H∞ preview control and fixed-lag smoothing problems are solved in general discrete time linear systems, via a reduction to equivalent open loop differential games. To prevent high order Riccati equations, found in some solutions, the state of the Hamilton-Jacobi system (HJS) resides in a quotient space of an auxiliary extended state space system. The dimension of that auxiliary space is equal t...

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second spac...

In this paper we study the vertex operator algebra Dch(H,Γ) constructed from fixed points of chiral differential operators on upper half plane which is holomorphic at all cusps, under action a congruence subgroup Γ. To end, introduce an SL(2,R)-invariant filtration labeled by partition pairs and its successive quotient. We show that quotient cuspidal condition isomorphic to space modular forms....

We provide a Hilbert-Mumford Criterion for the action of a reductive group G on a Q-factorial algebraic variety X, partially proving a conjecture stated by A. BiaÃlynicki-Birula. The result allows to construct G-invariant open subsets of X admitting a good quotient by G from certain open subsets admitting a good quotient by a maximal torus T of G. As an application, we indicate an explicit meth...

We study some geometric properties of actions on nonpositively curved spaces related to complete reducibility and semisimplicity, focusing on representations of a finitely generated group Γ in the group G of rational points of a reductive group over a local field, acting on the associated space (symmetric space or affine building). We prove that the space of completely reducible classes is the ...

Gromov constructed uncountably many pairwise non-isomorphic discrete groups with Kazhdan's property (T). We will show that no separable II 1-factor can contain all these groups in its unitary group. In particular, no separable II 1-factor can contain all separable II 1-factors in it. We also show that the full group C *-algebras of some of these groups fail the lifting property. We recall that ...

In this paper we study the problem of determining the homology groups of a quotient of a topological space by an action of a group. The method is to represent the original topological space as a homotopy limit of a diagram, and then act with the group on that diagram. Once it is possible to understand what the action of the group on every space in the diagram is, and what it does to the morphis...

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used...

The question of the dimension of almost Hilbertian subspaces is resolved in [1] where it is shown that every Banach space E of dimension n possesses almost Hilbertian subspaces of dimension c(logn), where c is an absolute constant, and that this estimate is the best possible. When the net is spread wider to include quotient spaces and subspaces of quotient spaces we should expect to find instan...