基于Riemann Zeta的电路连续实函数浪涌建模

Binesh Thankappan
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引用次数: 0

摘要

黎曼ζ被定义为一个复变量的函数,当实部大于1时,它解析地延续了狄利克雷级数的和。本文考虑了半径为2mm的自由落体水滴撞击平面时所具有的有限能量的黎曼ζ。提出了一种改进的zeta函数,并将其与球坐标相结合,进行了实际分析。通过实解析延拓,分析了液滴与平面接触瞬间的单点接触。zeta函数在drop的销毁点被提取,在那里它定义了一个唯一的实函数。对于某些连续函数,假设一个特殊的性质,其中函数的一阶导数和一阶积分在所有点上组合在一起为零。这种函数的近似反向合成产生了一种特殊的波形,称为死亡浪涌。将所提出的概念推广到一般连续实函数,得到了相应函数的死亡-浪涌模型的综合。与水滴相关的黎曼ζ函数也可以被建模为一个死亡浪涌。濒死电涌模型对应于波形的电挤压或压缩,它最初是在无限参数上定义的,被压缩到与定义的最终值和倒数值非常接近的参数的有限数量的值。最后给出了仿真软件的综合结果,并进行了分析。电路中浪涌的存在将对应于一些未知的连续的、真实的电流或电压函数的电压缩,该方法可以用来估计原始的未知函数。
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Riemann Zeta Based Surge Modelling of Continuous Real Functions in Electrical Circuits
Riemann zeta is defined as a function of a complex variable that analytically continues the sum of the Dirichlet series, when the real part is greater than unity. In this paper, the Riemann zeta associated with the finite energy possessed by a 2mm radius, free falling water droplet, crashing into a plane is considered. A modified zeta function is proposed which is incorporated to the spherical coordinates and real analysis has been performed. Through real analytic continuation, the single point of contact of the drop at the instant of touching the plane is analyzed. The zeta function is extracted at the point of destruction of the drop, where it defines a unique real function. A special property is assumed for some continuous functions, where the function’s first derivative and first integral combine together to a nullity at all points. Approximate reverse synthesis of such a function resulted in a special waveform named the dying-surge. Extending the proposed concept to general continuous real functions resulted in the synthesis of the corresponding function’s Dying-surge model. The Riemann zeta function associated with the water droplet can also be modeled as a dying–surge. The Dying- surge model corresponds to an electrical squeezing or compression of a waveform, which was originally defined over infinite arguments, squeezed to a finite number of values for arguments placed very close together with defined final and penultimate values. Synthesized results using simulation software are also presented, along with the analysis. The presence of surges in electrical circuits will correspond to electrical compression of some unknown continuous, real current or voltage function and the method can be used to estimate the original unknown function.
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International Journal of Circuits, Systems and Signal Processing
International Journal of Circuits, Systems and Signal Processing Engineering-Electrical and Electronic Engineering
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