Related papers: Elimination with applications to singularities in …
In this note, we provide a complete classification for entire area maximizing hypersurfaces having an isolated singularity. We also construct an interesting illustrated example. For area maximizing hypersurfaces over exterior domains, we…
This paper studies "pro-excision" for the K-theory of one-dimensional (usually semi-local) rings and its various applications. In particular, we prove Geller's conjecture for equal characteristic rings over a perfect field of finite…
We give an alternative proof of the theorem by Kuznetsov and Lunts, stating that any separated scheme of finite type over a field of characteristic zero admits a categorical resolution of singularities. Their construction makes use of the…
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to…
We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zero-dimensionality are shown to be equivalent. The part of this characterisation that…
We reduce the classification of finite extensions of function fields (of curves over finite fields) with the same class number to a finite computation; complete this computation in all cases except when both curves have base field…
This work focuses on the problem of exact model reduction of positive linear systems, by leveraging minimal realization theory. While determining the existence of a positive reachable realization remains in general an open problem, we are…
Let $K$ be a field, and $A=K[a_1,\ldots ,a_n]$ a solvable polynomial algebra in the sense of [K-RW, {\it J. Symbolic Comput.}, 9(1990), 1--26]. Based on the Gr\"obner basis theory for $A$ and for free modules over $A$, an elimination theory…
This paper summarizes the results at the present moment about singularities with respect to the Mather-Jacobian log discrepancies over algebraically closed field of arbitrary characteristic. The basic point is the Inversion of Adjunction…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
The purpose of this work is to investigate the consequences of quantum gravity for the singularity problem. We study the higher-derivative terms that invariably appear in any quantum field theoretical model of gravity, handling them both…
We show that a version of the desingularization theorem of Hironaka holds for certain classes of infinitely differentiable functions (essentially, for subrings that exclude flat functions and are closed under differentiation and the…
We study local behavior of positive solutions to the fractional Yamabe equation with a singular set of fractional capacity zero.
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meadow signature (this additional value can be interpreted as an…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…