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Author Archives: Shuhua Zhang
Monotonically increasing intervals
Problem A real sequence satisfies for all , where . Let be the length of the th interval. Show that there exists a unique such that for all . Remark This is a problem that arises from nonlinear quantization in … Continue reading
Posted in Analysis, mathematics, signal processing
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3D Matrix Multiplication Tricks
Recently, I came across times 3D matrix multiplication in Matlab. It is for frequency domain signal processing, specifically, frequencydependent multichannel Wiener filter. Here, 3D matrix multiplication means 2D matrix multiplication at each frequency (or other parameters): Given and which are … Continue reading
Dense Circle
Proposition 1. Let be an irrational number and denote the set of fractional parts of for all . Then is dense in . Proof. We shall first prove that is dense at , then proceed to the whole range of … Continue reading
Posted in Analysis, mathematics
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Originally posted on What's new:
I’ve just uploaded to the arXiv my paper “Every odd number greater than 1 is the sum of at most five primes“, submitted to Mathematics of Computation. The main result of the paper is…
Posted in mathematics
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Blacklist IPs that attack SSH and FTP services on a Linux machine
I manage a Linux server (Redhat EL4, kernel version 2.6.934). Yesterday, I found the server was attacked relentlessly from 121.101.223.211. It seemed to be a brutal force dictionary attack. What to do then? The obvious way is to manually add that IP … Continue reading