Elementary And Integral-elementary Functions

By an integral-elementary function we mean any real function that can be obtained from the constants, sin x, e(x), log x, and arcsin x (defined on (-1, 1)) using the basic algebraic operations, composition and integration. The rank of an integral-elementary function f is the depth of the formula defining f. The integral-elementary Functions of rank less than or equal to n are real-analytic and satisfy a common algebraic differential equation P-n(f, f',..., f((k))) = 0 with integer coefficients. We prove that every continuous function f: R --> R can be approximated uniformly by integral-elementary functions of bounded rank. Consequently, there exists an algebraic differential equation with integer coefficients such that its everywhere analytic solutions approximate every continuous function uniformly. This solves a problem posed by L. A. Rubel. Using the same basic functions as above, but allowing only the basic algebraic operations and compositions, we obtain the class of elementary functions. We show that every differentiable function with a derivative not exceeding an iterated exponential can be uniformly approximated by elementary functions of bounded rank. If we include the function arcsin x defined on [-1, 1], then the resulting class of naive-elementary functions will approximate every continuous function uniformly. We also show that every sequence can be uniformly approximated by elementary functions, and that every integer sequence can be represented in the form f(n), where f is naive-elementary

Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions

This is the author's accepted version. The final version is available from APS via the DOI in this recordWe present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two groups of (at least) two elements using a general method based on delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge theory for phase models and the dynamics of real-world oscillator networks.CB has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007–2013) under REA grant agreement no. 626111. IZK acknowledges support from National Science Foundation CHE-1465013 grant

Optical Identification of Inaccuracies Caused by Improper Handling on Type IV Gypsum Casts

Type IV gypsum (stone gypsum) is an essential material in prosthetic treatment. Improper handling can change hardness, expansion and compressive strength and it is the most common reason for inaccurate casts. In that case even the most perfect impressions will result in inadequate prosthetic treatment. Using optical instruments-digital camera (2.5 million pixels) and digital microscope we attempted to identify the visual appearance of inadequate casts and relate them to specific causes. All casts were poured in highly controlled conditions and only one factor, whose influence we tried to determine, was changed during the procedure. Most common mistakes are: outdated gypsum, incorrect powder to water ratio, mixing without a vacuummixer, pourring without a vibrator and etching by alginate acid. All the mistakes were visualised, easily recognized and categorized by using digital optical equipment

Alveolar Bone Loss on Abutment and Non-Abutment Teeth as Related to Removable Partial Denture Wearing. A Six Month Follow up Study

Loss of interdental alveolar bony septum can be determined directly from a radiograph as a percentage length of the interdental bony crest of the alveolus to the distance from cemento-enamel junction of the tooth to the tooth apex. The aim of this study was to measure the height of interdental alveolar bone around the abutment and nonabutment teeth in removable partial denture wearers (RPD) on dental panoramic radiographs (DPR) through a period of six months. Twenty RPD patients (5 males, 15 females participated in the study. The alveolarbone loss measurement was performed on DPRs, using Shei index, on each mandibular abutment and non-abutment tooth on its mesial and distal side, after the RPD delivery and six months later. Recordings of plaque index (PlI) were made at the mid-buccal, mid-palatal, mesio- and disto-palatal surfaces of each abutment and non-abutment teeth after the RPD delivery and six months later. The results revealed a decrease of Shei index values on both abutment and non-abutment teeth, which reached a statistically significant level for distal Shei index values of the abutment teeth and mesial and distal Shei index values of the non-abutment teeth (p<0.05) in a 6 month period. There was no statistically significant difference in PlI values between the first and the second measurement (p>0.05). We concluded that the decrease in bone support on both abutment and non-abutment teeth was attributed to the high levels of PlI and low level of oral hygiene than to RPD loading. Supported by the Ministry of Science and Technology, Republic of Croatia, Project No. 065911

Electromyographic Evaluation of the Influence of Denture Adhesive on Retention and Stability of Complete Dentures

Improving retention and stability of complete dentures is of considerable interest in prosthetic dentistry. Approaches to this problem over the years have included overdentures, implants and denture adhesives. Although denture adhesives are widely used, there are few quantitative data on the effects of an adhesive on denture retention and stability during normal functional activities. The purpose of this investigation was to study the influence of denture adhesive on the surface EMG activity of the masticatory muscles in a sample of complete denture wearers. In this study 6 denture wearers were investigated. Surface EMG recordings were obtained from left and right anterior temporal and masseter muscle and from the sub-mandibular group in the region of the anterior belly of the digastric muscle on the left and right side. Data were recorded during standardized jaw positions that included clenching in the position of maximal intercuspation of teeth (at 100%, 50% and 25% of the maximum activity), lateral eccentric positions, maximal lateral eccentric positions, protrusion, maximal protrusion and wide opening. The results demonstrated higher digastric muscle activity in protrusion with the teeth at an edge-toedge position after the use of adhesive (p0.05). This investigation demonstrated that patients were able to produce greater levels of muscle activity in protrusive and laterotrusive positions with the use of adhesive

Hafnia and alumina on sulphur passivated germanium

In this work hafnia (HfO2) and alumina (Al2O3) films were deposited on germanium, using either water or oxygen plasma as the oxidant, by atomic layer deposition at 250 °C with and without sulphur passivation of the substrate. X-ray photoelectron spectroscopy was carried out to investigate the interface between both HfO2 and Al2O3 films and germanium. The results show that for hafnia and alumina deposited with water on pre-sulphur treated germanium there is negligible GeOx formation when compared to films grown using oxygen plasma. The results support the case for sulphur passivation of the interface

Modeling regional sea level rise using local tide gauge data

2012-2013 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics