Domain of existence for the solution of some IVP's and BVP's by using an efficient ninth‐order iterative method

[EN] In this paper, we consider the problem of solving initial value problems and boundary value problems through the point of view of its continuous form. It is well known that in most cases these types of problems are solved numerically by performing a discretization and applying the finite difference technique to approximate the derivatives, transforming the equation into a finite-dimensional nonlinear system of equations. However, we would like to focus on the continuous problem, and therefore, we try to set the domain of existence and uniqueness for its analytic solution. For this purpose, we study the semilocal convergence of a Newton-type method with frozen first derivative in Banach spaces. We impose only the assumption that the Frechet derivative satisfies the Lipschitz continuity condition and that it is bounded in the whole domain in order to obtain appropriate recurrence relations so that we may determine the domains of convergence and uniqueness for the solution. Our final aim is to apply these theoretical results to solve applied problems that come from integral equations, ordinary differential equations, and boundary value problems.Spanish Ministry of Science and Innovation. Grant Number: MTM2014- 52016-C2-2-P Generalitat Valenciana Prometeo. Grant Number: 2016/089Cevallos, F.; Hueso, JL.; Martínez Molada, E.; Howk, CL. (2020). Domain of existence for the solution of some IVP's and BVP's by using an efficient ninth-order iterative method. Mathematical Methods in the Applied Sciences. 43(14):7934-7947. https://doi.org/10.1002/mma.5696793479474314Porter, D., & Stirling, D. S. G. (1990). Integral equations. doi:10.1017/cbo9781139172028Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2013). Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation. Mathematical and Computer Modelling, 57(7-8), 1950-1956. doi:10.1016/j.mcm.2012.01.012Ortega, J. M. (1968). The Newton-Kantorovich Theorem. The American Mathematical Monthly, 75(6), 658. doi:10.2307/2313800Ahmad, F., Rehman, S. U., Ullah, M. Z., Aljahdali, H. M., Ahmad, S., Alshomrani, A. S., … Sivasankaran, S. (2017). Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs. Complexity, 2017, 1-30. doi:10.1155/2017/9407656Argyros, I. K., & Hilout, S. (2013). On the local convergence of fast two-step Newton-like methods for solving nonlinear equations. Journal of Computational and Applied Mathematics, 245, 1-9. doi:10.1016/j.cam.2012.12.002Argyros, I. K., Ezquerro, J. A., Gutiérrez, J. M., Hernández, M. A., & Hilout, S. (2011). On the semilocal convergence of efficient Chebyshev–Secant-type methods. Journal of Computational and Applied Mathematics, 235(10), 3195-3206. doi:10.1016/j.cam.2011.01.005Ezquerro, J. A., Grau-Sánchez, M., Hernández, M. A., & Noguera, M. (2013). Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations. Journal of Mathematical Analysis and Applications, 398(1), 100-112. doi:10.1016/j.jmaa.2012.08.040Qin, X., Dehaish, B. A. B., & Cho, S. Y. (2016). Viscosity splitting methods for variational inclusion and fixed point problems in Hilbert spaces. Journal of Nonlinear Sciences and Applications, 09(05), 2789-2797. doi:10.22436/jnsa.009.05.74Zheng, L., & Gu, C. (2012). Semilocal convergence of a sixth-order method in Banach spaces. Numerical Algorithms, 61(3), 413-427. doi:10.1007/s11075-012-9541-6Polyanin, A. (1998). Handbook of Integral Equations. doi:10.1201/978142005006

Predictive Factors, Management, and Clinical Outcomes of Coronary Obstruction Following Transcatheter Aortic Valve Implantation Insights From a Large Multicenter Registry

Objectives This study sought to evaluate the main baseline and procedural characteristics, management, and clinical outcomes of patients from a large cohort of patients undergoing transcatheter aortic valve implantation (TAVI) who suffered coronary obstruction (CO). Background Very little data exist on CO following TAVI. Methods This multicenter registry included 44 patients who suffered symptomatic CO following TAVI of 6,688 patients (0.66%). Pre-TAVI computed tomography data was available in 28 CO patients and in a control group of 345 patients (comparisons were performed including all patients and a cohort matched 1: 1 by age, sex, previous coronary artery bypass graft, transcatheter valve type, and size). Results Baseline and procedural variables associated with CO were older age (p<0.001), female sex (p<0.001), no previous coronary artery bypass graft (p = 0.043), the use of a balloon-expandable valve (p = 0.023), and previous surgical aortic bioprosthesis (p = 0.045). The left coronary artery was the most commonly involved (88.6%). The mean left coronary artery ostia height and sinus of Valsalva diameters were lower inpatients with obstruction than in control subjects (10.6 +/- 2.1 mm vs. 13.4 Conclusions Symptomatic CO following TAVI was a rare but life-threatening complication that occurred more frequently in women, in patients receiving a balloon-expandable valve, and in those with a previous surgical bioprosthesis. Lower-lying coronary ostium and shallow sinus of Valsalva were associated anatomic factors, and despite successful treatment, acute and late mortality remained very high, highlighting the importance of anticipating and preventing the occurrence of this complication. (C

Malaria infection and feather growth rate predict reproductive success in house martins

Carry-over effects take place when events occurring in one season influence individual performance in a subsequent season. Blood parasites (e.g. Plasmodium and Haemoproteus) have strong negative effects on the body condition of their hosts and could slow the rate of feather growth on the wintering grounds. In turn, these winter moult costs could reduce reproductive success in the following breeding season. In house martins Delichon urbica captured and studied at a breeding site in Europe, we used ptilochronology to measure growth rate of tail feathers moulted on the winter range in Africa, and assessed infection status of blood parasites transmitted on the wintering grounds. We found a negative association between haemosporidian parasite infection status and inferred growth rate of tail feathers. A low feather growth rate and blood parasite infections were related to a delay in laying date in their European breeding quarters. In addition, clutch size and the number of fledglings were negatively related to a delayed laying date and blood parasite infection. These results stress the importance of blood parasites and feather growth rate as potentially mechanisms driving carry-over effects to explain fitness differences in wild populations of migratory birds