Related papers: Scalar actions in Lean's mathlib
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial…
Large Language Models (LLMs) are increasingly being adopted as tools for learning; however, most tools remain text-only, limiting their usefulness for domains where visualizations are essential, such as mathematics. Recent work shows that…
In this paper we investigate further the tableaux system for a deontic action logic we presented in previous work. This tableaux system uses atoms (of a given boolean algebra of action terms) as labels of formulae, this allows us to embrace…
Using the dilaton scalar and axion pseudoscalar fields we construct a number of scalars and differential forms which are symmetric under the $\mathbf{Z}_2$-subgroup of the group $SL(2, \mathbf{R})$. These invariants enable us to establish…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
In this paper we have considered the renormalized one-loop effective action for massless self-interacting scalar field in the 3-dimensional ball. The scalar field satisfies Dirichlet boundary condition on the ball. Using heat kernel…
In this review paper, we treat the topic of fine gradings of Lie algebras. This concept is important not only for investigating the structural properties of the algebras, but, on top of that, the fine gradings are often used as the starting…
The group $SL(n,{\bf Z})$ acts linearly on $\R^n$, preserving the integer lattice $\Z^{n} \subset \R^{n}$. The induced (left) action on the n-torus $\T^{n} = \R^{n}/\Z^{n}$ will be referred to as the ``standard action''. It has recently…
We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not…
In this article, we develop a calculus of Shubin type pseudodifferential operators on certain non-compact spaces, using a groupoid approach similar to the one of van Erp and Yuncken. More concretely, we consider actions of graded Lie groups…
We classify real-analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\leq n\leq m\leq2n-3$, which extends Fisher--Melnick's work for $\mathrm{SL}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally,…
Graded labels are ubiquitous in real-world learning-to-rank applications, especially in human rated relevance data. Traditional learning-to-rank techniques aim to optimize the ranked order of documents. They typically, however, ignore…
Functional logic languages can solve equations over user-defined data and functions. Thus, the definition of an appropriate meaning of equality has a long history in these languages, ranging from reflexive equality in early equational logic…
Active Learning (AL) methods seek to improve classifier performance when labels are expensive or scarce. We consider two central questions: Where does AL work? How much does it help? To address these questions, a comprehensive experimental…
We present a generalization of the symbol calculus from ordinary multiple polylogarithms to their elliptic counterparts. Our formalism is based on a special case of a coaction on large classes of periods that is applied in particular to…
We use machine learning to optimize LSM-tree structure, aiming to reduce the cost of processing various read/write operations. We introduce a new approach Camal, which boasts the following features: (1) ML-Aided: Camal is the first attempt…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra.