The existence of extremal metrics has been recently studied extensively on Kähler manifolds. The goal is to establish a sufficient and necessary condition for the existence of extremal metrics in the sense of Geometric Invariant Theory. There are many important works related to the necessary part ([Ti], [D1], [M1],[M2]). The sufficient part seems more difficult than the necessary part since the...

In this paper, using theorems on the continuous dependence of solution differential inclusions perturbation, we obtain high-order exact penalty for nonconvex extremal problems in space Banach-valued absolutely functions. Using type distance function classes

We consider configurations of D6-branes with D0-brane charge given by recent work of Taylor and compute interaction potentials with various D-brane probes using a 1-loop open string calculation. These results are compared to a supergravity calculation using the solution given by Sheinblatt of an extremal black hole carrying 0-brane and 6-brane charge.

We consider approximation of L p functions by Hardy functions on subsets of the circle, for 1 p < 1. After some preliminaries on the possibility of such an approximation which are connected to recovery problems of the Carleman type, we prove existence and uniqueness of the solution to a generalized extremal problem involving norm constraints on the complementary subset. problems in Hardy spaces.

The problem of constructing a feedback control algorithm for a parabolic variational inequality is considered. This algorithm should provide tracking a prescribed trajectory by a solution of the given inequality. Two solving algorithms, which are stable with respect to informational noises, are designed. The algorithms are based on the method of extremal shift, which is known in the theory of g...

We establish extremal values of a solution y of a second-order initial value problem as the coefficients vary in a nonconvex set. These results extend earlier work by M. Essen in particular by allowing a coefficient in the second derivative expression.

‎For a simple graph $G$‎, ‎the signless Laplacian Estrada index is defined as $SLEE(G)=sum^{n}_{i=1}e^{q^{}_i}$‎, ‎where $q^{}_1‎, ‎q^{}_2‎, ‎dots‎, ‎q^{}_n$ are the eigenvalues of the signless Laplacian matrix of $G$‎. ‎In this paper‎, ‎we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$'s and then determine the unique unicyclic graph with maximum $SLEE$ a...

As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes. Black hole thermodynam...

As in the grand canonical treatment of Reissner-Nordström black holes in anti-de Sitter spacetime, the canonical ensemble formulation also shows that non-extremal black holes tend to have lower action than extremal ones. However, some small non-extremal black holes have higher action, leading to the possibility of transitions between non-extremal and extremal black holes. Black hole thermodynam...

We consider maximal monotone diierential inclusions with memory. We establish the existence of extremal strong and then we show that they are dense in the solution set of the original equation. As an application, we derive a \bang-bang" principle for nonlinear control systems monitored by maximal monotone diierential equations.