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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...
ZERO LOCI OF ADMISSIBLE NORMAL FUNCTIONS WITH TORSION SINGULARITIES
NORMAL FUNCTIONS TORSION SINGULARITIES
2015/9/29
We show that the zero locus of a normal function on a smooth
complex algebraic variety S is algebraic provided that the normal function extends to a admissible normal function on a smooth compacti...
NON-COLLISION SINGULARITIES IN THE PLANAR TWO-CENTER-TWO-BODY PROBLEM
PLANAR TWO-CENTER-TWO-BODY PROBLEM NON-COLLISION SINGULARITIES
2015/9/29
Statement of the main result. We study a two-center two-body problem.
Consider two xed centers Q1 and Q2 of masses m1 = m2 = 1 located at distance
from each other and two small particles Q3 and Q4...
DISTRIBUTIONS WITH SINGULARITIES:Punctual and Local Study
DISTRIBUTIONS WITH SINGULARITIES Punctual and Local Study
2015/9/29
DISTRIBUTIONS WITH SINGULARITIES:Punctual and Local Study.
CURVATURE PINCHING ESTIMATE AND SINGULARITIES OF THE RICCI FLOW
SINGULARITIES CURVATURE PINCHING ESTIMAT
2015/8/17
In this paper, we first derive a pinching estimate on the traceless Ricci
curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then
we apply this estimate to study...
New Tight Frames of Curvelets and Optimal Representations of Objects with C2 Singularities
Curvelets wavelets second dyadic decomposition edges nonlinear approximation singularities thresholding Radon transform
2015/6/17
This paper introduces new tight frames of curvelets to address the problem of finding optimally sparse representations of objects with discontinuities along C2 edges.Conceptually, the curvelet transfo...
Singularities of generic mean curvature flow.
ON THE ABSENCE OF "SPLASH" SINGULARITIES IN THE CASE OF TWO-FLUID INTERFACES
SPLASH SINGULARITIES TWO-FLUID INTERFACES
2014/4/3
We show that "splash" singularities cannot develop in the case of locally smooth solutions of the two-uid interfaces in two dimensions. More precisely, we show that the scenario of formation of singul...
Hypersurfaces and their singularities in partial correlation testing
Hypersurfaces singularities partial correlation testing
2012/11/21
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volu...
An Adaptive Multilevel Method For Time-Harmonic Maxwell Equations With Singularities
Maxwell's equations singularities of solutions adaptive 痭 ite element method multigrid method
2012/8/8
We develop an adaptive edge 痭ite element method based on reliable and e眂ient
residual-based a posteriori error estimates for low-frequency time-harmonic Maxwell's equations with
singularities. The r...
Local invariants on quotient singularities and a genus formula for weighted plane curves
Local invariants quotient singularities genus formula weighted plane curves Algebraic Geometry
2012/6/30
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
On the asymptotics of a Toeplitz determinant with singularities
the asymptotics of a Toeplitz determinant singularities Functional Analysis
2012/6/25
We provide an alternative proof of the classical single-term asymptotics for Toeplitz determinants whose symbols possess Fisher-Hartwig singularities. We also relax the smoothness conditions on the re...
Singularities of duals of Grassmannians
Singularities of duals of Grassmannians Algebraic Geometry Differential Geometry
2012/6/21
Let $X$ be a smooth irreducible nondegenerate projective variety and let $X^*$ denote its dual variety. It is well known that $\sigma_2(X)^*$, the dual of the 2-secant variety of $X$, is a component o...
Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
Embedded $\mathbf{Q}$-Resolutions for Yomdin-Lê Surface Singularities
Quotient singularity weighted blow-up embedded Q-reso-lution Yomdin-Le singularity characteristic polynomial monodromy
2012/6/19
In a previous work we have introduced and studied the notion of embedded $\mathbf{Q}$-resolution, which essentially consists in allowing the final ambient space to contain abelian quotient singulariti...