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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
2023/11/14
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
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...
BEYOND MEAN FIELD: ON THE ROLE OF PAIR EXCITATIONS IN THE EVOLUTION OF CONDENSATES
BEYOND MEAN FIELD PAIR EXCITATIONS
2015/10/15
This paper is in part a summary of our earlier work
[17, 18, 19], and in part an announcement introducing a re nement
of the equations for the pair excitation function used in our previous work with...
Extremal Functions for a Mean Field Equation in Two Dimension
Extremal Functions a Mean Field Equation Two Dimension
2014/4/3
Let be a bounded piecewise C 2 simply-connected domain. In thisarticle, we give necessary and sucient conditions for the existence ofmaximizer ofJ8( ) = log Zedx!116Zj 5 j2dx for 2 H10(). We pro...
A large class of non constant mean curvature solutions of the Einstein constraint equations on an asymptotically hyperbolic manifold
Asymptotically hyperbolic manifold Constraint equations Conformal method
2010/12/31
We construct solutions of the constraint equation with non constant mean curvature on an
asymptotically hyperbolic manifold by the conformal method. Our approach consists in decreasing a certain expo...
Beurling-Hörmander Uncertainty Principle for the Spherical Mean Operator
Uncertainty principle Beurling-Hö rmander theorem Gelfand-Shilov theorem Cowling-Price theorem Fourier transform Spherical mean operator
2009/5/1
We establish the Beurling-Hörmander theorem for the Fourier transform connected with the spherical mean operator. Applying this result, we prove the Gelfand-Shilov and Cowling-Price type theorems...
Korovkin-type theorems are established, and consequently mean ergodic theorems are obtained.
On the Fourth Power Mean of the Character Sums Over Short Intervals
character sums short intervals fourth power mean asymptotic formula
2007/12/11
The main purpose of this paper is to study the mean value properties of the character sums over the interval $\left[1, \frac{p}{8}\right)$ by using the mean value theorems of the Dirichlet L-functions...
Mean value on the difference between a quadratic residue and its inverse modulo p
An integer and its inverse Bernoulli numbers Cochrane sums
2007/12/11
The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet $L$-functions to study the asymptotic property of the difference between...