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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arbitrarily high-order cut-off methods to preserve maximum bound principle for Allen-Cahn equations
Allen-Cahn equations 最大界限原理 任意高阶 截止方法
2023/4/14
A new class of high-order maximum principle preserving numerical methods is proposed for solving the semilinear Allen-Cahn equation. We start with the method consists of a $k$th-order multistep expone...
BOSE–EINSTEIN CONDENSATION BEYOND MEAN FIELD:MANY-BODY BOUND STATE OF PERIODIC MICROSTRUCTURE
Bose–Einstein condensation homogenization many-body perturbation theory two-scale expansion singular perturbation mean field limit bound state
2015/10/16
We study stationary quantum fluctuations around a mean field limit in trapped, dilute atomic gases of repulsively interacting bosons at zero temperature. Our goal is to describe quantum-mechanically t...
ERRATUM:BOSE–EINSTEIN CONDENSATION BEYOND MEAN FIELD:MANY-BODY BOUND STATE OF PERIODIC MICROSTRUCTURE
Bose–Einstein condensation homogenization many-body perturbation theory two-scale expansion singular perturbation mean field limit bound state
2015/10/16
This is a correction to the author’s article [Multiscale Model. Simul.,10 (2012), pp.383–417].
A bound from below for the temperature in compressible Navier-Stokes equations
below for the temperature compressible Navier-Stokes equations
2015/10/15
We consider the full system of compressible Navier-Stokes equations for heat conducting fluid. We show that the temperature is uniformly positive for t ≥ t0 (for any t0 > 0) for any solutions with fin...
Attainment of the multiple quantum Chernoff bound for certain ensembles of mixed states
multiple quantum Chernoff bound certain ensembles mixed states
2015/8/25
We consider the problem of detecting the true quantum state among r possible ones, based onmeasurements performed on n of copies of a finite dimensional quantum system. It is known that the exponent f...
AN ASYMPTOTIC ERROR BOUND FOR TESTING MULTIPLE QUANTUM HYPOTHESES
ASYMPTOTIC ERROR BOUND TESTING MULTIPLE QUANTUM HYPOTHESES
2015/8/25
We consider the problem of detecting the true quantum state among r possible ones, based of measurements performed on n copies of a finitedimensional quantum system. A special case is the problem of d...
THE CHERNOFF LOWER BOUND FOR SYMMETRIC QUANTUM HYPOTHESIS TESTING
CHERNOFF LOWER BOUND SYMMETRIC QUANTUM HYPOTHESIS TESTING
2015/8/25
We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system...
Minimax Risk: Pinsker Bound
COMMUNICATION THEORY, STATISTICAL DENSITY ESTIMATION FISHER INFORMATION KERNEL ESTIMATORS LINEAR ESTIMATORS, BAYES LOCAL ASYMPTOTIC NORMALITY METHOD OF SIEVES MINIMAX ESTIMATION NOISE (SIGNAL PROCESSING IN THE PRESENCE OF ) PREDICTION AND FILTERING LINEAR SIEVES, METHOD OF SPECTRAL ANALYSIS SHRINKAGE ESTIMATORS SMOOTHNESS PRIORS SOBOLEV SPACES SPLINE FUNCTIONS STATIONARY PROCESSES STEIN EFFECT
2015/8/25
We give an account of the Pinsker bound describing the exact asymptotics of the minimax risk in a class of nonparametric smoothing problems. The parameter spaces are Sobolev classes or ellipsoids, and...
Computation of the maximum H_infinity-norm of parameter-dependent linear systems by a branch and bound algorithm
Calculation algorithm parameter linear system a branch and bound algorithm linear system
2015/8/12
For linear systems that contain unspecified parameters that lie in given intervals, we present a branch and bound algorithm for computing the maximum H_infinity-norm over the set of uncertain paramete...
Branch-and-bound algorithm for computing the minimum stability degree of parameter-dependent linear systems
Branch and bound algorithm linear systems a robust nonlinear and linear system stability the parameters of linear system
2015/8/12
We consider linear systems with unspecified parameters that lie between given upper and lower bounds. Except for a few special cases, the computation of many quantities of interest for such systems ca...
A sharp bound on the L2 norm of the solution of a random elliptic difference equation
sharp bound L2 norm random elliptic difference equation
2015/7/14
We consider a stationary solution of the Poisson equation (λ − Lω)φλ(x; ω) = −∂∗b(x; ω), where λ > 0 and Lω is a random, discrete, elliptic operator given by Lωu(x) := ∂&...
An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions
the zero-counting formulae Dirichlet $L$-functions Dedekind zeta-functions Number Theory
2012/6/30
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet L-functions and Dedekind zeta-functions in rectangles.
The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation Probabilities
The Sharp Lower Bound Asymptotic Efficiency of Estimators the Zone of Moderate Deviation Probabilities Statistics Theory
2012/6/27
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower...
Collapsing 4-manifolds under a lower curvature bound
collapsing Gromov-Hausdorff convergence Alexandrov spaces topology of 4-manifolds
2012/5/24
In this paper we describe the topology of 4-dimensional closed orientable Riemannian manifolds with a uniform lower bound of sectional curvature and with a uniform upper bound of diameter which collap...
A sharp upper bound for the rainbow 2-connection number of 2-connected graphs
rainbow edge-coloring rainbow k-connection number 2-connected graph ear decomposition
2012/4/18
A path in an edge-colored graph is called {\em rainbow} if no two edges of it are colored the same. For an $\ell$-connected graph $G$ and an integer $k$ with $1\leq k\leq \ell$, the {\em rainbow $k$-c...