We design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time -delays without any el...

Let H be the closed real linear hull of {Xs : s ∈ R} in L2(Ω,F , P ). Then H is a real Hilbert space with inner product (Y1, Y2) := E[Y1Y2] and norm ‖Y ‖ := (Y, Y ). For I ⊂ R, put HI for the closed subspace of H spanned by {Xs : s ∈ I}, and PI for the orthogonal projection operator of H onto HI . We write P⊥ I for the projection operator onto the orthogonal complement H ⊥ I of HI , i.e., P⊥ I ...

This paper presents a new algorithm for the closed-loop H∞ composite control of singularly perturbed bilinear systems with time-varying parameter uncertainties and exogenous disturbance using the successive Galerkin approximation (SGA). The singularly perturbed bilinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale via singular perturbation theory, and then...

Measurements of ryanodine receptor (RyR) activity during dynamic changes of calcium concentration have suggested that RyR has at least four calcium binding sites, and that activation transpires as an increase in the activity within the high open probability H-mode. Binding of several Ca2+ ions within the H-mode should manifest itself in the steady-state RyR activity by the presence of multiple ...

Let E be a central extension of the form 0 → V → G → W → 0 where V and W are elementary abelian 2-groups. Associated to E there is a quadratic map Q : W → V given by the 2-power map which uniquely determines the extension. This quadratic map also determines the extension class q of the extension in H(W,V ) and an ideal I(q) in H(G,Z/2) which is generated by the components of q. We say E is Bock...

Video surveillance has been widely used in recent years to enhance public safety and privacy protection. A video surveillance system needs efficient transmission and storage of video data. Video compression techniques can be used to achieve this. State-of-the-art video compression methods such as H.264/AVC often lead to high computational complexity at the encoder, which is generally implemente...

The objects of study in this paper are Hopf algebras H which finitely generated over an algebraically closed field and extensions a commutative algebra A by finite dimensional H?:=H/A+H, where A+ is the augmentation ideal A. Basic structural homological properties recalled classes examples listed. structure theorem proved when (?) H? semisimple cosemisimple, showing that case noncommutativity a...

We generalize a result of Hochman in two simultaneous directions: Instead of realizing an effectively closed Z action as a factor of a subaction of a Z-SFT we realize an action of a finitely generated group analogously in any semidirect product of the group with Z. Let H be a finitely generated group and G = Z o H a semidirect product. We show that for any effectively closed H-dynamical system ...

S. P. Novikov developed an analog of the Morse theory for closed 1-forms. In this paper we suggest an analog of the Lusternik Schnirelman theory for closed 1-forms. For any cohomology class ξ ∈ H1(X,R) we define an integer cl(ξ) (the cuplength associated with ξ); we prove that any closed 1-form representing ξ has at least cl(ξ)− 1 critical points. The number cl(ξ) is defined using cup-products ...

We prove the existence of smooth closed hypersurfaces of prescribed mean curvature homeomorphic to S for small n, n ≤ 6, provided there are barriers. 0. Introduction In a complete (n+1)-dimensional manifold N we want to find closed hypersurfaces M of prescribed mean curvature. To be more precise, let Ω be a connected open subset of N , f ∈ C(Ω̄), then we look for a closed hypersurface M ⊂ Ω such...