Asymptotic representations for hypergeometric-Bessel type function and fractional integrals

AbstractThe paper is devoted to the study of asymptotic relations for the functionλγ,σ(β)(z)=βΓ(γ+1−1/β)∫1∞(tβ−1)γ−1/βtσe−ztdtgeneralising Tricomi confluent hypergeometric function and modified Bessel function of the third kind. The full asymptotic representations for λγ,σ(β)(z) at zero and infinity are established. Applications are given to obtain full asymptotic expansions near zero and infinity for the Liouville fractional integral(I−αf)(x)=1Γ(α)∫x∞f(t)dt(t−x)1−α(x>0;α∈C,Re(α)>0)and for the Erdelyi–Kober-type fractional integral(I−;β,ηαf)(x)=βxβηΓ(α)∫x∞tβ(1−α−η)−1f(t)dt(tβ−xβ)1−α(x>0;α∈C,(Re(α)>0)with β>0 and η∈C of power-exponential function f(t), and for three other fractional integrals

Attainments and limitations of an early childhood programme in Colombia

The Growth and Development Monitoring Programme is a longstanding early childhood social intervention in Colombia. The programme's goal is the prevention and early identification of problems affecting children’s health and nutrition. To achieve this aim, the programme’s basic strategy is to educate parents about the overall health care of infants. The objective of this study is to measure the impact of this programme on children’s nutrition and health status and maternal child-care practices. To address potential selection bias, we employ quasi-experimental techniques. This article uses data from the Demographic Health Survey of 2010. The evidence suggests that the programme improved immunization status and the likelihood of health care for acute respiratory infection or fever. As expected, the programme has a greater impact on children from among the poorest people in the country. In the most advanced regions and for the beneficiaries of private health care, the effects of the programme have tended to be negligible. In this sense, our central policy recommendation is to optimize the programme for the poorest households in the country

Controllability results for impulsive mixed type functional integro-differential evolution equations with nonlocal conditions

In this paper, we establish the controllability for a class of abstract impulsive mixed-type functional integro-differential equations with finite delay in a Banach space. Some sufficient conditions for controllability are obtained by using the Mönch fixed point theorem via measures of noncompactness and semigroup theory. Particularly, we do not assume the compactness of the evolution system. An example is given to illustrate the effectiveness of our results

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled

Can Fat Deposition After Myocardial Infarction Alter the Performance of RF Catheter Ablation of Scar-Related Ventricular Tachycardia?: Results from a Computer Modeling Study

Effect of Fat Deposition on the Performance in RF Ablation IntroductionThe outcomes of catheter ablation of scar-mediated ventricular tachycardia (VT) remain far from perfect. The presence of fat as a component of the underlying substrate for scar-mediated VT could be relevant since this entity can seriously impede the passage of RF current due to its low electrical conductivity. Methods and ResultsComputer models of RF ablation were built in order to investigate the means by which the spatial heterogeneity of different tissues represented within the ventricular infarct zone, including the viable myocardium, fibrous tissue, and fat, could influence temperature distributions during RF ablation. The results demonstrated that spatial distributions of different tissue types significantly alter the density of electrical current largely as a result of fat impeding the passage of current. However, the thermal lesions appear minimally unaffected by this phenomenon, with variations in depth of approximate to 1 mm. ConclusionWhile during RF ablation of scar-related ventricular tachycardia differences in tissue characteristics may affect the density of electrical current on a small-scale, overall this does not appear to significantly impact the size of the created thermal lesions.This work was supported by the Spanish "Plan Estatal de Investigacion, Desarrollo e Innovacion Orientada a los Retos de la Sociedad" under Grant TEC2014-52383-C3 (TEC2014-52383-C3-1-R).Pérez, JJ.; D'avila, A.; Aryana, A.; Trujillo Guillen, M.; Berjano, E. (2016). Can Fat Deposition After Myocardial Infarction Alter the Performance of RF Catheter Ablation of Scar-Related Ventricular Tachycardia?: Results from a Computer Modeling Study. Journal of Cardiovascular Electrophysiology. 27(8):947-952. https://doi.org/10.1111/jce.13006S947952278Aryana, A., & d’ Avila, A. (2014). 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Adipose tissue in myocardial infarction. Cardiovascular Pathology, 13(2), 98-102. doi:10.1016/s1054-8807(03)00134-0Suárez, A. G., Hornero, F., & Berjano, E. J. (2010). Mathematical Modeling of Epicardial RF Ablation of Atrial Tissue with Overlying Epicardial Fat. The Open Biomedical Engineering Journal, 4(1), 47-55. doi:10.2174/1874120701004020047PÉREZ, J. J., D’AVILA, A., ARYANA, A., & BERJANO, E. (2015). Electrical and Thermal Effects of Esophageal Temperature Probes on Radiofrequency Catheter Ablation of Atrial Fibrillation: Results from a Computational Modeling Study. Journal of Cardiovascular Electrophysiology, 26(5), 556-564. doi:10.1111/jce.12630Berjano, E. J. (2006). BioMedical Engineering OnLine, 5(1), 24. doi:10.1186/1475-925x-5-24Hasgall PA Di Gennaro F Baumgartner C Neufeld E Gosselin MC Payne D Klingenböck A Kuster N 10.13099/VIP21000-03-0 www.itis.ethz.ch/databaseGonzalez-Suarez, A., & Berjano, E. (2016). Comparative Analysis of Different Methods of Modeling the Thermal Effect of Circulating Blood Flow During RF Cardiac Ablation. IEEE Transactions on Biomedical Engineering, 63(2), 250-259. doi:10.1109/tbme.2015.2451178Salazar, Y., Bragos, R., Casas, O., Cinca, J., & Rosell, J. (2004). Transmural Versus Nontransmural In Situ Electrical Impedance Spectrum for Healthy, Ischemic, and Healed Myocardium. IEEE Transactions on Biomedical Engineering, 51(8), 1421-1427. doi:10.1109/tbme.2004.82803