We consider the diffusive single species growth in a plug flow reactor model with distributed delay. For small delay, existence and uniqueness of such wavefronts are proved when the convolution kernel assumes the strong generic delay kernel. The approaches used in this paper are geometric singular perturbation theory and the center manifold theorem.

In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander’s condition.

This article investigates the heat kernel of two-dimensional uniform spanning tree. We improve previous work by demonstrating occurrence log-logarithmic fluctuations around leading order polynomial behaviour for on-diagonal part quenched kernel. In addition we give two-sided estimates averaged kernel, and show that exponents appear in off-diagonal parts versions differ. Finally, derive various ...

In this paper, a homotopy perturbation method (HPM) and modified homotopy perturbation (MHPM) are proposed to solve singular integral equation with generalized Abel's kernel.

This paper investigates weak convergence of U -statistics via approximation in probability. The classical condition that the second moment of the kernel of the underlying U -statistic exists is relaxed to having 43 moments only (modulo a logarithmic term). Furthermore, the conditional expectation of the kernel is only assumed to be in the domain of attraction of the normal law (instead of the c...

We solve the logistic differential equation of fractional order and non-singular kernel. The analytical solution is obtained.

We primarily consider here the L mapping properties of a class of strongly singular Radon transforms on the Heisenberg group H; these are convolution operators on H with kernels of the form M(z, t) = K(z)δ0(t) where K is a strongly singular kernel on C . Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi. We also ...