Controller design to optimize a composite performance measure

This paper studies a mixed objective problem of minimizing a composite measure of thel ₁, ₂, andl -norms together with thel -norm of the step response of the closed loop. This performance index can be used to generate Pareto-optimal solutions with respect to the individual measures. The problem is analyzed for discrete-time, single-input single-output (SISO), linear time-invariant systems. It is shown via Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination that defines the performance measure is estabilished.This research was supported by the National Science Foundation under Grants No. ECS-92-04309, ECS-92-16690 and ECS-93-08481.     

L p c -concentration of blow-up solutions for the biharmonic nonlinear Schrödinger equation

This article is concerned with the blow-up solutions of the biharmonic Schrödinger equation with L ²-super critical nonlinearity. We obtain the nonexistence of strong limit of L ^{p _c} -norm and L ^{p _c} -concentration properties of the radially symmetric blow-up solutions, where L ^{p _c} is the invariant Lebesgue space.     

Epimorphisms and cowellpoweredness for separated metrically generated theories

For metrically generated constructs X we give an internal characterization of the regular closure operator on X, determined by the subconstruct X ₀, consisting of its T ₀ objects. This allows us to describe the epimorphisms in X ₀ and to show that all the constructs of that type are cowellpowered. We capture many known results but our method also gives solutions in cases where the epimorphism problem was still open. The third author is “research assistant” at the FWO-Vlaanderen.     

Lp-Lq DECAY ESTIMATES FOR HYPERBOLIC EQUATIONS WITH OSCILLATIONS IN COEFFICIENTS

This work is concerned with the proof of Lp -Lq decay estimates for solutions of the Cauchy problem for utt -λ2(t)b2(t)/Δu =0. The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. The authors‘ main interest is devoted to the critical case where one has an interesting interplay between the growing and the oscillating part.     

When Some Complement of a Submodule Is a Summand

A module M is said to satisfy the C ₁₁ condition if every submodule of M has a (i.e., at least one) complement which is a direct summand. It is known that the C ₁ condition implies the C ₁₁ condition and that the class of C ₁₁-modules is closed under direct sums but not under direct summands. We show that if M = M ₁ ⊕ M ₂, where M has C ₁₁ and M ₁ is a fully invariant submodule of M, then both M ₁ and M ₂ are C ₁₁-modules. Moreover, the C ₁₁ condition is shown to be closed under formation of the ring of column finite matrices of size Γ, the ring of m-by-m upper triangular matrices and right essential overrings. For a module M, we also show that all essential extensions of M satisfying C ₁₁ are essential extensions of C ₁₁-modules constructed from M and certain subsets of idempotent elements of the ring of endomorphisms of the injective hull of M. Finally, we prove that if M is a C ₁₁-module, then so is its rational hull. Examples are provided to illustrate and delimit the theory.     

Robust H ∞ control for singular systems with time-varying uncertainties

In this paper, we investigate the problem of robust H _∞ control for singular systems with polytopic time-varying parameter uncertainties. By introducing the notion of generalized quadratic H _∞ performance, the relationship between the existence of a robust H _∞ dynamic state feedback controller and that of a robust H _∞ static state feedback controller is given. By using matrix inequalities, the existence conditions of robust H _∞ static state feedback and dynamic output feedback controllers are derived. Moreover, the design methods for such controllers are provided in terms of the solutions of matrix inequalities. An example is also presented to demonstrate the validity of the proposed methods. __________ Translated from Journal of Northeastern University (Natural Science), 2004, 25(2): 110–113     

Gorenstein Injective and Projective Complexes with Respect to a Semidualizing Module

Let R be a commutative (possibly non-Noetherian) ring (in order to make things less technical) and C a semidualizing R-module. In this article, we introduce and investigate the notion of G _C -injective (G _C -projective) complexes. This extends Enochs and García Rozas's notion of Gorenstein injective (Gorenstein projective) complexes. We then show that a complex X is G _C -injective (G _C -projective) if and only if X ^m is a G _C -injective (G _C -projective) module for each m ∈ ?.     

A generalization of d’Alembert formula

In this paper we find a closed form of the solution for the factored inhomogeneous linear equation

Construction of Ternary H v -groups and Ternary P-hyperoperations

In this paper, we study the concept of ternary H _v -groups and some their properties. We give some examples of ternary H _v -groups. Also, we consider the fundamental relation β* on a ternary H _v -group and prove that β* is a compatible relation on a ternary H _v -group. In addition, we define the P-hyperoperation, and then, we construct a new ternary H _v -group.     

Localization of Frames

Motivated by Balan, Casazza, Heil, and Landau's results on localization of frames in a separable Hilbert space ?, we investigate the transitivity of localization relation of the frame ? = {f _i } _i∈I and sequence ? = {e _j } _j∈G in ? with respect to the associated map a: I → G, where G is a discrete abelian group and I is a index set. We also study some properties of ? _p -column decay, ? _p -row decay, weak homogeneous approximation property, and strong homogeneous approximation property of frame ? = {f _i } _i∈I , and sequence ? = {e _j } _j∈G , with respect to the associated map a.     

Modules Whose t-Closed Submodules Have a Summand as a Complement

We define and investigate T ₁₁-type modules as a generalization of t-extending modules, and modules satisfying C ₁₁ condition. A module M is said to be T ₁₁-type if every t-closed submodule of M has a complement which is a direct summand. Direct sums of T ₁₁-type modules inherit the property. Some equivalent conditions for a module M to be T ₁₁-type are given. We characterize a module M for which every direct summand satisfies T ₁₁ condition. If R _R is T ₁₁-type, then R/Z ₂(R _R ) is a C ₂ ring if and only if it is a von Neumann regular ring. Applying this result, we characterize a right t-extending (resp., finitely Σ-t-extending, or Σ-t-extending) ring R for which R/Z ₂(R _R ) is von Neumann regular.     

Characterization of varietal covering and stem groups

Let A _m be the variety of abelian groups of exponent m, where mis a square free positive integer. It is shown that every group G has an A _m -covering group, which generalizes the work of I. Schur (1904) and M.R. Jones (1973). Also, similar to the work of Yamazaki (1964) in the variety of abelian groups, if 1→ A → H → G → 1 is an A _m -stem extension, then we show that H is a homomorphic image of an A _m -covering group of G. Finally,in this variety some results of Hall's type will be proved.     

On Relative K 2-Group of Split Radical Ideals

Let I be a split radical ideal of a ring R. In this article, the exact sequence 1 → K ₂(R, I) → U _R (I) → V(R, I) → 1 is given by using the method of extension of groups, where U _R (I) is determined by generators and relations. The results of Maazen and Stienstra on the presentation for relative K ₂ group of split radical pairs are extended and amplified.     

Weakly G K -Perfect and Integral Closure of Ideals

Let R be a commutative Noetherian ring, K a nonzero finitely generated suitable R-module, and I an ideal of R. It is shown that if (R, ) is local, then  is G _K -perfect if and only if K is a canonical module for R. Furthermore, if I is integrally closed and G _K  ? dim _R I < ∞, then K _ is a canonical R _-module for every  ? Ass _R R/I whenever K satisfies Serre's condition (S ₁) or grade _K I > 0. Finally, it is shown that if CM ? dim _R I < ∞, then R _ is Cohen–Macaulay for every  ? Ass _R R/I.     

<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Observer-Based Control for a Class of Uncertain Neutral Time-Delay Systems via LMI Optimization Approach

In this paper, the H_∞ observer-based control for a class of uncertain neutral time-delay systems is considered. The linear matrix inequality (LMI) optimization approach is used to design the H_∞ robust control with disturbance attenuation. Two classes of observer-based controls are proposed and their H_∞-norm bounds are given. The control and observer gains are given from the LMI feasible solutions. A numerical example is given to illustrate the results. The research reported here was supported by the National Science Council of Taiwan under Grant NSC 93-2213-E-214-020.     

A new multivariable <Subscript><Emphasis Type="BoldItalic">6</Emphasis></Subscript><Emphasis Type="BoldItalic">ψ</Emphasis><Subscript><Emphasis Type="BoldItalic">6</Emphasis></Subscript> summation formula

By multidimensional matrix inversion, combined with an A _r extension of Jackson’s ₈ φ ₇ summation formula by Milne, a new multivariable ₈ φ ₇ summation is derived. By a polynomial argument this ₈ φ ₇ summation is transformed to another multivariable ₈ φ ₇ summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating ₆ φ ₅ summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey’s very-well-poised ₆ ψ ₆ summation formula. Partly supported by FWF Austrian Science Fund grants P17563-N13, and S9607 (the second is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”).     

Many Solutions of Elliptic Problems on R n of Irrational Slope

ABSTRACT

We consider the problem ? Δ u + F _u (x, u) = 0 on R ⁿ , where F is a smooth function periodic of period 1 in all its variables. We show that, under suitable hypotheses on F, this problem has a family of non-self-intersecting solutions u _D , which are at finite distance from a plane of slope (ω,0,…,0) with ω irrational. These solutions depend on a real parameter D; if D ≠ D ^′, then the closures of the integer translates of u _D and of u _{D ^′} do not intersect.     

Preparation, structure, magnetic properties and special magnetoresistance effect of Lao.67Sr0.33Mn03+δ/Pr0.7Cao.3 Mn03+δ/Lao.67Sro.33Mn03+δ trilayered thin films

The La_0,67Sr_0.33Mn0_{3 +δ}/Pr_0.7Ca_o.3Mn0_3+δ/La_0.67Sr_0.33Mn0_3+δ(LPL) trilayered films on (100)LaA-1O₃ substrates are prepared by using direct current (DC) magnetron sputtering method. The results obtained by means of X-ray powder diffractometer show that all films are the high quality epitaxial films. The results gained by SQUID magnetometer indicate that there is a magnetic coupling in the LPL trilayered films. The resistivities of LSMO, PC-MO and LPL films are measured using standard four-probe method and analyzed log_p-1/T curve. From the results it is concluded that the middle-layered PCMO which is ferromagnetic may play a role of intra-magnetic field, which weakens the paramagnetism of LSMO film, lowersp _max and enlargesT _p which is the transition temperature from metal to insulator, just as the applied magnetic field does. And the middle-layered PCMO may induce the change of the density of states in the LSMO’s gap. The two reasons above make the resistivity andT _p of the samples in zero field change with the thickness of PCMO layers. Project supported by the Chinese Academy of Sciences and the Foundation of State Science and Technology Commission of China.