Limits of brain–computer interface

Limits in modified categories of interest

‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...

Understanding the Limits and Benefits of a 3D Interface Specification

It is my belief that a specification for 3D interfaces is necessary for the continued advancement of the field. Such a specification stands to be severely limited however if care is not taken to understand the requirements of the domain. This paper explains my concerns about this topic as it is best to understand the benefits and limitations of a course of action prior to committing to it. I wi...

Exterior Boundary Value Problems as Limits of Interface Problems

It is proved that the solution to exterior Neumann boundary value problem can be obtained as the limit of the solutions of some problems in the whole space. 1 Consider the following problem: (V' + k*)u =f in f2, ul,=O, where f2 = R3\D. D is bounded domain with a smooth boundary r, fE C,(Q), k > 0. In [l] we proved the following: THEOREM 1. Consider the problem V=N in D N = const. > 0. =0 in Q, ...

On sharp interface limits for diffuse interface models for two-phase flows

We discuss the sharp interface limit of a diffuse interface model for a two-phase flow of two partly miscible viscous Newtonian fluids of different densities, when a certain parameter " > 0 related to the interface thickness tends to zero. In the case that the mobility stays positive or tends to zero slower than linearly in "we will prove that weak solutions tend to varifold solutions of a corr...

Generalized Covering Groups and Direct Limits