Practical Kedem-Katchalsky equations and their modification

The research problem presented in this work concerns modification of the Kedem-Katchalsky (K-K) equation for volume flow (J _v ) through system (h|M|l), consisting of a membrane M and boundary layers h and l. Such boundary layers appear in the vicinity of the membrane on both sides due to the lack of mixing of solutions. This paper also includes the derivation of the equation for volume flow (J _vr ) dissipated on concentration boundary layers h and l. The derivation of these equations concerns the case in which the substance transport through the membrane is generated by the osmotic pressure gradient . On the basis of the equations for the volume flows (J _v ) and (J _vr ), some calculations for a nephrophane membrane, used in medicine, and for aqueous glucose solutions have been carried out. In order to test the equations for (J _v ) and (J _vr ), we have also carried out calculations for the volume flow (J′ _v ) that is transferred through the membrane in the case of mixed solutions on both sides of the membrane. This volume flux has been calculated on the basis of the original (K-K) equation. The results are presented in Fig. 2.      

荧光偏振法研究脉冲电场对酿酒酵母细胞膜流动性影响

以DPH(1,6-二苯基-1,3,5-己三烯)为荧光探剂,采用荧光偏振法探讨了脉冲电场(0～25 kV·cm-1,0～266 ms)对酿酒酵母细胞膜流动性影响。经5 kV·cm-1电场处理后,酿酒酵母细胞膜的流动性显著减小,并且随电场强度和处理时间的增加而减小;通过平板计数法和紫外分光光度计法分别检测了脉冲电场对酿酒酵母细胞存活对数及膜通透性影响。结果显示,5 kV·cm-1虽然只能使少量的酵母致死,却能使酵母细胞膜的通透性显著增加,膜流动性显著降低。并且细胞的存活率随电场强度增大而减小,细胞膜的通透性随电场强度增大而增大。这表明细胞膜的流动性降低与细胞膜的通透性升高成正相关,与细胞的存活率成负相关。由此推测脉冲电场在对酿酒酵母灭菌过程中,细胞膜是其作用的一个关键位点,膜流动性减小,细胞膜通透性增强,是细胞死亡的主要原因。     

利用偏振度研究散射介质浓度及杂质比的数值分析

为了研究散射介质的粒子数浓度对散射光偏振度的影响以及杂质混合比与目标偏振度的关系,求解了当激光器输出波长处于近红外波段806 nm时目标的米勒矩阵及偏振度的数值解,结果表明偏振度随散射介质粒子数浓度的变化十分显著;通过建立混合目标模型,讨论了杂质比与偏振度的数值关系,并对目标的偏振度进行了归一化,而且实现了由归一化偏振度对杂质混合比的反演。本文的研究结果为利用散射光偏振度研究大气遥感提供了新的途径。     

Damage Evolution Modelling for Rock Materials Based on the Principle of Least Energy Dissipation Rate within Irreversible Thermodynamics

The nonlinear mechanical behavior of rock significantly influences the design and construction of underground structures. Due to the complexity and diversity of the damage mechanisms of rock, the damage variable directly defined by partial-damage mechanisms is insufficient in reflecting the progressive-failure process of rock comprehensively. So, in this paper, a novel damage variable is introduced into the plastic-strain rate based on the theoretical framework of irreversible thermodynamics to overcome this defect. The general expression is derived according to the least energy dissipation rate principle. The proposed damage variable can represent the irreversible energy dissipation process and has a strictly theoretical basis in mechanics. Moreover, the granite and marble stress-strain curves are simulated and compared with the Lemaitre damage model, Mazars damage model, and statistical damage model. The results show that the form of the proposed damage variable is practical and straightforward and can better reflect the entire stress-strain relationship of rock. Furthermore, the initial value of the inelastic response strain can be given directly through the proposed damage variable. The model presented here can overcome the issue that the current models need to select the damage threshold indirectly or assume it in advance and ensures that the damage evolution characteristics follow the first principle entirely.     

Dynamic Weight Strategy of Physics-Informed Neural Networks for the 2D Navier–Stokes Equations

When PINNs solve the Navier–Stokes equations, the loss function has a gradient imbalance problem during training. It is one of the reasons why the efficiency of PINNs is limited. This paper proposes a novel method of adaptively adjusting the weights of loss terms, which can balance the gradients of each loss term during training. The weight is updated by the idea of the minmax algorithm. The neural network identifies which types of training data are harder to train and forces it to focus on those data before training the next step. Specifically, it adjusts the weight of the data that are difficult to train to maximize the objective function. On this basis, one can adjust the network parameters to minimize the objective function and do this alternately until the objective function converges. We demonstrate that the dynamic weights are monotonically non-decreasing and convergent during training. This method can not only accelerate the convergence of the loss, but also reduce the generalization error, and the computational efficiency outperformed other state-of-the-art PINNs algorithms. The validity of the method is verified by solving the forward and inverse problems of the Navier–Stokes equation.     

Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations

In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair Xh×Mh. The method consists of transmitting the finite element solution (uh,ph) of the 3D steady Navier–Stokes equations into the finite element solution pairs (uhn,phn) based on the finite element space pair Xh×Mh of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair Xh×Mh satisfies the discrete inf-sup condition in a 3D domain Ω. Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution (uhn,phn) of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to (σ,h) of the FE solution (uhn,phn) to the exact solution (u,p) of the 3D steady Navier–Stokes equations in the H1−L2 norm. Finally, we also give the convergence order with respect to (σ,h) of the FE velocity uhn to the exact velocity u of the 3D steady Navier–Stokes equations in the L2 norm.     

Lanczos Potential for the van Stockung Space-Time

The Lanczos Potential is a theoretical useful tool to find the conformal Weyl curvature tensor C _abcd of a given relativistic metric. In this paper we find the Lanczos potential L _abc for the van Stockung vacuum gravitational field. Also, we show how the wave equation can be combined with spinor methods in order to find this important three covariant index tensor.     

固体核磁共振中膜蛋白双交叉极化效率与动力学参数相关的定量分析

固体核磁共振（NMR）中双交叉极化（DCP）是用于膜蛋白信号指认的多维异核相关实验的基本技术模块.DCP的效率在很大程度上决定了多维异核相关实验的效率.本文分析了3种典型的膜环境中的膜蛋白（AQPZ、DAGK和EV71 2B）的DCP效率及其影响因素.结果显示,在相同的实验条件下,3种蛋白样品的DCP效率存在明显差异：其中AQPZ的DCP效率最高（31%）,DAGK的效率次之（23%）,EV71 2B的效率最低（14%）.通过测量它们在旋转坐标下的自旋-晶格弛豫时间（T_1ρ）和偶极耦合常数（D_HN）,发现膜蛋白的运动会明显缩短T_1ρ,但对D_HN的影响较小.在实验的基础上,建立了T_1ρ与DCP效率相关的模型,并基于DCP动力学的定量分析,证明了运动导致的T_1ρ缩短是降低DCP效率的主要原因.因此,可以通过定量分析未知样品的T_1ρ来预测其DCP的最优效率,为DCP实验的优化提供依据.     

Comparative Analysis of Different Univariate Forecasting Methods in Modelling and Predicting the Romanian Unemployment Rate for the Period 2021–2022

Unemployment has risen as the economy has shrunk. The coronavirus crisis has affected many sectors in Romania, some companies diminishing or even ceasing their activity. Making forecasts of the unemployment rate has a fundamental impact and importance on future social policy strategies. The aim of the paper is to comparatively analyze the forecast performances of different univariate time series methods with the purpose of providing future predictions of unemployment rate. In order to do that, several forecasting models (seasonal model autoregressive integrated moving average (SARIMA), self-exciting threshold autoregressive (SETAR), Holt–Winters, ETS (error, trend, seasonal), and NNAR (neural network autoregression)) have been applied, and their forecast performances have been evaluated on both the in-sample data covering the period January 2000–December 2017 used for the model identification and estimation and the out-of-sample data covering the last three years, 2018–2020. The forecast of unemployment rate relies on the next two years, 2021–2022. Based on the in-sample forecast assessment of different methods, the forecast measures root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE) suggested that the multiplicative Holt–Winters model outperforms the other models. For the out-of-sample forecasting performance of models, RMSE and MAE values revealed that the NNAR model has better forecasting performance, while according to MAPE, the SARIMA model registers higher forecast accuracy. The empirical results of the Diebold–Mariano test at one forecast horizon for out-of-sample methods revealed differences in the forecasting performance between SARIMA and NNAR, of which the best model of modeling and forecasting unemployment rate was considered to be the NNAR model.     

Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator

With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. We arrive at a closed-form solution expressed through conditional moments, which can be extracted directly from time-series data with a finite sampling intervals. We provide all finite-time correction terms for parametric and non-parametric estimation of the Kramers–Moyal coefficients for discontinuous processes which can be easily implemented—employing Bell polynomials—in time-series analyses of stochastic processes. With exemplary cases of insufficiently sampled diffusion and jump-diffusion processes, we demonstrate the advantages of our arbitrary-order finite-time corrections and their impact in distinguishing diffusion and jump-diffusion processes strictly from time-series data.     

油雾浓度对激光偏振度的影响

基于斯托克斯矢量,通过测量偏振度,研究不同入射偏振态的激光分别在不同浓度油雾介质中传输后偏振特性的变化情况.实验采用波长为671nm和532nm的水平、45°、-45°、90°的线偏振光,使它们分别入射到5种不同浓度的油雾介质中,计算四种偏振态偏振光的偏振度变化情况.结果表明,在相同油雾浓度下,对于不同波长的激光,波长越长,线偏振度越高,然而每种波长随浓度的变化趋势是一样的;在相同波长情况下,随着浓度的改变,水平与垂直线偏振光的偏振度变化较大,可达50%,135°与45°线偏振光的偏振度变化较小,约为20%.     

About the Definition of the Local Equilibrium Lattice Temperature in Suspended Monolayer Graphene

The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case.     

Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogonality of eigenvectors. Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule.     

Numerical Analysis and Comparison of Four Stabilized Finite Element Methods for the Steady Micropolar Equations

In this paper, four stabilized methods based on the lowest equal-order finite element pair for the steady micropolar Navier–Stokes equations (MNSE) are presented, which are penalty, regular, multiscale enrichment, and local Gauss integration methods. A priori properties, existence, uniqueness, stability, and error estimation based on Fem approximation of all the methods are proven for the physical variables. Finally, some numerical examples are displayed to show the numerical characteristics of these methods.     

心肌膜电位的光学标测技术及实验研究

基于电压敏感染料膜电位光学标测的原理,建立了一套光标测系统,主要包括LED激发光源、以及由滤光片、CCD、A/D采集卡及计算机构成的荧光信号采集、处理部分.目前,整套系统已可自动完成图像采集、实时显示,以及部分后处理等工作,已获得兔心室组织细胞膜动作电位.另外,在建立系统的同时,研究了光学标测实验方法,对离体兔心脏急性缺血的主要电生理特征进行了标测实验,并结合仿真研究的结论说明了缺血后有效不应期时空异质性的存在以及组织中电兴奋传导速度的减慢是缺血导致折返性心律失常的主要机制.     

Solution of Duffin–Kemmer–Petiau Equation for the Step Potential

The Duffin–Kemmer–Petiau (DKP) equation for spin 0 and 1 in the pressence of the step potential is solved. The problem is reduced to the solution of an equation of Feshbach–Villars type.The reflection and transmission coefficients are correctly deduced. The Klein paradox persists and is discussed using the charge interpretation.     

Information Measures for Generalized Order Statistics and Their Concomitants under General Framework from Huang-Kotz FGM Bivariate Distribution

In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters γ1,…,γn are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics.     

Foundations of the Quaternion Quantum Mechanics

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.