Entropy generation in magnetohydrodynamic mixed convection flow over an inclined stretching sheet

This research focuses on entropy generation rate per unit volume in magneto-hydrodynamic (MHD) mixed convection boundary layer flow of a viscous fluid over an inclined stretching sheet. Analysis has been performed in the presence of viscous dissipation and non-isothermal boundary conditions. The governing boundary layer equations are transformed into ordinary differential equations by an appropriate similarity transformation. The transformed coupled nonlinear ordinary differential equations are then solved numerically by a shooting technique along with the Runge-Kutta method. Expressions for entropy generation (Ns) and Bejan number (Be) in the form of dimensionless variables are also obtained. Impact of various physical parameters on the quantities of interest is seen

Local convergence balls for nonlinear problems with multiplicity and their extension to eight-order of convergence

[EN] The main contribution of this study is to present a new optimal eighth-order scheme for locating zeros with multiplicity m > 1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth-order convergence of the proposed scheme. Moreover, a local convergence study for the optimal fourth-order method defined by the first two steps of the new method is presented, allowing us to obtain the radius of the local convergence ball. Finally, numerical tests on some real-life problems, such as a Van der Waals equation of state, a conversion Chemical engineering problem and two standard academic test problems are presented, which confirm the theoretical results established in this paper and the efficiency of this proposed iterative method. We observed from the numerical experiments that our proposed iterative methods have good values for convergence radii. Further, they have not only faster convergence towards the desired zero of the involved function but they also have both smaller residual error and a smaller difference between two consecutive iterations than current existing techniques.This research was partially supported by Ministerio de Economia y Competitividad under grant MTM2014-52016-C2-2-P and by the project of Generalitat Valenciana Prometeo/2016/089.Behl, R.; Martínez Molada, E.; Cevallos-Alarcon, FA.; Alshomrani, AS. (2019). Local convergence balls for nonlinear problems with multiplicity and their extension to eight-order of convergence. Mathematical Problems in Engineering. 2019:1-18. https://doi.org/10.1155/2019/1427809S1182019Petković, M. S., Neta, B., Petković, L. D., & Džunić, J. (2013). Basic concepts. Multipoint Methods, 1-26. doi:10.1016/b978-0-12-397013-8.00001-7Shengguo, L., Xiangke, L., & Lizhi, C. (2009). A new fourth-order iterative method for finding multiple roots of nonlinear equations. Applied Mathematics and Computation, 215(3), 1288-1292. doi:10.1016/j.amc.2009.06.065Neta, B. (2010). Extension of Murakami’s high-order non-linear solver to multiple roots. International Journal of Computer Mathematics, 87(5), 1023-1031. doi:10.1080/00207160802272263Li, S. G., Cheng, L. Z., & Neta, B. (2010). Some fourth-order nonlinear solvers with closed formulae for multiple roots. Computers & Mathematics with Applications, 59(1), 126-135. doi:10.1016/j.camwa.2009.08.066Zhou, X., Chen, X., & Song, Y. (2011). Constructing higher-order methods for obtaining the multiple roots of nonlinear equations. Journal of Computational and Applied Mathematics, 235(14), 4199-4206. doi:10.1016/j.cam.2011.03.014Sharifi, M., Babajee, D. K. R., & Soleymani, F. (2012). Finding the solution of nonlinear equations by a class of optimal methods. Computers & Mathematics with Applications, 63(4), 764-774. doi:10.1016/j.camwa.2011.11.040Soleymani, F., & Babajee, D. K. R. (2013). Computing multiple zeros using a class of quartically convergent methods. Alexandria Engineering Journal, 52(3), 531-541. doi:10.1016/j.aej.2013.05.001Soleymani, F., Babajee, D. K. R., & Lotfi, T. (2013). On a numerical technique for finding multiple zeros and its dynamic. Journal of the Egyptian Mathematical Society, 21(3), 346-353. doi:10.1016/j.joems.2013.03.011Zhou, X., Chen, X., & Song, Y. (2013). Families of third and fourth order methods for multiple roots of nonlinear equations. Applied Mathematics and Computation, 219(11), 6030-6038. doi:10.1016/j.amc.2012.12.041Hueso, J. L., Martínez, E., & Teruel, C. (2014). Determination of multiple roots of nonlinear equations and applications. Journal of Mathematical Chemistry, 53(3), 880-892. doi:10.1007/s10910-014-0460-8Behl, R., Cordero, A., Motsa, S. S., & Torregrosa, J. R. (2015). On developing fourth-order optimal families of methods for multiple roots and their dynamics. Applied Mathematics and Computation, 265, 520-532. doi:10.1016/j.amc.2015.05.004Zafar, F., Cordero, A., Quratulain, R., & Torregrosa, J. R. (2017). Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters. Journal of Mathematical Chemistry, 56(7), 1884-1901. doi:10.1007/s10910-017-0813-1Geum, Y. H., Kim, Y. I., & Neta, B. (2018). Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points. Journal of Computational and Applied Mathematics, 333, 131-156. doi:10.1016/j.cam.2017.10.033Geum, Y. H., Kim, Y. I., & Magreñán, Á. A. (2018). A study of dynamics via Möbius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions. Journal of Computational and Applied Mathematics, 344, 608-623. doi:10.1016/j.cam.2018.06.006Chun, C., & Neta, B. (2015). An analysis of a family of Maheshwari-based optimal eighth order methods. Applied Mathematics and Computation, 253, 294-307. doi:10.1016/j.amc.2014.12.064Thukral, R. (2013). Introduction to Higher-Order Iterative Methods for Finding Multiple Roots of Nonlinear Equations. Journal of Mathematics, 2013, 1-3. doi:10.1155/2013/404635Geum, Y. H., Kim, Y. I., & Neta, B. (2016). A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Applied Mathematics and Computation, 283, 120-140. doi:10.1016/j.amc.2016.02.029Argyros, I. (2003). On The Convergence And Application Of Newton’s Method Under Weak HÖlder Continuity Assumptions. International Journal of Computer Mathematics, 80(6), 767-780. doi:10.1080/0020716021000059160Zhou, X., Chen, X., & Song, Y. (2013). On the convergence radius of the modified Newton method for multiple roots under the center–Hölder condition. Numerical Algorithms, 65(2), 221-232. doi:10.1007/s11075-013-9702-2Bi, W., Ren, H., & Wu, Q. (2011). Convergence of the modified Halley’s method for multiple zeros under Hölder continuous derivative. Numerical Algorithms, 58(4), 497-512. doi:10.1007/s11075-011-9466-5Zhou, X., & Song, Y. (2014). Convergence radius of Osada’s method under center-Hölder continuous condition. Applied Mathematics and Computation, 243, 809-816. doi:10.1016/j.amc.2014.06.068Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062Balaji, G. V., & Seader, J. D. (1995). Application of interval Newton’s method to chemical engineering problems. Reliable Computing, 1(3), 215-223. doi:10.1007/bf02385253Shacham, M. (1989). An improved memory method for the solution of a nonlinear equation. Chemical Engineering Science, 44(7), 1495-1501. doi:10.1016/0009-2509(89)80026-

Analytical solutions for nonlinear systems using Nucci's reduction approach and generalized projective Riccati equations

In this study, the Nucci's reduction approach and the method of generalized projective Riccati equations (GPREs) were utilized to derive novel analytical solutions for the (1+1)-dimensional classical Boussinesq equations, the generalized reaction Duffing model, and the nonlinear Pochhammer-Chree equation. The nonlinear systems mentioned earlier have been solved using analytical methods, which impose certain limitations on the interaction parameters and the coefficients of the guess solutions. However, in the case of the double sub-equation guess solution, analytic solutions were allowed. The soliton solutions that were obtained through this method display real positive values for the wave phase transformation, which is a novel result in the application of the generalized projective Riccati method. In previous applications of this method, the real positive properties of the solutions were not thoroughly investigated

A preconditioned iterative method for solving systems of nonlinear equations having unknown multiplicity

A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented. We introduce preconditioners to nonlinear equations or a system of nonlinear equations and their corresponding Jacobians. The inclusion of preconditioners provides numerical stability and accuracy. The different selection of preconditioner offers a family of iterative methods. We modified an existing method in a way that we do not alter its inherited quadratic convergence. Numerical simulations confirm the quadratic convergence of the preconditioned iterative method. The influence of preconditioners is clearly reflected in the numerically achieved accuracy of computed solutions.Peer ReviewedPostprint (published version

Why do Saudi Nurses Leave Bedside Nursing: Findings from a Pilot Study

Aim: To explore the salient factors that account for Saudi nurses leaving bedside nursing to work in other fields of nursing.   Method: A non-experimental descriptive quantitative design was used to answer the research question of this pilot study. A valid and reliable questionnaire was used as an instrument for data collection. A snowball / purposive sample was used to collect the data from 46 Saudi nurses who had left bedside nursing in three hospitals in the Aseer region in southwest of Saudi Arabia. Data were analyzed by a professional statistician using descriptive statistics.   Findings: The salient factors for Saudi nurses’ decision to leave bedside nursing that were identified included: income (including allowances and financial incentives), administrative regulations, job satisfaction, and other miscellaneous factors   Conclusion: Although this pilot study has several limitations, the findings indicate that health care planners and policy staff, and nursing leaders in the Kingdom of Saudi Arabia need to develop strategies to address the issues expressed by Saudi nurses in regard to bedside nursing, particularly the need to improve (a) financial allowances and incentive systems, (b) the bedside work environment (e.g., by decreasing weekly working hours), and (c) the image of bedside Saudi nurses in the eyes of Saudi society.   Keywords: Saudi Nurses, Pilot Study, Bedside Nursing &nbsp

Antimicrobial Usage and Resistance in Makkah Region Hospitals: A Regional Point Prevalence Survey of Public Hospitals

(1) Background: Inappropriate use of antimicrobials and subsequently rise of antimicrobial resistance (AMR) remains a major public health priority. Over-prescribing of broad-spectrum antibiotics is one of the main contributing factors for the emergence of AMR. We sought to describe antimicrobial prescribing trends among patients in public hospitals in Makkah hospitals. (2) Method: We undertook a point prevalence survey (PPS) in six hospitals in Makkah, Saudi Arabia, from January 2019 to July 2019. The survey included all the inpatients receiving antimicrobials on the day of PPS. Data was collected using the Global point prevalence survey (PPS) tool developed by the University of Antwerp, Belgium. (3) Results: Of 710 hospitalized patients, 447 patients (61.9%) were treated with one or more antimicrobials during the study period. The average bed occupancy among six hospitals was 74.4%. The majority of patients received antimicrobials parenterally (90.3%). Of the total prescribed antimicrobials, 415 (53.7%) antimicrobials were used in medical departments, 183 (23.7%) in surgical departments, and 175 (22.6%) in ICUs. Pneumonia (17.3%), skin and soft tissue infections (10.9%), and sepsis (6.6.%) were three common clinical indications. Ceftriaxones were the most commonly used antibiotics that were prescribed in 116 (15%) of patients, followed by piperacillin, with an enzyme inhibitor in 84 (10.9%). (4) Conclusion: There was a high prevalence of antibiotic use in the hospitals of Makkah, which could be a potential risk factor for the incidence of resistant strains, particularly MRSA infection. Public health decision-makers should take these findings into consideration to update national policies for antibiotic use in order to reduce the risks of further increases of AMR

The impact of diabetes mellitus on the emergence of multi-drug resistant tuberculosis and treatment failure in TB-diabetes comorbid patients: a systematic review and meta-analysis

BackgroundThe existence of Type 2 Diabetes Mellitus (DM) in tuberculosis (TB) patients is very dangerous for the health of patients. One of the major concerns is the emergence of MDR-TB in such patients. It is suspected that the development of MDR-TB further worsens the treatment outcomes of TB such as treatment failure and thus, causes disease progression.AimTo investigate the impact of DM on the Emergence of MDR-TB and Treatment Failure in TB-DM comorbid patients.MethodologyThe PubMed database was systematically searched until April 03, 2022 (date last searched). Thirty studies met the inclusion criteria and were included in this study after a proper selection process.ResultsTuberculosis-Diabetes Mellitus patients were at higher risk to develop MDR-TB as compared to TB-non-DM patients (HR 0.81, 95% CI: 0.60–0.96, p < 0.001). Heterogeneity observed among included studies was moderate (I2 = 38%). No significant change was observed in the results after sub-group analysis by study design (HR 0.81, 95% CI: 0.61–0.96, p < 0.000). In the case of treatment failure, TB-DM patients were at higher risk to experience treatment failure rates as compared to TB-non-DM patients (HR 0.46, 95% CI: 0.27–0.67, p < 0.001).ConclusionThe results showed that DM had a significant impact on the emergence of MDR-TB in TB-diabetes comorbid patients as compared to TB-non-DM patients. DM enhanced the risk of TB treatment failure rates in TB-diabetes patients as compared to TB-non-DM patients. Our study highlights the need for earlier screening of MDR-TB, thorough MDR-TB monitoring, and designing proper and effective treatment strategies to prevent disease progression

On Generalized Fourier’s and Fick’s Laws in Bio-Convection Flow of Magnetized Burgers’ Nanofluid Utilizing Motile Microorganisms

This article describes the features of bio-convection and motile microorganisms in magnetized Burgers’ nanoliquid flows by stretchable sheet. Theory of Cattaneo–Christov mass and heat diffusions is also discussed. The Buongiorno phenomenon for nanoliquid motion in a Burgers’ fluid is employed in view of the Cattaneo–Christov relation. The control structure of governing partial differential equations (PDEs) is changed into appropriate ordinary differential equations (ODEs) by suitable transformations. To get numerical results of nonlinear systems, the bvp4c solver provided in the commercial software MATLAB is employed. Numerical and graphical data for velocity, temperature, nanoparticles concentration and microorganism profiles are obtained by considering various estimations of prominent physical parameters. Our computations depict that the temperature field has direct relation with the thermal Biot number and Burgers’ fluid parameter. Here, temperature field is enhanced for growing estimations of thermal Biot number and Burgers’ fluid parameter

Optimal control strategy of HIV-1 epidemic model for recombinant virus

In this work, an optimal control strategy is developed to eliminate the spread of HIV-1. To do this, two control variables are used such as the efficaciousness of drug therapy in reducing the infection of new cells and decreasing the production of new viruses. Existence for the optimal control pair is accomplished and the Pontryagins Maximum Principle is used to characterize these optimal controls. Objective functional is constituted to minimize the densities of infected cells and free virus and to maximize the density of healthy cells. The optimality system is derived and solved numerically