Songs with a single rhyme

I was listening to some Mandarin Chinese songs and noticed that the song "絲路" (Silk Road) by 梁靜茹 (Fish Leong) and the song 陪我看日出 (Watching the Sunrise With Me) by 蔡淳佳 (Joi Chua) share something interesting. All the rhymes in both songs end with the same vowel (the vowel u in IPA). Is this common in Mandarin Chinese songs? Does it occur frequently in other languages as well?

Happy π approximation day 2022!

Today is π approximation day (also known as casual π day). I talked about this 2 years ago in this blog post.

I first learned about the approximation 22/7 of π as a child and was fascinated with such approximations. I remember using a handheld calculator to find fractions that better approximates π by multiplying π with larger and larger integers and check when the result is close to an integer. This of course is a tedious process, but I was able to find some good approximations. A much better approach is to use continued fractions. The continued fraction expansion of π produces convergents which are the best rational fractions that approximates π. 

In countries using YY/MM, this whole month is π approximation month!

 I have recently uploaded 2 python modules to pypi:

1. OEISsequences: Python functions to generate The On-Line Encyclopedia of Integer Sequences (OEIS) sequences. Available at: OEISsequences · PyPI. Functions are available to compute the n-th term of a sequence or generate subsequence terms (and sometimes both) depending on what is more efficient.

2. algebraic-connectivity-directed: Python functions to compute various notions of algebraic connectivity of directed graphs. Available at: algebraic-connectivity-directed · PyPI. I defined an extension of Fiedler's seminal algebraic connectivity concept (1973) to directed graphs in a 2005 Linear and Multilinear Algebra paper and have refined the concept in subsequent papers over the years to better capture the connectivity of directed graphs especially when they are "far" from being undirected. More information on these various notions of algebraic connectivity of directed graphs can be found in the following references:

1. C. W. Wu, "Synchronization in coupled arrays of chaotic oscillators with nonreciprocal coupling", IEEE Transactions on Circuits and Systems-I, vol. 50, no. 2, pp. 294-297, 2003.

2. C. W. Wu, "Algebraic connecivity of directed graphs", Linear and Multilinear Algebra, vol. 53, no. 3, pp. 203-223, 2005.

3. C. W. Wu, "On Rayleigh-Ritz ratios of a generalized Laplacian matrix of directed graphs", Linear Algebra and its applications, vol. 402, pp. 207-227, 2005.

4. C. W. Wu, "Synchronization in networks of nonlinear dynamical systems coupled via a directed graph", Nonlinearity, vol. 18, pp. 1057-1064, 2005.

5. C. W. Wu, "Synchronization in Complex Networks of Nonlinear Dynamical Systems", World Scientific, 2007.

6. C. W. Wu, "Synchronization in dynamical systems coupled via multiple directed networks," IEEE Transactions on Circuits and Systems-II: Express Briefs, vol. 68, no. 5, pp. 1660-1664, 2021.