某型机进近段高精度相对姿态实时测量技术

某型机在飞行训练过程中，进近段的二维相对姿态数据对于该型机安全着陆有着至关重要的作用。基于无线网络电台的双向数据传输系统能够实时获取进近段飞机相对理想着陆点的水平、垂直相对位置数据。通过上行链路上传着陆点的姿态数据，下行链路实时下传动动差分后的差分数据,最后在中心控制站进行二次数据处理。该技术获得的进近段二维相对姿态精度达到厘米级，满足飞行训练的需求。同时结合飞机显控数据以及视景图，以多角化动态关联的方式将实时获取的姿态数据等呈现给指挥员，更好地辅助指挥员进行着陆指挥工作。     

Properties of bounded stochastic processes employed in biophysics

Abstract

Realistic stochastic modeling is increasingly requiring the use of bounded noises. In this work, properties and relationships of commonly employed bounded stochastic processes are investigated within a solid mathematical ground. Four families are object of investigation: the Sine-Wiener (SW), the Doering–Cai–Lin (DCL), the Tsallis–Stariolo–Borland (TSB), and the Kessler–Sørensen (KS) families. We address mathematical questions on existence and uniqueness of the processes defined through Stochastic Differential Equations, which often conceal non-obvious behavior, and we explore the behavior of the solutions near the boundaries of the state space. The expression of the time-dependent probability density of the Sine-Wiener noise is provided in closed form, and a close connection with the Doering–Cai–Lin noise is shown. Further relationships among the different families are explored, pathwise and in distribution. Finally, we illustrate an analogy between the Kessler–Sørensen family and Bessel processes, which allows to relate the respective local times at the boundaries.     

Analytical solution of stochastic differential equation by multilayer perceptron neural network approximation of Fokker–Planck equation

The Fokker–Planck equation is a useful tool to analyze the transient probability density function of the states of a stochastic differential equation. In this paper, a multilayer perceptron neural network is utilized to approximate the solution of the Fokker–Planck equation. To use unconstrained optimization in neural network training, a special form of the trial solution is considered to satisfy the initial and boundary conditions. The weights of the neural network are calculated by Levenberg–Marquardt training algorithm with Bayesian regularization. Three practical examples demonstrate the efficiency of the proposed method.     

无绝缘高温超导双饼线圈的瞬态电热特性分析

无绝缘高温超导线圈具有良好的电热稳定性和机械紧凑性,但其充电过程中却有明显的磁场延迟现象。为详细了解无绝缘高温超导线圈励磁过程的瞬态特性,建立了无绝缘高温超导线圈的同轴圆环等效电路模型。通过绕制一个670匝的无绝缘高温超导双饼线圈,在液氮温度下进行不同充电速率的励磁实验,初步验证了等效电路模型的正确性。基于该模型,针对线圈励磁过程的充电和恒流阶段,仿真得到了线圈各匝的径向电流分布规律和电热损耗特性。     

Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory

Abstract

This article contains the nonlocal elasticity theory to capture size effects in functionally graded (FG) nano-rod under magnetic field supported by a torsional foundation. Torque effect of an axial magnetic field on an FG nano-rod has been defined using Maxwell’s relation. The material properties were assumed to vary according to the power law in radial direction. The Navier equation and boundary conditions of the size-dependent FG nano-rod were derived by the Hamilton’s principle. These equations were solved by employing the generalized differential quadrature method (GDQM). Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. The effects of some parameters, such as inhomogeneity constant, magnetic field and small-scale parameter, were studied. As an important result of this study can be stated that an FG nano-rod model based on the nonlocal elasticity theory behaves softer and has smaller natural frequency.     

Eigenvalues of a Differential Operator and Zeros of the Riemann $\zeta$-Function

The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same.     

Turing patterns for a coupled two-cell generalized Schnakenberg model

ABSTRACT

We consider a system for a generalized Schnakenberg model, showing Turing pattern formation for a wide class of nonlinearities.     

Multi-variable special polynomials using an operator ordering method

Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.