Related papers: A general context for Goodwillie Calculus
In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…
Mumford defined a rational pullback for Weil divisors on normal surfaces, which is linear, respects effectivity, and satisfies the projection formula. In higher dimensions, the existence of small resolutions of singularities precludes such…
We introduce the basic elements of the theory of parametrized $\infty$-categories and functors between them. These notions are defined as suitable fibrations of $\infty$-categories and functors between them. We give as many examples as we…
In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical…
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional…
This paper presents a generalized version of a theorem of Grzegorek and Labuda in category bases and also endeavours to establish a variant formulation of the same in Marczewski structures.
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We give sufficient conditions for a general Dirichlet series to be universal with respect to translations or rearrangements.
We use generalized Taylor formulae in order to give some simple constructions in the real closure of an \ovfz. We deduce a new, simple quantifier elimination algorithm for \rcvfs and some theorems about constructible subsets of real…
Pearl's front-door criterion provides a set of sufficient conditions for estimating the total causal effect from observational data in the presence of latent confounding, using the functional P(y | do(x := x*)) = \sum_z P(z | x*) \sum_x P(y…
This paper presents a sound and completecalculus for causal relevance, based onPearl's functional models semantics.The calculus consists of axioms and rulesof inference for reasoning about causalrelevance relationships.We extend the set of…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
The purpose of this paper is to investigate the generalized formulation of weighted optimal guidance laws with impact angle constraint. From the generalized formulation, we explicitly find the feasible set of weighting functions that lead…
The main purpose of this article is to study conditions for a curve on a submanifold $M\subset\mathbb{R}^n$, constructed in a particular way involving the Euclidean distance to $M$, to be a geodesic. We also present the naturally arising…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
A new categorical setting is defined in order to characterize the subrecursive classes belonging to complexity hierarchies. This is achieved by means of coercion functors over a symmetric monoidal category endowed with certain recursion…