Which infinite abelian groups admit an almost maximally almost-periodic group topology?

A topological group G is said to be almost maximally almost-periodic if its von Neumann radical is non-trivial, but finite. In this paper, we prove that every abelian group with an infinite torsion subgroup admits a (Hausdorff) almost maximally almost-periodic group topology. Some open problems are also formulated

Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time- and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made equiripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design examples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach

A Simple Proof of the Alternation Theorem

A simple proof of the alternation theorem for minimax FIR filter design is presented in this paper. It requires no background on mathematical optimization theory, and is based on easily understood properties of filters with equiripple behavior. The method is similar to the classical counting argument used in early mathematics literature. The contribution here is a simplified presentation which directly uses filter design language

Maximally decimated perfect-reconstruction FIR filter banks with pairwise mirror-image analysis (and synthesis) frequency responses

Structures are presented for the perfect-reconstruction quadrature mirror filter bank that are based on lossless building blocks. These structures ensure that the frequency responses of the analysis (and synthesis) filters have pairwise symmetry with respect to π/2 and require fewer parameters than recently reported structures (also based on lossless building blocks). The design time for the proposed structures is correspondingly much less than for the earlier methods, which did not incorporate such symmetry

Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters

Two perfect-reconstruction structures for the two-channel quadrature mirror filter (QMF) bank, free of aliasing and distortions of any kind, in which the analysis filters have linear phase, are described. The structure in the first case is related to the linear prediction lattice structure. For the second case, new structures are developed by propagating the perfect-reconstruction and linear-phase properties. Design examples, based on optimization of the parameters in the lattice structures, are presented for both cases

A 'trick' for the design of FIR half-band filters

Based on a well-known property of FIR half-band filters, this correspondence shows how the design time for equiripple half-band filters can be reduced by a considerable amount. The observation which leads up to this improved procedure also places in evidence new implementation schemes, which simultaneously ensure low passband and stopband sensitivities. Extension of the method to Mth-band filter design is also outlined

Fatigue tests on big structure assemblies of concorde aircraft

Fatigue tests on structural assemblies of the Concorde supersonic transport aircraft are reported. Two main sections of the aircraft were subjected to pressure, mechanical load, and thermal static tests. The types of fatigue tests conducted and the results obtained are discussed. It was concluded that on a supersonic aircraft whose structural weight is a significant part of the weight analysis, many fatigue and static strength development tests should be made and fatigue and thermal tests of the structures are absolutely necessary

An isogeometric analysis for elliptic homogenization problems

A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational expenses while using traditional finite element methods. The isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in this paper is regarded as an alternative approach to the standard Finite Element Heterogeneous Multiscale Method (FE-HMM) which is currently an effective framework to solve these problems. The method utilizes non-uniform rational B-splines (NURBS) in both macro and micro levels instead of standard Lagrange basis. Beside the ability to describe exactly the geometry, it tremendously facilitates high-order macroscopic/microscopic discretizations thanks to the flexibility of refinement and degree elevation with an arbitrary continuity level provided by NURBS basis functions. A priori error estimates of the discretization error coming from macro and micro meshes and optimal micro refinement strategies for macro/micro NURBS basis functions of arbitrary orders are derived. Numerical results show the excellent performance of the proposed method