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The interventional cardiac catheterization for treating congenital heart disease has evolved. Complications following interventional procedures might need emergency surgery as a bailout. Here, we report a case of cardiac perforations in three different sites following device closure of atrial septal defect (ASD). In literature, the major sites of ASD device erosion are at the roof of the right atrium (RA), left atrium (LA), or at the atrial junction with the aorta. In our patient, the device eroded at all three sites: the roof of the LA, RA, and the aorta, causing hemopericardium.

Objective: To determine the optimal letrozole regimen for ovulation induction (OI) in women with polycystic ovary syndrome (PCOS) Design: Retrospective cohort study. Setting: Single academic fertility clinic from 2015–2022. Patient(s): A total of 189 OI cycles in 52 patients with PCOS Intervention(s): Patients were prescribed 1 of 4 letrozole regimens (group 1: 2.5 mg for 5 days, group 2: 2.5 mg for 10 days, group 3: 5 mg for 5 days, and group 4: 5 mg for 10 days). Main outcome measure(s): The primary outcome was ovulation, and secondary outcomes included multifollicular development, and clinical pregnancy rate, which were analyzed with binary logistic regression. Kaplan-Meier cumulative response curves and a Cox proportional hazard regression model were used for time-dependent analyses. Results: Mean age was 30.9 years (standard deviation [SD], 3.6) and body mass index was 32.1 kg/m2 (SD, 4.0). Group 2 (odds ratio [OR], 9.12; 95% confidence interval [CI], 1.92–43.25), group 3 (OR, 3.40; 95% CI, 1.57-7.37), and group 4 (OR, 5.94; 95% CI, 2.48–14.23) had improved ovulation rates after the starting regimen as compared with group 1. Cumulative ovulation rates exceeded 84% in all groups, yet those who received 5 mg and/or 10 days achieved ovulation significantly sooner. Multifollicular development was not increased in groups 2–4 as compared with group 1. Groups 2–4 also demonstrated improved time to pregnancy. Conclusions: Ovulation rates are improved when starting with letrozole at 5 mg and/or a 10-day extended course as compared with the frequently-used 2.5 mg for 5 days. This may shorten time to ovulation and pregnancy.

Objective: To compare the consistency of endometrial receptivity array (ERA) and histologic dating among 3 spatially distinct endometrial samples obtained during a cycle of exogenous estrogen and progesterone. Design: Prospective blinded study. Setting: University practice. Patients: Twelve patients undergoing a mock frozen embryo transfer cycle. Intervention: Endometrial biopsy was performed in a manner that provided a spatially organized endometrial specimen, corresponding to the fundus, middle, and lower segment. Each of these 3 sections was further divided into immediately adjacent specimens for ERA and histology. Main Outcome Measure: Consistency of the ERA and histology results among fundal, mid, and lower endometrial biopsy specimens. Results: The ERA showed variability in outcome among different patients but dated all specimens originating from the same patient identically. Histologic dating showed variability between patients as well as between different locations within the uterus. When comparing average dating results for each patient, we saw a positive correlation between histologic and ERA dating (Spearman Rho = 0.45); however, this did not reach statistical significance. The ERA results from upper, mid, and lower uterine biopsy specimens were identical for each autologous biopsy, whereas histologic dating showed variability with an average standard deviation of 0.71 days. Conclusions: The increased heterogeneity of histologic dating is likely to be attributed to the subjectivity of the test. Furthermore, we did not observe a consistent lag or advancement in histologic or ERA dating between the fundal or lower uterine biopsies. Overall, clinicians should be reassured that endometrial tissue will return consistent ERA results independent of the location within the uterus in which it was obtained.

The Cohen–Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann–Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequalities about both the quadratic function and the absolute values functions and their fractional derivatives with respect to another function are proved and they are based on an appropriate modification of the Razumikhin method. These inequalities are applied to obtain the bounds of the norms of any solution of the model. In particular, we apply the squared norm and the absolute values norms. These bounds depend significantly on the function applied in the fractional derivative. We study the asymptotic behavior of the solutions of the model. In the case when the function applied in the fractional derivative is increasing without any bound, the norms of the solution of the model approach zero. In the case when the applied function in the fractional derivative is equal to the current time, the studied problem reduces to the model with the classical Riemann–Liouville fractional derivative and the obtained results gives us sufficient conditions for asymptotic behavior of the solutions for the corresponding model. In the case when the function applied in the fractional derivative is bounded, we obtain a finite bound for the solutions of the model. This bound depends on the initial function and the solution does not approach zero. An example is given illustrating the theoretical results.

In this paper, we consider an integro-differential model of nerve conduction which presents the propagation of impulses in the nerve’s membranes. First, we approximate the original problem via cellular nonlinear networks (CNNs). The dynamics of the CNN model is investigated by means of local activity theory. The edge of chaos domain of the parameter set is determined in the low-dimensional case. Computer simulations show the bifurcation diagram of the model and the dynamic behavior in the edge of chaos region. Moreover, stabilizing control is applied in order to stabilize the chaotic behavior of the model under consideration to the solutions related to the original behavior of the system.

The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y′,y″,y‴), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.

Background : Junctional ectopic tachycardia (JET) is the most common arrhythmia after pediatric open-heart surgeries (OHS), causing high morbidity and mortality. As diagnosis is often missed in patients with minimal hemodynamic instability, its incidence depends on active surveillance. A prospective randomized trial evaluated the efficacy and safety of prophylactic amiodarone and dexmedetomidine to prevent and control postoperative JET. Methods : Consecutive patients aged under 12 years were randomized into amiodarone, dexmedetomidine (initiated during anesthetic induction) and control groups. Outcome measures included incidence of JET, inotropic score, ventilation, and intensive care unit (ICU) duration and hospital stay, as well as adverse drug effects. Results : Two hundred and twenty-five consecutive patients with a median age of 9 months (range 2 days–144 months) and a median weight of 6.3 kg (range 1.8 kg–38 kg) were randomized with 70 patients each to amiodarone and dexmedetomidine groups, and the rest were controls. Ventricular septal defect and Fallot's tetralogy were the common defects. The overall incidence of JET was 16.4%. Syndromic patients, hypokalemia, hypomagnesemia, longer bypass, and cross-clamp duration were the risk factors for JET. Patients with JET had significantly prolonged ventilation (P = 0.043), longer ICU (P = 0.004), and hospital stay (P = 0.034) than those without JET. JET was less frequent in amiodarone (8.5%) and dexmedetomidine (14.2%) groups compared to controls (24.7%) (P = 0.022). Patients receiving amiodarone and dexmedetomidine had significantly lower inotropic requirements, lower ventilation duration (P = 0.008), ICU (P = 0.006), and hospital stay (P = 0.05). Adverse effects such as bradycardia and hypotension after amiodarone and ventricular dysfunction after dexmedetomidine were not significantly different from controls. Conclusion : Prophylactic amiodarone or dexmedetomidine started before OHS is effective and safe for the prevention of postoperative JET.

Riemann-Liouville fractional differential equations with impulses are useful in modeling the dynamics of many real world problems. It is very important that there are good and consistent theoretical proofs and meaningful results for appropriate problems. In this paper we consider a boundary value problem for integro-differential equations with Riemann-Liouville fractional derivative of orders from (1,2). We consider both interpretations in the literature on the presence of impulses in fractional differential equations: With fixed lower limit of the fractional derivative at the initial time point and with lower limits changeable at each impulsive time point. In both cases we set up in an appropriate way impulsive conditions which are dependent on the Riemann-Liouville fractional derivative. We establish integral presentations of the solutions in both cases and we note that these presentations are useful for furure studies of existence, stability and other qualitative properties of the solutions.

Abstract Background Diabetes Mellitus (DM) is a major cause of maternal, fetal, and neonatal morbidities. Our objective was to estimate the effect of both pre-pregnancy and gestational DM on the growth parameters of newborns in the Qatari population. Methods In this population-based cohort study, we compared the data of neonates born to Qatari women with both pre-pregnancy and gestational diabetes mellitus in 2017 with neonates of healthy non-diabetic Qatari women. Results Out of a total of 17020 live births in 2017, 5195 newborns were born to Qatari women. Of these, 1260 were born to women with GDM, 152 were born to women with pre-pregnancy DM and 3783 neonates were born to healthy non-diabetic (control) women. The prevalence of GDM in the Qatari population in 2017 was 24.25%. HbA1C% before delivery was significantly higher in women with pre-pregnancy DM (mean 6.19 ± 1.15) compared to those with GDM (mean 5.28 ± 0.43) (P 4000 gm) was observed in 2.7% of the control group compared to 4.8% in infants born to women with GDM, and 4.6% in infants born to women with pre-pregnancy DM (P= 0.001). Multivariate logistic regression analysis demonstrated that higher maternal age (adjusted OR 2.21, 95% CI 1.93, 2.52, P

A nonlinear Riemann–Liouville fractional differential equation with constant delay is studied. Initially, some existence results are proved. Three Ulam type stability concepts are defined and studied. Several sufficient conditions are obtained. Some of the obtained results are illustrated on fractional biological models.

Abstract A system of linear Riemann–Liouville fractional differential equations with constant delay is studied. The initial condition is set up similar to the case of the ordinary derivative. Explicit formulas for the solutions are obtained for various initial functions.

Introduction: A number of guidelines are available for management of congenital heart diseases from infancy to adult life. However, these guidelines are for patients living in high-income countries. Separate guidelines, applicable to Indian children, are required when recommending an intervention for congenital heart diseases, as often these patients present late in the course of the disease and may have co-existing morbidities and malnutrition. Process: Guidelines emerged following expert deliberations at the National Consensus Meeting on Management of Congenital Heart Diseases in India, held on the 10th and 11th of August, 2018 at the All India Institute of Medical Sciences. Objectives: The aim of the study was to frame evidence-based guidelines for (i) indications and optimal timing of intervention in common congenital heart diseases and (ii) follow-up protocols for patients who have undergone cardiac surgery/catheter interventions for congenital heart diseases. Recommendations: Evidence-based recommendations are provided for indications and timing of intervention in common congenital heart diseases, including left-to-right shunts, obstructive lesions, and cyanotic congenital heart diseases. In addition, protocols for follow-up of postsurgical patients are also described. Keywords: Congenital heart disease, Intervention, Surgery

In this paper, we consider neural networks in the case when the neurons are subject to a certain impulsive state displacement at fixed moments and the duration of this displacement is not negligible small (these are known as non-instantaneous impulses). We examine some stability properties of the equilibrium of the model. Several sufficient conditions for uniform Lipschitz stability of the equilibrium of neural networks with time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. These sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable. The case of non-Lipschitz activation functions is also studied. The theory is illustrated on particular nonlinear neural networks.

A number of guidelines are available for the management of congenital heart diseases (CHD) from infancy to adult life. However, these guidelines are for patients living in high-income countries. Separate guidelines, applicable to Indian children, are required when recommending an intervention for CHD, as often these patients present late in the course of the disease and may have coexisting morbidities and malnutrition. Guidelines emerged following expert deliberations at the National Consensus Meeting on Management of Congenital Heart Diseases in India, held on August 10 and 11, 2018, at the All India Institute of Medical Sciences. The meeting was supported by Children's HeartLink, a nongovernmental organization based in Minnesota, USA. The aim of the study was to frame evidence-based guidelines for (i) indications and optimal timing of intervention in common CHD; (ii) follow-up protocols for patients who have undergone cardiac surgery/catheter interventions for CHD; and (iii) indications for use of pacemakers in children. Evidence-based recommendations are provided for indications and timing of intervention in common CHD, including left-to-right shunts (atrial septal defect, ventricular septal defect, atrioventricular septal defect, patent ductus arteriosus, and others), obstructive lesions (pulmonary stenosis, aortic stenosis, and coarctation of aorta), and cyanotic CHD (tetralogy of Fallot, transposition of great arteries, univentricular hearts, total anomalous pulmonary venous connection, Ebstein's anomaly, and others). In addition, protocols for follow-up of postsurgical patients are also described, disease wise. Guidelines are also given on indications for implantation of permanent pacemakers in children.

The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics, chemistry, biology, etc. In this paper, the presence of noninstantaneous impulses in differential equations with generalized proportional Caputo fractional derivatives is discussed. Generalized proportional Caputo fractional derivatives with fixed lower limits at the initial time as well as generalized proportional Caputo fractional derivatives with changeable lower limits at each impulsive time are considered. The statements of the problems in both cases are set up and the integral representation of the solution of the defined problem in each case is presented. Ulam-type stability is also investigated and some examples are given illustrating these concepts.

The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when the control input is acting continuously as well as when it is acting instantaneously at the impulsive times. We defined the global Mittag–Leffler synchronization as a generalization of exponential synchronization. We obtained some sufficient conditions for Mittag–Leffler synchronization. Our results are illustrated with examples.

Practical stability properties of generalized proportional Caputo fractional differential equations with bounded delay are studied in this paper. Two types of stability, practical stability and exponential practical stability, are defined and considered, and also some sufficient conditions to guarantee stability are presented. The study is based on the application of Lyapunov like functions and their generalized proportional Caputo fractional derivatives among solutions of the studied system where appropriate Razumikhin like conditions are applied (appropriately modified in connection with the fractional derivative considered). The theory is illustrated with several nonlinear examples.

In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fractional differential equation with the GPFD is considered as a comparison equation, and some comparison results are proven. Sufficient conditions for stability and asymptotic stability were obtained. Examples illustrating the results and ideas in this paper are also provided.

Abstract In this paper, we present further generalizations of the beta function; Riemann–Liouville, Caputo and Kober–Erdelyi fractional operators by using confluent hypergeometric function with six parameters. We also define new generalizations of the Gauss F, Appell F1 $F_{1}$, F2 $F_{2}$ and Lauricella FD3 $F_{D}^{3}$ hypergeometric functions with the help of new beta function. Then we obtain some generating function relations for these generalized hypergeometric functions by using each generalized fractional operators, separately. One of the purposes of the present investigation is to give a chance to the reader to compare the results corresponding to each generalized fractional operators.

Duplication of atrioventricular valves involves the mitral valve more often than the tricuspid valve and is often associated with other cardiac defects. Double-orifice tricuspid valve (DOTV) is often identified in surgery or autopsy and missed on echocardiography, as the two orifices are orthogonal to the imaging plane. If suspected on echocardiography, it masquerades as mild tricuspid hypoplasia. Three-dimensional echocardiography and magnetic resonance imaging of a DOTV are presented.

Cervicothoracic thymic cysts are rare and difficult to diagnose preoperatively. We report a case of a cervicothoracic thymic cyst presenting as a lateral neck mass and mimicking a laryngocele in a 3-year-old boy and its definitive management.

In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results.

First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. We define stability in time and generalize Mittag-Leffler stability for RL fractional differential equations and we study stability properties by an appropriate modification of the Razumikhin method. Two different types of derivatives of Lyapunov functions are studied: the RL fractional derivative when the argument of the Lyapunov function is any solution of the studied problem and a special type of Dini fractional derivative among the studied problem.

Stability of the solutions to a nonlinear impulsive Caputo fractional differential equation is studied using Lyapunov like functions. The derivative of piecewise continuous Lyapunov functions among the nonlinear impulsive Caputo differential equation of fractional order is defined. This definition is a natural generalization of the Caputo fractional Dini derivative of a function. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability of the solution are established. Some examples are given to illustrate the results.

If the atrial appendages lie adjacent to each other on same side of the great arteries, instead of encircling their roots, they are referred as juxtaposed. Right juxtaposition of atrial appendages is less common than left juxtaposition. The images demonstrate the classical radiological, echocardiographic, and surgical images of juxtaposed atrial appendages. Their clinical incidence, associations, and relevance during interventional and surgical procedures are discussed.

Background: Conventional methods of closure of ventricular septal defects involve placement of sutures 4-5 mm from the posterior inferior margin. This study compares the conventional method with an alternative technique wherein sutures are placed along the edge of the defect thereby “excluding” the conduction system and the tensor apparatus of the tricuspid valve from the suture line. Materials and Methods: Between January 2013 and January 2016, 409 consecutive patients were retrospectively reviewed and divided into two matched groups. Group A (n = 174) underwent closure using the alternative technique and Group B (n = 235) with the conventional technique. Patients with isolated ventricular septal defects (VSDs) (n = 136) were separately analyzed as were infants within this subset. Results: Immediate postoperative results were similar with no statistically significant differences in either group in terms of incidence of residual defects or postoperative tricuspid regurgitation. There was however a significantly increased incidence of post operative complete heart block (CHB) among patients in the conventional group (P = 0.02). Incidence of temporary heart block that reverted to sinus rhythm was also more in the conventional method group (Group B) (P = 0.03) as was right bundle branch block (P ≤ 0.05) in all the subsets of patients analyzed. Conclusion: Surgical closure of VSDs can be accomplished by placing sutures along the margins or away with comparable results. The incidence of CHB, however, seems to be less when the “excluding” technique is employed.

Fractional differential equations with impulses arise in modeling real world phenomena where the state changes instantaneously at some moments. Often, these instantaneous changes occur at random moments. In this situation the theory of Differential equations has to be combined with Probability theory to set up the problem correctly and to study the properties of the solutions. We study the case when the time between two consecutive moments of impulses is exponentially distributed. In connection with the application of the Riemann–Liouville fractional derivative in the equation, we define in an appropriate way both the initial condition and the impulsive conditions. We consider the case when the lower limit of the Riemann–Liouville fractional derivative is fixed at the initial time. We define the so called p-moment Mittag–Leffler stability in time of the model. In the case of integer order derivative the introduced type of stability reduces to the p–moment exponential stability. Sufficient conditions for p–moment Mittag–Leffler stability in time are obtained. The argument is based on Lyapunov functions with the help of the defined fractional Dini derivative. The main contributions of the suggested model is connected with the implementation of impulses occurring at random times and the application of the Riemann–Liouville fractional derivative of order between 0 and 1. For this model the p-moment Mittag–Leffler stability in time of the model is defined and studied by Lyapunov functions once one defines in an appropriate way their Dini fractional derivative.

The initial value problem for a special type of scalar nonlinear fractional differential equation with a Riemann–Liouville fractional derivative is studied. The main characteristic of the equation is the presence of the supremum of the unknown function over a previous time interval. This type of equation is difficult to be solved explicitly and we need approximate methods for its solving. In this paper, initially, mild lower and mild upper solutions are defined. Then, based on these definitions and the application of the monotone-iterative technique, we present an algorithm for constructing two types of successive approximations. Both sequences are monotonically convergent from above and from below, respectively, to the mild solutions of the given problem. The suggested iterative scheme is applied to particular problems to illustrate its application.

Nonlinear scalar Riemann-Liouville fractional differential equations with a constant delay and impulses are studied and initial conditions and impulsive conditions are set up in an appropriate way. The definitions of both conditions depend significantly on the type of fractional derivative and the presence of the delay in the equation. We study the case of a fixed lower limit of the fractional derivative and the case of a changeable lower limit at each impulsive time. Integral representations of the solutions in all considered cases are obtained. Existence results on finite time intervals are proved using the Banach principle.

In this work, the thermal conductivity of Al _2 O _3 nanofluids has been investigated for the sensitivity towards neutron irradiation. The solution combustion method has been used for the synthesis of Al _2 O _3 nanoparticles that have been used for the preparation of the nanofluids. Prepared nanofluids have been neutron-irradiated for 7 and 14 days. Dynamic Light Scattering, Scanning Electron Microscopy, and Ultraviolet-Visible Spectroscopy have been used to ascertain the change in properties before and after neutron-irradiation. Thermal conductivity has been measured for un-irradiated and neutron-irradiated nanofluids at 30 °C using a KD2 pro thermal properties analyzer. The decrease in thermal conductivity has been observed after neutron-irradiation that further decreases with increased duration of exposure and concentration of nanoparticles. 5 and 10% decrease in thermal conductivity has been recorded after 7 and 14 days of neutron irradiation for change in concentration from 0 to 2 volume percent. Neutron-irradiation sensitivity analysis revealed that heat transfer characteristics are sensitive at higher concentrations and during initial exposure of neutron-irradiations.

In this paper, we study Linear Riemann-Liouville fractional differential equations with a constant delay. The initial condition is set up similarly to the case of ordinary derivative. Explicit formulas for the solutions are obtained for various initial functions.

In this paper, we apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory to establish the existence of unbounded solutions for the following fourth order three-point boundary value problem on a half-line \begin{align*} &x''''(t)+q(t) f(t, x(t), x'(t), x''(t),x'''(t))=0, \qquad \hbox{$t\in(0,+\infty)$,} \\ &x''(0)=A,\qquad x(\eta)=B_1,\qquad x'(\eta)=B_2, \qquad x'''(+\infty)=C, \end{align*} where $\eta\in(0,+\infty),$ but fixed, and $f\colon [0,+\infty)\times \mathbb{R}^4\rightarrow\mathbb{R}$ satisfies Nagumo's condition. We present easily verifiable sufficient conditions for the existence of at least one solution, and at least three solutions of this problem. We also give two examples to illustrate the importance of our results.

Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability with initial time difference are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations are employed. Several examples are given to illustrate the theory.

Objective: Reconstruction of branch pulmonary arteries (PAs) can be challenging in redo congenital heart surgeries. Treatment options like percutaneous stent implantation and surgical patch angioplasty may yield suboptimal results. We present our experience with hybrid intraoperative stenting which may be an effective alternative option. Methods: We retrospectively analyzed data of all patients with PA stenosis who underwent intraoperative PA branch stenting in our institution between January 2011 and December 2012. Results: Ten patients [6 females, median age 10 (1.4 to 37) years], underwent hybrid stenting of the PA. Primary cardiac diagnoses were pulmonary atresia with ventricular septal defect (VSD) in three patients, pulmonary atresia with intact ventricular septum in two, Tetralogy of Fallot (TOF) in one, Double outlet right ventricle (DORV) with pulmonary stenosis (PS) in one, complex single ventricle in two and VSD with bilateral branch PA stenosis in one patient. Concomitant surgeries were revision/reconstruction of RV-PA conduit in 4, Fontan completion in 4, repair of TOF with conduit placement in 1 and VSD closure in 1 patient. The left PA was stented in 7, the right in 2 and both in 1, with a total of 11 stents. There were no complications related to stent implantation. Two early postoperative deaths were unrelated to stent implantation. At mean follow-up period of 14.8 (12–26) months, stent position and patency were satisfactory in all survivors. None of them needed repeat dilatation or surgical reintervention. Conclusion: Hybrid stenting of branch PA is a safe and effective option for PA reconstruction in redo cardiac surgeries. With meticulous planning, it can be safely performed without fluoroscopy.

In this paper a nonlinear system of Riemann−Liouville (RL) fractional differential equations with non-instantaneous impulses is studied. The presence of non-instantaneous impulses require appropriate definitions of impulsive conditions and initial conditions. In the paper several types of initial value problems are considered and their mild solutions are given via integral representations. In the linear case the equivalence of the solution and mild solutions is established. Conditions for existence and uniqueness of initial value problems are presented. Several examples are provided to illustrate the influence of impulsive functions and the interpretation of impulses in the RL fractional case.

In this paper, we study Lipschitz stability of Caputo fractional differential equations with non-instantaneous impulses and state dependent delays. The study is based on Lyapunov functions and the Razumikhin technique. Our equations in particular include constant delays, time variable delay, distributed delay, etc. We consider the case of impulses that start abruptly at some points and their actions continue on given finite intervals. The study of Lipschitz stability by Lyapunov functions requires appropriate derivatives among fractional differential equations. A brief overview of different types of derivative known in the literature is given. Some sufficient conditions for uniform Lipschitz stability and uniform global Lipschitz stability are obtained by an application of several types of derivatives of Lyapunov functions. Examples are given to illustrate the results.

This work is concerned with oscillation of a class of fourth-order nonlinear delay dynamic equations on a time scale. A new comparison theorem is established that improves related results reported in the literature.

We consider the following complementary Lidstone boundary value problem $$\begin{array}{c}(-1)^{m}y^{(2m+1)}(t)= F(t,y(t), y'(t)),~~t\in[0,1]\\ y(0)=0, y^{(2k-1)}(0)=y^{(2k-1)}(1)=0, 1\leq k\leq m. \end{array}$$ The nonlinear term $F$ depends on $y'$ and this derivative dependence is seldom investigated in the literature. Using a variety of fixed point theorems, we establish the existence of one or more positive solutions for the boundary value problem. Examples are also included to illustrate the results obtained.

Cardiac hybrid procedures are performed in modern, spacious, and highly equipped hybrid suites in developed countries. Organizing such expensive suites in countries with an emerging economy is difficult from both a financial and logistics point of view. We share our experience of safely performing a Hybrid stage I palliation procedure for Aortic atresia with ventricular septal defect on a 2-month-old infant weighing 3.35 kg using minimal resources in a conventional catheterization laboratory.

In this paper, we consider a four-point coupled boundary value problem for systems of the nonlinear semipositone fractional differential equation \begin{gather*}\left\{ \begin{array}{ll} \mathbf{D}_{0+}^\alpha u+\lambda f(t,u,v)=0,\quad 00,\\ \mathbf{D}_{0+}^\alpha v+\lambda g(t,u,v)=0,\\ u^{(i)}(0)=v^{(i)}(0)=0, 0\leq i\leq n-2,\\ u(1)=av(\xi), v(1)=bu(\eta), \xi,\eta\in(0,1) \end{array}\right.\end{gather*} where $\lambda$ is a parameter, $a, b, \xi,\eta$ satisfy $\xi,\eta\in(0,1)$, $0

By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85⁻87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich⁻Rus⁻Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121⁻124; Boll. Unione Mat. Ital. 1972, 4, 26⁻42 and Boll. Unione Mat. Ital. 1971, 4, 1⁻11.) is not applicable.

One approach to study various stability properties of solutions of nonlinear Caputo fractional differential equations is based on using Lyapunov like functions. A basic question which arises is the definition of the derivative of the Lyapunov like function along the given fractional equation. In this paper, several definitions known in the literature for the derivative of Lyapunov functions among Caputo fractional differential equations are given. Applications and properties are discussed. Several sufficient conditions for stability, uniform stability and asymptotic stability with respect to part of the variables are established. Several examples are given to illustrate the theory.

The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

The Cohen and Grossberg neural networks model is studied in the case when the neurons are subject to a certain impulsive state displacement at random exponentially-distributed moments. These types of impulses significantly change the behavior of the solutions from a deterministic one to a stochastic process. We examine the stability of the equilibrium of the model. Some sufficient conditions for the mean-square exponential stability and mean exponential stability of the equilibrium of general neural networks are obtained in the case of the time-varying potential (or voltage) of the cells, with time-dependent amplification functions and behaved functions, as well as time-varying strengths of connectivity between cells and variable external bias or input from outside the network to the units. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. The theory relies on a modification of the direct Lyapunov method. We illustrate our theory on a particular nonlinear neural network.

One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.