Related papers: Transseries for beginners
Looking forward to introducing an analysis in Galois Fields, discrete functions are considered (such as transcendental ones) and MacLaurin series are derived by Lagrange's Interpolation. A new derivative over finite fields is defined which…
Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…
The large proper-time behaviour of expanding boost-invariant fluids has provided many crucial insights into quark-gluon plasma dynamics. Here we formulate and explore the late-time behaviour of nonequilibrium dynamics at the level of…
For a Riemann integrable function on an interval and for a point therein,we define 'Fourier series at the point on the interval' and bring out how and when the function element becomes expressible as Fourier series.In this process,we also…
In this paper we give a new definition of symmetric special multiserial algebras in terms of defining cycles. As a consequence, we show that every special multiserial algebra is a quotient of a symmetric special multiserial algebra.
Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to…
Butcher series, also called B-series, are a type of expansion, fundamental in the analysis of numerical integration. Numerical methods that can be expanded in B-series are defined in all dimensions, so they correspond to \emph{sequences of…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
One of the main applications of resurgence in physics is the decoding of nonperturbative effects through large order relations. These relations connect perturbative asymptotic expansions of observables to expansions around other saddle…
Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…
A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of…
I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…
From any given sequence of finite or infinite graphs, a nonstandard graph is constructed. The procedure is similar to an ultrapower construction of an internal set from a sequence of subsets of the real line, but now the individual entities…
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straight forward definition of a general geometric Fourier transform covering most versions in the literature.…
This is a proposal of an algebra which aims at distributed array processing. The focus lies on re-arranging and distributing array data, which may be multi-dimensional. The context of the work is scientific processing; thus, the core…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
Near-vector spaces extend linear algebra tools to non-linear algebraic structures, enabling the study of non-linear problems. However, explicit constructions remain rare. This paper introduces a broad computable family of near-vector…