Quantum alpha-determinants and q-deformed hypergeometric polynomials

The quantum $\alpha$-determinant is defined as a parametric deformation of the quantum determinant. We investigate the cyclic $\mathcal{U}_q(\mathfrak{sl}_2)$-submodules of the quantum matrix algebra $\mathcal{A}_q(\mathrm{Mat}_2)$ generated by the powers of the quantum $\alpha$-determinant. For such a cyclic module, there exists a collection of polynomials which describe the irreducible decomposition of it in the following manner: (i) each polynomial corresponds to a certain irreducible $\mathcal{U}_q(\mathfrak{sl}_2)$-module, (ii) the cyclic module contains an irreducible submodule if the parameter is a root of the corresponding polynomial. These polynomials are given as a $q$-deformation of the hypergeometric polynomials. This is a quantum analogue of the result obtained in our previous work [K. Kimoto, S. Matsumoto and M. Wakayama, Alpha-determinant cyclic modules and Jacobi polynomials, to appear in Trans. Amer. Math. Soc.].Comment: 10 page

Implementing 64-bit Maximally Equidistributed F2\mathbb{F}_2-Linear Generators with Mersenne Prime Period

CPUs and operating systems are moving from 32 to 64 bits, and hence it is important to have good pseudorandom number generators designed to fully exploit these word lengths. However, existing 64-bit very long period generators based on linear recurrences modulo 2 are not completely optimized in terms of the equidistribution properties. Here we develop 64-bit maximally equidistributed pseudorandom number generators that are optimal in this respect and have speeds equivalent to 64-bit Mersenne Twisters. We provide a table of specific parameters with period lengths from $2^{607}-1$ to $2^{44497}-1$. (An online appendix is available at http://www.ritsumei.ac.jp/~harase/melg-64-app.pdf)Comment: 11 Page

Human cell line (HGC-27) derived from the metastatic lymph node of gastric cancer

A cell line (HGC-27) was established by culture of the metastatic lymph node from a gastric cancer patient diagnosed histologically as undifferentiated carcinoma. HGC-27 cells were polygonal or short spindle-shaped and adhered to glass surfaces as a monolayer. The cells were probably derived from gastric cancer cells, as their origin from mesenchymal tissues can be excluded morphologically and enzyme-histochemically. Enzyme activities were generally negative or low, except for adenosine triphosphatase, lactic dehydrogenase and leucine aminopeptidase. These scanty findings might reflect the undifferentiated character of the original tumor cells. The cloning efficiency was 5.3% in liquid medium and 1.0% in soft agar. The doubling time was about 17 hr. Chromosomal analysis revealed a mode of 109 and 110 chromosomes.</p