deals with the determination of an initial condition in degenerate hyperbolic equation from final observations. With the aim of reducing the execution time, this inverse problem is solved using an approach based on double regularization: a Tikhonov’s regularization and regularization in equation by viscose-elasticity. So, we obtain a sequence of weak solutions of degenerate linear viscose-elastic problems. Firstly, we prove the existence and uniqueness of each term of this sequence. Secondly, we prove the convergence of this sequence to the weak solution of the initial problem. Also we present some numerical experiments to show the performance of this approach.     

Channel estimation and tracking with nested sampling for fast-moving users in millimeter-wave communication

Channel estimation is very challenging in millimeter-wave (mmWave) communications since the receiver is usually equipped with a limited number of radio-frequency (RF) chains and a large number of antennas. The receiver can only observe a low-dimensional projection of the received signals due to the huge gap between the numbers of RF chains and antennas. Instead of using the phase-shifter which is not a simple circuit at mmWave, we employ a switch network for analog design, which is equivalent to an antenna selection process. To increase the resolution and accuracy, a nested sampling strategy is used to formulate a virtual array with a larger aperture, aiming to reduce the complexity and power consumption of the system. We also consider the Doppler effect caused by the fast-moving user which may seriously deteriorate the channel estimation accuracy. Based on the covariance fitting criterion, a joint Doppler and channel estimation method is proposed without need of discretizing the angle space, and thus the model mismatch effect can be totally eliminated. Finally, we excavate the temporal variation law of the user to estimate the line-of-sight (LoS) channel in the current time slot by using the estimates from the previous two time slots. Numerical simulation results are provided to demonstrate the effectiveness and superiority of our proposed method.     

On global Hessenberg based methods for solving Sylvester matrix equations

In the first part of this paper, we investigate the use of Hessenberg-based methods for solving the Sylvester matrix equation $AX+XB=C$. To achieve this goal, the Sylvester form of the global generalized Hessenberg process is presented. Using this process, different methods based on a Petrov–Galerkin or on a minimal norm condition are derived. In the second part, we focus on the SGl-CMRH method which is based on the Sylvester form of the Hessenberg process with pivoting strategy combined with a minimal norm condition. In order to accelerate the SGl-CMRH method, a preconditioned framework of this method is also considered. It includes both fixed and flexible variants of the SGl-CMRH method. Moreover, the connection between the flexible preconditioned SGl-CMRH method and the fixed one is studied and some upper bounds for the residual norm are obtained. In particular, application of the obtained theoretical results is investigated for the special case of solving linear systems of equations with several right-hand sides. Finally, some numerical experiments are given in order to evaluate the effectiveness of the proposed methods.     

On the Barzilai-Borwein basic scheme in FFT-based computational homogenization

Building upon the equivalence of the basic scheme in the work of Moulinec and Suquet with gradient descent methods, we investigate the effect of using the celebrated Barzilai-Borwein step size selection technique in this context. We provide an overview of recent convergence theory and present efficient implementations in the context of computational micromechanics, with and without globalization. In contrast to polarization schemes and fast gradient methods, no lower bound on the eigenvalues of the material tangent is necessary for the Barzilai-Borwein scheme. We demonstrate the power of the proposed method for linear elastic and inelastic large scale problems with finite and infinite material contrast.     

Studying the effect of particle size on the antibacterial activity of some N-nicotinyl phosphoric triamides

Using ultrasonic top-to-down method, nanoparticles of two N-nicotinyl phosphoric triamides: C₅H₄NC(O)NHP(O)R, R?=?4-CH₃-NC₅H₁₀ (1), (CH₃)₃CNH₂ (2) were prepared for the first time and characterized by ³¹P, ¹³C, ¹H NMR, FTIR, scanning electron microscopy, energy dispersive X-ray. The average particle size of 1 and 2 were 60–70 and 40–50?nm, respectively, and the morphology was spherical for 1 and rod for 2. Solid state (powder) antibacterial effect of these compounds and two other similar reported ones, in their macro- and nanosizes, were evaluated with colony counting method on one Gram-positive (Staphylococcus aureus) and one Gram-negative (Escherichia coli) bacteria in Brain–Heart infusion culture medium. Results showed that all the macro- and nanosized compounds, except macrosized 1, were antibacterial and all nanoscaled ones had stronger antibacterial activity than their macroscaled analogues. The most effect of the particle size was observed for 1: by decreasing the particle sizes, the antibacterial activity state of 1 was changed from inactive (for macro) to potent (for nano).     

载气热提取法测定熔敷金属中扩散氢收集条件的探究

探究了GB/T 3965—2012《熔敷金属中扩散氢测定方法》中载气热提取法收集条件对测定扩散氢含量的影响,并与水银法进行了对比。研究结果表明,样本炉温设定为400℃,A型试块的内部温度大约在51 min时稳定在358℃左右,B型试块内部温度大约在27 min时稳定在391℃左右;载气热提取法电信号曲线收集结束点的电信号及斜率均接近0时获得的结果与水银法具有较好的一致性。