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Applications of operational calculus: Equations for rectangular arrays of four and five data
Interpolation shifting operator rectangular data array operational equations
2010/11/1
Selections of equations for four or five data in rectangular array are seldom encountered in textbooks. New methods illustrate polynomial and exponential equations for the two designs. The methods are...
Exponential Convergence Rates of Second Quantization Semigroups and Applications
Convergence rate tail norm entropy second quantization L´ evy processes
2011/2/28
Exponential convergence rates in the L2-tail norm and entropy are characterized for the second quantization semigroups by using the corresponding base Dirichlet form. This supplements the well known r...
This paper presents a self-contained account for coupling arguments and ap-plications in the context of Markov processes. We first use coupling to describe the transport problem, which leads to the co...
Applications of operational calculus: Trigonometric interpolating equation for the eight-point cube
interpolation operational equations prismatic array
2010/9/21
A general method for obtaining a trigonometric-type interpolating equation for the eight-point cubical array is illustrated. It can often be used to reproduce a ninth datum at an arbitrary point near ...
Applications of fractional calculus
fractional derivative fractional Integral differintegrals
2010/9/21
Different definitions of fractional derivatives and fractional Integrals (Differintegrals) are considered. By means of them explicit formula and graphs of some special functions are derived. Also we r...
Applications of operational calculus: Rectangular prisms and the estimation of a missing datum
Interpolation data replacement operational equations
2010/9/21
Operational equations can be used for the estimation of data missing from prismatic arrays. This paper continues the discussion of that subject. New interpolating equations for data in prismatic and r...
Applications of operational calculus: trigonometric interpolating equation for the nine-point prism and robust center point formulas
operational equations prismatic array central tendency
2010/9/26
The derivation of a trigonometric equation for the nine-point, rectangular prismatic array is illustrated. In many cases, the equation can be used to reproduce a ninth datum at an arbitrary point near...
Applications of fractional differential equations
fractional derivative fractional differential equations
2010/9/27
By considering different definitions of fractional derevatives, we study some kind of fractional differential equations and also give some of there applications.
Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models with applications to parameter estimation
Non-asymptotic deviation inequalities smoothed additive functionals in non-linear state-space parameter estimation
2011/2/22
Approximating joint smoothing distributions using particle-based methods is a well-known issue in statistical inference when operating on general state space hidden Markov models (HMM). In this paper ...
An Inverse Power Method for Nonlinear Eigenproblems with Applications in 1-Spectral Clustering and Sparse PCA
Inverse Power Method Nonlinear Eigenproblems
2011/1/4
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding cri...
Approximate tail probabilities of the maximum of a chi-square field on multi-dimensional lattice points and their applications to detection of loci interactions
Approximate tail probabilities a chi-square field multi-dimensional lattice points
2011/1/4
Define a chi-square random field on a multi-dimensional lattice points index set with a direct-product covariance structure, and consider the distribution of the maximum of this random field. We provi...
Explicit formula for the solution of the Szegö equation on the real line and applications
Szeg¨o equation integrable systems Lax pair Hankel operators soliton resolution
2011/1/21
We consider the cubic Szeg¨o equation i@tu = (|u|2u) in the Hardy space L2 +(R) on the upper half-plane, where is the Szeg¨o projector.
Some aspects of the $m$-adic analysis and its applications to $m$-adic stochastic processes
$m$-adic analysis applications to $m$-adic stochastic processes
2011/1/18
In this paper we consider a generalization of analysis on p-adic numbers field to the m case of m-adic numbers ring. The basic statements, theorems and formulas of p-adic analysis can be used for the ...
Applications of Differential Chains to Complex Analysis and Dynamics
Differential Chains Complex Analysis Dynamics
2011/2/28
First and foremost, I would like to thank my advisor Sarah Koch for being so generous with her time and energy.
Computations and Applications of eta invariants
Computations Applications of eta invariants
2010/11/24
We give a survey on eta invariants including methods of computation and applications in differential topology.