Remarks on star countable discrete closed spaces

summary:In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming $2^{\aleph _0}=2^{\aleph _1}$, there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable

Generalized Reed-Solomon Codes with Sparsest and Balanced Generator Matrices

We prove that for any positive integers $n$ and $k$ such that $n\!\geq\! k\!\geq\! 1$, there exists an $[n,k]$ generalized Reed-Solomon (GRS) code that has a sparsest and balanced generator matrix (SBGM) over any finite field of size $q\!\geq\! n\!+\!\lceil\frac{k(k-1)}{n}\rceil$, where sparsest means that each row of the generator matrix has the least possible number of nonzeros, while balanced means that the number of nonzeros in any two columns differ by at most one. Previous work by Dau et al (ISIT'13) showed that there always exists an MDS code that has an SBGM over any finite field of size $q\geq {n-1\choose k-1}$, and Halbawi et al (ISIT'16, ITW'16) showed that there exists a cyclic Reed-Solomon code (i.e., $n=q-1$) with an SBGM for any prime power $q$. Hence, this work extends both of the previous results

The progress of Celani's experiment replication project in China

Abstract only.Francesco Celani demonstrated his LENR device using H2 gas and a specially treated constantan wire during the NIWeek 2012 and ICCF-17, showing a peak excess heat power of about 20W at an input power of 48W. Since then, a replication of Celani's work has been launched through a project called MFMP (Martin Fleischmann Memorial Project) in an open method named "live open science" by the author. Thanks to the wire granted by Celani, a similar replication project is carried out at Delta Energy Technologies in China this year, aimed at observing significant amount of anomalous heat production as Celani did. The experiment setup is presented and the instruments are illustrated here. The methods of calorimeter are discussed and will be adopted in the experiment. The project progress is briefly introduced and the plan is shortly listed