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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part II discrete case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In the second part, I will mainly focus on two semi-discrete models: Ablowitz-Ladik equation and fully discrete NLS equation. First, I will clarify the connection of these two discrete models with dis...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach: Part I continuous case
KP-户田约简法 NLS类型 方程孤子解 统一方法 离散情况
2023/4/27
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
GALERKIN AND RUNGE{KUTTA METHODS: UNIFIED FORMULATION, A POSTERIORI ERROR ESTIMATES AND NODAL SUPERCONVERGENCE
Continuous discontinuous Galerkin methods
2015/12/11
We unify the formulation and analysis of Galerkin and Runge{Kutta
methods for the time discretization of parabolic equations. This, together with
the concept of reconstruction of the approximate sol...
A Unified Near-Optimal Estimator For Dimension Reduction in lα (0 < α ≤ 2) Using Stable Random Projections
Near-Optimal Estimator Dimension Reduction Stable Random Projections
2015/8/21
Many tasks (e.g., clustering) in machine learning only require the lα distances instead of the original data. For dimension reductions in the lα norm (0 < α ≤ 2), the method of stable random projectio...
A Unified Generating Function of the q-Genocchi Polynomials with their Interpolation Functions
Genocchi numbers and polynomials q-Genocchi numbers and polynomials Number Theory
2011/9/23
Abstract: The purpose of this paper is to construct of the unification q-extension Genocchi polynomials. We give some interesting relations of this type of polynomials. Finally, we derive the q-extens...
A unified approach to the plus-construction, Bousfield localization, Moore spaces and zero-in-the-spectrum examples
plus-construction Bousfield localization Moore spaces zero-in-the-spectrum K-Theory and Homology
2011/9/14
Abstract: We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. T...
A unified treatment of ODEs under Osgood and Sobolev type conditions
DiPerna–Lions theory Sobolev regularity Osgood condition regular Lagrangian flow transport equation
2011/9/5
Abstract: In this paper we prove the existence, uniqueness and regularity of the DiPerna--Lions flow generated by a vector field which is "almost everywhere Osgood continuous", following Crippa and de...
On a unified formulation of completely integrable systems
integrable systems Hamiltonian dynamics linear normal forms
2011/7/7
The purpose of this article is to show that a $\mathcal{C}^1$ differential system on $\R^n$ which admits a set of $n-1$ independent $\mathcal{C}^2$ conservation laws defined on an open subset $\Omega\...
A Unified Analysis of Transmission with Transceiver Distortion and Some Applications
Unified Analysis of Transmission Transceiver Distortion Applications
2011/1/19
A unified analysis is presented for information transmission over Gaussian channels with memoryless nonlinear transceiver distortion, which encompasses various distortion models including transmit-sid...
Generating functions for the Bernstein polynomials: A unified approach to deriving identities for the Bernstein basis functions
Bernstein polynomials generating function Szasz-Mirakjan basis functions
2011/2/28
The main aim of this paper is to provide a unified approach to deriving identities for the Bernstein polynomials using a novel generating function. We derive various functional equations and different...
A Unified MGF-Based Capacity Analysis of Diversity Combiners over Generalized Fading Channels
Unified MGF-Based Capacity Analysis Diversity Combiners Generalized Fading Channels
2011/1/21
Unified exact average capacity results for L-branch coherent diversity receivers including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel gener...
A Unified MGF-Based Capacity Analysis of Diversity Combiners over Generalized Fading Channels
MGF-Based Capacity Analysis Diversity Combiners Generalized Fading Channels
2011/1/4
Unified exact average capacity results for L-branch coherent diversity receivers including equal-gain combining (EGC) and maximal-ratio combining (MRC) are not known. This paper develops a novel gener...
Towards a unified characterization of phenological phases: fluctuations and correlations with temperature
Biological Physics (physics.bio-ph) Adaptation and Self-Organizing Systems (nlin.AO) Data Analysis, Statistics and Probability (physics.data-an)
2010/11/11
Phenological timing -- i.e. the course of annually recurring development stages in nature -- is of particular interest since it can be understood as a proxy for the climate at a specific region; moreo...
On a unified theory of numbers
unified theory numbers
2010/12/13
In 1873 James Clerk Maxwell combined electricity and magnetism using the Maxwell's Equations into a single force called electromagnetism and since then,physicists have been trying to discover the elus...
Solutions of matrix NLS systems and their discretisations: A unified treatment
matrix NLS difference equations bidifferential graded algebra
2010/4/1
Using a bidifferential graded algebra approach to integrable partial differential or difference equations, a unified treatment of continuous, semi-discrete (Ablowitz-Ladik) and fully discrete matrix N...