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Singularities of Flat Dual Surfaces of Cuspidal Edges in the Three-Sphere from Duality Viewpoint
We focus on investigating the differential geometric properties of cuspidal edge in the three-sphere from a viewpoint of duality. Using Legendrian...
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Historical steps of development of convexity as a field
In this chapter we will show historical steps of the development of convexity as a field and, in addition, developments of the relations between...
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Poincaré Duality
Recall that our goal is to find a solution to the following problem. Problem 4.1. Let X be a finite CW-complex. When is X homotopy equivalent to a...
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Deciding whether a lattice has an orthonormal basis is in co-NP
We show that the problem of deciding whether a given Euclidean lattice L has an orthonormal basis is in NP and co-NP. Since this is equivalent to...
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From duality in mathematical programming to Fenchel duality and convex analysis: Duality as a force of inspiration in the creation of new mathematics
“Duality” is an intriguing notion in the history of mathematics that refers to a variety of phenomena in many different areas and sub-disciplines of...
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Duality theorems in topology
The present chapter is devoted to the early work on duality phenomena in topology. Of course, topology is a field which emerged from geometry during...
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Dualizing spheres for compact p-adic analytic groups and duality in chromatic homotopy
The primary goal of this paper is to study Spanier–Whitehead duality in the K ( n )-local category. One of the key players in the K ( n )-local category is...
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Unitless Frobenius Quantales
It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define Frobenius quantales...
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Polar Degrees
The notion of polar degrees is fundamental for assessing the algebraic complexity of polynomial optimization problems of a metric origin.We already...
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A Duality-Based Proof of the Triangle Inequality for the Wasserstein Distances
This short note gives a proof of the triangle inequality based on the Kantorovich duality formula for the Wasserstein distances of exponent
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DNA codes over two noncommutative rings of order four
In this paper, we describe a new type of DNA codes over two noncommutative rings E and F of order four with characteristic 2. Our DNA codes are based...
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Sha**, Revisited
In this chapter, I review the argument of “The Sha** of Deduction in Greek Mathematics,” explaining its elements that may be construed as...
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Local Projective Positivity of Local Function Systems
AbstractThe present paper is devoted to the local projective positivity in the category of the local function systems or commutative local operator...
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The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary
We give two proofs that appropriately defined congruence subgroups of the map** class group of a surface with punctures/boundary have enormous...
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A Note on the Global Dimension of Shifted Orders
We consider the dominant dimension of an order over a Cohen-Macaulay ring in the category of centrally Cohen-Macaulay modules. There is a canonical...
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Several characterizations of left Köthe rings
We study classical Köthe’s problem, concerning the structure of non-commutative rings with the property that: “every left module is a direct sum of...
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