Superconvergence error estimates of discontinuous Galerkin time stepping for singularly perturbed parabolic problems

Numerical Algorithms - A parabolic convection-diffusion-reaction problem is discretized by the non-symmetric interior penalty Galerkin (NIPG) method in space and discontinuous Galerkin (DG) method...     

Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

Lauricella hypergeometric series $$F_A^{(n)}$$ F A ( n ) over finite fields

The Ramanujan Journal - In this paper, we develop a finite field analogue for one of the Lauricella series, $$F^{(n)}_A$$ . Extending results of Greene, a finite field analogue for the multinomial...     

Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Divisibility of certain $$\ell $$ -regular partitions by 2

The Ramanujan Journal - For a positive integer $$\ell $$ , let $$b_{\ell }(n)$$ denote the number of $$\ell $$ -regular partitions of a nonnegative integer n. Motivated by some recent conjectures...     

Lines of curvature near umbilical points on surfaces immersed in R4

LetM be a compact orientable surface,I:M R⁴ an immersion of classC ^r and a normal unitary smooth vector field. We prove that in the space of pairs (I, ) the family of pairs all whose umbilical points are Darbouxian is generic.     

Steering forces on undriven tractor wheel

The steering forces on an undriven, angled wheel mounting a 6-16 8PR tire were measured on a wheel test carriage at zero camber angle and at 1.5 km/h forward speed in a soil bin with sandy clay loam soil. The lateral force developed was found to be a function of slip angle, normal load, and inflation pressure for a particular soil condition. An exponential relationship could estimate the coefficient of lateral force of the 6-16 tire. The coefficients of this equation were found to be linearly related to inflation pressure. Rolling resistance of the wheel tested was found to be a function of slip angle, normal load, and inflation pressure for the soil condition tested. A linear relationship existed between the rolling resistance and slip angle, where the coefficients were found to be a function of inflation pressure and normal load. The generalized equations developed in the present study for estimating coefficients of lateral force and rolling resistance by taking both the tire and operating parameters into account, were found to be reasonably good by looking at the high coefficient of determination between experimental and estimated values.     

On nonoscillation of canonical or noncanonical disconjugate functional equations

Qualitative comparison of the nonoscillatory behavior of the equations

Synthesis of 1-(5-phenyl-2H-tetrazol-2-ylacetyl)-4-substituted thiosemicarbazides as possible antiinflammatory agents

A series of 1-(5-phenyl-2H-tetrazol-2-ylacetyl)-4-substituted thiosemicarbazids were prepared as possible antiinflammatory agents. Their antiproteolytic activity was reported.     

Synthesis of some newer 5-(5-aryl-2H-tetrazol-2-ylmethyl)-4-substituted-s-triazole-3-thiols as possible antiinflammatory agents

Several 1-(5-aryl-2H-tetrazol-2-ylacetyl)-4-substituted thiosemicarbazides and 5-(5-aryl-2H-tetrazol-2-yl-methyl)-4-substituted-s-triazole-3-thiols were synthesized as possible antiinflammatory agents. These compounds were characterized by their elemental, infrared and nuclear magnetic resonance analysis.