相关论文: Algebraic Analysis Applied to the Theory of Linear…

Initially introduced by Peter Hammer, Logical Analysis of Data is a methodology that aims at computing a logical justification for dividing a group of data in two groups of observations, usually called the positive and negative groups.…

This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…

Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced…

We unify Linear Algebra by proposing a definition of determinants via one equation that implies all known properties of them:\\ 1. Cramer's Rule,\\ 2. Cofactor expansion,\\ 3. Antisymmetry of determinants,\\ 4. Linearity of determinants,\\…

In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean…

We develop some foundations for the theory of formal derived algebraic geometry, which parallel the theory of formal spectral algebraic geometry by Jacob Lurie. For this, we establish a close connection between algebro-geometric objects in…

Orbit determination (OD) from three position vectors is one of the classical problems in astrodynamics. Early contributions to this problem were made by J. Willard Gibbs in the late 1800s and OD of this type is known today as ``Gibbs…

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…

The general class of the graded Lie algebras is defined. These algebras could be constructed using an arbitrary dynamical systems with discrete time and with invarinat measure. In this papers we consider the case of the central extension of…

We introduce an algebraic analogue of dynamical systems, based on term rewriting. We show that a recursive function applied to the output of an iterated rewriting system defines a formal class of models into which all the main architectures…

The purpose of a program analysis is to compute an abstract meaning for a program which approximates its dynamic behaviour. A compositional program analysis accomplishes this task with a divide-and-conquer strategy: the meaning of a program…

Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…

In various subjects, there exist compact and consistent relationships between input and output parameters. Discovering the relationships, or namely compact laws, in a data set is of great interest in many fields, such as physics, chemistry,…

This paper presents a brief historical survey of iterative methods for solving linear systems of equations. The journey begins with Gauss who developed the first known method that can be termed iterative. The early 20th century saw good…

A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…

A theorem prover without an extensive library is much less useful to its potential users. Algebra, the study of algebraic structures, is a core component of such libraries. Algebraic theories also are themselves structured, the study of…

Ergodic theory, Higher order Fourier analysis and the hyper graph regularity method are three possible approaches to Szemer\'edi type theorems in abelian groups. In this paper we develop an algebraic theory that creates a connection between…

We develop an algebraic language theory based on the notion of an Eilenberg--Moore algebra. In comparison to previous such frameworks the main contribution is the support for algebras with infinitely many sorts and the connection to logic…

We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…

This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…