The salience of bilateral symmetry to humans has led to the suggestion that camouflage may be enhanced in asymmetrical patterns. However, the importance of bilateral symmetry in visual signals (and overall morphology) may constrain the evolution of asymmetrical camouflage, resulting in the bilaterally symmetrical cryptic patterns that we see throughout the animal kingdom. This study investigate...

A posteriori error estimates are derived for unsteady convection-diffusion equations discretized with the non-symmetric interior penalty and the local discontinuous Galerkin methods. First, an error representation formula in a user specified output functional is derived using duality techniques. Then, an Lt (L 2 x) a posteriori estimate consisting of elementwise residual-based error indicators ...

The generalized Bernstein basis in the space Πn of polynomials of degree at most n, being an extension of the q-Bernstein basis introduced recently by G.M. Phillips, is given by the formula (see S. Lewanowicz & P. Woźny, BIT 44 (2004), 63–78) Bn i (x;ω| q) := 1 (ω; q)n [ n i ] q x (ωx−1; q)i (x; q)n−i (i = 0, 1, . . . , n). We give explicitly the dual basis functions Dn k (x; a, b, ω| q) for th...

We prove a posteriori error estimates for a nite element method for steady-state, energy dependent, Fokker-Planck and Fermi pencil beam equations in two space dimensions and with a forward-peaked scattering (i.e., with velocities varying within the right unit semicircle). Our estimates are based on a transversal symmetry assumption, together with a strong stability estimate for an associated du...

This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The resulting forward equation is a boundary value problem on the positive half-line that involves a negative Riemann-Liouville fractional derivative in space, and a fr...

Abstract The primal-dual method of Chambolle and Pock is a widely used algorithm to solve various optimization problems written as convex-concave saddle point problems. Each update step involves the application both forward linear operator its adjoint. However, in practical applications like computerized tomography, it often computationally favourable replace adjoint by more efficient approxima...