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Geometry of jet spaces and integrable systems
jet spaces integrable systems Geometry
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2010/4/2
An overview of some recent results on geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space...
Recent Development on the Geometry of the Teichuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
Geometry of the Teichuller Moduli Spaces Riemann Surfaces Polarized Calabi-Yau Manifolds
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2018/4/19
The moduli spaceMg,k of Riemann surfaces of genus g with k punctures plays an important role in many area of mathematics and theoretical physics.In this article we first survey some of our recent work...
Integrable GL(2) Geometry and Hydrodynamic Partial Differential Equations
Integrable GL(2) Geometry Hydrodynamic Partial Differential Equations
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2010/4/7
This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). ...
Visually Dynamic Presentation of Proofs in Plane Geometry Part 1. Basic Features and the Manual Input Method
Geometry theorem proving Visually dynamic presentation of proof Dynamic geometry Unordered geometry Gelernter Java Geometry Expert Morley’s theorem Feuerbach’s theorem Pythagorean theorem Pedal triangle
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2013/9/9
With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In asingle diagram for the proof, when the proof text goes on step b...
Visually Dynamic Presentation of Proofs in Plane Geometry
Geometry theorem proving Proof with hierarchical structures Visually dynamic presentation of proof Dynamic geometry Full-angle Deductive database Fixpoint Unordered geometry Hilbert geometry Tarski geometry
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2013/9/9
We present the method for automated generation of visually dynamic presentations of plane geometry proofs based on the full-angle method. The proof generated by the full-angle method is organized hier...
New Results on the Geometry of the Moduli Space of Riemann Surfaces
MSC(2000)
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2018/4/20
In this paper we briefly survey our recent results about the Mumford goodness of several canonical metrics on the moduli spaces of Riemann surfaces. We will also prove the dual Nakano negativity of th...
THE GEOMETRY OF HIGHER PATH-SPACES
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2007/12/13
<正> IntroductionThe geometry in a space R_n(x~1,…, x~n)in whit.h there is givena system of differential equations of the r-th order:(?)has recently been studied by various writers.It seems to me thatt...
NOTE ON THE PROJECTIVE DIFFERENTIAL GEOMETRY OF SPACE CURVES
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2007/12/13
<正> INTRODUGTION.1.In the proiective theory of a curve in ordinary space thereare introduced various systems of tetrahedrons associated to a pointof the curve.Most of them are,more or less,artificial ...
PROJECTIVE DIFFERENTIAL GEOMETRY OF SINGULARITIES OF PLANE CURVES
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2007/12/12
<正> In a recent paper the present author has established somerepresentations for a plane curve C in the neighbourhood of a singularpoint O characterized by the property that the tangent t(?) of C at O...
PROJECTIVE DIFFERENTIAL GEOMETRY
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2007/12/12
<正> By hypothesis the curve C_m has with C a contact of order m+1;the constant term and the coefficient of the term s in the expansion off/s~m must vanish,namely……
HILBERT SPACE OF PROBABILITY DENSITY FUNCTIONS BASED ON AITCHISON GEOMETRY
Bayes' theorem Fourier coefficients Haar basis Aitchison distance Simplex Least squares approximation
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2007/12/12
The set of probability functions is a convex subset of $L^1$ and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise wh...
Test of the Possible Application of the Half-Way Bounce-Back Boundary
Condition for Lattice Boltzmann Methods in Complex Geometry
lattice Boltzmann method
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2007/8/15
2001Vol.35No.5pp.593-596DOI:
Test of the Possible Application of the Half-Way Bounce-Back Boundary
Condition for Lattice Boltzmann Methods in Complex Geometry
WAN Rong-Zheng and F...
SO(d,d;Z) Transformation Property for Gauge Fluxes and
Ramond-Ramond Fields in Noncommutative Geometry
SO(d d Z) spinor noncommutative geometry
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2007/8/15
2002Vol.37No.2pp.173-178DOI:
SO(d,d;Z) Transformation Property for Gauge Fluxes and
Ramond-Ramond Fields in Noncommutative Geometry
WANG Pei
Institute of Modern Physics,...
NEUMANN SERIES SOLUTION TO A NEUTRON TRANSPORT EQUATION OF SLAB GEOMETRY
Neutron transport equation series soluti
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2007/8/7
This paper deals with the solution to an energy, dependent stationary neutron transport equation of slab geometry. In L~p space, the equation is converted into an equivalent integral equation. By the ...
A REMARK ON SOME NUMERICAL RESULTS IN COMPLEX DIFFERENTIAL GEOMETRY
REMARK NUMERICAL RESULTS COMPLEX DIFFERENTIAL GEOMETRY
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2018/4/20
In order to find explicit numerical approximation of K¨ahler-Einstein metric of projective manifolds, Donaldson introduced in [3] various operators with good properties to approximate classical operat...