A Generalized Euler Probability Distribution

含尺度导数变分问题的广义Euler-Lagrange方程

Generalized Euler-Lagrange equations for variational problems with scale derivatives

我们得到几个欧拉-拉格朗日方程的变分泛函定义在一组Hölder曲线。当拉格朗日包含多个尺度导数，取决于一个参数，或包含高阶尺度导数的情况下被认为是。

用欧拉-拉格朗日变分原理推导广义牛顿流体的流动关系

Using Euler-Lagrange Variational Principle to Obtain Flow Relations for Generalized Newtonian Fluids

利用欧拉-拉格朗日变分原理，得到了圆柱管内流动的解析关系和数值关系。该方法是基于最小化的总应力在流动管道中使用的应力和应变率之间的流体本构关系。牛顿和非牛顿流体模型，其中包括幂律，宾厄姆，赫歇尔-Bulkley，Carreau和十字架，用于演示。

Addition formulas for the $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with arbitrary parameters and their Kummer- and Euler-type transformations

We obtain addition formulas for $_{p}F_{p}$ and $_{p+1}F_{p}$ generalized hypergeometric functions with general parameters. These are utilized in conjunction with integral representations of these functions to derive Kummer- and Euler-type transformations that express $_{p}F_{p}\left(x\right)$ and $_{p+1}F_p\left(x\right)$ in the form of sums of $_{p}F_{p}\left(-x\right)$ and $_{p+1}F_p\left(-x\right)$ functions, respectively.

A modified Euler-Maclaurin formula in 1D and 2D with applications in statistical physics

The Euler-Maclaurin summation formula is generalized to a modified form by expanding the periodic Bernoulli polynomials as its Fourier series and taking cuts, which includes both the Euler-Maclaurin summation formula and the Poission summation formula as special cases. By making use of the modified formula, a numerical summation method is obtained and the error can be controlled. The modified formula is also generalized from one dimention to two dimentions. Examples of its applications in statistical physics are also discussed.

用于哈密顿系统幺正控制的广义欧拉角

Generalized Euler angles for a unitary control of the Hamiltonian system

本研究通过逐次应用KAK分解，提出了推广$\textrm{SU}(2)$欧拉角的$\textrm{SU}(2^{n})$角度参数化方法，并推导了对应哈密顿量指数曲线的广义欧拉角参数曲线的一阶微分代数约束方程，该方程类似第二类正则坐标的Wei-Norman方程。

Limit theorems and fluctuations for point vortices of generalized Euler equations

We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

紧李群：Euler构造和广义Dyson猜想

Compact Lie groups: Euler constructions and generalized Dyson conjecture

紧李群的广义欧拉参数化是一种从极大李群开始参数化群的方法，它允许参数范围的简单表征。本文研究了一类全紧连通李群。我们提出了一个通用的方法，实现他们的广义欧拉参数化从任何对称嵌入的李群。我们的建设是基于这些群体的几何形状的详细分析。作为一个副产品，这引起了一个有趣的连接与某些戴森积分。特别是，我们获得了一个Macdonald猜想的几何为基础的证明关于戴森积分对应的根系与所有不可约对称空间。作为我们的一般方法的应用，我们明确参数化类的简单，单连通紧李群的所有群体。我们提供了一个表格，给出了所有这些欧拉参数化的所有必要成分。

欧拉方程的粘性正则化与熵原理

Viscous regularization of the Euler equations and entropy principles

本文研究了可压缩欧拉方程的一类一般粘性正则化。一个独特的正则化是兼容的所有广义熵a la Harten，并满足最小熵原理。与最近H.布伦纳是做。

广义Euler-Poinsot刚体方程的显式椭圆解

The generalized Euler-Poinsot rigid body equations: explicit elliptic solutions

刚体动力学的经典Euler-Poinsot情形允许一类简单但非平凡的可积推广，它修改了描述物体在空间中运动的Poisson方程。这些推广具有第一积分是多项式的角动量。我们将修正的Poisson方程看作一个椭圆系数线性方程组，并证明了它的所有解都是单值的。利用向量推广的Picard定理，我们推导出的解决方案显式的sigma函数的相应的椭圆曲线。最后给出了数值算例。我们还比较了广义Poisson方程与经典三阶Hüssen方程的某些推广。

关于SU（N）的欧拉角

On the Euler angles for SU(N)

本文重新考虑酉群的Euler参数化问题。在用广义角构造了一般群元之后，我们计算了SU（N）上的不变测度，然后用拓扑和几何方法确定了参数的全范围.特别是，我们表明，给定的参数化实现了作为纤维化的U（N）在复杂的射影空间$\mathbb{CP}^n$的组$SU(N+1)$。这证明了将参数解释为广义欧拉角是合理的。

带表面摩擦的二维定常高超声速极限 Euler 流过斜坡的广义 Newton-Busemann 定律

Generalized Newton-Busemann Law For Two-Dimensional Steady Hypersonic-limit Euler Flows Passing Ramps With Skin-Frictions

本文研究了带表面摩擦的二维定常高超声速极限 Euler 流过斜坡问题，通过构造包含 Dirac 测度的 Radon 测度解来表示无限薄激波层，从而推广了高超声速空气动力学中的 Newton-Busemann 定律以计算斜坡上的阻力和升力分布。

Geometric Lagrangian averaged Euler-Boussinesq and primitive equations

In this article we derive the equations for a rotating stratified fluid governed by inviscid Euler-Boussinesq and primitive equations that account for the effects of the perturbations upon the mean. Our method is based on the concept of geometric generalized Lagrangian mean recently introduced by Gilbert and Vanneste, combined with generalized Taylor and horizontal isotropy of fluctuations as turbulent closure hypotheses. The models we obtain arise as Euler-Poincaré equations and inherit from their parent systems conservation laws for energy and potential vorticity. They are structurally and g…

Emergence of generalized hydrodynamics in the non-local Luttinger model

We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all…