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SOME SPECTRAL PROPERTIES OF PSEUDO-DIFFERENTIAL OPERATORS ON THE SIERPINSKI GASKET
Analysis on fractals localized eigenfunctions Sierpiński gasket Szego limit theorem
2015/12/10
We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
For each ˉeld k, we deˉne a category of rationally decomposed mixed
motives with Z-coe±cients. When k is ˉnite, we show that the category is Tannakian, and we prove formulas relating the behaviour of...
关于平方数的戴德金ζ函数系数的和式余项
戴德金$\zeta$函数 代数数域 平方数
2018/2/6
设 $E$ 是有理数域 $\mathbb{Q}$ 上的一个代数数域. $a(n)$ 为 $E$上范数 $n$ 的整理想的个数. 再设 $\Delta(x)$ 为和式 $\sum_{n\le x}(a(n^2))^l$ 渐近式的余项. 本文利用解析方法得到了$$\int_1^X \Delta^2 (x)dx$$的一个比较好的上界. 该结果在均值上改进了吕广世等人 [J. Number Theory,...
Solvable model for pair excitation in trapped Boson gas at zero temperature
Solvable model pair excitation trapped Boson gas zero temperature
2015/10/16
In Bose–Einstein condensation (BEC), particles occupy a single-particle quantum state, , macroscopically. At zero temperature, the wavefunction for is usually described via a nonlinear Schrodinger ...
KINETIC HIERARCHIES AND MACROSCOPIC LIMITS FOR CRYSTALLINE STEPS IN 1+1 DIMENSIONS
kinetic theory epitaxial growth crystal surface Burton–Cabrera–Frank model particle system Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy closure evaporation-condensation surface diffusion correlation function step chemical potential macroscopic limit propagation of chaos
2015/10/16
We apply methods of kinetic theory to study the passage from particle systems to nonlinear partial differential equations (PDEs) in the context of deterministic crystal surface relaxation. Starting wi...
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...
We show that a certain class of varieties with origin in Physics,
generates (additively) the Denef-Loeser ring of Motives. In particular, this
disproves a conjecture of Kontsevich on the number of p...
We show that the coefficients in the Laurent series of the
Igusa local zeta functions I(s) = R
C
f
sω are periods. This is proved by
first showing the existence of functional equation...
A SHORT PROOF OF ROST NILPOTENCE VIA REFINED CORRESPONDENCES
ROST NILPOTENCE VIA REFINED CORRESPONDENCES
2015/9/29
I generalize the standard notion of the composition g ◦f of
correspondences f : X → Y and g : Y → Z to the case that X and Z are
arbitrary varieties but Y is smooth and projective. Using this ...
ON MOTIVIC DECOMPOSITIONS ARISING FROM THE METHOD OF BIA LYNICKI-BIRULA
DECOMPOSITIONS ARISING BIA LYNICKI-BIRULA
2015/9/29
Recently, V. Chernousov, S. Gille and A. Merkurjev have
obtained a decomposition of the motive of an isotropic smooth projective
homogeneous variety analogous to the Bruhat decomposition. Using the
...
We prove that the zero locus of an admissible normal
function over an algebraic parameter space S is algebraic in the
case where S is a curve.
SINGULARITIES OF ADMISSIBLE NORMAL FUNCTIONS (WITH AN APPENDIX BY NAJMUDDIN FAKHRUDDIN)
NORMAL FUNCTIONS NAJMUDDIN FAKHRUDDIN
2015/9/29
In a recent paper, M. Green and P. Griths used R. Thomas’ work on nodal
hypersurfaces to sketch a proof of the equivalence of the Hodge conjecture and the existence of certain singular admissible no...
ON THE ALGEBRAICITY OF THE ZERO LOCUS OF AN ADMISSIBLE NORMAL FUNCTION
ZERO LOCUS ADMISSIBLE NORMAL FUNCTION
2015/9/29
We show that the zero locus of an admissible normal function on
a smooth complex algebraic variety is algebraic.
THE LOCUS OF HODGE CLASSES IN AN ADMISSIBLE VARIATION OF MIXED HODGE STRUCTURE
ADMISSIBLE VARIATION HODGE CLASSES
2015/9/29
We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure.