Approximate analytical solutions of systems of PDEs by homotopy analysis method

AbstractIn this paper, the homotopy analysis method (HAM) is applied to obtain series solutions to linear and nonlinear systems of first- and second-order partial differential equations (PDEs). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown in particular that the solutions obtained by the variational iteration method (VIM) are only special cases of the HAM solutions

Series Solution of the Multispecies Lotka-Volterra Equations by Means of the Homotopy Analysis Method

The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given

Construction of (n+ 1) -dimensional dual-mode nonlinear equations: multiple shock wave solutions for (3 + 1) -dimensional dual-mode Gardner-type and KdV-type

The goal of this study is to offer an exclusive functional conversion to produce (n+ 1) -dimensional dual-mode nonlinear equations. This transformation has been implemented and new (3 + 1) -dimensional dual-mode Gradner-type and KdV-type have been established. Finally, the simplified bilinear method is used to tell the necessary conditions on these new models to have multiple singular-solitons. - 2019, The Author(s).This work is financially supported by UKM Grant: DIP-2017-011 and Ministry of Education Malaysia Grant FRGS/1/2017/STG06/UKM/01/1.Scopu

Modified Step Variational Iteration Method for Solving Fractional Biochemical Reaction Model

A new method called the modification of step variational iteration method (MoSVIM) is introduced and used to solve the fractional biochemical reaction model. The MoSVIM uses general Lagrange multipliers for construction of the correction functional for the problems, and it runs by step approach, which is to divide the interval into subintervals with time step, and the solutions are obtained at each subinterval as well adopting a nonzero auxiliary parameter ℏ to control the convergence region of series' solutions. The MoSVIM yields an analytical solution of a rapidly convergent infinite power series with easily computable terms and produces a good approximate solution on enlarged intervals for solving the fractional biochemical reaction model. The accuracy of the results obtained is in a excellent agreement with the Adam Bashforth Moulton method (ABMM)

Association of vital pulp therapy outcomes with tooth type, arch location, treatment type, and number of surfaces destroyed in deciduous teeth: A retrospective study

There is a paucity of information concerning vital pulp treatment outcomes in the undergraduate teaching setting. This study aimed to determine which type of deciduous molar, arch location, type of vital pulp therapy, and the number of carious surfaces involved had a better prognosis when carried out by undergraduate dental students. The method used was the review of clinical records of 590 patients with 600 deciduous molars, that visited the outpatient undergraduate dental clinics for vital pulp therapy. Statistical analysis used to determine the associations of tooth type, arch location, treatment type, and the number of carious surfaces involved in successful outcomes was logistic regression analysis with significance set at p < 0.05. According to the regression analysis model results, there was a significant association based on tooth type (p < 0.05) and arch location (p = 0.003). In addition, there was a significant association based on the type of treatment performed (p = 0.036). However, there was no significant association in success rates based on the number of carious surfaces involved (p = 0.873). In conclusion, second deciduous molars and maxillary deciduous molars had a better overall prognosis, and indirect pulp therapy was revealed to be more highly associated with successful treatment outcomes in comparison to ferric sulfate pulpotomy in our setting

Effects of Cryogenic Aging on a Rapid Prototyped (RP) Polymer

Little research has been done on the post-processing (aging) of rapid prototyped (RP) polymers at temperatures below 123K (–238˚F). Test specimens of RP thermosetting resin (DSM-Somos 8110) were fabricated and cryogenically aged from 10-25 hours. The tensile strength and impact toughness were measured. This work will study the effect of cryogenic aging on yield strength of Somos 8110. This paper will also discuss our interpretation of the data based on fractography.The work was funded by an NSF Grant under Research Experiences for Undergraduates (REU).Mechanical Engineerin

Microstructural and Elemental Characterization of Root Canal Sealers Using FTIR, SEM, and EDS Analysis

Background: Root canal sealers and repair materials should have the desirable physical, chemical, and biological characteristics, and an antibacterial effect if possible. There is little information available on the biocompatibility of new sealers on the market. Fourier transform infrared spectroscopy (FTIR) can offer trustworthy data to examine chemical structures; another technique for revealing the elements in the constituents that may contribute to the cytotoxicity of these sealers is scanning electron microscopy (SEM), with the goal of elemental mapping utilizing energy-dispersive X-ray spectroscopy (EDX). Methodology: All the root canal sealers were mixed as per the manufacturers’ instructions and allowed to set in molds for 24 h. Then, the samples were placed into an incubator (Memmert GmbH + Co. KG, Schwabach, Germany for 72 h, in a moist environment to allow complete chemical setting of the sealers. The organic and inorganic components of the sample were identified using FTIR with the wavelength length in the infra-red region measuring 400–450 nm. The finely crushed samples were coated with gold metal; following that, the sealer samples were examined under a scanning electron microscope (SEM) at 5000×, 10,000×, and 20,000× magnification, followed by energy-dispersive X-ray spectroscopy. Results: The surfaces of BioRoot and DiaRoot sealers revealed a relatively uniform distribution of irregular micro-sized particles aggregated in clusters, with the particle size ranging from 1 to 65 µm and 0.4 to 55 µm, respectively. OneFill, iRoot, and CeraSeal demonstrated irregularly shaped particles with particle sizes of 0.5 to 105 µm, 0.5 to 195 µm, and 0.3 to 68 µm, respectively. The EDX microanalysis revealed that oxygen, calcium, and carbon were found in all the tested sealer materials. Silicone and zirconium were absent in DiaRoot, but DiaRoot contained fluoride and ytterbium. Moreover, aluminum was noted in DiaRoot, One Fill, and CeraSeal, and chloride was only observed in BioRoot. FTIR analysis revealed strong absorption bands at 666 cm−1 and 709 cm−1 in BioRoot. Bands at 739 cm−1, 804 cm−1, 863 cm−1, 898 cm−1, and 1455 cm−1 were observed in DiaRoot. Bands at 736 cm−1 and 873 cm−1 in OneFill suggested the presence of C-H bending. Similarly, bands were observed at 937 cm−1, 885 cm−1, 743 cm−1, and 1455 cm−1 in iRoot, representing C-H stretching. Conclusions: All root canal sealers had diverse surface morphologies that contained irregular, micro-sized particles that were uniformly distributed, and they lacked heavy metals. All the experimental sealers comprised mainly calcium, oxygen, and carbon