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Minkowski’s Fundamental Theorem and Its Applications
Given a real valued function \(F(x_{1},x_{2},\ldots ,x_{n})\)...
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Galois Theory (II)—The Fundamental Theorem
In this chapter, the fundamental theorem of Galois theory is stated and proven. Additionally, we prepare for application to the question of a...
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An algebraic approach to the Fundamental Theorem of Algebra
In this paper, we investigate the algebraic counterpart of the Fundamental Theorem of Algebra. We explore the concept of real-closed fields and...
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Fundamental theorem of asset pricing with acceptable risk in markets with frictions
We study the range of prices at which a rational agent should contemplate transacting a financial contract outside a given market. Trading is subject...
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Fundamental Theorem for (A, H)-dimodules
Let k be a field, H a Hopf algebra with a bijective antipode, and A an H -dimodule algebra. We assume that there is an H -colinear algebra map from H ...
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Fundamental Theorem of Asset Pricing under fixed and proportional costs in multi-asset setting and finite probability space
The Fundamental Theorem of Asset Pricing is extended to a market model over a finite probability space with many assets that can be exchanged into...
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A Fundamental Theorem
The fundamental theorem of this chapter constructs a splitting field for a given polynomial. Stated differently, for polynomials whose coefficients...
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The Fundamental Theorem of Calculus
From Chapter 29 we recognize that there is a relationship between the accumulation function and the...
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Fundamental Theorem of Calculus
In Chap. 15 , we have seen the construction and properties of Riemann integrals. We have also seen some...
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Two-Sided Fundamental Theorem of Affine Geometry
The fundamental theorem of affine geometry says that if a self-bijection f of an affine space of dimenion n over a possibly skew field takes left...
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The Fundamental Theorem of Algebra
The field \(\mathbb {C}\) of complex numbers...
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Fundamental group of complex hypocycloids
The Zariski–van Kampen theorem allows us to provide a presentation of the fundamental group for the complement of algebraic plane curves. However,...
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The Fundamental Theorem of Arithmetic
In Chapter 2, we made extensive use of the fact that every positive integer can be written in one and only one way as a product of powers of distinct...
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Fundamental Groupoid and van Kampen’s Theorem
In many geometrically relevant situations, a space can be decomposed into smaller spaces. This might either mean that one has a suitable cover by...
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Fundamental Theorem for Explicit Eigenvalue Bounds
This chapter details a Galerkin projection-based method for obtaining explicit eigenvalue bounds in the form:...
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Social Construction: The Fundamental Theorem
The troubled history of the concept “social construction” in science studies begins in earnest with the milestone publication in 1979 of Laboratory...
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Brooks' Theorem Graph Coloring and Critical Graphs
Brooks' Theorem (1941) is one of the most famous and fundamental theorems in graph theory – it is mentioned/treated in all general monographs on...