相关论文: How to write a coequation

Kinetic equations bridge the gap between a microscopic description and a macroscopic description of the physical reality. Due to the high dimensionality the construction of numerical methods represents a challenge and requires a careful…

Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…

This article discusses several erroneous claims which appear in textbooks on numerical methods and computational physics. These are not typos or mistakes an individual author has made, but widespread misconceptions. In an attempt to stop…

Mathematics formalisation is the task of writing mathematics (i.e., definitions, theorem statements, proofs) in natural language, as found in books and papers, into a formal language that can then be checked for correctness by a program. It…

An important step in learning to use math in science is learning to see physics equations as not just calculational tools, but as ways of expressing fundamental relationships among physical quantities, of coding conceptual information, and…

The study of register in computational language research has historically been divided into register analysis, seeking to determine the registerial character of a text or corpus, and register synthesis, seeking to generate a text in a…

This article is intended as a guide for new graduate students in the field of computational science. With the increasing influx of students from diverse backgrounds joining the ever-popular field, this short guide aims to help students…

This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…

In functional programming languages, the classic form of annotation is a single type constraint on a term. Intersection types add complications: a single term may have to be checked several times against different types, in different…

We find, motivated by real-world applications, that the well-known request-response specification comes with multiple variations, and that these variations should be distinguished. As the first main contribution, we introduce a…

Citation recommendation describes the task of recommending citations for a given text. Due to the overload of published scientific works in recent years on the one hand, and the need to cite the most appropriate publications when writing…

Complexes and cohomology, traditionally central to topology, have emerged as fundamental tools across applied mathematics and the sciences. This survey explores their roles in diverse areas, from partial differential equations and continuum…

Boolean and quantum circuits have commonalities and differences. To formalize the syntactical commonality we introduce syntactic circuits where the gates are black boxes. Syntactic circuits support various semantics. One semantics is…

Floating-point addition on a finite-precision machine is not associative, so not all mathematically equivalent summations are computationally equivalent. Making this assumption can lead to numerical error in computations. Proper ordering…

Different ways to describe a permutation, as a sequence of integers, or a product of Coxeter generators, or a tree, give different choices to define a simple permutation. We recollect few of them, define new types of simple permutations,…

This article explores a generic framework of well-typed and well-scoped syntaxes, with a signature-axiom approach resembling traditional abstract algebra. The boilerplate code needed in defining operations on syntaxes is identified and…

Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…

The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…

It is well-known that any permutation can be written as a product of two involutions. We provide an explicit formula for the number of ways to do so, depending only on the cycle type of the permutation. In many cases, these numbers are sums…