We devise a framework which leads to the formulation of a unified theory of normality (regularity), semi-normality (semi-regularity), s-normality (s-regularity), feeblynormality (feebly-regularity), pre-normality (pre-regularity), and others. Certain aspects of theory are given by unified proof.

Certain rheological behavior of fluids in engineering sciences is modeled by power law ansatz with p ∈ (1, 2]. In the present paper a semi-implicit time discretization scheme for such fluids is proposed. The main result is the optimal O(k2) error estimate, where k is the time step size. This improves results in [L. Diening, A. Prohl, and M. Růžička, SIAM J. Numer. Anal., 44 (2006), pp. 1172–119...

In this paper, an H1-Galerkin mixed finite element method is proposed and analyzed for parabolic partial differential equations with nonselfadjoint elliptic parts. Compared to the standard H1-Galerkin procedure, C1-continuity for the approximating finite dimensional subspaces can be relaxed for the proposed method. Moreover, it is shown that the finite element approximations have the same rates...

An H1Galerkin mixed finite element method is discussed for a class of second order hyperbolic problems. It is proved that the Galerkin approximations have the same rates of convergence as in the classical mixed method, but without LBB stability condition and quasi-uniformity requirement on the finite element mesh. Compared to the results proved for one space variable, the L∞(L2)-estimate of the...

We study a class of monotone numerical schemes for time-dependent HamiltonJacobi equations with weak Dirichlet boundary conditions. We get a convergence rate of 1 2 under some usual assumptions on the data, plus an extra assumption on the Hamiltonian H(Du, x) at the boundary ∂Ω. More specifically the mapping p→ H(p, x) must satisfy a monotonicity condition for all p in a certain subset of Rn gi...

This paper considers the global classical solvability (well-posedness) of a mixed initial-boundary value problem for semilinear hyperbolic systems with nonlinear reaction coupling of Lotka–Volterra type. The reaction nonlinearity is not globally Lipschitz in L2 and has Lipschitz properties depending on an L∞-norm bound. The well-posedness problem is reformulated in an abstract setting as a modi...

Existing semantic segmentation methods mostly rely on per-pixel supervision, unable to capture structural regularity present in natural images. Instead of learning to enforce semantic labels on individual pixels, we propose to enforce affinity field patterns in individual pixel neighbourhoods, i.e., the semantic label patterns of whether neighbouring pixels are in the same segment should match ...

We define a class of deformations in W (Ω,R), p > n−1, with positive Jacobian that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality Det = det (that the distributional determinant coincides with the pointwise determinant of the gradient). Maps in this class are shown to satisfy a property of weak monotonicity, and, as...

A hyperoval of a point-line geometry is a nonempty set of points meeting each line in either 0 or 2 points. In this paper, we study hyperovals in line Grassmannians of finite polar spaces of rank 3, hereby often imposing some extra regularity conditions. We determine an upper bound and two lower bounds for the size of such a hyperoval. If equality occurs in one of these bounds, then there is an...