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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fields with a generic multiplicative endomorphism
通用乘法 自同态 域
2023/5/4
The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I wi...
Critical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale
Critical Gaussian Multiplicative Chaos Convergence of the Derivative Martingale Probability
2012/6/29
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching rand...
Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization
nonnegative matrix factorization algorithms multiplicative updates hierarchical alternating least squares
2011/9/21
Abstract: Nonnegative matrix factorization (NMF) is a data analysis technique used in a great variety of applications such as text mining, image processing, hyperspectral data analysis, computational ...
Multiplicative white noise functionals and the Krylov-Veretennikov expansion for coalescing stochastic flows
Krylov-Veretennikov expansion coalescing stochastic flows Probability
2011/9/20
Abstract: In this article we consider multiplicative operator-valued white noise functionals related to a stochastic flow. A generalization of the Krylov-Veretennikov expansion is presented. An analog...
Additive decompositions induced by multiplicative characters over finite fields
Characters Residuacity Finite Fields
2011/8/26
Abstract: In 1952, Perron showed that quadratic residues in a field of prime order satisfy certain ad- ditive properties. This result has been generalized in different directions, and our contribution...
Abstract: Fix integers $b>a\geq1$ with $g:=\gcd(a,b)$. A set $S\subseteq\mathbb{N}$ is \emph{$\{a,b\}$-multiplicative} if $ax\neq by$ for all $x,y\in S$. For all $n$, we determine an $\{a,b\}$-multipl...
Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
Harnack inequality functional solution delay SDE strong Feller property
2011/2/28
By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong...
Towards the Capacity Region of Multiplicative Linear Operator Broadcast Channels
Capacity Region Multiplicative Linear Operator Broadcast Channels
2011/2/28
Recent research indicates that packet multicasting employing random linear network coding can be regarded as transmitting subspaces as codewords over a linear operator channel (LOC).
Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential
Nonlinear Schr¨odinger equation Nash-Moser Theory
2011/1/19
We prove the existence of quasi-periodic solutions for Schr¨odinger equations with a multiplicative potential on Td, d ≥ 1, merely differentiable nonlinearities, and tangential frequencies constrained...
Delooping totalization of a multiplicative operad
multiplicative operads totalization colored operads
2011/3/1
The paper shows that under some conditions the totalization of a cosimplicial space obtained from a multiplicative operad is a double loop space of the space of derived morphisms from the associative ...
Transference inequalities for multiplicative Diophantine exponents
Transference inequalities multiplicative Diophantine exponents
2011/1/20
In this paper we prove inequalities for multiplicative analogues of Diophantine exponents, similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if...
Multiplicative zero-one laws and metric number theory
Zero-one laws metric Diophantine approximation
2011/1/18
We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete ‘multiplicative’ zero-one law is established akin to the ‘simultaneous’ zero-one law...
Rough Burgers-like equations with multiplicative noise
Rough Burgers-like equations multiplicative noise
2011/1/18
We construct solutions to Burgers type equations perturbed by a multiplicative spacetime white noise in one space dimension.
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
suprema of Gaussian processes omega results random multiplicative function
2011/1/17
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic,but supply strong information when one is only ...
On the limit distributions of some sums of a random multiplicative function
limit distributions of some sums of random multiplicative function
2011/1/17
We study sums of a random multiplicative function; this is an example,of number-theoretic interest, of sums of products of independent random variables (chaoses).