Exactness of penalization for exact minimax penalty function method in nonconvex programming

The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.

基于UHPLC-Q Exactive Orbitrap/MS结合多元统计方法分析不同基原淫羊藿化学成分的差异

目的:建立超高效液相色谱-四极杆-静电场轨道阱高分辨质谱联用(UHPLC-Q Exactive Orbitrap/MS)结合多元统计分析技术对5种不同基原淫羊藿化学成分差异分析的方法。方法:对5种基原30批淫羊藿样品的UHPLC-Q Exactive Orbitrap/MS全扫描数据进行多元统计分析。利用SIMCA软件进行主成分分析(PCA)和正交偏最小二乘法-判别分析(OPLS-DA)。结果:5种基原淫羊藿的化学成分具有差异性,根据相关参考文献及谱图信息,共鉴定出27种化学成分。所建立的OPLS-DA模型具有良好的数据描述能力和预测能力。柔毛淫羊藿化学成分具有显著性差异,而朝鲜淫羊藿与箭叶淫羊藿,淫羊藿与巫山淫羊藿之间的化学成分及含量具有相似性。经过筛选与分析,确定8种差异化学成分。结论:建立的方法可分析出5种基原淫羊藿化学成分的差异性,操作简便,方法准确,可为不同基原淫羊藿的质量控制及开发应用提供理论依据。

参仙升脉口服液化学成分的UHPLC-Q Exactive Focus MS/MS快速分析

目的探究参仙升脉口服液的化学物质基础。方法利用超高效液相色谱-四极杆/静电场轨道阱高分辨质谱(UHPLC-Q Exactive Focus MS/MS)对参仙升脉口服液的化学成分进行整体、系统辨识。采用Thermo Accucore aQ C_(18)色谱柱(150 mm×2.1 mm,2.6μm),流动相0.1%甲酸水溶液(A)-甲醇(B)梯度洗脱,洗脱程序为0-13 min,5%-60%B;13-27 min,60%-95%B;27-30 min,95%B,流速0.3 mL·min^(-1),柱温30°C;质谱分析离子化方式为加热电喷雾离子化(H-ESI),扫描模式为正、负离子切换,扫描范围m/z 120-1800,碰撞能量30 eV、50 eV、70 eV。结果共鉴定出160个化学成分,包括29个黄酮类成分,24个有机酸类成分,21个生物碱类成分,19个萜类成分,15个苯丙素类成分,12个皂苷类成分和40个其他类成分;其中6个化学成分(芦丁、补骨脂苷、异补骨脂苷、补骨脂素、异补骨脂素和补骨脂酚)经对照品比对确认。结论该研究借助UHPLC-Q Exactive Focus MS/MS技术实现了参仙升脉口服液化学成分准确、快速、系统的分析和鉴定,为其化学物质基础的阐明和质量控制提供了重要依据。

Two become one:combination of two risk factors in a new glaucoma animal model

Glaucoma is a group of eye diseases characterized by progressive loss of retinal ganglion cells(RGCs)and optic nerve degeneration.During this process,the visual field is reduced,and blindness may ultimately occur.Worldwide,glaucoma is the second leading cause of blindness,with about 80 million people affected.Glaucoma is a multifactorial disease and due to its complexity,the exact pathomechanisms are not fully understood yet.However,different risk factors,such as elevated intraocular pressure(IOP),age,or myopia,have been identified to date(EGS,2021).

Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model

Due to the novel applications of flexible pipes conveying fluid in the field of soft robotics and biomedicine,the investigations on the mechanical responses of the pipes have attracted considerable attention.The fluid-structure interaction(FSI)between the pipe with a curved shape and the time-varying internal fluid flow brings a great challenge to the revelation of the dynamical behaviors of flexible pipes,especially when the pipe is highly flexible and usually undergoes large deformations.In this work,the geometrically exact model(GEM)for a curved cantilevered pipe conveying pulsating fluid is developed based on the extended Hamilton's principle.The stability of the curved pipe with three different subtended angles is examined with the consideration of steady fluid flow.Specific attention is concentrated on the large-deformation resonance of circular pipes conveying pulsating fluid,which is often encountered in practical engineering.By constructing bifurcation diagrams,oscillating shapes,phase portraits,time traces,and Poincarémaps,the dynamic responses of the curved pipe under various system parameters are revealed.The mean flow velocity of the pulsating fluid is chosen to be either subcritical or supercritical.The numerical results show that the curved pipe conveying pulsating fluid can exhibit rich dynamical behaviors,including periodic and quasi-periodic motions.It is also found that the preferred instability type of a cantilevered curved pipe conveying steady fluid is mainly in the flutter of the second mode.For a moderate value of the mass ratio,however,a third-mode flutter may occur,which is quite different from that of a straight pipe system.

UPLC-Q Exactive静电场轨道阱高分辨质谱法同时测定金胆片中6种成分的含量

目的 建立UPLC-Q Exactive静电场轨道阱高分辨质谱法同时测定金胆片中龙胆苦苷、虎杖苷、芦丁、白藜芦醇、槲皮素、山柰素的含量。方法 分析采用HYPERSIL GOLD C18色谱柱(2.1 mm×100 mm, 1.9μm);流动相甲醇-0.2%甲酸,梯度洗脱;体积流量0.3 mL/min;柱温35℃;电喷雾离子源;负离子扫描。结果 6种成分在各自范围内线性关系良好(r≥0.999 03),平均加样回收率96.4%~97.9%,RSD 0.6%~2.0%。结论 该方法快速简便,精密度好,灵敏度高,可用于金胆片的质量控制。

Exact controllability of rational expectations model with multiplicative noise and input delay

This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.

Frequentist and Bayesian Sample Size Determination for Single-Arm Clinical Trials Based on a Binary Response Variable: A Shiny App to Implement Exact Methods

Sample size determination typically relies on a power analysis based on a frequentist conditional approach. This latter can be seen as a particular case of the two-priors approach, which allows to build four distinct power functions to select the optimal sample size. We revise this approach when the focus is on testing a single binomial proportion. We consider exact methods and introduce a conservative criterion to account for the typical non-monotonic behavior of the power functions, when dealing with discrete data. The main purpose of this paper is to present a Shiny App providing a user-friendly, interactive tool to apply these criteria. The app also provides specific tools to elicit the analysis and the design prior distributions, which are the core of the two-priors approach.

Calculation of Two-Tailed Exact Probability in the Wald-Wolfowitz One-Sample Runs Test

The objectives of this paper are to demonstrate the algorithms employed by three statistical software programs (R, Real Statistics using Excel, and SPSS) for calculating the exact two-tailed probability of the Wald-Wolfowitz one-sample runs test for randomness, to present a novel approach for computing this probability, and to compare the four procedures by generating samples of 10 and 11 data points, varying the parameters n0 (number of zeros) and n1 (number of ones), as well as the number of runs. Fifty-nine samples are created to replicate the behavior of the distribution of the number of runs with 10 and 11 data points. The exact two-tailed probabilities for the four procedures were compared using Friedman’s test. Given the significant difference in central tendency, post-hoc comparisons were conducted using Conover’s test with Benjamini-Yekutielli correction. It is concluded that the procedures of Real Statistics using Excel and R exhibit some inadequacies in the calculation of the exact two-tailed probability, whereas the new proposal and the SPSS procedure are deemed more suitable. The proposed robust algorithm has a more transparent rationale than the SPSS one, albeit being somewhat more conservative. We recommend its implementation for this test and its application to others, such as the binomial and sign test.

Pyroelectric Plate with Magnetoelectric Effect

In dynamic problems the electric and magnetic fields are inseparable. At the same time, a multitude of electrostatic and magnetostatic effects permit mutually independent description. This separation appears to be possible and thermodynamically consistent when the bulk energy density depends only on the polarization density or, alternatively, on the magnetization density. However, when the bulk energy density depends simultaneously on the both densities, then, the electrostatic and magnetostatic effects should be studied together. There appear interesting cross-effects;among those are the change of the internal electrostatic field inside a specimen under the influence of the external magnetic fields, and vice versa. Below, in the framework of thermodynamic approach the boundary value problem for magnetoelectric plate is formulated and analyzed. The exact solution is established for the isotropic pyroelectric plate.

ABSOLUTE STABLE HOMOTOPY FINITE ELEMENT METHODS FOR CIRCULAR ARCH PROBLEM AND ASYMPTOTIC EXACTNESS POSTERIORI ERROR ESTIMATE

In this paper, HFEM is proposed to investigate the circular arch problem. Optimal error estimates are derived, some superconvergence results are established, and an asymptotic exactness posteriori error estimator is presented. In contrast with the classical displacement variational method, the optimal convergence rate for displacement is uniform to the small parameter. In contrast with classical mixed finite element methods, our results are free of the strict restriction on h(the mesh size) which is preserved by all the previous papers. Furtheremore we introduce an asymptotic exactness posteriori error estimator based on a global superconvergence result which is discovered in this kind of problem for the first time.

On exactness and unbiasedness of confidence bands for a continuous distribution function

We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.

酒制蜂胶中6种活性成分体内药动学研究及其代谢产物鉴定

目的研究酒制蜂胶中乔松素、白杨素、高良姜素、对香豆酸、山柰酚、柚皮素体内药动学,并鉴定其代谢产物。方法大鼠灌胃给予酒制蜂胶(10 g/kg),于0033、0083、025、05、075、1、15、2、4、6、9、12、24、36 h采血,采用UPLC-Q Exactive Orbitrap MS法测定6种活性成分血药浓度,计算主要药动学参数,并对其代谢产物进行分析。结果乔松素、白杨素、高良姜素、对香豆酸、山柰酚、柚皮素AUC0~t分别为17952、27730、43093、2177814、5976、77835 ng/mL·h,Tmax均在030 h以内。共鉴定出15种代谢产物,主要涉及葡萄糖醛酸化、硫酸酯化等途径。结论该方法准确可靠,可为明确酒制蜂胶药效物质及其体内过程提供依据。各活性成分不仅以原型成分入血,又可通过Ⅰ、Ⅱ相代谢发挥药效。

The Local Theory of Completely 1-Summing Mapping Spaces

In this paper, we investigate local properties in the system of completely 1-summing mapping spaces. We introduce notions of injectivity, local reflexivity, exactness, nuclearity and finite-representability in the system of completely 1-summing mapping spaces. First we obtain that if V has WEP, V is locally reflexive in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if it is locally reflexive in the system (Ⅰ(⋅,⋅), t(⋅)). Furthermore we prove that an operator space V ⊆ B(H) is exact in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)). At last, we show that an operator space V is finitely representable in {Mn}n∈N in the system (Ⅱ1(⋅,⋅), π1(⋅)) if and only if V = C.

UHPLC-Q Exactive高分辨质谱联用法分析淫羊藿中的化学成分

目的采用UHPLC-Q Exactive四极杆-静电场轨道阱高分辨质谱联用技术鉴定分析淫羊藿药材成分。方法采用Thermo Hypersil GLOD C_(18)(100 mm×2.1 mm,1.9μm)色谱柱,体积分数0.1%甲酸水溶液-乙腈溶液为流动相进行梯度洗脱,流速为0.3 mL·min^(-1),柱温为40℃,电喷雾正、负离子模式扫描。结果共分析和鉴定出79个化合物,包括黄酮类、生物碱类、有机酸类和木脂素类化合物,其中16个化合物经与对照品比对鉴定。鉴定的黄酮类包括46个异戊烯基黄酮醇类化合物,异戊烯基黄酮醇类负离子模式二级特征碎片为m/z 367、351、513、353和323。初步鉴定化合物41、54、76、65和69为新的异戊烯基黄酮。结论淫羊藿中异戊烯基黄酮醇类多具有淫羊藿素或8-异戊烯基山奈酚苷元母核结构,该结果为淫羊藿成分的系统分析提供了数据支持。

基于UPLC-Q Exactive Orbitrap-MS的不同产地半枝莲药材差异分析

目的采用超高效液相色谱-四极杆-静电场轨道阱高分辨质谱(UPLC-Q Exactive Orbitrap-MS)技术,结合多元统计分析半枝莲药材不同产地的差异代谢物,为分析影响药材质量的指标控制提供依据。方法采集不同产地半枝莲质谱数据,以热图Pearson聚类、主成分分析(Principal components analysis,PCA)、偏最小二乘法判别分析(Partial least squares discriminant analysis,PLS-DA)等多元统计分析手段,确定不同产地半枝莲药材的差异成分。结果通过数据库比对共鉴别39个化合物,聚类热图结果表明21批样品可以分为5类,且在31个化合物上存在明显差异,PCA结果分析得到3个主成分可以实现不同产地半枝莲的区分,累积解释率为93.68%,其中野黄芩苷对主成分1影响较大,黄芩苷、芹菜素对主成分2影响较大。PLS-DA可以实现5个产地样本的分离,通过特征值大于1,得到关键差异化合物与PCA结果一致。结论所建立的方法能用于不同产地半枝莲药材差异分析及质量评价。

Three Dimensional Coupling between Elastic and Thermal Fields in the Static Analysis of Multilayered Composite Shells

This new work aims to develop a full coupled thermomechanical method including both the temperature profile and displacements as primary unknowns of the model.This generic full coupled 3D exact shell model permits the thermal stress investigation of laminated isotropic,composite and sandwich structures.Cylindrical and spherical panels,cylinders and plates are analyzed in orthogonal mixed curved reference coordinates.The 3D equilibrium relations and the 3D Fourier heat conduction equation for spherical shells are coupled and they trivially can be simplified in those for plates and cylindrical panels.The exponential matrix methodology is used to find the solutions of a full coupled model based on coupled differential relations with respect to the thickness coordinate.The analytical solution is based on theories of simply supported edges and harmonic relations for displacement components and sovra-temperature.The sovra-temperature magnitudes are directly applied at the outer faces through static state hypotheses.As a consequence,the sovra-temperature description is assumed to be an unknown variable of themodel and it is calculated in the sameway as the three displacements.The final systemis based on a set of coupled homogeneous differential relations of second order in the thickness coordinate.This system is reduced in a first order differential relation system by redoubling the number of unknowns.Therefore,the exponential matrix methodology is applied to calculate the solution.The temperature field effects are evaluated in the static investigation of shells and plates in terms of displacement and stress components.After an appropriate preliminary validation,new benchmarks are discussed for several thickness ratios,geometrical data,lamination sequences,materials and sovra-temperature values imposed at the outer faces.Results make evident the accordance between the uncoupled thermo-mechanical model and this new full coupled thermo-mechanical model without the need to separately solve the Fourier heat conduction relation.Both effects connected with the thickness layer and the related embedded materials are included in the conducted thermal stress analysis.

Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows

In this paper, the problem of finding exact solutions to the magnetohydrodynamic(MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation(PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.

Modifications of the Optimal Auxiliary Function Method to Fractional Order Fornberg-Whitham Equations

In this paper,we present a new modification of the newly developed semi-analytical method named the Optimal Auxilary Function Method(OAFM)for fractional-order equations using the Caputo operator,which is named FOAFM.The mathematical theory of FOAFM is presented and the effectiveness of this method is proven by using it with well-known Fornberg-Whitham Equations(FWE).The FOAFM results are compared with other method results along with their exact solutions with the help of tables and plots to prove the validity of FOAFM.A rapidly convergent series solution is obtained from FOAFMand is validated by comparison with other results.The analysis proves that ourmethod is simply applicable,contains less computationalwork,and is rapidly convergent to the exact solution at the first iteration.A series solution to the problem is obtained with the help of FOAFM.The validity of FOAFM results is validated by comparing its results with the results available in the literature.It is observed that FOAFM is simply applicable,contains less computational work,and is fastly convergent.The convergence and stability are obtained with the help of optimal constants.FOAFM is very easy in applicability and provides excellent results at the first iteration for complex nonlinear initial/boundary value problems.FOAFM contains the optimal auxiliary constants through which we can control the convergence as FOAFM contains the auxiliary functions D_(1),D_(2),D_(3)...in which the optimal constants G_(1),G_(2),...and the control convergence parameters exist to play an important role in getting the convergent solution which is obtained rigorously.The computational work in FOAFM is less when compared to other methods and even a low-specification computer can do the computational work easily.

On numerical stationary distribution of overdamped Langevin equation in harmonic system

Efficient numerical algorithm for stochastic differential equation has been an important object in the research of statistical physics and mathematics for a long time.In this work we study the highly accurate numerical algorithm for the overdamped Langevin equation.In particular,our interest is in the behaviour of the numerical schemes for solving the overdamped Langevin equation in the harmonic system.Based on the large friction limit of the underdamped Langevin dynamic scheme,three algorithms for overdamped Langevin equation are obtained.We derive the explicit expression of the stationary distribution of each algorithm by analysing the discrete time trajectory for both one-dimensional case and multi-dimensional case.The accuracy of the stationary distribution of each algorithm is illustrated by comparing with the exact Boltzmann distribution.Our results demonstrate that the“BAOA-limit”algorithm generates an accurate distribution of the harmonic system in a canonical ensemble,within a stable range of time interval.The other algorithms do not produce the exact distribution of the harmonic system.