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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...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
MATHEMATICAL DEVELOPMENTS FROM THE ANALYSIS OF RIFFLE SHUFFLING
Mathematical analysis development ripples shuffling
2015/7/8
Introduction The most common method of mixing cards is the ordinary riffle shuffle, in which a deck of n cards (often n = 52) is cut into two parts and the
parts are riffled together. A sharp mathema...
Micro-local Analysis for the Metropolis Algorithm
Convergence rate algorithm random eigenvalues and eigenvectors
2015/7/8
We prove sharp rates of convergence to stationarity for a simple case of the Metropolis algorithm: the placement of a single disc of radius h randomly into the
interval [−1 − h, 1 + h], w...
On the spectral analysis of second-order Markov chains
second order Markov chains trajectorial reversibility spectrum of non-reversible Markov kernels spectral gap improvement of speed of convergence discrete position-speed Markov chains homogeneous and Abelian second order Markov chains
2015/7/7
Second order Markov chains which are trajectorially reversible are considered. Contrary to the reversibility notion for usual Markov chains, no symmetry property can be deduced for the corresponding t...
A Spectral Analysis Approach for Experimental Designs
In this paper we show how the approach of spectral analysis generalizes the standard ANOVA-based techiques for studying data from designed experiments. Several examples are worked out in detail including a thorough analysis of Calvin's famous ice cream data.
2015/7/7
In this paper we show how the approach of spectral analysis generalizes the standard ANOVA-based techiques for studying data from designed experiments.Several examples are worked out in detail, includ...
THE INTEGRAL K-THEORETIC NOVIKOV CONJECTURE FOR GROUPS WITH FINITE ASYMPTOTIC DIMENSION
K-THEORETIC integral
2015/7/7
The goal of this paper is to apply the techniques developed by the first author
in [3] to verify the integral Novikov conjecture for groups with finite asymptotic
dimension as defi...
Twisted Weyl Group Multiple Dirichlet Series: The Stable Case
Stable Case Multiple Dirichlet Series
2015/7/6
Weyl group multiple Dirichlet series were associated with a root system Φ and a number
field F containing the n-th roots of unity by Brubaker, Bump, Chinta, Friedberg and Hoffstein [3] an...
Given a root system Φ of rank r and a global field F containing the n-th
roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose
coefficients are n-th ...
Weyl Group Multiple Dirichlet Series, Eisenstein Series and Crystal Bases
Eisenstein Series Crystal Bases
2015/7/6
If F is a local eld containing the group n of n-th roots of unity, and if G is a split
semisimple simply connected algebraic group, then Matsumoto [27] de ned an n-fold
covering group of G(F), tha...
Gis-supported Precise Spatio-temporal Modelling from Airborne Sar Imagery
SAR modelling Temporal
2015/7/6
Precise spatio-temporal model can make it easy to obtain precise temporal and spatial information just like the true world, and it is of
much importance to the planning and designing of Civil Enginee...
THE BASIC TOPOLOGY MODEL OF SPHERICAL SURFACE DIGITAL SPACE
SGDM manifold spherical surface digital space
2015/7/6
SGDM (Sphere Grid Data Model) is an efficient method to deal with the global data because of the advantages of multi-resolution and
hierarchy. However, SGDM has no distinct descriptions and lack of r...
Let Re(s)﹦π(n)／n,(n﹦2), and Im(s)﹦((π(n)﹣π(2))㏒n)i,(n＞2)， Riemann hypothesis is proved.
Speaking in and about mathematics classrooms internationally: The technical vocabulary of students and teachers
Speaking mathematics classrooms
2015/5/29
This presentation takes patterns of
language use as the entry point for
the consideration of discourses in and
about the mathematics classroom.
These patterns of language take the
form of di...
Identifying cognitive processes important to mathematics learning but often overlooked
overlooked mathematics learning
2015/5/29
This presentation introduces a set
of mathematical competencies that
deserve to be given more attention
in our mathematics classrooms, on
the grounds that the possession of
these competencie...