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Updated: Jun 5, 2025

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小N系列在零维O模型中:构造扩展和跨系列

Dario Benedetti1, Razvan Gurau1,2, Hannes Keppler2

  • 1CPHT, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France.

Annales Henri Poincare
|December 16, 2024
PubMed
概括

本研究分析了零维四边形O(N) 矢量模型的分区函数和自由能量. 我们利用构造性场理论来证明博雷尔相加性,并探索跨序列扩张,为更高维的量子场理论奠定基础.

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Convergence of Fourier Series01:21

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
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Inverse z-Transform by Partial Fraction Expansion

The inverse z-transform is a crucial technique for converting a function from its z-domain representation back to the time domain. One effective method for finding the inverse z-transform is the Partial Fraction Method, which involves decomposing a function into simpler fractions with distinct coefficients. These fractions correspond to known z-transform pairs, facilitating the inverse transformation process.
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Exponential Fourier series

In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
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Routh-Hurwitz Criterion II01:19

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In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Discrete-Time Fourier Series

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