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1.
In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.  相似文献   
2.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.  相似文献   
3.
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn.  相似文献   
4.
张月荣  袁晓 《物理学报》2021,(4):349-359
标度拓展经典负半阶分抗逼近电路,可实现具有任意分数阶微积算子运算功能的分抗逼近电路,但牺牲了运算恒定性.从电路网络的角度分析具有恒定运算性能的负半阶Carlson分形格分抗逼近电路.根据标度分形格分抗逼近电路的等效无源双口网络,探讨该双口网络右侧端口的运算有效性,设计具有高运算恒定性的任意阶标度分形格分抗逼近电路.结合负实零极点对基元系统的零极点分布及其局域化特性,阐述具有任意实数阶微积算子运算功能的标度分形格分抗逼近电路运算振荡现象的物理本质,并从理论上分析有效抑制频域运算振荡现象的方法.结合对称阻容T型节电路优化理论及方法,对任意阶对称格型级联双口网络的频域逼近性能进行优化,获得具有高逼近效益的任意阶标度分形格分抗逼近电路.具有低振荡幅度的任意阶对称格型级联双口网络为高运算恒定性的分抗逼近电路设计及应用提供了一种新方法及思路.  相似文献   
5.
Fractional-order calculus is about the differentiation and integration of non-integer orders. Fractional calculus (FC) is based on fractional-order thinking (FOT) and has been shown to help us to understand complex systems better, improve the processing of complex signals, enhance the control of complex systems, increase the performance of optimization, and even extend the enabling of the potential for creativity. In this article, the authors discuss the fractional dynamics, FOT and rich fractional stochastic models. First, the use of fractional dynamics in big data analytics for quantifying big data variability stemming from the generation of complex systems is justified. Second, we show why fractional dynamics is needed in machine learning and optimal randomness when asking: “is there a more optimal way to optimize?”. Third, an optimal randomness case study for a stochastic configuration network (SCN) machine-learning method with heavy-tailed distributions is discussed. Finally, views on big data and (physics-informed) machine learning with fractional dynamics for future research are presented with concluding remarks.  相似文献   
6.
Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.  相似文献   
7.
We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.  相似文献   
8.
从教具制作、定量实验探究和教学启示等三方面来探究匀速圆周运动的向心加速度公式,即利用自制教具探究向心加速度a c与圆周运动半径r和角速度ω之间的定量关系.实验发现,结果非常好地符合理论预期.最后讨论了该教具所蕴含的教学启示,可以将其设计成适合高中物理教学的验证性、探究性实验及课外科创活动,从而培养学生的科学探究能力、科学推理能力、动手协作能力和问题解决能力.本教具还提供了测量当地重力加速度的一种新方法.  相似文献   
9.
In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.  相似文献   
10.
Hao Wang 《中国物理 B》2022,31(11):114206-114206
As concepts closely related to microwave absorption properties, impedance matching and phase matching were rarely combined with material parameters to regulate properties and explore related mechanisms. In this work, reduction-diffusion method was innovatively applied to synthesize rare earth alloy Y$_{2}$Fe$_{17}$. In order to regulate the electromagnetic parameters of absorbers, the Y$_{2}$Fe$_{17}$N$_{3-\delta }$ particles were coated with silica (Y$_{2}$Fe$_{17}$N$_{3-\delta }$@SiO$_{2}$) and absorbers with different volume fractions were prepared. The relationship between impedance matching, matching thickness, and the strongest reflection loss peak (${\rm RL}_{\rm min}$) was presented obviously. Compared to the microwave absorption properties of Y$_{2}$Fe$_{17}$N$_{3-\delta }$/PU absorber, Y$_{2}$Fe$_{17}$N$_{3-\delta }$@SiO$_{2}$/PU absorbers are more conducive to the realization of microwave absorption material standards which are thin thickness, light weight, strong absorbing intensity, and broad bandwidth. Based on microwave frequency bands, the microwave absorption properties of the absorbers were analyzed and the related parameters were listed. As an important parameter related to perfect matching, reflection factor ($\sqrt {ărepsilon_{\rm r}/\mu_{\rm r}}$) was discussed combined with microwave amplitude attenuation. According to the origin and mathematical model of bandwidth, the formula of EAB (${\rm RL}<-10$ dB) was derived and simplified. The calculated bandwidths agreed well with experimental results.  相似文献   
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