关于Gauss’s law的物理内涵

本文就高斯定理的物理内函进行了阐述 ,对电磁学的教学。

A Spectral Convolutional Neural Network Model Based on Adaptive Fick’s Law for Hyperspectral Image Classification

Hyperspectral image classification stands as a pivotal task within the field of remote sensing,yet achieving highprecision classification remains a significant challenge.In response to this challenge,a Spectral Convolutional Neural Network model based on Adaptive Fick’s Law Algorithm(AFLA-SCNN)is proposed.The Adaptive Fick’s Law Algorithm(AFLA)constitutes a novel metaheuristic algorithm introduced herein,encompassing three new strategies:Adaptive weight factor,Gaussian mutation,and probability update policy.With adaptive weight factor,the algorithmcan adjust theweights according to the change in the number of iterations to improve the performance of the algorithm.Gaussianmutation helps the algorithm avoid falling into local optimal solutions and improves the searchability of the algorithm.The probability update strategy helps to improve the exploitability and adaptability of the algorithm.Within the AFLA-SCNN model,AFLA is employed to optimize two hyperparameters in the SCNN model,namely,“numEpochs”and“miniBatchSize”,to attain their optimal values.AFLA’s performance is initially validated across 28 functions in 10D,30D,and 50D for CEC2013 and 29 functions in 10D,30D,and 50D for CEC2017.Experimental results indicate AFLA’s marked performance superiority over nine other prominent optimization algorithms.Subsequently,the AFLA-SCNN model was compared with the Spectral Convolutional Neural Network model based on Fick’s Law Algorithm(FLA-SCNN),Spectral Convolutional Neural Network model based on Harris Hawks Optimization(HHO-SCNN),Spectral Convolutional Neural Network model based onDifferential Evolution(DE-SCNN),SpectralConvolutionalNeuralNetwork(SCNN)model,and SupportVector Machines(SVM)model using the Indian Pines dataset and PaviaUniversity dataset.The experimental results show that the AFLA-SCNN model outperforms other models in terms of Accuracy,Precision,Recall,and F1-score on Indian Pines and Pavia University.Among them,the Accuracy of the AFLA-SCNN model on Indian Pines reached 99.875%,and the Accuracy on PaviaUniversity reached 98.022%.In conclusion,our proposed AFLA-SCNN model is deemed to significantly enhance the precision of hyperspectral image classification.

Magnetic Monopoles, the Poynting Vector and Lenz’s Law

The Poynting vector includes time-independent contributions which, since they represent photons of zero frequency, need to be absent;this removal resolves several paradoxes that arise when they are left in place;furthermore, magnetic monopoles, if they existed, would be accompanied by a Lenz’s law that defies conservation of energy suggesting that magnetic charges might not be found in Nature.

Gauss's Law for Magnetism &Law of Universal Magnetism: Calculate the Charge of a Monopole

This paper describes a mathematical proof that Gauss’s Law for Magnetism can be derived from the Law of Universal Magnetism [1]. A second reciprocal proof also shows that the Law of Universal Magnetism can be derived from Gauss’s Law for Magnetism. These two complimentary proofs confirm that the Law of Universal Magnetism is a valid equation rooted in Gaussian law. The paper also confirms the theoretical existence of the magnetic monopole and calculates its magnetic charge using the ratio of the electromagnetic field and the speed of light. Using the mass-to-charge ratio of an electron, the mass and radius of the magnetic monopole are determined. The monopole is found to have the same radius as the electron and can also be found in the electromagnetic spectrum range known as gamma rays. Lightning is a natural source of gamma rays and could prove fruitful in the search for monopoles.

Gauss’s Law: Re-Examination and Its Consequences

Gauss’s law is modified to take into account the absorption of the electric field by vacuum. It has important consequences as the absorbed energy becomes a part of the vacuum energy and excites the energy of strings in a form of quantum harmonic oscillators. Thus, vacuum becomes an excitable medium and this helps to understand the basic mechanisms for the conservation of the charge of the electron, electrostatic attraction or repulsion and the energy associated with vacuum.

EXPERIMENTAL STUDY ON DARCY′S LAW IN HELE-SHAW CELLS

The basic physics of unsteady Hele-Shaw flow at high Reynolds numbers is mainly studied by an experimental measurement. In order to confirm the Darcy′s law in Hele-Shaw cell, since there is an analogy between flow in cells and that in porous media, progressive water waves are utilized to build an unsteady flow in a Hele-Shaw cell, and which complex wave number is measured by a wave height gauge. Meanwhile, theoretical analyses are used to compare with experimental data. Result shows Darcy′s Law is not exactly correct for unsteady Hele-Shaw flows, and it is expected to conduct a modified Darcy′s Law.

基于Gauss伪谱法的空空导弹最优中制导律设计

研究Gauss伪谱法在空空导弹最优中制导律设计中的应用。建立空空导弹中制导律设计问题最优控制模型,首次提出采用Gauss伪谱法求解最优中制导律设计问题的思路,详细阐述了求解流程,通过仿真算例验证了求解方法的有效性,并同比例导引、打靶法等传统方法进行了对比。仿真结果表明,综合考虑性能指标、计算精度、计算效率等因素,Gauss伪谱法具有明显优势,Gauss伪谱法求解结果和求解效率与配点个数密切相关。研究结果为空空导弹中制导律设计提供理论参考。

5维Gauss-Bonnet-AdS黑洞的热力学和临界现象

把宇宙学常数理解为压强,利用标准的热力学方法讨论了5维Gauss-Bonnet-Ad S黑洞系统的热力学和临界现象.把Bekenstein-Hawking熵作为黑洞系统的熵,发现在5维球对称的Gauss-Bonnet-Ad S黑洞中存在相变现象.进一步计算了相变点的临界指数,发现他们满足热力学普适标度规律.

一类广义Gauss型求积公式

基于被积函数在n次第一类和第二类Chebyshev多项式的零点处的差商,该本构造了两种Gauss型求积公式,这些求积公式包含了某些已知结果作为特例。更重要的是这些新结果与Gauss-Turán求积公式有密切的联系。

Gauss-Newton法的半局部收敛性

设f:Rn→Rm 是Frechet可微的 ,m≥n .则非线性最小二乘问题可描述为下面的极小化问题 :minF(x) :=12 f(x) Tf(x) .Gauss Newton法是求解非线性最小二乘问题的最基本的方法之一 ,其n + 1步迭代定义为 :xn + 1=xn - f′(xn) Tf′(x) -1f′(xn) Tf(xn) .本文主要研究解非线性最小二乘问题的Gauss Newton法的半局部收敛性 .假设f(x)在B(x0 ,r)内连续可导且f′(x0 )满秩 ,若f的导数满足Lipschitz连续F′(x) -f′(x′)≤γx -x′ , x ,x′∈B(x0 ,r) .在一个关于初始点x0 的判断准则c =f(x0 ) ,β =f′T(x0 )f′(x0 ) -1f′(x0 ) T ,β2 cγ <1 1 0下 ,Gauss Newton法产生的序列 {xn}收敛到一个驻点x ,从而给出了Gauss Newton法的半局部收敛性 .

与Gauss-Turán求积公式有关的极小值

对于给定的权函数 dμ(x) ,若存在 n次首 1多项式 P*n (x) (称为 s-正交多项式 )使下列积分F(s,μ) =∫R[Pn(x) ]2 s+ 2 dμ(x)达到极小 ,Pn(x) =xn +an- 1 xn- 1 +… +a1 x +a0 ,则以多项式 P*n (x)的 n个不同零点 x1 >x2 >… >xn- 1 >xn 作为节点的下列求积公式 (称为 Gauss-Turán求积公式 )∫Rf (x) dμ(x) =∑2 sj=0 ∑nk=1Ajkf ( j) (xk) +E2 s,n(f ) .具有代数精确度 2 (s+1 ) n -1 .但我们对 F (s,μ)所知不多 .Milovanovic′在他最近的一篇文章里提出计算 F(s,μ)的值 .

电子产品可靠性评估的Gauss-幂律加速退化模型

主要研究了电子产品的加速退化失效可靠性评估问题。提出了Gauss-幂律加速退化模型,并利用加速退化数据得出正常应力水平下的可靠性指标,同时给出了一个应用实例表明该模型的适用性和有效性。

Benford’s Law在煤矿安全数据真实性判定中的应用和优化研究

首先阐述了对煤矿安全数据进行真实性判定的重要性.然后,提出了基于Benford’s Law的煤矿安全数据真实性的判定方法,并通过对淮南地矿井安全数据的分析,证明了该方法的科学性和有效性.最后,对该方法进行优化,使得优化后的方法在煤矿安全数据的真实性判定上,不仅区分度高而且运算量小.

Gauss分布函数模型及其在教学设计中的应用

将生长曲线应用于设计教育方案。分析了生长曲线的特征,依据教育规律建立了Gauss分布函数的人才培养模型,结合高等职业教育实际给出专业教学计划的设计方法和步骤,运用相关分析对模型进行优化。

THE LAW OF ITERATED LOGARITHM FOR R/S STATISTICS

A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.

PRECISE RATES IN THE LAW OF THE ITERATED LOGARITHM FOR R/S STATISTICS

Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.

结合Cannikin’s Law的离线数据增广方法研究

数据增广是提升深度学习模型性能的有效方法之一。针对多类别目标检测任务中检测性能不平衡问题,提出一种针对“短板类别”(检测性能远低于模型平均检测性能的类别)的离线数据增广方法。受Cannikin’s Law的启发,采用基于复制粘贴(copy-paste)机制的场景多样性增广方法。随机采集训练集中“短板类别”实例区域,通过相似性度量机制选取训练集中增广目标样本进行随机粘贴。为了降低随机粘贴导致的遮挡问题,采用基于自遮挡(cut-replace)机制的增广方法提升模型遮挡表达能力。通过截取样本自身区域,对特征表达最显著区域进行遮挡。实验表明,FCOS目标检测框架在PASCAL VOC数据上的平均检测精度(mean average precision,mAP)从79.10%提升到83.90%,其中短板类别更为显著,提升了20.8个百分点。在MS-COCO数据上平均检测精度提升了0.9个百分点。

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

PHOTOREALISTIC COMPUTER GRAPHICS FORENSICS BASED ON LEADING DIGIT LAW

As the advent and growing popularity of image rendering software,photorealistic computer graphics are becoming more and more perceptually indistinguishable from photographic images.If the faked images are abused,it may lead to potential social,legal or private consequences.To this end,it is very necessary and also challenging to find effective methods to differentiate between them.In this paper,a novel leading digit law,also called Benford's law,based method to identify computer graphics is proposed.More specifically,statistics of the most significant digits are extracted from image's Discrete Cosine Transform(DCT) coefficients and magnitudes of image's gradient,and then the Support Vector Machine(SVM) based classifiers are built.Results of experiments on the image datasets indicate that the proposed method is comparable to prior works.Besides,it possesses low dimensional features and low computational complexity.

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton＇s canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether＇s theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.