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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the preservation of second integrals by RK methods
RK方法 保存 第二积分
2023/4/25
One can elucidate integrability properties of ODEs by knowing the existence of second integrals. However, little is known about how they are preserved, if at all, under numerical methods. In this talk...
THE GROMOV-WITTEN POTENTIAL OF A POINT, HURWITZ NUMBERS, AND HODGE INTEGRALS
Hurwitz numbers Gromov-Witten potential moduli space
2015/7/14
It is the Deligne-Mumford compacti cation of the moduli space Mg;n of smooth
n-pointed genus g curves. It has n natural line bundles Li (roughly, the cotangent
space to the ith marked point) and a n...
HODGE INTEGRALS AND HURWITZ NUMBERS VIA VIRTUAL LOCALIZATION
HODGE INTEGRALS HURWITZ NUMBERS
2015/7/14
We give another proof of Ekedahl, Lando, Shapiro, and Vainshtein's remarkable formula expressing Hurwitz numbers (counting covers of
P1 with speci ed simple branch points, and speci ed branching over...
Upper bounds for the number of zeroes for some Abelian integrals
Abelian integrals Weak 16th Hilbert’s Problem limit cycles
2011/2/25
Consider the vector field x′ = −yG(x, y), y′ = xG(x, y), where the set of critical points {G(x, y) = 0} is formed by K straight lines, not passing through the origin and parallel to one or two o...
On absolute convergence of multiple Fourier integrals
Fourier integral Fourier multiplier Hardy-Steklov
2011/2/25
New sufficient conditions for representation of a func-tion of several variables as an absolutely convergent Fourier integral are obtained in the paper.
Feynman integrals and motives of configuration spaces
Feynman integrals motives of configuration spaces
2011/2/28
We formulate the problem of renormalization of Feynman integrals and its relation to periods of motives in configuration space instead of momentum space.
The iterated integrals of ln(1 + x^2)
Iterated integrals harmonic numbers recurrences valuations
2011/2/21
For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x2), arithmetic properties of cer...
Quadratic harnesses from generalized beta integrals
Quadratic conditional moments generalized beta integrals harnesses
2010/12/13
We use generalized beta integrals to construct examples of Markov processes with linear regressions, and quadratic second conditional moments.
Local Zeta Functions and Oscillatory Integrals for Non-degenerate Laurent Polynomials Over p-adic Fields
exponential sums mod p p-adic oscillatory integrals Laurent polynomials
2010/12/8
In this article, we study exponential sums mod p m, or more generally,p-adic oscillatory integrals attached to Laurent polynomials which are non-degenerate with respect to its Newton polytope at infin...
DESCENDENT INTEGRALS AND TAUTOLOGICAL RINGS OF MODULI SPACES OF CURVES
DESCENDENT INTEGRALS TAUTOLOGICAL RINGS MODULI SPACES CURVES
2018/4/19
The main objective of this paper is to give a summary of our recent work on recursion formulae for intersection numbers on moduli spaces of curves and their applications.We also present a conjectural ...
We present an explicit formula for integrals of the open 2D Toda lattice of type $A_n$. This formula is applicable for various reductions of this lattice. To illustrate the concept we find integrals o...
State and parameter estimation using Monte Carlo evaluation of path integrals
parameter estimation path integrals Monte Carlo
2010/4/6
Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path in...
Singular Integrals and Commutators in Generalized Morrey Spaces
generalized Morrey spaces singular integrals commutators Calder\'on--Zygmund kernel BMO VMO
2007/12/13
We consider a singular an integral operator ${\mathscr K}$ with a variable Calder\'on--Zygmund type kernel $k(x;\xi),$ $x\in {\Bbb R}^n,$ $\xi\in {\Bbb R}^n\sm\{0\},$ satisfying a mixed homogeneity co...
On Rough Singular Integrals Along Surfaces on Product Domains
Singular Integrals Product Domains
2010/2/26
In this paper, we study a class of singular integrals along surfaces on product domains with kernels in L(log L)2(Sn-1 \times Sm-1). We formulate a general theorem concerning the Lp boundedness of the...
On a proof of a conjecture of Marino-Vafa on Hodge integrals
a proof of a conjecture Marino-Vafa Hodge integrals
2018/4/20
We outline a proof of a remarkable formula for Hodge integrals conjectured by Mari˜no and Vafa based on large N duality.