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Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence
Gene regulation is a key factor in gaining a full understanding of molecular biology. microRNA (miRNA), a novel class of non-coding RNA, has recently been found to be one crucial class of post-transac...
In rotor walk on a finite directed graph, the exits from each vertex follow a prescribed periodic sequence. Here we consider the case of rotor walk where a particle starts from a designated source ver...
RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE
Copy number variations (CNVs) are gains and losses of DNA se-quence of a genome, which result in the abnormality of the cell or individual. The data from single nucleotide polymorphism (SNP) microar...
Using the link surgery formula for Heegaard Floer homology we find a spectral sequence from the lattice homology of a plumbing tree to the Heegaard Floer homology of the corresponding 3-manifold. This...
A local-global sequence for Chow groups of zero-cycles involving Brauer groups has been conjectured to be exact for all proper smooth algebraic varieties. We apply existing methods to construct severa...
In this paper, we investigate the necessary sufficient conditions for the exactness of the homotopy sequence of Nori's fundamental group and apply these to various special situations to regain some cl...
We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of...
In this paper we listed a sequence of odd numbers up to 300,000 by a computer calculating and it could be find that the density of prime numbers is decreased as odd number increases and that there exi...
In this paper a pseudo sequence of odd numbers had been advanced, and the number of pseudo prime numbers in it are largely less than the real prime numbers in the real sequence of odd numbers. This ps...
Abstract: We study the limit of the stochastic model for two dimensional second grade fluids subjected to the periodic boundary conditions as the stress modulus tends to zero. We show that under suita...
Abstract: We consider the second of Mullin's sequences of prime numbers related to Euclid's proof that there are infinitely many primes. We show in particular that it omits infinitely many primes, con...
Abstract: We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere $S_{n-1}\subset\mathbb{R}^{n}$ and we obtain a Central Limit Theorem for a sequence of...
Let [x] be the greatest integer not exceeding x. In the paper we introduce the sequence {Un} given by U0 = 1 and Un = −2P[n/2] k=1 􀀀 n 2kUn−2k (n  1), and establish many recursi...

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