关于Neyman-Pearson基本引理的几个注记

本文探讨了Neyman-Pearson基本引理.通过论证总体参数θ只有θ₀或θ₁两种可能时最优检验功效函数的唯一性,得到了两种假设T₁:θ=θ₀←→θ=θ₁和T₂:θ=θ₁←→θ=θ₀各自对应最优检验的两类错误概率可以互换的结论.     

交叉积群代数模范畴的左部分和右部分(英文)

设G是一个有限群,k为一个特征不整除G的阶数的域,∧是一个扭kG-模代数,且∧*_σG（简写为∧*G）是一个交叉积代数.设L_∧（R_∧）为代数∧的模范畴中前缀（后缀）的投射（内射）维数至多为1的所有有限生成的不可分解模.本文主要研究了交叉积代数∧*G的模范畴左（右）部分L_∧*G(R_∧*G)与代数∧的左（右）部分L_∧（R_∧）之间的关系.最后,利用本文得到的结果,考察了代数∧的相关性质在交叉积扩张下在代数∧*G中的保持性.     

易被忽视的三角最值的求法

<正>若函数y=f（x）+g（x）,当f（x）、g（x）同时在某个自变量x₀处取得最大（小）值,则在自变量x₀处,函数y取得最大（小）值为f（x₀）+ g（x₀）.本文仅例探该结论在三角函数求最值方面的应用.     

Zalcman引理在随机迭代函数族动力系统中的应用

本文根据Schwick的思想，利用Zalcman引理讨论了随机迭代函数族动力系统，指出了函数族随机迭代动力系统的Fatou集和函数族衍生半群动力系统的Fatou集定义差别明显但却等价.并获得了如下正规定则，设F={f_i|f_i为C（C）上的非线性解析函数，i ∈ M}，其中M为非空指标集，Σ_M={（j₁，j₂，…，j_n，…）|j_i ∈ M，i ∈ N}，若对任意的指标序列σ=（j₁，j₂，…，j_n，…）∈ Σ_M，迭代序列{W_σⁿ=f_jn º f_jn-1 º … ºf_j1（z）|n ∈ N}在点z处正规，则函数族F本身在点z处正规.     

Goodman公式的推广

1959年,Goodman发现了任一p阶图中k₃与k₃的个数之和,即f₃,仅是顶点的度d_i的函数之和（1≤i≤p）.人们总企图求得k₄的个数与k₄个数之和的公式f₄.首先,证明f₄并不仅是d_i的函数之和（1≤i≤p）;然后,求了f₄的公式,但它们还依赖一个自同构图c₁₁.     

空间非齐次白噪声驱动的分数阶随机热方程的矩估计

该文主要研究如下伴有Cauchy初值条件的分数阶随机热方程■其中a∈(1,2]为算子D_δ^α的阶数,δ(|δ|≤2-α)称为偏度参数,扩散系数g(·):R→R是非随机的可测函数:?²/?_t?_xw_ρ(t,x)表示空间非齐次白噪声,在关于非齐次布朗单w_ρ(t,x)催化测度ρ的适当假设下,证明了该方程解的存在性、唯一性和H?lder连续性.同时,也证明了方程解的矩估计.     

关于分数因子两个开问题的解答

本文指出极小连通二部分数1-因子不一定是极小2-连通图.研究了σ₂（G）与分数k-因子存在性之间的关系,指出存在一个特例在满足阶数n≥4k-5,δ（G）≥k且σ₂（G）≥n条件下,图G不存在分数k-因子.     

由2010年高考题中不等式所想到的

（2010年辽宁理21）已知函数f（x）=（a+1）lnx+ax²+1.（1）讨论函数f（x）的单调性;（2）设a<-1.如果对任意x₁,x₂∈（0,+∞）,|f（x₁）-f（x+2）|≥4|x₁-x+2|,求a的取值范围.（2010年湖北理21）已知函数f（x）=ax+b/x+c（a>0）的图像在点（1,f（1））处的切线方     

一类对称函数的Schur凸性与应用

对x=（x₁,x₂,…,x_n）∈R₊ⁿ及r∈{1,2,…,n},定义了对称函数F_n（x,r）=F_n（x₁,x₂,…,x_n;r）=∑_1≤i12…r≤n(∏₍j=1 x_ij/₁+x_ij^1/r,其中i₁,i₂,…,i_n是正整数.本文讨论了F_n（x,r）的Schur凸性、Schur几何凸性和Schur调和凸性,并借助于控制理论建立了若干不等式.     

控制数固定的树的谱半径(英文)

阶数为n,控制数为γ的树的集合记为T_n,γ（其中n≥max{12,2γ+1},γ≥3）。本文给出了T_n,γ中前三大的邻接谱半径以及它们对应的图。     

Analysis of equations of state for a real gas based on the notion of division of strain into free and elastic strains

It is established that, in a general case, the equations of state of a real gas are identical to the constitutive equations of cubic strain of a deformable material. Based on this, we use the fundamental notion of deformation mechanics of the division of strain into free and elastic strain. As a result, we reduce the equation of cubic strain to the form of a generalization of the ideal gas law. We establish specific features of the gaseous state as compared with the solid and liquid states. In particular, the continuum physical meaning of an ideal gas and the universal gas constant is revealed. We construct two-parameter expressions for the compressibility coefficient for an arbitrary state of aggregation, which reveal the physical meaning of the corresponding experimental data and agree with the notions of the molecularkinetic theory of gases.     

随机Hamilton系统同胚流的大偏差原理

在非Lipschitz条件下得到随机微分方程同胚流的大偏差原理.作为应用,本文同时给出了随机Hamilton系统同胚流的大偏差原理.特别地,以下二阶非线性随机振荡方程同胚流的大偏差原理也同样成立:Z_t=C_0Z_t-Z_t~3+Θ(Z_t)W_t,(Z_0,Z_0)=(z,u)∈R~2,其中C_0为任意常数,Θ为一阶导数有界的二阶连续可微函数,W_t是一维Brown白噪声.     

高阶齐次线性微分方程解的零点

研究了一类高阶齐次线性微分方程解的零点收敛指数,并得到当方程的系数A_0为整函数,其泰勒展式为缺项级数,并且A_0起控制作用时,方程f~((k))+A_(k-2)f~((k-2))+…+A_1f′+A_0f=0的任意两个线性无关解f_1,f_2满足max{λ(f_1),λ(f_2)}=∞,其中λ(f)表示亚纯函数.f的零点收敛指数.     

小波神经网络模型预测二氧化碳+水溶液体系界面张力

二氧化碳+水溶液体系界面张力(IFT)是影响地层中气水两相运移特性的重要参数之一,对二氧化碳捕集、埋存至关重要.为了快速准确地确定二氧化碳+水溶液体系IFT,对已有IFT实验结果进行了统计整理,得到了1 677组样本数据,考虑了压力,温度,气体中甲烷、氮气含量,水溶液中一价阳离子(Na+,K+)浓度、二价阳离子(Ca2+,Mg2+)浓度6个因素对IFT的影响,建立了小波神经网络（WNN）预测模型对二氧化碳+水溶液体系IFT进行预测.模拟结果表明,随机选取839组数据作为训练集样本,得到的小波神经网络结构为6-16-1,该模型预测IFT的平均绝对误差(M_MAE)、平均相对误差(M_MARE)、方差(M_MSE)和相关度(R2)分别为1.23 mN/m,3.30%,2.30 mN2/m2,0.988.与最新提出的多元拟合模型和BP神经网络模型对比结果表明,小波神经网络模型预测精度最高.     

Responses of SDOF Structures With SPIS-Ⅱ Dampers Under Random Seismic Excitation北大核心CSCD

A closed-form solution of responses of SDOF structures with SPIS-Ⅱ dampers under seismic excitation modeled with the Clough-Pezien spectrum was proposed, and the shock absorption performance and influential factors of this system were studied based on the proposed method. Firstly, the motion equation for the SPIS-Ⅱ damper was established, and the unified expressions of frequency domain solutions of structural responses, such as the structural displacement and the inerter force, were obtained. Secondly, based on the rational expression decomposition and the residue theorem, the quadratic orthogonal equations of the frequency response eigenvalue function and the Clough-Pezien spectrum were obtained respectively, and in turn the quadratic orthogonal equation of the structural response power spectrum was deduced. Thirdly, the concise closed-form solutions of the 0~2nd-order spectral moments of the structural responses were acquired. The proposed method and the virtual excitation method were used to analyze a case respectively, which verifies the correctness of the proposed method. Finally, the proposed method was used to analyze the effects of the inerter parameters on the seismic performances of the structure. The research shows that, the proposed method gives closed-form solutions better than those given by the virtual excitation method in terms of computation efficiency and accuracy. The damping performance will improve with the increase of µm and µξ for a constant µω and the damping performance will reach the optimum for µω=1. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A direct method for determining the mass of gases in ICF shell

In the present paper, the defects of dew point method for measuring the mass of gas filled in ICF shells are analyzed. An accurate state equation for gas D2 is deduced from Benedict-Webb-Rubin (BWR) equation and experimental data in planar phase. A direct method to determine gas mass in ICF shells via measuring the temperature and pressure outside the shells and solving the equation of state by numerical method is proposed. It overcomes the theoretical defects of dew point method and the complexities of equipment. In the present method, the state equation can be improved by more accurately measuring P-V-T values of gas D2, so the measuring precision of the mass of gas in the shells can also be improved. The present method is effective for treating mix gases filled in the shells as well. The errors between the computational results and experimental data are very small. Some cases in the filling process are predicted, and the proper temperature and pressure for filling gases effectively are also suggested.     

混合型裂纹的疲劳扩展

本文对受单向拉伸疲劳载荷的中心斜裂纹L₃铝试板进行了研究。根据Erdogan和Sih的最大拉应力理论,推导出以△K作为参变量,以裂纹角β₀进行修正的Paris形式的扩展速率表达式。并且进一步论证以更简单的用裂纹长度在x轴上投影的Paris方程来表示。初始裂纹角β₀有20°、30°、45°、60°、80°、90°等各种角度,裂纹尖端有经预制疲劳裂纹尖端与未经预制疲劳裂纹尖端两种情况,比较了这两种情况下疲劳扩展轨迹及疲劳扩展速率。     

Fluctuations of deformed Wigner random matrices

Let X_n be a standard real symmetric (complex Hermitian) Wigner matrix, y₁, y₂, . . . , y_n a sequence of independent real random variables independent of X_n. Consider the deformed Wigner matrix H_n,α = n^-1/2X_n + n^-α/2 diag (y₁, . . . , y_n), where 0<α<1. It is well known that the average spectral distribution is the classical Wigner semicircle law, i.e., the Stieltjes transform m_n,α(z) converges in probability to the corresponding Stieltjes transform m(z). In this paper, we shall give the asymptotic estimate for the expectation Em_n,α(z) and varianceVar(m_n,α(z)), and establish the central limit theorem for linear statistics with sufficiently regular test function. A basic tool in the study is Stein’s equation and its generalization which naturally leads to a certain recursive equation.     

非线性抛物方程混合有限元方法的高精度分析

采用双线性元及零阶Raviart-Thomas元（Q₁₁+Q₁₀×Q₀₁）对非线性抛物方程讨论了一种H¹-Galerkin混合有限元方法.提出一个线性化的二阶格式,利用数学归纳法有技巧的导出了原始变量u在H¹（Ω）模意义下及流量p=▽u在L²（Ω）模意义下的O（h²+τ²）阶超逼近性质.引入一个有关初始点的时间离散方程,并利用其得到了▽ ·在L²（Ω）模意义下的O（h²+τ²）阶的超逼近结果.同时利用插值后处理技巧得到整体超收敛.最后,数值算例结果验证了理论分析（其中,h是剖分参数,τ是时间步长）.     

Maxwell方程的多余阶次与恰当解

设pu=f在Ω内对任意f有解,其中p是任意线性常系数偏微分算子.在本文中我们证明Maxwell方程相当于四阶方程,齐次Maxwell方程的一般解为 其中φ_i满足□φ_i=0 i=1.2.