相关论文: Various notions of point derivations in Banach alg…
Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular,…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
The (parallel linear) transports in tensor spaces generated by derivations of the tensor algebra along paths are axiomatically described. Certain their properties are investigated. Transports along paths defined by derivations of the tensor…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
We shall study backward stochastic differential equations and we will present a new approach for the existence of the solution. This type of equation appears very often in the valuation of financial derivatives in complete markets.…
We suggest a few projects for studying vertex algebras with emphasis on finite group viewpoints.
In this paper, we introduce directed networks called `divergence network' in order to perform graphical calculation of divergence functions. By using the divergence networks, we can easily understand the geometric meaning of calculation…
We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm…
The slope variety of a graph is an algebraic set whose points correspond to drawings of a graph. A complement-reducible graph (or cograph) is a graph without an induced four-vertex path. We construct a bijection between the zeroes of the…
This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…
In this paper, we study the existence of the random fixed points for lower semicontinuous condensing random operators defined on Banach spaces. Our results extend corresponding ones present in literature.
We discuss the relationship between Hopf superalgebras and Hopf algebras. We list the braided vector spaces of diagonal type with generalized root system of super type and give the defining relations of the corresponding Nichols algebras.
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Using dual perturbation theory in a non-sun-reflexive context, we establish a correspondence between 1. a class of nonlinear abstract delay differential equations (DDEs) with unbounded linear part and an unknown taking values in an…
Given a Banach Algebra $A$ and $a\in A$, several relations among the Drazin spectrum of $a$ and the Drazin spectra of the multiplication operators $L_a$ and $R_a$ will be stated. The Banach space operator case will be also examined.…
An algebraic deformation theory of dialgebra morphisms is obtained.