Related papers: Approximate derivations of order $n$
The main purpose of this paper is to give characterization theorems on derivations as well as on linear functions. Among others the following problem will be investigated: Let $n\in\mathbb{Z}$, $f, g\colon\mathbb{R}\to\mathbb{R}$ be…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
This paper presents an algebraic approach to characterizing higher-order differential operators. While the foundational Leibniz rule addresses first-order derivatives, its extension to higher orders typically involves identities relating…
Weighted finite-state machines are a fundamental building block of NLP systems. They have withstood the test of time -- from their early use in noisy channel models in the 1990s up to modern-day neurally parameterized conditional random…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…
The main purpose of the present work is solving the characterization problem which consist of identification of necessary and sufficient conditions on the scattering data ensuring that the reconstructed potential belongs to a particular…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…
A generalization of the Gr\"{u}nwald difference approximation for fractional derivatives in terms of a real sequence and its generating function is presented. Properties of the generating function are derived for consistency and order of…
We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.
We present a higher well-ordering principle which is equivalent (over Simpson's set theoretic version of $\text{ATR}_0$) to the existence of transitive models of Kripke-Platek set theory, and thus to $\Pi^1_1$-comprehension. This is a…
Let $\mathcal M=(M,<,...)$ be a linearly ordered first-order structure and $T$ its complete theory. We investigate conditions for $T$ that could guarantee that $\mathcal M$ is not much more complex than some colored orders (linear orders…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
Let $R$ be an integral domain of characteristic zero. We prove that a function $D\colon R\to R$ is a derivation of order $n$ if and only if $D$ belongs to the closure of the set of differential operators of degree $n$ in the product…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…
Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…