Related papers: $F$-singularities: applications of characteristic …

Let $X \subset\mathbb{P}^r$ be a projective $d$-variety with isolated determinantal singularities and $\omega$ be a $1$-form on $X$ with a finite number of singularities (in the stratified sense). Under some technical conditions on $r$ we…

Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities,…

A review of the superstatistics concept is provided, including various recent applications to complex systems.

P-resolutions of two-dimensional, cyclic quotient singularities have been introduced to study deformation theory. Those P-resolutions (as well as the singularities themselves) are toric varieties. In the present paper we give a straight,…

Applications of the principle of reduction of couplings to the standard model and supersymmetric grand unified theories are reviewed. Phenomenological applications of renormalization group invariant sum rules for soft supersymmetry-breaking…

The first examples of exceptional terminal singularities are constructed.

In this paper, we will use investigate the existence of compactifications with particular convergence properties - pseudoradial, radial, sequential and Fr\'echet-Urysohn - through the use of spoke systems.

After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…

In this article, we explore the structure of IR singularity of Feynman diagrams at one loop via power counting in loop momentum. The emphasis is on many known results which follow from this simple analysis.

In this paper we study nodal deformations of singular surfaces $S\subset \mathbb P^3$. In particular we consider the case in which $S$ has an isolated singularity of multiplicity $m$ and the case in which $S$ has only ordinary singularities…

Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.

Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modelled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path…

We study the isolated singularities of functions satisfying (E) (--$\Delta$) s v$\pm$|v| p--1 v = 0 in $\Omega$\{0}, v = 0 in R N \$\Omega$, where 0 < s < 1, p > 1 and $\Omega$ is a bounded domain containing the origin. We use the…

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.

Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…

A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.

In this essay, we provide an overview of methodological considerations necessary to lay out the foundation for our PhD research on uncertainty and risk-aware adaptation.

We consider the parameterization ${\mathbf{f}}=(f_0,f_1,f_2)$ of a plane rational curve $C$ of degree $n$, and we want to study the singularities of $C$ via such parameterization. We do this by using the projection from the rational normal…

We study the Lorenz model from the viewpoint of its accessible singularities and local index.

Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic…