Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation.

A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral equations to a system of algebraic equations that has an easy solved. The present algorithm is extended to solve the one and two-dimensional mixed Volterra-Fredholm integral equations. Convergence analysis for the present method is discussed and confirmed the exponential convergence of the spectral algorithm. Various numerical examples are approached to demonstrate the powerful and accuracy of the technique.

Association between hidradenitis suppurativa and hospitalization for psychiatric disorders: a cross-sectional analysis of the National Inpatient Sample.

BACKGROUND: Hidradenitis suppurativa (HS) is associated with pain, disfigurement, psychosocial distress and poor quality of life, all of which may lead to a higher likelihood of mental health (MH) disorders. However, little is known about the MH comorbidities of HS. OBJECTIVES: To determine the MH disorders and cost burden associated with HS. METHODS: Data were examined from the 2002-2012 National Inpatient Sample, comprising approximately a 20% sample of all U.S. paediatric and adult hospitalizations (87 053 155 admissions). RESULTS: MH disorders were much more common in inpatients with vs. without HS (34·27% vs. 20·05%). In multivariable logistic regression models controlling for sex, age, race/ethnicity and insurance status, HS was associated with significantly higher odds of an MH disorder (adjusted odds ratio 2·53, 95% confidence interval 2·42-2·63), including 10 of 15 MH disorders examined. In contrast, HS was not associated with primary hospitalization for an MH disorder overall (odds ratio 0·95, 95% confidence interval 0·84-1·07), but it was associated with primary hospitalization for eight of 15 MH disorders examined. Among inpatients with HS, primary admission for an MH disorder was associated with female sex, public or no insurance and more chronic diseases, but inversely associated with older age and nonwhite race/ethnicity. HS was associated with > $38 million (USD) of excess mean annual costs of hospitalization for MH disorders. CONCLUSIONS: Inpatients with HS had increased odds of comorbid MH disorders, overall, and multiple primary MH admissions, in particular, which were associated with considerable excess costs.