The Dirichlet problem for the time-fractional advection-diffusion equation in a half-space

The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically

The fundamental solutions to the central symmetric time-fractional heat conduction equation with heat absorption

The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically

The Dirichlet problem for the time-fractional advection-diffusion equation in a half-space

The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically

The fundamental solutions to the central symmetric time-fractional heat conduction equation with heat absorption

The time-fractional heat conduction equation with heat absorption proportional to temperature is considered in the case of central symmetry. The fundamental solutions to the Cauchy problem and to the source problem are obtained using the integral transform technique. The numerical results are presented graphically

Fundamental solution to the Cauchy problem for the time-fractional advection-diffusion equation

The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered. The fundamental solution to the Cauchy problem is obtained using the integral transform technique. The numerical results are illustrated graphically

Spectrum of steroid-resistant and congenital nephrotic syndrome in children: The podoNet registry cohort

Background and objectives Steroid-resistant nephrotic syndrome is a rare kidney disease involving either immune-mediated or genetic alterations of podocyte structure and function. The rare nature, heterogeneity, and slow evolution of the disorder are major obstacles to systematic genotype-phenotype, intervention, and outcome studies, hampering the development of evidence-based diagnostic and therapeutic concepts. To overcome these limitations, the PodoNet Consortium has created an international registry for congenital nephrotic syndrome and childhood-onset steroid-resistant nephrotic syndrome. Design, setting, participants, & measurements Since August of 2009, clinical, biochemical, genetic, and histopathologic information was collected both retrospectively and prospectively from 1655 patients with childhood-onset steroid-resistant nephrotic syndrome, congenital nephrotic syndrome, or persistent subnephrotic proteinuria of likely genetic origin at 67 centers in 21 countries through an online portal. Results Steroid-resistant nephrotic syndrome manifested in the first 5 years of life in 64% of the patients. Congenital nephrotic syndrome accounted for 6% of all patients. Extrarenal abnormalities were reported in 17% of patients. The most common histopathologic diagnoses were FSGS (56%), minimal change nephropathy (21%), and mesangioproliferative GN (12%). Mutation screening was performed in 1174 patients, and a genetic disease cause was identified in 23.6% of the screened patients. Among 14 genes with reported mutations, abnormalities in NPHS2 (n=138), WT1 (n=48), and NPHS1 (n=41) were most commonly identified. The proportion of patients with a genetic disease cause decreased with increasing manifestation age: from 66% in congenital nephrotic syndrome to 15%-16% in schoolchildren and adolescents. Among various intensified immunosuppressive therapy protocols, calcineurin inhibitors and rituximab yielded consistently high response rates, with 40%-45% of patients achieving complete remission. Confirmation of a genetic diagnosis but not the histopathologic disease type was strongly predictive of intensified immunosuppressive therapy responsiveness. Post-transplant disease recurrence was noted in 25.8% of patients without compared with 4.5% (n=4) of patients with a genetic diagnosis. Conclusions The PodoNet cohort may serve as a source of reference for future clinical and genetic research in this rare but significant kidney disease. © 2015 by the American Society of Nephrology