The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee ...

In this article we study some aspects of dispersive and concentration phenomena for the Schrödinger equation posed on the hyperbolic space H n , in order to see if the negative curvature of the manifold gets the dynamics stabler than in the Euclidean case. It is indeed the case : we prove that the dispersion inequality is valid, in a stronger form than the one on R n. However, the geometry is n...

In this paper we modify the maximum principal of (Galloway, 2000) for totally geodesic null hypersurfaces by proving a geometric maximum principle which obeys mean curvature inequalities of a family of totally umbilical null hypersurfaces of a spacetime manifold (Theorem 6). As a physical interpretation we show that, in particular, for a prescribed class of spacetimes the geometric inequality o...

Basic properties of von Neumann entropy around the strong subadditivity (SSA) are studied for the CAR systems. An entropy inequality named MONO-SSA equivalent to SSA for the tensor-product systems can fail for the CAR systems. However, if the state of the CAR systems is even, MONO-SSA is shown to be equivalent to SSA due to the symmetric purification, and is valid for such a state. Mailing addr...

Let ir(G) and γ(G) be the irredundance number and domination number of a graph G, respectively. The number of vertices and leafs of a graph G is denoted by n(G) and n1(G). If T is a tree, then Lemańska [4] presented in 2004 the sharp lower bound γ(T ) ≥ n(T ) + 2− n1(T ) 3 . In this paper we prove ir(T ) ≥ n(T ) + 2− n1(T ) 3 for an arbitrary tree T . Since γ(T ) ≥ ir(T ) is always valid, this ...

Estimation of distribution algorithms (EDAs) are population-based heuristic search methods that use probabilistic models of good solutions to guide their search. When applied to constrained optimization problems, most evolutionary algorithms use special techniques for handling invalid solutions. This paper presents PolyEDA, a new EDA approach that is able to directly consider linear inequality ...

When osmotic pressure across an artificial membrane, produced by a permeable electrically neutral solute on one side of it, is balanced by an external pressure difference so that there is no net volume flow across the membrane, it has been found that there will be a net flux of a second electrically neutral tracer solute, present at equal concentrations on either side of the membrane, in the di...

A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous-time, uncertain, gridded, linear parameter-varying (LPV) systems. Integral quadratic constraints (IQCs) are used to describe the uncertainty. Since gridded LPV systems do not have a valid frequencydomain interpretation, the time-domain, dissipation inequality approach is followed. The...

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...

Given an integer polyhedron PI ⊂ R, an integer point x̄ ∈ PI , and a point x∗ ∈ R \ PI , the primal separation problem is the problem of finding a linear inequality which is valid for PI , violated by x∗, and satisfied at equality by x̄. The primal separation problem plays a key role in the primal approach to integer programming. In this paper we examine the complexity of primal separation for se...