Rubick’s Cube Solves Itself

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Bett’s Dance

I have posted a link to Bert Jansch playing Bett’s Dance here before:
Jansch and Renbourn live

Here is another live version:

… and (probably) a studio version, included on the album  “Living in the Shadows, Part 1”, which is available on vinyl or CD from the link below:

Bett’s Dance at Earth Recordings

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Numerical Integration; Tanh-Sinh Quadrature v. 4.42

Back to Newton and Excel.

I recently received a new update to the Tanh-Sinh Quadrature spreadsheet from Graeme Dennes, which may be downloaded from:

Tanh_Sinh Quadrature.

From the Readme:

The Tanh-Sinh quadrature workbook has been enhanced as follows:

  1. The Tanh-Sinh integrator in the workbook may be the fastest finite-interval integrator on the planet!!
  2. The speed of the DE programs has been doubled.
  3. A fast finite interval program TINT has been added. It runs at over twice the speed of the Gauss-Kronrod program.
  4. The speed of the Gauss-Kronrod program has been improved through modifications developed by Berntsen, Espelid and Sorevik.
  5. The Romberg integrator, written by the author, may be the fastest and most accurate Romberg integrator on the planet!!
  6. Now includes over 1200 test integrals with true results. This may be the largest set of diverse test integrals available at no cost. It includes several of the “standard” sets of test integrals in wide use.
  7. The Plotter worksheet now shows two plots: the plot of the selected function over the finite interval (a,b), and the plot of the selected function after being transformed by the Tanh-Sinh function.
  8. Minor change to allow compatibility with Excel 2007.
  9. Minor correction.

Graeme Dennes

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Mini-tours of India 9

To Jaipur. The capital and largest city of Rasjasthan, also known as the Pink City:

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… and finally, we follow a monkey on a moped back to New Delhi, the airport, and home.

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Mini-tours of India 8

We arrive in Jodhpur, the Blue City, and the second largest in Rajasthan:

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Mini-tours of India 7

On the way to Jodhpur, we visit the Ranakpur Jain Temple, and the village of Kherwa, staying at the old Palace Hotel:

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Mini-tours of India 6

From Bijaipur we move on to the UNESCO World Heritage listed Chittor Fort, or Chittorgah, then the city of Udaipur, known as the City of Lakes, or the Venice of the East:

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