相关论文: Local Hypercomplex Analyticity

Complex analyticity is generalized to hypercomplex functions, quaternion or octonion, in such a manner that it includes the standard complex definition and does not reduce analytic functions to a trivial class. A brief comparison with other…

We extend to Gaussian distributions a result providing smoothed analysis estimates for condition numbers given as relativized distances to illposedness. We also introduce a notion of local analysis meant to capture the behavior of these…

The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…

We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…

This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…

We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are provided of different concrete notions of…

In this paper, we explore connections between interpretable machine learning and learning theory through the lens of local approximation explanations. First, we tackle the traditional problem of performance generalization and bound the…

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.

We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested.…

In the first half of twentieth century the theory of complex analytic functions and of their zerosets was fully developed. The definition of holomorphic function has a local nature. Germs of holomorphic functions form a distinguished…

The notion of supershift (in itself a generalization of the notion of superoscillation arising in quantum mechanics) expresses the fact that the sampling of a function in an interval allows to compute the values of the function far from the…

We provide combinatorial/topological formula for the multiplicity of a complex analytic normal surface singularity whenever the analytic structure on the fixed topological type is generic.

This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity…

We propose definitions of hypercomplex analytic spaces and hypercomplex schemes. We show that such a hypercomplex space is canonically associated to the quotient of a hypercomplex manifold by a finite group action.

Contextuality in quantum physics provides a key resource for quantum information and computation. The topological approach in [Abramsky and Brandenburger, New J. Phys., 2011, Abramsky et al., CSL 2015, 2015] characterizes contextuality as…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

The cluster analysis of very large objects is an important problem, which spans several theoretical as well as applied branches of mathematics and computer science. Here we suggest a novel approach: under assumption of local convergence of…

The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…

A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…