Related papers: A Grothendieck topos of generalized functions I: b…
The result of performing integrations over connection type variables in the path integral for the discrete field theory may be poorly defined in the case of non-compact gauge group with the Haar measure exponentially growing in some…
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is…
As a generalization of geodesic function, in the present paper, we introduce the notion of geodesic $\varphi$-convex function and deduce some basic properties of $\varphi$-convex function and geodesic $\varphi$-convex function. We also…
We develop a calculus based on graph enumeration for $S_n$-equivariant motivic invariants of graphically stratified moduli spaces. We apply our theory to the Deligne--Mumford moduli space $\overline{\mathcal{M}}_{g, n}$ and to the space of…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
In the framework of the generalized measure theory the decomposable probabilistic-valued set functions are introduced with triangle functions $\tau$ in an appropriate probabilistic metric space as natural candidates for the "addition",…
In this expository note, we revisit several classical arithmetic functions - namely Euler's totient function, the divisor sum functions and Dedekind's $\psi$-function - within a unifying algebraic framework that highlights their connections…
In the early 1960's, Moreau and Rockafellar introduced a concept of called \emph{subgradient} for convex functions, initiating the developments of theoretical and applied convex analysis. The needs of going beyond convexity motivated the…
We present an extension of the methods of classical Lie group analysis of differential equations to equations involving generalized functions (in particular: distributions). A suitable framework for such a generalization is provided by…
Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…
This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…
The aim of this article is to give a rather extensive, and yet nontechnical, account of the birth of the regularity theory for generalized minimal surfaces, of its various ramifications along the decades, of the most recent developments,…
Inspired by the theories of Kaplansky-Hilbert modules and probability theory in vector lattices, we generalise functional analysis by replacing the scalars $\mathbb{R}$ or $\mathbb{C}$ by a real or complex Dedekind complete unital…
We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonality of morphisms, which we hope might be of use in the…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
The space of Schwartz distributions of finite order is represented as a factor space of the space of, what we call, Mikusinski functions. The point of Mikusinski functions is that they admit a multiplication by convergent Laurent series. It…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
This paper explores generalized slice monogenic functions by introducing their operator symbols, representation formula, and integral formula. The study extends the Teodorescu transform to a broader class of theorems and inferences,…
We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally…