Related papers: Power Series in Several Complex Variables
These notes are the outgrowth of a series of lectures given at MSRI in January 1995 at the beginning of the special semester in complex dynamics and hyperbolic geometry. In these notes, the primary aim is to motivate the study of complex…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
We propose an approach for deriving a broad class of propagation models for inhomogeneously, linearly polarized ``vector'' beams. Our formulation leverages a complex scalar potential along with an appropriately constructed Lagrangian energy…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
I present my viewpoint on complexity, stressing general arguments and using a rather simple language.
Given a power series in finitely many variables that is algebraic over the corresponding polynomial ring over a subfield of the reals, we show that its convergence domain is semialgebraic over the real closure of the subfield. This gives in…
Complex systems thinking is applied to a wide variety of domains, from neuroscience to computer science and economics. The wide variety of implementations has resulted in two key challenges: the progenation of many domain-specific…
The main object of this paper is to find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria…
The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
It will be shown a different way to find infinite series for Pi involving complex conjugates.
Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects…
If a is a point in the domain of convergence of a planar power series f in a single variable x one con expand f into a planar power series in the variable (x-a). One arrives at the notion of planar analytic functions on any domain D in the…
Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…
The purpose of this note is to show that the subvarieties of small degree inside a general hypersurface of large degree come from intersecting with linear spaces or other varieties.
This paper provides a precise and scientific definition of complexity and coupling, grounded in the functional domain, particularly within industrial control and automation systems (iCAS). We highlight the widespread ambiguity in defining…