We provide simple formulas that can be used to calculate ideal bootstrap or exact recombination estimates of group statistics from experimental data. When resampling is done over small numbers of groups, the ideal bootstrap is more accurate than the exact recombinant estimate, however the former is biased. For large sample sizes there is no discernable difference between the two approaches and ...

This article is concerned with the global exact controllability for ideal incompressible magnetohydrodynamics in a rectangular domain where controls are situated both vertical walls. First, via boundary established related Elsässer type system by applying return method, introduced [Coron J.M., Math. Control Signals Systems, 5(3) (1992) 295--312]. Similar results then inferred original help of s...

Book Reviews classical medical training. Following a six year apprenticeship in an English country surgery and a brief period in London, he returned to Berkeley in 1792 to practice variolation, a method that had been popularized to com-The Eradication of Small Pox: Edward bat the smallpox. As the author points out, variolation Jenner and the First and Only Eradication was a highly dangerous pra...

Let V be a vector space over some field k, and let α : V V be a linear map (an ‘endomorphism of V ’). Given any polynomial p with coefficients in k, there is an endomorphism p(α) of V , and we say that p is an annihilating polynomial for α if p(α) = 0. Our first major goal is to see that for any α, the annihilating polynomials can easily be classified: they’re precisely the multiples of a certa...

In this paper, we study the nonlinear inverse problem of estimating spectrum a system matrix, that drives finite-dimensional affine dynamical system, from partial observations single trajectory data. noiseless case, prove an annihilating polynomial whose roots are subset spectrum, can be uniquely determined We then which eigenvalues matrix recovered and derive various sufficient necessary condi...

Our paper presents an attempt to axiomatise signal processing. Our long-term goal is to formulate signal processing algorithms for an ideal world of exact computation and prove properties about them, then interpret these ideal formulations and apply them without change to real world discrete data. We give models of the axioms that are based on Gaussian functions, that allow for exact computatio...