Unidimensional continuous-variable quantum key distribution with discrete modulation

In this paper, we proposed an unidimensional continuous-variable quantum key distribution (CV-QKD) protocol with discrete modulation, which waives the necessity in one of the quadrature modulations and further simplified the implementation of the CV-QKD protocol. On the basis of the Heisenberg uncertainty relation, we analyze the boundary between the unphysical and physical region. Besides, we utilize a novel proof approach to achieve a lower bound valid of transmission distance. This scheme shows an available method to further simplified the implementation of the QKD.     

Discrete Fourier Transform Analysis of Chronoamperometric Currents Obtained Under Ultrasound

A discrete Fourier transform (DFT) technique was used to analyze chronoamperometric currents at a Pt microdisk electrode (Ø=15 μm) in an electrolyte containing [Fe(CN)₆]^3?/[Fe(CN)₆]^4? under ultrasound at a frequency of 26.3 kHz and the powers of 0–50 W. The currents were measured by a high‐speed data acquisition card. Considering the effects of acoustic vibrations and cavitations on the limiting currents, a microdisk electrode and a high frequency sampling (10 MHz) were used to collect the current signals to restrain the deviation of average from sampling period in other methods. The results show that the amplitudes at 0 Hz and 26.3 kHz are related to the decay of ultrasound at constant power output when the separation between sono‐horn and electrode increases, and also related to the reactant concentration at the same ultrasonic conditions. The frequency signals are always shown in frequency spectrum despite different ultrasonic conditions. The amplitudes reflect the intensity of ultrasound and the concentration of reactant in solution, so they can be called specific frequencies. This method can be used to analyze quantitatively the effects of ultrasound on electrochemical reaction, determine the reactant concentration and measure the distribution of ultrasonic intensity in a solution.     

轴对称弹性体扭转问题的无网格自然邻接点Petrov-Galerkin法

本文将无网格自然邻接点Petrov-Galerkin 法应用于轴对称弹性体扭转问题的求解．无网格自然邻接点Petrov-Galerkin 法采用自然邻接点插值构造试函数，并且采用三角形线性单元的形函数作为加权残值法的加权函数．自然邻接点插值构造的试函数满足Kronecker delta 函数性质，因此本质边界条件的施加十分方便．由于几何形状和边界条件的轴对称特点，原来的空间问题简化为二维问题求解，因此计算时只需要横截面上离散节点的信息．数值算例结果表明，所提出的方法对求解轴对称弹性体扭转问题是行之有效的．     

Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations

This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and two-phase granular systems, such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes. The unique capability of MR to not only image the solids’ distribution (voidage) but also the velocity of the particulate phase is clearly shown. It is demonstrated that MR can provide measurements over different length and time scales. With the MR equipment used for the studies summarized here, temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres, respectively. Besides providing crucial data required for an improved understanding of the underlying physics of granular flows, multi-scale MR measurements were also used to validate numerical simulations of granular systems. It is shown that predictions of time-averaged properties, such as voidage and velocity of the particulate phase, made using the Discrete Element Model agree very well with MR measurements.     

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

It is shown that, depending upon the orientation of the end tangents t₀,t₁ relative to the end point displacement vector p=p₁–p₀, the problem of G¹ Hermite interpolation by PH cubic segments may admit zero, one, or two distinct solutions. For cases where two interpolants exist, the bending energy may be used to select among them. In cases where no solution exists, we determine the minimal adjustment of one end tangent that permits a spatial PH cubic Hermite interpolant. The problem of assigning tangents to a sequence of points p₀,...,p_n in R³, compatible with a G¹ piecewise-PH-cubic spline interpolating those points, is also briefly addressed. The performance of these methods, in terms of overall smoothness and shape-preservation properties of the resulting curves, is illustrated by a selection of computed examples.     

一类排序问题的求解及效果评估

对一类排序问题给出了一种有效的排序方法.我们将该类排序问题中的属性分为正向属性和负向属性,建立了属性规范化处理的数学模型,得到属性之间无差异的偏好比重,并对偏好比重进行汇总,得到对象之间的排序.最后,利用带自然边界条件的三次样条插值的三弯矩算法对该排序方法进行误差估计.     

Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals

In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals.     

Efficient Laguerre and Hermite Spectral Methods for Odd-Order Differential Equations in Unbounded Domains

Laguerre dual-Petrov-Galerkin spectral methods and Hermite Galerkin spectral methods for solving odd-order differential equations in unbounded domains are proposed. Some Sobolev bi-orthogonal basis functions are constructed which lead to the diagonalization of discrete systems. Numerical results demonstrate the effectiveness of the suggested approaches.     

Linearization of the interaction principle: Analytic Jacobians in the “Radiant” model

In this paper we present a new linearization of the Radiant radiative transfer model. Radiant uses discrete ordinates for solving the radiative transfer equation in a multiply-scattering anisotropic medium with solar and thermal sources, but employs the adding method (interaction principle) for the stacking of reflection and transmission matrices in a multilayer atmosphere. For the linearization, we show that the entire radiation field is analytically differentiable with respect to any surface or atmospheric parameter for which we require Jacobians (derivatives of the radiance field). Derivatives of the discrete ordinate solutions are based on existing methods developed for the LIDORT radiative transfer models. Linearization of the interaction principle is completely new and constitutes the major theme of the paper. We discuss the application of the Radiant model and its linearization in the Level 2 algorithm for the retrieval of columns of carbon dioxide as the main target of the Orbiting Carbon Observatory (OCO) mission.