A metric space is said to be locally non-compact if every neighborhood contains a sequence that is bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non-compact iff it is without isolated points. The result has an interesting consequence in computable analysis: If a complete me...

We shall prove the following theorem concerning compact connected abelian groups: For any element x in a compact connected abelian group there is an element y such that the closure of the cyclic group generated by y is connected and contains x. This is a generalisation of the well known fact that any compact connected group whose topology admits a basis of at most continuum cardinality is monot...

Many of the definitions and results concerning connected im kleinen continua become useful only when these continua are locally compact. This is especially true in the cyclic element theory. For if a continuous curve M is not locally compact, it is not necessarily true that a simple closed curve in M belongs to a cyclic element of M. Furthermore, if a continuous curve M is not locally compact, ...

Performance evaluation of direction-of-arrival (DOA) estimation algorithms has continuously drawn significant attention in the past years. Most previous studies were conducted under the situation that antenna element separation is about half wavelength in order to avoid the appearance of grating lobes. On the other hand, recent developments in wireless communications have favoured the use of po...

Let D be a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Let v : M → g = LieG be an equivariant map, such that the corresponding vector field on M does not vanish outside of a compact subset. These data define an element of K-theory of the transversal cotangent bundle to M . Hence, by embedding of M into a compact manifold, one c...

A nonconforming finite element method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose [2] is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenizati...

It is known that an approximation in non-compact sets not guaranteed always same true for concave which do guarantee get the uniqness of a best element. In this papers we introduce new method to semi-compact and pre-concave set metric spaces. This accomplished by prove some theorems used properties above guarantees existences uniqueness element any set, where these semi-compactness pre-concavit...

In the paper, an extremely compact multiple-input-multiple-output (MIMO) antenna is proposed for portable wireless ultrawideband (UWB) applications. The prototype consists of four monopole elements, which are placed perpendicularly to achieve polarization diversity. addition, mutual coupling between elements suppressed by designing gap radiation element and ground plane. Moreover, a matching st...

INTRODUCTION Computational modelling in orthopaedic biomechanics often uses continuum homogenised finite element models of the bone which require accurate definitions of its elastic properties. In this study the variation of the orthotropic elastic constants of cortical bone from the female anterior femoral midshaft were evaulated. Micro-finite-element (μFE) analysis of bone samples from 27 fem...