套代数子空间的端点

设d为套代数AlgN的子空间且包含AlgN的所有一秩算子．利用预零化子d⊥中一秩算子,我们给出了单位球d1中端点的刻画．     

The influence of some fuzzy implication operators on the accuracy of a fuzzy model-Part I

The problem of the influence of fuzzy implication operators and connective also on the accuracy of a fuzzy model of a d.c. series motor is considered. Several typical fuzzy implication operators are used to construct the fuzzy model of a d.c. series motor. A root-mean-square error is adopted as the criterion of the model's adequacy to the real system. The best typical fuzzy relations are selected.     

The algebraic structure of relative twisted vertex operators

Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, “relativized” twisted vertex operators are constructed in a general context based on isometries of rational lattices, and a generalized twisted Jacobi identity is established for them. This result generalizes many previous results. Relatived untwisted vertex operators had been studied in a monograph by the authors. The present paper includes as a special case the proof of the main relations among twisted vertex operators based on even lattices announced some time ago by the second author.     

The influence of some fuzzy implication operators on the accuracy of a fuzzy model-part II

The influence of fuzzy implication operators and the connective Also on the accuracy of a fuzzy model of a d.c. series motor is considered. Some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d.c. series motor. A root-mean-square error is used as the criterion of the fuzzy model's adequacy to the real system. A number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model's applicability if estimated from the point of view of computing techniques. The best types of fuzzy relations, representing fuzzy models of a real system, are chosen in order to secure the least root-mean-square error with minimal number of mathematical operations necessary for computer implementation.     

A priori estimates for solution operators of diffusion equations

The diffusion equation [d]=Au is considered, where u=u(t,x), t>0, and A is a second order uniformly elliptic differential operator in R^m Whose coefficients are bounded. Other conditions are prescribed on A to generate known soiution operators. We derive growth estimates for these solution operators in certain function spaces together with estimates for their derivatives in t and also estimates on the products of the first two spatial derivatives with these solution operators. Bounds on the solution operators are given which depmd only upon the i.u.b.'s for the ternination coefficients of A and the formal adjoint A_ * of A : These estimates are best with respect to each function space considered in the sense that equality holds for a particular solution operator     

Wavelet-Like Transforms for Admissible Semi-Groups; Inversion Formulas for Potentials and Radon Transforms

We introduce a family of wavelet-like transforms associated to certain admissible semigroups of operators acting on L_p-spaces, and prove the corresponding reproducing formula of Calderòn’s type. The new transforms constitute a unified approach to inversion of a wide class of integral operators in analysis and applications. We illustrate the general theory by considering Riesz and Bessel potentials (associated to the ordinary and the generalized translation), and the k-plane Radon transform on ℝⁿ.     

Some asymptotic results for the combination of evidence problem

The combination of evidence problem is treated here as the construction of a posterior possibility function (or probability function, as a special case) describing an unknown state parameter vector of interest. This function exhibits the appropriate components contributing to knowledge of the parameter, including conditions or inference rules, relating the parameter with observable characteristics or attributes, and errors or confidences of observed or reported data. Multivalued logic operators - in particular, disjunction, conjunction, and implication operators, where needed – are used to connect these components and structure the posterior function. Typically, these operators are well-defined for only a finite number of arguments. Yet, often in the problem at hand, a number of observable attributes represent probabilistic concepts in the form of probability density functions. This occur, for example, for attributes representing ordinary numerical measurements- as opposed to those attributes representing linguistic-based information, where non-probabilistic possibility functions are used. Thus the problem of discretization of probabilistic attributes arises, where p.d.f.'s are truncated and discretized to probability functions. As the discretization process becomes finer and finer, intuitively the posterior function should better and better represent the information available. Hence, the basic question that arises is: what is the limiting behavior of the resulting posterior functions when the level of discretization becomes infinitely fine, and, in effect, the entire p.d.f.'s are used?It is shown in this paper that under mild analytic conditions placed upon the relevant functions and operators involved, nontrivial limits in the above sense do exist and involve monotone transforms of statistical expectations of functions of random variable corresponding to the p.d.f.'s for the probabilistic attributes.     

Transmission problems for Maxwell's equations with weakly Lipschitz interfaces

We prove sufficient conditions on material constants, frequency and Lipschitz regularity of interface for well posedness of a generalized Maxwell transmission problem in finite energy norms. This is done by embedding Maxwell's equations in an elliptic Dirac equation, by constructing the natural trace space for the transmission problem and using Hodge decompositions for operators d and δ on weakly Lipschitz domains to prove stability. We also obtain results for boundary value problems and transmission problems for the Hodge–Dirac equation and prove spectral estimates for boundary singular integral operators related to double layer potentials. Copyright © 2005 John Wiley & Sons, Ltd.     

Strong polynomiality of resource constraint propagation

Constraint-based schedulers have been widely successful in tackling complex, disjunctive, and cumulative scheduling applications by combining tree search and constraint propagation. The constraint-propagation step is a fixpoint algorithm that applies pruning operators to tighten the release and due dates of activities using precedence or resource constraints. A variety of pruning operators for resource constraints have been proposed; they are based on edge finding or energetic reasoning and handle a single resource.

Complexity results in this area are only available for a single application of these pruning operators, which is problematic for at least two reasons. On the one hand, the operators are not idempotent, so a single application is rarely sufficient. On the other hand, the operators are not used in isolation but interact with each other. Existing results thus provide a very partial picture of the complexity of propagating resource constraints in constraint-based scheduling.

This paper aims at addressing these limitations. It studies the complexity of applying pruning operators for resource constraints to a fixpoint. In particular, it shows that: (1) the fixpoint of the edge finder for both release and due dates can be reached in strongly polynomial time for disjunctive scheduling; (2) the fixpoint can be reached in strongly polynomial time for updating the release dates or the due dates but not both for the cumulative scheduling; and (3) the fixpoint of “reasonable” energetic operators cannot be reached in strongly polynomial time, even for disjunctive scheduling and even when only the release dates or the due dates are considered.     

Browder’s Theorems through Localized SVEP

A bounded linear operator T ∈ L(X) on aBanach space X is said to satisfy “Browder’s theorem” if the Browder spectrum coincides with the Weyl spectrum. T ∈ L(X) is said to satisfy “a-Browder’s theorem” if the upper semi-Browder spectrum coincides with the approximate point Weyl spectrum. In this note we give several characterizations of operators satisfying these theorems. Most of these characterizations are obtained by using a localized version of the single-valued extension property of T. In the last part we shall give some characterizations of operators for which “Weyl’s theorem” holds.     

Spectral theory of difference operators with almost constant coefficients

The spectrum of higher even order difference operators with almost constant coefficients is determined. With appropriate smoothness and decay conditions on the coefficients, we show that singular continuous spectrum is absent and that the absolutely continuous spectrum agrees with that of the constant coefficient limiting operator. For such operators, the absolutely continuous spectrum is determined uniquely by the range of the characteristic polynomial. This result extends a similar result for even order differential operators. The methods of proof are closely related likewise. Finally, some results on fourth order operators with unbounded coefficients are shown.     

THE QUASI-GEOSTROPHIC EQUATION AND ITS TWO REGULARIZATIONS

Abstract

A symbolic calculus for the transposes of a class of bilinear pseudodifferential operators is developed. The calculus is used to obtain boundedness results on products of Lebesgue spaces. A larger class of pseudodifferential operators that does not admit a calculus is also considered. Such a class is the bilinear analog of the so-called exotic class of linear pseudodifferential operators and fail to produce bounded operators on products of Lebesgue spaces. Nevertheless, the operators are shown to be bounded on products of Sobolev spaces with positive smoothness, generalizing the Leibniz rule estimates for products of functions.     

Weighted boundedness of the 2‐fold product of Hardy–Littlewood maximal operators

We study new weighted estimates for the 2‐fold product of Hardy–Littlewood maximal operators defined by . This operator appears very naturally in the theory of bilinear operators such as the bilinear Calderón–Zygmund operators, the bilinear Hardy–Littlewood maximal operator introduced by Calderón or in the study of pseudodifferential operators. To this end, we need to study Hölder's inequality for Lorentz spaces with change of measures Unfortunately, we shall prove that this inequality does not hold, in general, and we shall have to consider a weaker version of it.     

Samuel multiplicity and the structure of essentially semi-regular operators: A note on a paper of Fang

Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang’s results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang’s 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang’s paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang’s 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ ∈ ? in an essentially semi-regular domain.     

Stress state in multilayer cylindrical tubes made of elastically compressible linear viscoelastic material

Through the use of Abel's operators and э operators, the authors obtained an implicit solution for N-layered cylindrical tubes with alternating elastic and viscoelastic layers under conditions of elastic compressibility of the viscoelastic medium. Explicit expressions were written for the reactive pressures in 3- and 2-layered cylindrical tubes with alternating elastic and viscoelastic layers; these are analyzed in detail. Based on the solution obtained earlier for a condition where the viscoelastic operator corresponding to Poisson's coefficient is taken as a constant, it has been shown that the hypotheses discussed will lead in time to qualitatively different stress states. The overall results obtained are illustrated on an example.     

Rotenberg模型中迁移半群的本质谱

在Lp（1（≤）p＜＋∞）空间中,本文运用半群理论研究了Rotenberg模型中具光滑边界条件的迁移半群的本质谱.采用半群方法和比较算子等方法,证明了对任意的t＞0,s＞0,算子[UH（t）-U0（t）]U0（s）[UH（t）-U0（t）]在Lp（1＜p＜＋∞）在空间中紧和在L1空间弱紧,得到迁移半群VH（t）与V0（t）有相同的本质谱型.     

On factoring an operator using elements of its kernel

A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the derivation ? acting on some ring of functions, this paper considers the more general situation of an endomorphism 𝔇 acting on a unital associative algebra. The operators considered, analogous to differential operators, are those which can be written as a finite sum of powers of 𝔇 followed by left multiplication by elements of the algebra. Assume that the set of such operators is closed under multiplication and that a Wronski-like matrix produced from some finite list of elements of the algebra is invertible (analogous to the linear independence condition). Then, it is shown that the set of operators whose kernels contain all of those elements is the left ideal generated by an explicitly given operator. In other words, an operator has those elements in its kernel if and only if it has that generator as a right factor. Three examples demonstrate the application of this result in different contexts, including one in which 𝔇 is an automorphism of finite order.     

Hypercyclic Sequences of Differential and Antidifferential Operators

In this paper, we provide some extensions of earlier results about hypercyclicity of some operators on the Fréchet space of entire functions of several complex variables. Specifically, we generalize in several directions a theorem about hyper- cyclicity of certain infinite order linear differential operators with constant coefficients and study the corresponding property for certain kinds of “antidifferential” operators which are introduced in the paper. In addition, the existence of hypercyclic functions for certain sequences of differential operators with additional properties, for instance, boundedness or with some nonvanishing derivatives, is established.     

Accretive operators which are always single-valued in normed spaces

Set-valued accretive operators in Banach spaces have been extensively studied for several decades. Our main purpose in this paper is to establish a quite revealing result that says that every set-valued lower semi-continuous accretive mapping defined on a normed space is, indeed, single-valued on the interior of its domain. No reference to the well-known Michael’s Selection Theorem is needed. This result is used to extend known theorems concerning the existence of zeros for such operators, as well as showing existence of solutions for variational inclusions.     

Concerning the convergence of inexact Newton methods

In this study, we use inexact Newton methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a partially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover, this approach allows us to derive from the same theorem, on the one hand, semi-local results of Kantorovich type, and on the other hand, global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved, on the one hand, we cover a wider range of problems, and on the other hand, by choosing our operators appropriately, we can find sharper error bounds on the distances involved than before. Furthermore, we show that special cases of our results reduce to the corresponding ones already in the literature. Finally, our results are used to solve integral equations that cannot be solved with existing methods.