Lyapunov-type inequalities for a class of nonlinear higher order differential equations
Jun Zheng; Haofan Wang
| In this work, we establish several Lyapunov-type inequalities for a class of nonlinear higher order differential equations having a form \begin{align*} (\psi(u^{(m)}(x)))'+\sum_{i=0}^nr_i(x)f_i(u^{(i)}(x))=0, %\ \ \ \ \text{or}\ \ \ \ (\psi(u^{(m)}))^{(m)}+r_i(x)f(u)=0, \end{align*} with anti-periodic boundary conditions, where $m> n\geq 0$ are integers, $\psi$ and $f_i (i=0,1,2,...,n)$ satisfy certain structural conditions such that the considered equations have general nonlinearities. The obtained inequalities are extensions and complements of the existing results in the literature. |
Lyapunov-type inequalities for ψ−Laplacian equations
Zheng, Jun; Guo, Xu
| In this work, we present several Lyapunov-type inequalities for a class of $\psi-$Laplacian equations of the form \begin{align*} (\psi(u'(x)))'+r(x)f(u(x))=0, \end{align*} with Dirichlet boundary conditions, where $\psi$ and $f$ satisfies certain structural conditions with general nonlinearities. We do not require any sub-multiplicative property of $\psi$, and any convexity of $\frac{1}{\psi(t)}$ or $\psi (t)t$ in the establishment of Lyapunov-type inequalities. The obtained inequalities can be seen as extensions and complements of the existing results in the literature. |
| 本文通过严格数学分析找出了逻辑回归过拟合的成因：边界样本的损失贡献比重大且随法向量增长而加速增大、边界样本分布散乱，顺便理清了正则项的作用机理。 利用过拟合机制，本文提出一种反拉方法，既能缓解过拟合，又能减少训练步数，在MNIST数据集上实现加速38.25倍，在CIFAR10数据集上实现加速5.61倍。 |
T-Area-Marker for Scientific Images
陈光; 郭春芳
| Labeled images are one of the most important means of scientific communication and education. However, traditional markers (arrows, lines) are point markers; do not include information about how large the feature is. We designed an efficient marker system for labeling scientific images (electron or light microscopy, CT, MRI, ultrasonography, camera pictures, etc), called the “T Area Marker, (TAM)”. The basic TAM marker looks like a “T”, composed of a line segment and a small tick on one end; it defines an imagined circle that stands on the tickless end and the diameter of the circle is equal to the length of the line segment. Thus the TAM can define an exact area rather than a single point; and the imagined circle does not break the continuity of the image (unlike traditional visible circles, rectangles, etc). A TAM with N ticks (N>1) means the diameter equals to N times the length of TAM. A TAM may also have a tail and/or several tail branches to define translation of the imagined circle, thus define complicated areas. tAreaMarker.py is free software that combines the drawing and reading of TAMs, although in most cases TAMs are easily interpreted without computer assistance. |
Gibbsian representation of knowledge in infinite dimensional random neural networks(IDRNN)
xi guangcheng
| Abstract. In studying of a class of random neural network, some of relative researchers have proposed Markov model of neural network. Wherein Markov property of the neural network is based on “assuming”. To reveal mechanism of generating of Markov property in neural network, it is studied how infinite-dimensional random neural network (IDRNN) forms inner Markov representation of environment information in this paper.Because of equivalence between markov property and Gibbsian our conclusion is that knowledge is eventually expressed by extreme Gibbs probability measure—ergodic Gibbs probability measure in IDRNN. This conclusion is also applicable to quantum mechanical level of IDRNN. Hence one can see “ concept “- “ consciousness” is generated at particle(ion) level in the brain and is experienced at the level of the neurons; We have discussed also ergodicity of IDRNN with random neural potential. |
| 本文通过严格数学分析找出了逻辑回归过拟合的成因：边界样本的损失贡献比重大且随法向量增长而加速增大、边界样本分布散乱，顺便理清了正则项的作用机理。 利用过拟合机制，本文提出一种反拉方法，既能缓解过拟合，又能减少训练步数，在MNIST数据集上实现加速38.25倍，在CIFAR10数据集上实现加速5.61倍。 |
| 本文利用代数和组合的相关理论对超平面配置理论的自由性做出了相关研究，给出圈图所对应的图配置的生成元和导模的具体形式，并以图论的形式对圈图配置的导模及其自由解做出相关的组合解 释. |
Upper bounds for Z$_1$-eigenvalues of generalized Hilbert tensors
孟娟; 宋义生
| In this paper, we introduce the concept of Z$_1$-eigenvalue to infinite dimensional generalized Hilbert tensors (hypermatrix) $\mathcal{H}_\lambda^{\infty}=(\mathcal{H}_{i_{1}i_{2}\cdots i_{m}})$, $$ \mathcal{H}_{i_{1}i_{2}\cdots i_{m}}=\frac{1}{i_{1}+i_{2}+\cdots i_{m}+\lambda},\ \lambda\in \mathbb{R}\setminus\mathbb{Z}^-;\ i_{1},i_{2},\cdots,i_{m}=0,1,2,\cdots,n,\cdots, $$ and proved that its $Z_1$-spectral radius is not larger than $\pi$ for $\lambda>\frac{1}{2}$, and is at most $\frac{\pi}{\sin{\lambda\pi}}$ for $\frac{1}{2}\geq \lambda>0$. Besides, the upper bound of $Z_1$-spectral radius of an $m$th-order $n$-dimensional generalized Hilbert tensor $\mathcal{H}_\lambda^n$ is obtained also, and such a bound only depends on $n$ and $\lambda$. |
| 大气对红外辐射传输的影响引起的红外成像灰度变化，是红外目标跟踪应用需要应对的问题。本文的研究目的是对红外成像灰度变化规律进行李群建模，对设计高效、鲁棒的目标跟踪算法有重要意义。首先分析了红外辐射传输模型，并结合红外成像机理，得到红外成像灰度变化模型。进一步从理论上证明了大气影响下红外成像灰度变化规律符合李群结构，提出了红外图像灰度动态变化的一种非欧数学表征。最后根据红外成像灰度变化模型对不同环境下采集到的外场实验数据进行拟合，回归分析结果表明了该模型的准确性，进而说明了本文对红外成像灰度变化规律进行李群表达的合理性。 |
Partial generalizations of some Conjectures in locally symmetric Lorentz spaces
孙忠洋
| 这篇文章中，首先给出了局部对称Lorentz空间中线性 Weingarten类空超曲面的数量曲率和平均曲率的关系。进而，我们研究了局部对称Lorentz空间中满足一定曲率的完备或者紧致线性 Weingarten类空超曲面，通过修改Cheng-Yau的算子，给出了一些新的估计。最终，我们在局部对称Lorentz空间中给出了一些猜想的部分推广。 |