This paper describes the design of FIR delay filters with prescribed number of zeros at ω = π and prescribed magnitude and group delay flatness at ω = 0 that minimize a squared error. Even though the flatness constraints are in general non-linear functions of the filter coefficients, we show the remarkable fact that for a subclass of the filters a simple orthogonal projection of least squared e...

Our paper, ‘Human Geography without Scale’ (Marston et al. 2005), is developed in two parts: a critique that is immanent to scale, where we show that, even on the grounds of contemporary spatial theory, the concept is deficient; and a critique that is extrinsic to those grounds, where we make a contribution to an alternative ontology that does not rely on the transcendental abstraction of scale...

The dual flatness for Riemannian metrics in information geometry has been extended to Finsler metrics. The aim of this paper is to study the dual flatness of the so-called (α, β)-metrics in Finsler geometry. By doing some special deformations, we will show that the dual flatness of an (α, β)-metric always arises from that of some Riemannian metric in dimensional n ≥ 3.

PURPOSE To compare the sensitivity of flatness based energy metrics versus an attenuation based metric (percent depth dose) as a function of energy changes from the linac's nominal clinical energy. METHODS Energy changes were accomplished by adjusting the bending magnet current (BMI) ±15% away from the value used clinically. Two metrics for flatness, relative flatness in the central 80% of th...

We present a novel method for desiging multiwavelength pumped fiber Raman amplifiers with optimal gain-flatness and gain-bandwidth performance. We show that by solving the inverse amplifier design problem, relative gain flatness well below 1% can be achieved over bandwidths of up to 12 THz without any gain equalization devices. This constitutes a substantial improvement in gain flatness compare...

Abstract In this chapter, we will prove that the regular part of free boundary Reg ( ∂ Ω u ) (defined in Sect. 6.4 is C 1, α regular, for every ∈ (0, 1∕2).

This work describes the replacement of Tissue Phantom Ratio (TPR) measurements with beam profile flatness measurements to determine photon beam quality during routine quality assurance (QA) measurements. To achieve this, a relationship was derived between the existing TPR15/5 energy metric and beam flatness, to provide baseline values and clinically relevant tolerances. The beam quality was var...

If a connected metric space S is locally separable, then S is separable. If a connected, locally connected, metric space S is locally peripherally separable, then S is separable. Furthermore if a connected, locally connected, complete metric space S satisfies certain "flatness" conditions, it is known to be separable. These "flatness" conditions are rather strong and involve both im kleinen and...

this paper works on the concept of flatness and its practical application for the design of an optimal transient controller in a synchronous machine. the feedback linearization scheme of interest requires the generation of a flat output from which the feedback control law can easily be designed. thus the computation of the flat output for reduced order model of the synchronous machine with simp...