Characterization of the generalized Chebyshev-type polynomials of first kind

Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials. In this paper, we characterize the generalized Chebyshev-type polynomials of the first kind $\mathscr{T}_{n}^{(M,N)}(x),$ then we provide a closed form of the constructed polynomials in term of the Bernstein polynomials $B_{k}^{n}(x).$ We conclude the paper with some results on the integration of the weighted generalized Chebyshev-type with the Bernstein polynomials.Comment: Modified the title, One reference added, few additions, change in tex

Generalized Chebyshev polynomials of the second kind

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the paper with some results concerning integrals of the generalized Chebyshev-II and Bernstein polynomials.Comment: Change the title (Tschebyscheff to Chebyshev), and adding few comments. Adding the Journal reference

Monitoring and control of cardiovascular responses by using portable devices

University of Technology, Sydney. Faculty of Engineering and Information Technology.Interval training is an effective training protocol which helps strengthening and improving the athletes cardiovascular. Heart rate (HR) and oxygen uptake (VO₂) are major indicators of human cardiovascular response to exercises, observing these two factors can help predict energy expenditure (EE) which is an important factor in improving cardiovascular health. HR and VO₂ measurements can also aid early detection of cardiac diseases. The measurements of oxygen uptake and heart rate during sport or life activities are of great interest for development of training programs and the study of their effects on elite athletes or for assessing the efficacy of a rehabilitation therapy. A common method for evaluating the effects of endurance training is the monitoring of various respiratory parameters during exercise. One difficulty to achieve this goal during sport or different life activities is to use a reliable and valid portable system to measure the HR in a field setting. Such a portable apparatus may also be useful to determine the energy cost of many sport and real life activities. In this thesis, a portable device from Texas Instruments has been used to measure the Heart Rate. The eZ430-Chronos watch was reprogrammed and customized to measure the heart rate and to respond accordingly to eliminate any risk while exercising and to develop the exerciser cardiovascular fitness

Screening of Irish Fruit and Vegetable Germplasm for Novel Anti-tumour and Pesticidal Compounds

Conference paperPhytochemicals are a rich source of novel therapeutic and insecticidal agents (McLaughlin and Chang, 1999). Considerable research effort has been directed at screening exotic and medicinal plants in the search for novel products. However, plants which have traditional food uses have been little explored. In addition the range, type and level of individual bioactive compounds can vary significantly between different species, different cultivars of the same species and different tissue types of the plant (Reilly, in press) Therefore, the objective of this study was to screen a range of fruits and vegetables which can be grown in Ireland for novel bioactive compounds for use in food production and as bio-pesticides.The author wishes to acknowledge the financial support from the Dublin Institute of Technology through an ABBEST fellowshi

Fatty acids as biological markers for symbiotic bacteria in Phyllidia varicosa and Phyllidiella pustulosa

The fatty acid (FA) composition of Phyllidia varicosa and Phyllidiella pustulosa (notum and viscera) was investigated. Samples were collected from coastal water of Balok - Pahang - Malaysia. This study was conducted to test the hypothesis that nudibranchs species host symbiotic bacteria by using fatty acids as biological markers. A high level of fatty acids group specific to the bacteria were detected in the selected species that called odd- branched chain fatty acids. Among them, high levels of iso- anteiso-C15:0, C15:0, iso-C16:0, C17:0, iso-C17:0, iso C17:1(n-5), iso C18:0, 14-methyl-C18:0 and iso-C18:0) were found and their percentages in the notum are significantly different compared to viscera. The total odd- branched chain fatty acids were 29.64% in P. varicosa and 30.66% in P. pustulosa compared to another group of fatty acids such as saturated FA, monounsaturated FA and polyunsaturated FA. The present study deals with the identification of cyclopropane FA in the nudibranch tissue for the first time which cyclopropaneoctanoic acid 2-hexyl and cyclopropaneoctanoic acid 2-octyl were detected. We suggest that symbiotic bacteria associated with the nudibranchs tissue originate these fatty acids

Genetic dissection of photoperiod response based on GWAS of pre-anthesis phase duration in spring barley

Heading time is a complex trait, and natural variation in photoperiod responses is a major factor controlling time to heading, adaptation and grain yield. In barley, previous heading time studies have been mainly conducted under field conditions to measure total days to heading. We followed a novel approach and studied the natural variation of time to heading in a world-wide spring barley collection (218 accessions), comprising of 95 photoperiod-sensitive (Ppd-H1) and 123 accessions with reduced photoperiod sensitivity (ppd-H1) to long-day (LD) through dissecting pre-anthesis development into four major stages and sub-phases. The study was conducted under greenhouse (GH) conditions (LD; 16/8 h; ∼20/∼16°C day/night). Genotyping was performed using a genome-wide high density 9K single nucleotide polymorphisms (SNPs) chip which assayed 7842 SNPs. We used the barley physical map to identify candidate genes underlying genome-wide association scans (GWAS). GWAS for pre-anthesis stages/sub-phases in each photoperiod group provided great power for partitioning genetic effects on floral initiation and heading time. In addition to major genes known to regulate heading time under field conditions, several novel QTL with medium to high effects, including new QTL having major effects on developmental stages/sub-phases were found to be associated in this study. For example, highly associated SNPs tagged the physical regions around HvCO1 (barley CONSTANS1) and BFL (BARLEY FLORICAULA/LEAFY) genes. Based upon our GWAS analysis, we propose a new genetic network model for each photoperiod group, which includes several newly identified genes, such as several HvCO-like genes, belonging to different heading time pathways in barley

Enhancing Weather-Related Outage Prediction and Precursor Discovery Through Attention-Based Multi-Level Modeling

Electric grid continually monitors spatiotemporal data from sparse service areas. As power systems grow and get more complex, and with the deployment of more sensors and data collection capabilities, monitoring and analyzing data streams for outage prediction will get more complicated. In addition, the burden on human operators to analyze such data is getting challenging. Furthermore, climate change introduces new challenges to power grid reliability and makes the human grid operators’ task more critical. To address some of these challenges, this research proposes a novel model to jointly predict power grid outages and discover precursors from spatiotemporal data using multi-level data. The new method utilizes multi-task learning (MTL) and multi-instance learning (MIL) to jointly predict outages and learn event precursors. This is achieved by introducing distance-aware self-attention to capture relationships between locations and improve event detection and precursor discovery while utilizing multi-level data (local weather data, global demand, and forecast data) in a sparse setting. Experiments are conducted using five years of data collected in the U.S. Pacific Northwest. The proposed methodology achieves an Area Under the Precision-Recall Curve (AU-PRC) of 0.97 using 12 hours of data before the event. Experiments showed that the proposed model could predict events several hours ahead with high accuracy, where such early predictions allow grid operators to deploy outage mitigation plans. In addition, the new framework effectively discovers spatiotemporal precursors for power outages. Grid operators can use such event precursors to help mitigate outages and improve grid reliability.Temple University. College of Science and TechnologyComputer and Information Science