Related papers: Local Hypercomplex Analyticity
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a…
A number of prototypical optimization problems in multi-agent systems (e.g., task allocation and network load-sharing) exhibit a highly local structure: that is, each agent's decision variables are only directly coupled to few other agent's…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
In the present paper, classical tools of convex analysis are used to study the solution set to a certain class of set-inclusive generalized equations. A condition for the solution existence and global error bounds is established, in the…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
This paper develops various foundational results in the locally analytic representation theory of p-adic groups. In particular, we define the functor ``pass to locally analytic vectors'', which attaches to any continuous representation of a…
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…
This paper reviews local and global optimality conditions in polynomial optimization. We summarize the relationship between them.
We consider a subanalytic subset A of a complex analytic manifold M (when M is viewed as a real manifold) and formulate conditions under which A is a complex analytic subset of M.
We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation…
This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multiple objectives, local constraints as well as local variables, and they are…
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the shortest parallel computation required to construct a…
In this work we study the Cauchy problem in Gevrey spaces for a generalized class of equations that contains the case $b=0$ of the $b$-equation. For the generalized equation, we prove that it is locally well-posed for initial data in Gevrey…
A new kind of numbers called Hyper Space Complex Numbers and its algebras are defined and proved. It is with good properties as the classic Complex Numbers, such as expressed in coordinates, triangular and exponent forms and following the…
Building on the concept of local lexing the concept of parameterized local lexing is introduced.
We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H. We…
A complex-analytic structure within the unit disk of the complex plane is presented. It can be used to represent and analyze a large class of real functions. It is shown that any integrable real function can be obtained by means of the…
We develop the basic formalism of complex $q$-analysis to study the solutions of second order $q$-difference equations which reduce, in the $q\rightarrow 1$ limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After…
Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…