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Numerical Solutions of Nonlinear Ordinary Differential Equations by Using Adaptive Runge-Kutta Method
Get PDFWe present a study on numerical solutions of nonlinear ordinary differential equations by applying Runge-Kutta-Fehlberg (RKF) method, a well-known adaptive Runge-kutta method. The adaptive Runge-kutta methods use embedded integration formulas which appear in pairs. Typically adaptive methods monitor the truncation error at each integration step and automatically adjust the step size to keep the error within prescribed limit. Numerical solutions to different nonlinear initial value problems (IVPs) attained by RKF method are compared with corresponding classical Runge-Kutta (RK4) approximations in order to investigate the computational superiority of the former. The resulting gain in efficiency is compatible with the theoretical prediction. Moreover, with the aid of a suitable time-stepping scheme, we show that the RKF method invariably requires less number of steps to arrive at the right endpoint of the finite interval where the IVP is being considered
Editorial, Volume 17 (2019)
No full textOn behalf of the Editorial Board, it is with great pride and sincere privilege that I am writing this message to present the volume 17 (2019) of the JOURNAL OF ADVANCES IN MATHEMATICS The issue comes from a long process, and we took all the necessary steps to make it a high-caliber scientific publication. We are relying on the collaboration of all our Editors, reviewers, and contributors to make it a contemporary, lively, and relevant publication
Solutions of Some Difference Equations Systems and Periodicity
Get PDFIn this article, analysis and investigation have been conducted on the periodic nature as well as the type of the solutions of the subsequent schemes of rational difference equations
with a nonzero real numbers initial conditions
Supra Soft b-Compact and Supra Soft b-Lindle÷F Spaces
Get PDFThe purpose of this paper is to introduce and study the concepts of supra soft b-compact and supra soft b-Lindelˆf spaces. Also we study several of their properties and characterizations in details. Furthermore, the invariance of these kinds of spaces under some types of supra soft mappings and their hereditary properties are also investigate
Natural Mathematics, the Fibonacci Numbers and Aesthetics in Art
Get PDFThe Mathematics of beauty and beauty in mathematics are important ingredients in learning in the liberal arts. The Fibonacci numbers play an important and useful role in this. This paper seeks to present and illustrate a grounding of visual aesthetics in natural mathematical principles, centered upon the Fibonacci numbers. The specific natural mathematical principles investigated are the Fibonacci numbers, the Fibonacci Spiral, and the Cosmic Bud
Combined Cycle Consisting of Closed Processes Based Cycle Powered by A Reversible Heat Pump that Exceed Carnot Factor
Get PDFThis article deals with the task of analysing a feasible reversible combined cycle composed of a heat pump as the primary cycle and a non-condensing mode thermal engine characterized by operating under a closed processes based cycle that work by adding and releasing heat, as the secondary cycle. Two case studies are analysed and compared. According to the results, the case study based on the combination of a heat pump cycle with an organic Rankine cycle, is the paradigm of a reversible 100% efficient combined cycle. The case study based on a heat pump cycle and a reversible heating-cooling based cycle is the paradigm of a super-efficient combined cycle that yields a 1.486 power ratio (PR) or 148.6% efficiency. Further, the case based on a heat pump cycle with a regenerative irreversible heating-cooling based cycle, is the paradigm of energy conversion and energy generation that yields a 1.29 PR or 129% efficiency assuming limited irreversibilities.
This article deals with the task of analysing a feasible reversible combined cycle composed of a heat pump as the primary cycle and a non-condensing mode thermal engine characterized by operating under a closed processes based cycle that work by adding and releasing heat, as the secondary cycle. Two case studies are analysed and compared. According to the results, the case study based on the combination of a heat pump cycle with an organic Rankine cycle, is the paradigm of a reversible 100% efficient combined cycle. The case study based on a heat pump cycle and a reversible heating-cooling based cycle is the paradigm of a super-efficient combined cycle that yields a 1.486 power ratio (PR) or 148.6% efficiency. Further, the case based on a heat pump cycle with a regenerative irreversible heating-cooling based cycle, is the paradigm of energy conversion and energy generation that yields a 1.29 PR or 129% efficiency assuming limited irreversibilities
Preparation, Characterization and Antibacterial Efficiency of Olive Leaves Extract and Chitosan-Silver Nanoparticles using Electrochemical Method
Get PDFThe present work involves the improvement of chitosan-olive leaves extract and silver nanoparticles (Cs-OLE-AgNPs) using electrochemical approach followed by UV-irradiation reduction. The formation of silver nanoparticles (AgNPs) was characterized via UV–vis spectroscopy, Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), differential scanning calorimetry (DSC), EDX, thermal gravimetric analysis (TGA) and Swelling. The obtained nanoparticles average size was 36.19 nm. UV Spectroscopy show increase of peaks at 320 and 345 nm indicate the formation of a large cluster of AgNPs. Cs-OLE and Cs-OLE-AgNPs also demon started a relativity high antibacterial against both Escherichia coli (E. coli) and Staphylococcus aureus (S. aureus) bacteria. AgNPs show broadspectrum antibacterial activity at lower concentration (0.56%) and may be regarded as a good alternative therapeutic approach in the future
Dielectric and Electrical Properties of Poly (?-Caprolactone)/ Organomodified Clay Bionanocomposites Prepared in Open Air by in Situ Polymerization
Get PDFDielectric and electrical properties of bio-nanocomposites based on poly (?-caprolactone) (PCL) with different amounts of organomodified montmorillonite clay (MMT-ODA) were investigated by broadband dielectric spectroscopy in the frequency range from 1Hz to 1MHz and in the temperature range from -100 to 25°C. These nanocomposites were prepared by in situ Ring Opening polymerization of ?-caprolactone in open air by using titanium alkoxide as a catalyst. Due to the semicrystalline structure of PCL, the high number of modes and its overlap, the relaxation patterns observed on dielectric spectra were complicated. These relaxation data were modeled using the H-N empirical equation with the contribution of conductivity. The local dynamics of PCL were unaffected by the increase of nano-clay amount, in agreement with the DSC values of glass transition temperature. The PCL/MMT-ODA 3 wt% exhibited the lowest value of dielectric strength, indicating the strongest adhesion between PCL matrix and organo-modified clay. As for PCL/MMT-ODA 5 wt%, the presence of agglomerate made the adhesion between PCL and MMT-ODA very weak. The obtained findings were congruent FTIR and XRD results. The electrical conductivity of PCL was analysed according to the Jonscher’s law. The obtained exponent s values referred to three models corresponding to different temperature ranges
Structural, Optical and Electrical Properties of MnO2 / MWCNTs/PVA Nanocomposite
Get PDFManganese dioxide/multi-walled carbon nanotubes MnO2/ MWCNTs nanocomposite are synthesized by hydrothermal method. The crystallographic information of the acid-treated MWCNTs and the MnO2/ modified MWCNTs nanocomposite were characterized by X-ray diffraction (XRD),Transmission electron microscope (TEM )and FT-IR spectra. Optical and electrical properties of MnO2 / MWCNTs / PVA nanocomposite thin film with different concentration were studied .UV-VIS absorption spectra shift, at different exposing time , indicated the sensitivity to UV radiation. Optical band gap decreases with increasing time of radiation. Electrical properties of MnO2 / MWCNTs / PVA nanocomposite thin films with different concentration according to different frequency and exposing time of UV radiation showed semiconducting properties and sensitivity to UV radiation
The Cause To The Tides
No full textCurrent theories towards the cause of the tides show to be contrary to the laws of nature and that of motion. The correct version for the tides are herewith shown with supporting evidence.