The Lawson Algorithm and Extensions

George Lawson and

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Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces

Recently Penskoi [J. Geom. Anal. 25 (2015), 2645–2666, arXiv:1308.1628] generalized the well known two-parametric family of Lawson tau-surfaces τr,m minimally immersed in spheres to a three-parametric family Ta,b,c of tori and Klein bottles minimally immersed in spheres. It was remarked that this family includes surfaces carrying all extremal metrics for the first non-trivial eigenvalue of the ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The Metropolitan-Hastings Algorithm and Extensions

2. The Metropolis-Hastings Algorithm. Metropolis’ idea is to start with a Markov chain Xn on the state space X with a fairly arbitrary Markov transition density q(x, y)dy and then modify it to define a Markov chain X∗ n that has π(x) as a stationary measure. By definition, q(x, y) is a Markov transition density if q(x, y) ≥ 0 and ∫ y∈X q(x, y)dy = 1. If the transformed random walk X ∗ n is irre...

The Metropolitan-Hastings Algorithm and Extensions