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Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
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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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In classical mechanics, motion is often described through relationships between spatial coordinates and time. A car moving along a straight highway with constant acceleration serves as a simple case where velocity is an explicit function of time. This scenario results in a linear equation, enabling straightforward analysis using basic differentiation techniques.In contrast, a satellite in circular orbit follows a path defined by an implicit function. The position of the satellite is constrained...
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Elliptical arches are fundamental in architectural and structural engineering, offering aesthetic appeal and structural efficiency. The shape of an elliptical arch follows a constrained geometric relationship where the height and horizontal position are implicitly related. This means that the height y cannot be explicitly expressed as a function of the horizontal position x, necessitating implicit differentiation for slope and curvature analysis.The equation of an ellipse centered at the origin...
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The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
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The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
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Related Experiment Video

Updated: Apr 5, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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A Derivative-Free Riemannian Powell's Method, Minimizing Hartley-Entropy-Based ICA Contrast.

Amit Chattopadhyay, Suviseshamuthu Easter Selvan, Umberto Amato

    IEEE Transactions on Neural Networks and Learning Systems
    |August 21, 2015
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a faster method for source separation using an extended Powell

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    Area of Science:

    • Signal Processing
    • Optimization Theory

    Background:

    • Hartley-entropy-based contrast functions ensure unmixing local minima for source separation.
    • Nonsmooth optimization methods for these functions face computational challenges.

    Purpose of the Study:

    • To overcome computational bottlenecks in source separation.
    • To develop a faster optimization technique for Hartley-entropy-based contrast functions.

    Main Methods:

    • Extended Powell's derivative-free optimization method to a Riemannian manifold (oblique manifold).
    • Applied the extended method to minimize the Hartley-entropy-based contrast function for source recovery.

    Main Results:

    • The proposed scheme demonstrates faster convergence compared to existing algorithms.
    • Achieved impressive source separation results in simulations.
    • Successfully recovered quasi-correlated sources with finite-support distributions and correlated images.

    Conclusions:

    • The Riemannian manifold extension of Powell's method offers an efficient solution for source separation.
    • This approach significantly improves upon existing nonsmooth optimization techniques for this task.