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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonsplitting of the Hilbert Exact Sequence and the Principal Chebotarev Density Theorem
希尔伯特精确序列 主切 博塔列夫密度定理 非分裂
2023/4/18
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
Integrative approaches for microRNA target prediction: combining sequence information and the paired mRNA and miRNA expression profiles
miRNA target prediction expression profile integrative analysis
2016/1/25
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...
LOCAL-TO-GLOBAL PRINCIPLES FOR THE HITTING SEQUENCE OF A ROTOR WALK
LOCAL-TO-GLOBAL PRINCIPLES HITTING SEQUENCE ROTOR WALK
2015/8/14
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。
A Statistical Test on Capability of SNP Microarray Detecting CNVs: A Comparison to Sequence
Statistical Test Sequence
2014/12/5
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...
A spectral sequence on lattice homology
Lattice homology Heegaard Floer homology spectral sequence
2012/6/29
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...
The local-global exact sequence for Chow groups of zero-cycles
zero-cycles local-global principle Brauer–Manin obstruction
2012/6/27
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...
The Homotopy Sequence of Nori's Fundamental Group
The Homotopy Sequence of Nori's Fundamental Group Algebraic Geometry
2012/6/18
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...
The irregular distribution of primes up to 300,000 in the sequence of odd numbers
prime distribution of primes
2011/9/19
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...
The distribution of pseudo prime numbers up to 300,000 in pseudo sequence of odd numbers
prime pseudo prime distribution of pseudo primes
2011/9/19
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...
Convergence of a sequence of solutions of the stochastic two-dimensional equations of second grade fluids
stochastic two-dimensional equations second grade fluids Analysis of PDEs
2011/9/23
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...
A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in $\mathbb{R}^{n}$
Central Limit Theorem Brownian motion in the unit sphere in Rn OrnsteinUhlenbeck processes
2011/9/13
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...
Identities and congruences for a new sequence
congruence Euler polynomial identity p-regular function
2011/2/22
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...