منابع مشابه
Nonlinear Root Finding
There has always been a close relationship between mathematics and the sciences (astronomy, chemistry, engineering, physics, etc.). When applying mathematics to study some physical phenomenon, it is often the case that we arrive at a mathematical model (an equation or set of equations) of the phenomenon that cannot be conveniently solved with exact formulas. The following classical example from...
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In this paper, we rst show that there are several equivalent keys for t + 1 chosen plaintexts if the degree of the reduced cipher is t?1. This is against the claim by Jakobsen and Knudsen. We also derive an upper bound on the number of equivalent last round keys for t + 1 chosen plaintexts. We further show an eecient method which nds all the equivalent keys by using Rabin's root nding algorithm...
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Root isolation of univariate polynomials is one of the fundamental problems in computational algebra. It aims to find disjoint regions on the real line or complex plane, each containing a single root of a given polynomial, such that the union of the regions comprises all roots. For root solving over the field of complex numbers, numerical methods are the de facto standard. They are known to be ...
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Platelets are blood elements that play a key role in coagulation and participate directly in the processes of thrombosis and atherosclerosis (1-3). However, the physiologic mechanisms governing platelet formation and release from megakaryocytes remain largely unknown (4). Platelets are nonnucleated cells with only a vestigial protein synthetic apparatus, and therefore most of the structural and...
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We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials—given by a list of coefficients in binary—can be computed to a given accuracy by a uniform TC algorithm (a uniform family of constant-depth polynomial-size threshold circuits). The basic idea is to compute the inverse function of the polynomial by a power series. We also discuss an ...
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ژورنال
عنوان ژورنال: Blood
سال: 2017
ISSN: 0006-4971,1528-0020
DOI: 10.1182/blood-2017-04-776351