Fourier Series Expansions of Powers of the Trigonometric Sine and Cosine Functions

In this paper, Fourier series expansions of powers of sine and cosine functions are established for any possible power real or complex or positive integer. Recurrence relations are established to facilities the computations of the coefficients of expansions formulae. Numerical applications for real and complex powers are also included , the accuracy of the computed values are at least of order . While the applications for positive integer powers are given as exact analytical expressions

Footwear-integrated force sensing resistor sensors: A machine learning approach for categorizing lower limb disorders

Lower limb disorders are a substantial contributor to both disability and lower standards of life. The prevalent disorders affecting the lower limbs include osteoarthritis of the knee, hip, and ankle. The present study focuses on the use of footwear that incorporates force-sensing resistor sensors to classify lower limb disorders affecting the knee, hip, and ankle joints. The research collected data from a sample of 117 participants who wore footwear integrated with force-sensing resistor sensors while walking on a predetermined walkway of 9 meters. Extensive preprocessing and feature extraction techniques were applied to form a structured dataset. Several machine learning classifiers were trained and evaluated. According to the findings, the Random Forest model exhibited the highest level of performance on the balanced dataset with an accuracy rate of 96%, while the Decision Tree model achieved an accuracy rate of 91%. The accuracy scores of the Logistic Regression, Gaussian Naive Bayes, and Long Short-Term Memory models were comparatively lower. K-fold cross-validation was also performed to evaluate the models’ performance. The results indicate that the integration of force-sensing resistor sensors into footwear, along with the use of machine learning techniques, can accurately categorize lower limb disorders. This offers valuable information for developing customized interventions and treatment plans

Robust, distributed and optimal control of smart grids

These lecture notes provide an overview of recent research on the modeling and control of smart grids using distributed algorithms. In particular, energy-based modeling of general AC power networks using the framework of port-Hamiltonian systems theory is presented, and the relevance of such a formulation for stability analysis and control design is discussed. Low-level control design aspects (at a physical layer) for DC microgrids are also considered, achieving objectives such as fair load sharing among distributed generation units and (average) voltage regulation using limited data and measurements from the system. Finally, general frameworks for the optimal control of smart grids are introduced to consider both physical and economic constraints and exploit the flexibility brought up by storage devices and demand response from the grid’s prosumers

Conventional And Cognitive Radio Based Disaster Response Networks, A Comparative Study

The need for the deployment of reliable and efficient telecommunication systems in extreme emergency scenarios such as disaster response networks imposes a set of emerging unusual communication and routing challenges and obstacles that questions the performance of existing traditional and commercial telecommunication systems and networks in such scenarios, the revolution of telecommunication and networks industry witnessed the development of enormous telecommunication and networking services and systems that shaped their implementations in various domains of applications , in this paper, we study most of these communication standards in terms of their pros and cons, we also analyze the potentials of these standards in for Disaster Response networks in comparison with Cognitive Radio technology that has distinct capabilities and functionalities that enabled such a technology to be highly applicable for such harsh and unexpected scenario

Fabrication of alternating copolymers based on cyclopentadithiophene-benzothiadiazole dicarboxylic imide with reduced optical band gap: synthesis, optical, electrochemical, thermal, and structural properties

A series of alternating copolymers containing cyclopentadithiophene (CPDT) flanked by thienyl moieties as electron-donor units and benzothiadiazole dicarboxylic imide (BTDI) as electron-acceptor units were designed and synthesized for solar cell applications. Different solubilizing side chains, including 2-ethylhexyl chains and n-octyl chains were attached to CPDT units, whereas 3,7-dimethyloctyl chains and n-octyl chains were anchored to the BTDI moieties. The impact of these substituents on the solubilities, molecular weights, optical and electrochemical properties, and thermal and structural properties of the resulting polymers was investigated. PCPDTDTBTDI-EH, DMO was synthesized via Suzuki polymerization, whereas PCPDTDTBTDI-8, DMO, and PCPDTDTBTDI-EH, 8 were prepared through direct arylation polymerization. PCPDTDTBTDI-8, DMO has the highest number average molecular weight (Mn = 17,400 g mol−1) among all polymers prepared. The PCPDTDTBTDI-8, DMO and PCPDTDTBTDI-8, 8 which have n-octyl substituents on their CPDT units have comparable optical band gaps (Eg ~ 1.3 eV), which are around 0.1 eV lower than PCPDTDTBTDI-EH, DMO analogues that have 2-ethylhexyl substituents on their CPDT units. The polymers have their HOMO levels between −5.10 and −5.22 eV with PCPDTDTBTDI-EH, DMO having the deepest highest occupied molecular orbital (HOMO) energy level. The lowest unoccupied molecular orbital (LUMO) levels of the polymers are between −3.4 and −3.5 eV. All polymers exhibit good thermal stability with decomposition temperatures surpassing 350 °C. Powder X-ray diffraction (XRD) studies have shown that all polymers have the amorphous nature in solid state

Performance Evaluation of a Direct Absorption Collector for Solar Thermal Energy Conversion

The solar absorption efficiency of water as a base-fluid can be significantly improved by suspending nanoparticles of various materials in it. This experimental work presents the photo thermal performance of water-based nano-fluids of graphene oxide (GO), zinc oxide (ZnO), copper oxide (CuO), and their hybrids under natural solar flux for the first time. Nanofluid samples were prepared by the two-step method and the photothermal performance of these nanofluid samples was conducted under natural solar flux in a particle concentration range from 0.0004 wt % to 0.0012 wt %. The photothermal efficiency of water-based 0.0012 wt % GO nanofluid was 46.6% greater than that of the other nanofluids used. This increased photothermal performance of GO nanofluid was associated with its good stability, high absorptivity, and high thermal conductivity. Thus, pure graphene oxide (GO) based nanofluid is a potential candidate for direct absorption solar collection to be used in different solar thermal energy conversion applications

Effect of mutation and vaccination on spread, severity, and mortality of COVID-19 disease

Coronavirus disease 2019 (COVID-19) has had different waves within the same country. The spread rate and severity showed different properties within the COVID-19 different waves. The present work aims to compare the spread and the severity of the different waves using the available data of confirmed COVID-19 cases and death cases. Real-data sets collected from the Johns Hopkins University Center for Systems Science were used to perform a comparative study between COVID-19 different waves in 12 countries with the highest total performed tests for severe acute respiratory syndrome coronavirus 2 detection in the world (Italy, Brazil, Japan, Germany, Spain, India, USA, UAE, Poland, Colombia, Turkey, and Switzerland). The total number of confirmed cases and death cases in different waves of COVID-19 were compared to that of the previous one for equivalent periods. The total number of death cases in each wave was presented as a percentage of the total number of confirmed cases for the same periods. In all the selected 12 countries, Wave 2 had a much higher number of confirmed cases than that in Wave 1. However, the death cases increase was not comparable with that of the confirmed cases to the extent that some countries had lower death cases than in Wave 1, UAE, and Spain. The death cases as a percentage of the total number of confirmed cases in Wave 1 were much higher than that in Wave 2. Some countries have had Waves 3 and 4. Waves 3 and 4 have had lower confirmed cases than Wave 2, however, the death cases were variable in different countries. The death cases in Waves 3 and 4 were similar to or higher than Wave 2 in most countries. Wave 2 of COVID-19 had a much higher spread rate but much lower severity resulting in a lower death rate in Wave 2 compared with that of the first wave. Waves 3 and 4 have had lower confirmed cases than Wave 2; that could be due to the presence of appropriate treatment and vaccination. However, that was not reflected in the death cases, which were similar to or higher than Wave 2 in most countries. Further studies are needed to explain these findings

In-situ regeneration of activated carbon with electric potential swing desorption (EPSD) for the H 2 S removal from biogas

In-situ regeneration of a granular activated carbon was conducted for the first time using electric potential swing desorption (EPSD) with potentials up to 30 V. The EPSD system was compared against a standard non-potential system using a fixed-bed reactor with a bed of 10 g of activated carbon treating a gas mixture with 10,000 ppm H2S. Breakthrough times, adsorption desorption volume, capacities, effect of regeneration and desorption kinetics were investigated. The analysis showed that desorption of H2S using the new EPSD system was 3 times quicker compared with the no potential system. Hence, physical adsorption using EPSD over activated carbon is efficient, safe and environmental friendly and could be used for the in-situ regeneration of granular activated carbon without using a PSA and/or TSA system. Additionally, adsorption and desorption cycles can be obtained with a classical two column system, which could lead towards a more efficient and economic biogas to biomethane process