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Hybrid Transforms of Constructible Functions
We introduce a general definition of hybrid transforms for constructible functions. These are integral transforms combining Lebesgue integration and...
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Constructible sheaves and functions up to infinity
We introduce the category of b-analytic manifolds, a natural tool to define constructible sheaves and functions up to infinity. We study with some...
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Stratifications of real vector spaces from constructible sheaves with conical microsupport
Interpreting the syzygy theorem for tame modules over posets in the setting of derived categories of subanalytically constructible sheaves proves two...
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Constructible Sheaf Complexes in Complex Geometry and Applications
We present a detailed introduction of the theory of constructible sheaf complexes in the complex algebraic and analytic setting. All concepts are...
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A Sheaf-Theoretic Construction of Shape Space
We present a sheaf-theoretic construction of shape space—the space of all shapes. We do this by describing a homotopy sheaf on the poset category of...
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Rouquier dimension is Krull dimension for normal toric varieties
We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull...
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All Melodies Are Lost – Recognizability for Weak and Strong \(\alpha \) -Register Machines
For exponentially closed ordinals \(\alpha \) ,...
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Sets of real numbers closed under Turing equivalence: applications to fields, orders and automorphisms
In the first half of this paper, we study the way that sets of real numbers closed under Turing equivalence sit inside the real line from the...
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Measurability Properties of Mazurkiewicz Sets
In this chapter we consider the family of Mazurkiewicz subsets of the Euclidean plane ℝ2 from the measure-theoretical point of view. In particular,...
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Structural Properties of Minimum Multi-source Multi-Sink Steiner Networks in the Euclidean Plane
Given two finite sets A and B of points in the Euclidean plane, a minimum multi-source multi-sink Steiner network in the plane, or a minimum ( A , B )-ne...
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Hausdorff approximations and volume of tubes of singular algebraic sets
We prove bounds for the volume of neighborhoods of algebraic sets, in the euclidean space or the sphere, in terms of the degree of the defining...
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Bijective Continuous Images of Absolute Null Sets
In modern mathematics there are various notions of so-called small sets (small spaces). In classical real analysis, Lebesgue measure theory, and...
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Bilinear forms with trace functions over arbitrary sets and applications to Sato-Tate
We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves, where the supports of two variables can be...
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Riemann–Roch formulas for universal bivariant theories
This is a survey of Fulton–MacPherson’s bivariant theory, focusing on an important notion called Riemann–Roch formula . In Yokura (Int J Math...
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Other Structures
In the first part of this chapter we consider some properties of the class of global semianalytic sets in...
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Cyclicity of the Limit Periodic Sets for a Singularly Perturbed Leslie–Gower Predator–Prey Model with Prey Harvesting
In this paper, we study the Leslie–Gower predator–prey model with Michaelis–Menten type prey harvesting. Our main focus is on the cyclicity of...
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Borel Isomorphisms of Analytic Sets
According to the commonly used terminology, a topological space E is Polish if E is homeomorphic to some complete separable metric space. Recall that...
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Complete Sets
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is...
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Linear approximation method for solving split inverse problems and its applications
We study the problem of finding a common element that solves the multiple-sets feasibility and equilibrium problems in real Hilbert spaces. We...