Method of Detecting System Function by Measuring Frequency Response

Methods of rapidly measuring an impedance spectrum of an energy storage device in-situ over a limited number of logarithmically distributed frequencies are described. An energy storage device is excited with a known input signal, and aresponse is measured to ascertain the impedance spectrum. An excitation signal is a limited time duration sum-of-sines consisting of a select number offrequencies. In one embodiment, magnitude and phase of each frequency ofinterest within the sum-of-sines is identified when the selected frequencies and sample rate are logarithmic integer steps greater than two. This technique requires a measurement with a duration of one period of the lowest frequency. In another embodiment, where selected frequencies are distributed in octave steps, the impedance spectrum can be determined using a captured time record that is reduced to a half-period of the lowest frequency.

Applicative theories for logarithmic complexity classes

We present applicative theories of words corresponding to weak, and especially logarithmic, complexity classes. The theories for the logarithmic hierarchy and alternating logarithmic time formalise function algebras with concatenation recursion as main principle. We present two theories for logarithmic space where the first formalises a new two-sorted algebra which is very similar to Cook and Bellantoni's famous two-sorted algebra B for polynomial time [4]. The second theory describes logarithmic space by formalising concatenation- and sharply bounded recursion. All theories contain the predicates WW representing words, and VV representing temporary inaccessible words. They are inspired by Cantini's theories [6] formalising B.

A novel colourimetric technique to assess chewing function using two-coloured specimens: Validation and application

OBJECTIVES Chewing efficiency may be evaluated using cohesive specimen, especially in elderly or dysphagic patients. The aim of this study was to evaluate three two-coloured chewing gums for a colour-mixing ability test and to validate a new purpose built software (ViewGum©). METHODS Dentate participants (dentate-group) and edentulous patients with mandibular two-implant overdentures (IOD-group) were recruited. First, the dentate-group chewed three different types of two-coloured gum (gum1-gum3) for 5, 10, 20, 30 and 50 chewing cycles. Subsequently the number of chewing cycles with the highest intra- and inter-rater agreement was determined visually by applying a scale (SA) and opto-electronically (ViewGum©, Bland-Altman analysis). The ViewGum© software determines semi-automatically the variance of hue (VOH); inadequate mixing presents with larger VOH than complete mixing. Secondly, the dentate-group and the IOD-group were compared. RESULTS The dentate-group comprised 20 participants (10 female, 30.3±6.7 years); the IOD-group 15 participants (10 female, 74.6±8.3 years). Intra-rater and inter-rater agreement (SA) was very high at 20 chewing cycles (95.00-98.75%). Gums 1-3 showed different colour-mixing characteristics as a function of chewing cycles, gum1 showed a logarithmic association; gum2 and gum3 demonstrated more linear behaviours. However, the number of chewing cycles could be predicted in all specimens from VOH (all p<0.0001, mixed linear regression models). Both analyses proved discriminative to the dental state. CONCLUSION ViewGum© proved to be a reliable and discriminative tool to opto-electronically assess chewing efficiency, given an elastic specimen is chewed for 20 cycles and could be recommended for the evaluation of chewing efficiency in a clinical and research setting. CLINICAL SIGNIFICANCE Chewing is a complex function of the oro-facial structures and the central nervous system. The application of the proposed assessments of the chewing function in geriatrics or special care dentistry could help visualising oro-functional or dental comorbidities in dysphagic patients or those suffering from protein-energy malnutrition.

Classical solutions for a logarithmic fractional diffusion equation

We prove global existence and uniqueness of strong solutions to the logarithmic porous medium type equation with fractional diffusion ?tu + (?)1/2 log(1 + u) = 0, posed for x ? R, with nonnegative initial data in some function space of LlogL type. The solutions are shown to become bounded and C? smooth in (x, t) for all positive times. We also reformulate this equation as a transport equation with nonlocal velocity and critical viscosity, a topic of current relevance. Interesting functional inequalities are involved.

Introducing the Logarithmic finite element method: a geometrically exact planar Bernoulli beam element

We propose a novel finite element formulation that significantly reduces the number of degrees of freedom necessary to obtain reasonably accurate approximations of the low-frequency component of the deformation in boundary-value problems. In contrast to the standard Ritz–Galerkin approach, the shape functions are defined on a Lie algebra—the logarithmic space—of the deformation function. We construct a deformation function based on an interpolation of transformations at the nodes of the finite element. In the case of the geometrically exact planar Bernoulli beam element presented in this work, these transformation functions at the nodes are given as rotations. However, due to an intrinsic coupling between rotational and translational components of the deformation function, the formulation provides for a good approximation of the deflection of the beam, as well as of the resultant forces and moments. As both the translational and the rotational components of the deformation function are defined on the logarithmic space, we propose to refer to the novel approach as the “Logarithmic finite element method”, or “LogFE” method.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.