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1900s–1930s: Branch Curves and the Italian School of Algebraic Geometry
In contrast to the separate beginnings during the nineteenth century presented in the previous chapter, the twentieth century saw the consolidation...
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Differential Algebraic Equations
This chapter documents how to formulate and solve optimization problems with differential and algebraic equations (DAEs). The pyomo.dae package...
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A Categorical Aspect of the Analogy Between Quantifiers and Modalities
The formal analogy relating existential quantification to a modal possibility operator, and universal quantification to a modal necessity operator,...
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A survey of semisimple algebras in algebraic combinatorics
This is a survey of semisimple algebras of current interest in algebraic combinatorics, with a focus on questions which we feel will be new and...
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On Certain Algebraic Structures Associated with Lie (Super)Algebras
In this paper we exhibit a survey of constructions of Lie (super)algebras associated with certain triple systems, several examples and a historical...
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Algebraic Versus Geometric Thought and Expression in the Early Calculus
The language of the early calculus was much more geometrical than the analytic and algebraic style that was pioneered by Euler and still dominates...
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Stable recovery of planar regions with algebraic boundaries in Bernstein form
We present a new method for the stable reconstruction of a class of binary images from a small number of measurements. The images we consider are...
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Rational Liouvillian Solutions of Algebraic Ordinary Differential Equations of Order One
We give a necessary and sufficient condition for an autonomous first-order AODE to have a rational liouvillian solution. We also give an algorithm to...
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On the Superstability of an Interval Family of Differential-Algebraic Equations
AbstractWe consider an interval family of differential-algebraic equations (DAE) under assumptions that guarantee the coincidence of the structure...
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Algebraic Properties of Invariancy Regions
In this chapter we utilize concepts from the field of Semi-algebraic Geometry and Algebraic Topology in order to show that the dimension of an...
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Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
In the 1970s of the last century, the progress in powerful simulation software for mechanical multibody systems and for electrical circuits led to a...
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Emphases in Algebraic Analysis After Euler
Jean-Baptiste le Rond d’Alembert (1717–1783), another first-rate mathematician, was a slightly younger contemporary of Euler. He was also active as a...
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Brief History of Algebraic Topology: Motivation of the Subject and Historical Development
This chapter conveys the history of emergence of the concepts leading to the development of algebraic topology as a subject with their motivations....
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A new algebraic approach to genome rearrangement models
We present a unified framework for modelling genomes and their rearrangements in a genome algebra, as elements that simultaneously incorporate all...
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On the Topology of the Intersection Curve of Two Real Parameterized Algebraic Surfaces
Let $$\mathcal {S}_{\Gamma } : = {\operatorname {Im}} (\Gamma ) =...
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Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry
Infinite-dimensional Lie algebras (such as Kac-Moody, Virasoro etc.) govern, in many ways, various moduli spaces associated to algebraic curves. To...
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Problematic of Mathematics, Social Sciences, and Arts: A Ubiquitous Constructive Interaction in Algebraic Modeling
In this opening chapter, we reflect on the nature of mathematics and its contribution to society through two important ways of doing mathematics:...
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Martin Kneser’s Work on Quadratic Forms and Algebraic Groups
This article provides an overview of the research work of Martin Kneser on the arithmetic theory of quadratic forms and algebraic groups, focusing on...
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Paths of rectangles inscribed in lines over fields
We study rectangles whose vertices lie in sequence on four lines in the plane by parametrizing these rectangles in two ways, one involving slope and...
