Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator

The O( N) invariant quartic anharmonic oscillator is shown to be exactly solvable if the interaction parameter satisfies special conditions.The problem is directly related to that of a quantum double well anharmonic oscillator in an external field.A finite dimensional matrix equation for the problem is constructed explicitly,along with analytical expressions for some excited states in the system.The corresponding Niven equations for determining the polynomial solutions for the problem are given.

Interplay between spin frustration and magnetism in the exactly solved two-leg mixed spin ladder

We study a mixed spin-（3/2,1） ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction.The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system.Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0,1/5,2/5,3/5,1.Moreover,an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play.It is shown that the double-peak phenomenon at zero-field for the case of AF2 ground-state arises from the very strong antiferromagnetic rung coupling,while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.

exactly与to the day能连用吗?

[问][380]在《大学英语》(修订本)精读第三册(1998年8月第2次印刷)p.213上Cloze练习中有一个句子:It was April 30,1945,exactly 12years and 3 months to the day Hitler had initiated theenormous power of the Third Reich.请问句中exactly与to the day能连用吗? [答]句中的exactly与to the day不能连用。

An Exactly Solvable Algebraic Model for Single Quantum Well Treatments

We propose an algebraic model, presenting individual contributions separately in the system of interest, for the exact solutions of one-dimensional Poisson-Schr?dinger equations used generally in semiconductor device simulations. The model presented here reveals an interesting relation between the corresponding Poisson and Schr?dinger equation for the physical structure considered, which leads to closed solutions without solving the required electrostatic equation.

Generation of Exactly Solvable Potentials of Position-Dependent Mass Schrödinger Equation from Hulthen Potential

Exactly Solvable Potentials (ESPs) of Position-Dependent Mass (PDM) Schrodinger equation are generated from Hulthen Potential (parent system) by using Extended Transformation (ET) method. The method includes a Co-ordinate Transformation (CT) followed by Functional Transformation (FT) of wave function. Mass function of parent system gets transformed to that of generated system. Two new ESPs are generated. The explicit expressions of mass functions, energy eigenvalues and corresponding wave functions for newly generated potentials (systems) are derived. System specific regrouping method is also discussed.

Exactly Solved Anderson Lattice Model

A solvable Anderson lattice model is formulated.The exact eigenstates of model Hamiltonian are constructed by using the Bethe ansatz.The Be the ansatz equations are obtained from the periodic boundary conditions.

Pseudo-Hermitian Matrix Exactly Solvable Hamiltonian

The non PT-symmetric exactly solvable Hamiltonian describing a system of a fermion in the external magnetic field which couples to a harmonic oscillator through some pseudo-hermitian interaction is considered. We point out all properties of both of the original Mandal and the original Jaynes-Cummings Hamitonians. It is shown that these Hamiltonians are respectively pseudo-hermitian and hermitian REF _Ref536606452 \r \h \* MERGEFORMAT [1] REF _Ref536606454 \r \h [2]. Like the direct approach to invariant vector spaces used in Refs. REF _Ref536606456 \r \h [3] REF _Ref536606457 \r \h [4], we reveal the exact solvability of both the Mandal and Jaynes-Cummings Hamiltonians after expressing them in the position operator and the impulsion operator.

A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field

A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral meshes.In this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal MHD.Since the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this treatment.We propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD equations.Some numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.

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.

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。

Existence of Exactly n+1 Simple 4-Periodic Solutions of the Differential Delay Equation x(t)=-f(x(t-1))

By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).

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。

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.

ENUMERATION OF EXACTLY k-REDUCIBLE n-TOURNAMENTS

An n-tournament T_n is called k-reducible if auy of its (n--k+1)-subtourna-ments is reducible. An n-tournament T_n is called exactly k-reducible if it is k-reducible but not (k+1)-reducible. The numbers of all isomorphic classes of ntournaments and strong n-tournaments arc denoted by t(n) and s(n) respectively.

An exactly solvable model for two-dimensional non-Hermitian quasicrystals

The phenomenon Anderson localization explains the metalinsulator transition in a material with the increase of disorder and its electrons’transport change from diffusive into localized.The study of the Anderson localization has been extended to many fields of physics,including the quasiperiodic or incommensurate systems.

A RKDG Method for 2D Lagrangian Ideal Magnetohydrodynamics Equations with Exactly Divergence-Free Magnetic Field

In this paper,we present a Runge-Kutta Discontinuous Galerkin(RKDG)method for solving the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations under the Lagrangian framework.The fluid part of the ideal MHD equations along with z-component of the magnetic induction equation are discretized using a DG method based on linear Taylor expansions.By using the magnetic fluxfreezing principle which is the integral form of the magnetic induction equation of the ideal MHD,an exactly divergence-free numerical magnetic field can be obtained.The nodal velocities and the corresponding numerical fluxes are explicitly calculated by solving multidirectional approximate Riemann problems.Two kinds of limiter are proposed to inhibit the non-physical oscillation around the shock wave,and the second limiter can eliminate the phenomenon of mesh tangling in the simulations of the rotor problems.This Lagrangian RKDG method conserves mass,momentum,and total energy.Several numerical tests are presented to demonstrate the accuracy and robustness of the proposed scheme.

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.