We consider a discrete bridge from (0, 0) to (2N, 0) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order N with α > 0. We provide a classification of the static and dynamic behaviour of this model according to the value of the parameter α. Our main results concern the hydrodynamic limit and the fluctuations of the bridge. For α < 1,...

1 The " convex " KKT theorem: a recapitulation We recall the Karush-Kuhn-Tucker theorem for convex programming, as treated in the previous lecture (see Corollary 3.5 of [OSC]).

We present a new version of first order necessary optimality conditions for a static minmax problem with inequality constraints in the parametric constraint case. These conditions, after some modification, turn out to characterize strict local minimizers of order one for the given problem.

| Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. Th...

Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution of the anisotropic discrete Dirichlet boundary value problem. Our results generalize and improve those of [16]. Math Subject Classifications: 39A10, 34B18, 58E30.

In this paper, we illustrated one scenario to modify the Ivanenko-LandauKähler equation. Since Ivanenko and Landau introduced the equation in 1928, the equation has been regarded as having a certain role as a fermion in particular in the discrete Lattice. Also, although it correctly is formulated as an alternative classical field equation by the Ideal projection for the Dirac equation in the Mi...

Several fundamental concepts such as the basic constraint qualification (BCQ), the strong conical hull intersection property (CHIP), and the perturbations for convex systems of inequalities in Banach spaces (over R or C) are extended and studied; here the systems are not necessarily finite. Their relationships with each other in connection with the best approximations are investigated. As appli...

Assume that there exists a hypersurface singularity which cannot be resolved by iterated monoidal transformations in positive characteristic. We show that in the set of defining functions of hypersurface singularities which cannot be resolved, we can find a function satisfying very strong conditions. By these conditions we may be able to deduce a contradiction under the above assumption. Beside...

We consider an optimal control problem for a diffuse interface model of tumor growth. The state equations couples a Cahn-Hilliard equation and a reaction-diffusion equation, which models the growth of a tumor in the presence of a nutrient and surrounded by host tissue. The introduction of cytotoxic drugs into the system serves to eliminate the tumor cells and in this setting the concentration o...