A method for enclosing solutions of overdetermined systems of linear interval equations is described. Several aspects of the problem (algorithm, enclosure improvement, optimal enclosure) are studied.

This article introduces a methodology for designing the geometry of diffuse-walled radiant enclosures through nonlinear programming. In this application, the enclosure is represented parametrically using B-spline curves, while the radiosity distribution is solved by infinitesimal-area analysis. The enclosure geometry is repeatedly adjusted with a gradientbased minimization algorithm until a nea...

One of the main problems of interval computations is, given a function f(x 1 problem is feasible for linear functions f, but for generic polynomials, it is known to be computationally intractable. Because of that, traditional interval techniques usually compute the enclosure of y, i.e., an interval that contains y. The closer this enclosure to y, the better. It is desirable to describe cases in...

The voltage on a single-turn loop inside an enclosure characterizes the enclosure shielding effectiveness against a lightning insult. In this paper, the maximum induced voltage on a single-turn loop inside an enclosure from lightning coupling to a metal enclosure wall is expressed in terms of two multiplicative factors: (A) the normalized enclosure wall peak penetration ratio (i.e., ratio of th...

─ This paper deals with an impact of receiving antenna placed in a metal enclosure on an electromagnetic field distribution within the enclosure, and thus on its shielding effectiveness. In an experimental setup, a frequently used tool for measuring the electromagnetic field level at certain points within the enclosure is a dipole antenna connected to a measuring instrument via a coaxial cable....

The classical Lusternik-Schnirelman-Borsuk theorem states that if a d-sphere is covered by d + 1 closed sets, then at least one of the sets must contain a pair of antipodal points. In this paper, we prove a combinatorial version of this theorem for hypercubes. It is not hard to show that for any cover of the facets of a d-cube by d sets of facets, at least one such set contains a pair of antipo...

Coquand’s cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. We show that the underlying cube category is the opposite of the Lawvere theory of De Morgan algebras. The topos of cubical sets itself classifies the theory of ‘free De Morgan algebras’...

Department of Mechanical Engineering, The Hong Kong Polytechnic University Hung Home, Kowloon, Hong Kong, SAR of China Email address: [email protected]. Abstract This paper examines the influence of the internal resistance of a Helmholtz resonator on the noise control in a small enclosure. The absorptive process mainly occurring within the neck of a Helmholtz resonator provides the resonator w...