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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Purity and torsors over Prüfer bases
纯度 扭转器 普吕弗底座
2023/4/21
In algebraic geometry, purity refers to a diverse range of phenomena in which certain invariants or categories associated to geometric objects are insensitive to the removal of closed subsets of large...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Purity and torsors over Prüfer bases
纯度 扭转器 普吕弗底座
2023/4/23
In algebraic geometry, purity refers to a diverse range of phenomena in which certain invariants or categories associated to geometric objects are insensitive to the removal of closed subsets of large...
Stability Theorems for Fourier Frames and Wavelet Riesz Bases
Frames Riesz basis nonharmonic series wavelets
2015/9/29
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type co...
Ideal Denoising in an orthonormal basis chosen from a library of bases
Wavelet Packets Cosine Packets weak-` p spaces
2015/8/20
Suppose we have observations yi = si +zi, i = 1; :::; n, where (si) is signal and (zi)
is i.i.d. Gaussian white noise. Suppose we have available a library L of orthogonal
bases, such as the Wavelet ...
Markov bases for noncommutative Fourier analysis of ranked data
Calibration markov chain monte carlo techniques data sets and statistical analysis
2015/7/8
To calibrate Fourier analysis of S5 ranking data by Markov chain Monte Carlo techniques, a set of moves (Markov basis) is needed. We calculate this basis, and use it to provide a new statistical analy...
Let A0 be a complete characteristic (0; p) discrete valuation ring with absolute rami cation degree e and a perfect residue eld. We are interested in studying the category FFA0 of nite
at commutat...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
Kashiwara de ned the notion of a crystal, and gave examples of crystal structures
associated with bases of representations of quantum groups. We recommend the
expository article Kashiwara [7], writt...
Optimal Decentralized Control of Linear Systems via Groebner Bases and Variable Elimination
Groebner Bases and Variable via
2015/6/19
e consider the problem of optimal decentralized controller synthesis. There are several classes of such problems for which effective algorithms are known, including the quadratically invariant cases. ...
Grobner bases for operads
Grobner bases operads
2015/3/25
We define a new monoidal category on collections (shuffle composition). Monoids in this category (shuffle operads) turn out to bring a new insight in the theory of symmetric operads. For this category...
Higher connectivity of fiber graphs of Grobner bases
Higher connectivity fiber graphs Grobner bases
2012/11/23
Fiber graphs of Gr\"obner bases from contingency tables are important in statistical hypothesis testing, where one studies random walks on these graphs using the Metropolis-Hastings algorithm. The con...
Strong pseudoprimes to the first 9 prime bases
Strong Pseudoprimes Chinese Remainder Theorem
2012/7/9
Define $\psi_m$ to be the smallest strong pseudoprime to the first $m$ prime bases. The exact value of $\psi_m$ is known for $1\le m \le 8$. Z. Zhang have found a 19-decimal-digit number $Q_{11}=3825\...
Mutually unbiased bases as submodules and subspaces
Mutually unbiased bases submodules and subspaces Combinatorics
2012/6/19
Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most o...
Frames and Bases in Tensor Product of Hilbert Spaces
Frame bases Tensor product Frame operator Dual frame Hilbert space
2012/4/17
In this article we develop a theory for frames in tensor product of Hilbert spaces. We show that like bases if Y_1, Y_2, \cdot \cdot \cdot, Y_n are frames for H_1,H_2, \cdot \cdot \cdot, H_n, respecti...
Monomial bases of quantized enveloping algebras of finite type
quantized enveloping algebra Hall algeba monomial basis
2011/9/28
In this paper we present a systematic construction of monomial bases for all quantized enveloping algebras of finite type, which generalizes the main result in [4] for simply laced case.