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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear potentials at the fractional scale:sharp regularity
分数尺度 非线性势 尖锐 正则性
2023/11/29
Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with potentials
Calabi-Yau 曲线计数 4-folds
2023/4/23
I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4...
New Paper Published in Nature Communications titled, “Exact exchange-correlation potentials from ground-state electron densities”
Published titled Exact potentials electron densities
2019/10/10
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a ...
Consider a point mass falling vertically on an infinitely heavy
horizontal plate which oscillates periodically with period 2π in the vertical direction
and interacts with the particle by the l...
DIFFERENTIAL HARNACK ESTIMATES FOR TIME-DEPENDENT HEAT EQUATIONS WITH POTENTIALS
EQUATIONS WITH POTENTIALS DIFFERENTIAL HARNACK
2015/8/17
In this paper, we prove a differential Harnack inequality for positive
solutions of time-dependent heat equations with potentials. We also prove a gradient
estimate for the positive solution o...
DIFFERENTIAL HARNACK ESTIMATES FOR BACKWARD HEAT EQUATIONS WITH POTENTIALS UNDER THE RICCI FLOW
HARNACK ESTIMATES WITH POTENTIALS UNDER THE RICCI FLOW
2015/8/17
In this paper, we derive a general evolution formula for possible Harnack quantities. As a consequence, we prove several differential Harnack inequalities
for positive solutions of backward hea...
FEATURE TYPE EFFECTS IN SEMANTIC MEMORY: AN EVENT RELATED POTENTIALS STUDY
Differential the semantics of the senses nerve tissue semantic concepts biological systems
2015/7/31
It is believed that the N400 elicited by concepts belonging to Living is larger than N400 to Objects. This is considered as evidence that concepts are organized, in the brain, on the basis of categori...
Exploring the potentials and limitations of the time-reversal imaging of finite seismic sources
potentials time-reversal imaging
2014/12/31
The characterisation of seismic sources with timereversed wave fields is developing into a standard technique
that has already been successful in numerous applications.
Anti-Diabetic Potentials of Phenolic Enriched Chilean Potato and Select Herbs of Apiaceae and Lamiaceae Families
Type II Diabetes Hyperglycemia Hypertension Chilean Potato Apiaceae Lamiaceae
2014/12/12
The incidence of diabetes mellitus and cardiovascular diseases is increasing at a worrisome rate globally. Diabetes mellitus is known to occur due to high blood glucose levels, caused by defects in in...
The Nexus Land-Use model version 1.0, an approach articulating biophysical potentials and economic dynamics to model competition for land-use
Demand for food. Biomass energy Forest protection Land use Model equation biophysics
2014/12/10
Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes, regionally and globally. This study presents a new model called Nexus Land-U...
Existence, Stability, and Dynamics of Solitary Waves in Nonlinear Schroedinger Models with Periodic Potentials
Non-square lattices, Nonlinear waves Photonic lattices
2014/12/8
The focus of this dissertation is the existence, stability, and resulting dynamical evolution of localized stationary solutions to Nonlinear Schr¨odinger (NLS) equations with periodic confining potent...
On the boundedness of effective potentials arising from string compactifications
the boundedness of effective potentials string compactifications Mathematical Physics
2012/6/30
We study effective potentials coming from compactifications of string theory. We show that, under mild assumptions, such potentials are bounded from below in four dimensions, giving an affirmative ans...
Soliton dynamics of NLS with singular potentials
Nonlinear Schrodinger equation soliton dynamics singular potentials
2012/6/30
We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.
Quivers with potentials associated to triangulated surfaces, part IV: Removing boundary assumptions
Quivers potentials triangulated surfaces Removing boundary assumptions Combinatorics
2012/6/30
We prove that the quivers with potentials associated by the author to ideal triangulations of punctured surfaces with empty boundary are non-degenerate, provided the number of punctures is 1 or greate...
A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials
Schrodinger equation Bloch decomposition time-splitting spectral method semiclassical asymptotics lattice potential
2012/5/24
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schr\"odinger equations with periodic potentials. This is a prominent model in solid state physics ...