CONTROLLABILITY AND OPTIMALITY OF LINEAR TIME-INVARIANT NEUTRAL CONTROL SYSTEMS WITH DIFFERENT FRACTIONAL ORDERS

Control systems governed by linear time-invariant neutral equations with different fractional orders are considered. Sufficient and necessary conditions for the controllability of those systems are established. The existence of optimal controls for the systems is given. Finally, two examples are provided to show the application of our results.

A REGULAR VALUE OF COMPACT DEFORMATION

Sufficient conditions were given to assert that between any two Banach spaces over K, Fredholm mappings share at least one .value in a specific open ball. The proof of the result is constructive and based upon continuation methods.

Impulsive perturbation and bifurcation of solutions for a model of chemostat with variable yield

In this paper, we consider a variable yield model of a single-species growth in a well-stirred tank containing fresh medium, assuming the instances of time as triggering factors in which the nutrient refilling process and the removal of microorganisms by the uptake of lethal external antibiotic are initiated. It is also assumed that the periodic nutrient refilling and the periodic antibiotic injection occur with the same periodicity, but not simultaneously. The model is then formulated in terms of autonomous differential equations subject to impulsive perturbations. It is observed that either the population of microorganisms essentially washes out, or more favorably, the system is permanent. To describe this dichotomy, some biologically significant integral conditions are introduced. Further, it is shown that in a certain critical situation, a nontriviai periodic solution emerges via a bifurcation phenomenon. Finally, the dynamics of the model is illustrated with numerical experiments and computer simulations.

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE: MAXIMALITY AND MULTIPLIERS

We prove that, as in the finite dimensional case, the space of Bloch functions on the unit ball of a Hilbert space contains, under very mild conditions, any semi-Banach space of analytic functions invariant under automorphisms. The multipliers for such Bloch space are characterized and some of their spectral properties are described.

On Finite Rank Operators on Centrally Closed Semiprime Rings

We prove that the multiplication ring of a centrally closed semiprime ring R has a finite rank operator over the extended centroid C iff R contains an idempotent q such that qRq is finitely generated over C and, for each , there exist and e an idempotent of C such that xz=eq.

Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.

Calderón–Zygmund Operators in the Bessel Setting for All Possible Type Indices

We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-PMey-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, CalderSn-Zygmund operators for all possible values of type parameter λ, in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.

The ρ-variation of the Hermitian Riesz Transform

In this paper we prove the behaviour in weighted Lp spaces of the oscillation and variation of the Hilbert transform and the Riesz transform associated with the Hermite operator of dimension 1. We prove that this operator maps LP（R, w（x）dx） into itself when w is a weight in the Ap class for 1 〈 p 〈 ∞. For p = 1 we get weak type for the A1 class. Weighted estimated are also obtained in the extreme case p = ∞.

Variable exponent Hardy spaces associated with discrete Laplacians on graphs

In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.

Real Renormings on Complex Banach Spaces

The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but it is still not a complex norm.

A Note on Extreme Points in Dual Spaces

Given a normed space X it can be easily proven that every extreme point in Bx＊, the unit ball of X＊, is the restriction of an extreme point in Bx Our purpose is to study when the restrictions of extreme points in Bx＊＊＊ are extreme points in Bx＊. Namely, we characterize Ll-preduals satisfying the aforementioned property.