Canonical conservative state/signal shift realizations of passive discrete time behaviors

A passive linear discrete time invariant s/s (state/signal) system Σ=(V;X,W) consists of a Hilbert (state) space X, a Kre?n (signal) space W, a maximal nonnegative (generating) subspace V of the Kre?n space K:=−X[?]X[?]W. The sets of trajectories (x(⋅);w(⋅)) generated by V on the discrete time intervals I⊂Z are defined by

     

Periodic solutions of second order nonlinear difference equations with discrete -Laplacian

We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second order difference equations involving discrete -Laplacian. We obtain in particular upper and lower solutions theorems, Ambrosetti–Prodi type multiplicity results, sharp existence conditions for nonlinearities which are bounded from below or from above and necessary and sufficient conditions for the existence of positive periodic solutions when the nonlinearity is singular at 0.     

Geometric realizations of curvature models by manifolds with constant scalar curvature

We show any pseudo-Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and -scalar curvature.     

The maximum asymptotic bias of S-estimates for regression over the neighborhoods defined by certain special capacities

The maximum asymptotic bias of an S-estimate for regression in the linear model is evaluated over the neighborhoods (called (c,γ)-neighborhoods) defined by certain special capacities, and its lower and upper bounds are derived. As special cases, the (c,γ)-neighborhoods include those in terms of -contamination, total variation distance and Rieder's (,δ)-contamination. It is shown that when the model distribution is normal and the (,δ)-contamination neighborhood is adopted, the lower and upper bounds of an S-estimate (including the LMS-estimate) based on a jump function coincide with the maximum asymptotic bias. The tables of the maximum asymptotic bias of the LMS-estimate are given. These results are an extension of the corresponding ones due to Martin et al. (Ann. Statist. 17 (1989) 1608), who used -contamination neighborhoods.     

Existence and multiplicity results for some nonlinear problems with singular -Laplacian

Using Leray–Schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems

where l(u,u^′)=0 denotes the Dirichlet, periodic or Neumann boundary conditions on [0,T], is an increasing homeomorphism, (0)=0. The Dirichlet problem is always solvable. For Neumann or periodic boundary conditions, we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions, upper and lower solutions theorems, Ambrosetti–Prodi type results. We prove Lazer–Solimini type results for singular nonlinearities and periodic boundary conditions.     

On the distributions of the form ∑i (δpi−δni)

We present some properties of the distributions T of the form ∑_i (δ_pi−δ_ni), with ∑_i d(p_i,n_i)<∞, which arise in the study of the 3-d Ginzburg–Landau problem; see Bourgain et al. (C. R. Acad. Sci. Paris, Ser. I 331 (2000) 119–124). We show that there always exists an irreducible representation of T. We also extend a result of Smets (C. R. Acad. Sci. Paris, Ser. I 334 (2002) 371–374) which says that T is a measure iff T can be written as a finite sum of dipoles.     

Finite element analysis of an A– method for time-dependent Maxwell’s equations based on explicit-magnetic-field scheme

In this paper, error analysis of a finite element A– method for the time-dependent Maxwell’s equations is presented. An explicit-magnetic-field scheme is applied. Provided that the time-stepsize τ is sufficiently small, the proposed algorithm yields for finite time T an error of in the L²-norm for the electric field E and the magnetic field H, where h is the mesh size.     

Continuity in G

For a discrete group G, we consider βG, the Stone– ech compactification of G, as a right topological semigroup, and G^*=βGG as a subsemigroup of βG. We study the mappings λ_p^* :G^*→G^*and μ^* :G^*→G^*, the restrictions to G^* of the mappings λ_p :βG→βG and μ :βG→βG, defined by the rules λ_p(q)=pq, μ(q)=qq. Under some assumptions, we prove that the continuity of λ_p^* or μ^* at some point of G^* implies the existence of a P-point in ω^*.     

-stability of discrete hybrid systems via variational Lyapunov method

The aim of this paper is to give some results on ₀-stability for discrete hybrid systems via a variational cone-valued Lyapunov method.     

The equation on weakly pseudo-convex CR manifolds of dimension 3

Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of dimension 3, embedded in (N2), of codimension one or more, and endowed with the induced CR structure. Assuming that the tangential Cauchy-Riemann operator has closed range in L²(M) in order to rule out the Rossi example, we push regularity up to show has closed range in H^s(M) for all s>0. We then use the Szegö projection to show there is a smooth solution for the problem given smooth data. The results are obtained via microlocalization by piecing together estimates for functions and (0,1) forms that hold on different microlocal regions.     

Nonlinear structure of some classical quasi-Banach spaces and -spaces

We investigate the Lipschitz structure of ℓ_p and L_p for 0<p<1 as quasi-Banach spaces and as metric spaces (with the metric induced by the p-norm) and show that they are not Lipschitz isomorphic. We prove that the -space L₀ is not uniformly homeomorphic to any other L_p space, that the L_p spaces for 0<p<1 embed isometrically into one another, and reduce the problem of the uniform equivalence amongst L_p spaces to their Lipschitz equivalence as metric spaces.     

The Cuntz semigroup and comparison of open projections

We show that a number of naturally occurring comparison relations on positive elements in a C^?-algebra are equivalent to natural comparison properties of their corresponding open projections in the bidual of the C^?-algebra. In particular we show that Cuntz comparison of positive elements corresponds to a comparison relation on open projections, that we call Cuntz comparison, and which is defined in terms of—and is weaker than—a comparison notion defined by Peligrad and Zsidó. The latter corresponds to a well-known comparison relation on positive elements defined by Blackadar. We show that Murray-von Neumann comparison of open projections corresponds to tracial comparison of the corresponding positive elements of the C^?-algebra. We use these findings to give a new picture of the Cuntz semigroup.     

Well-posedness and regularity of generalized Navier-Stokes equations in some critical Q-spaces

We study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space , , which is larger than some known critical homogeneous Besov spaces. Here is a space defined as the set of all measurable functions with

     

The SC property of an expected residual function arising from stochastic complementarity problems

The stochastic nonlinear complementarity problem has been recently reformulated as an expected residual minimization problem which minimizes an expected residual function defined by an NCP function. In this work, we show that the expected residual function defined by the Fischer–Burmeister function is an function.     

Representation type of the blocks of category in types and

In this paper a complete classification of the representation type of the infinitesimal blocks of the parabolic category for the complex simple Lie algebras of types F₄ and G₂ is given.     

On nonatomic submeasures on . II

It is shown that if two submeasures on that are lim sup's of sequences of measures have the same zero sets, and one is nonatomic, so is the other, and they are (ε-δ)-equivalent. Moreover, if a submeasure η is the lim sup of a sequence of lower semi-continuous (lsc) submeasures and is 0-dominated by the so-called core γ^• of an lsc submeasure γ, then η is also (ε-δ)-dominated by γ^•. And if a submeasure η of this type is 0-dominated by a nonatomic submeasure, then it is nonatomic as well.