摘要:

The Quasi-Steady-State Approximation (QSSA) is a method of getting approximate solutions to differential equations, developed heuristically in biochemistry early this century. It can produce acceptable and important results even when formal analytic and numerical procedures fail. It has become associated with singular perturbation theory [1], which provides a means of assessing the accuracy and validity of the QSSA, but this involves rather complicated mathematics. In contrast, it is shown here how the necessary safeguards against misuse can be based on a simpler intuitive approach to singular perturbation theory, allied to the powerful numerical mathematical packages which have become available in recent years. This approach has been subjected to rigorous analysis and has been applied to problems in transport theory and chemical kinetics. In this note, examples are restricted to the case of ordinary differential equation systems involving only a few dependent variables. Use of the QSSA is described ab initio.

ISSN:1607-3606    

DOI:10.2989/16073600009485963

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Each finite closure system, whence each finite lattice, can be described in terms of "implicational bases" (called "covers of functional dependencies" in relational database theory). Although a NP - complete problem in general, it turns out that formodularlattices an optimal implicational base can be computed in polynomial time.

ISSN:1607-3606    

DOI:10.2989/16073600009485964

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The motivation for the present work is provided by Giuli and Salbany's work on the categoryBTOP0ofT0?bitopological spaces wherein they identified a cogenerator Q and a closure operator and used these to obtain, among other things, two interesting epireflective subcategories ofBTOP0consisting of objects which they referred to as 'absolutely 2T0-closed' and 'bisober' respectively. Moreover, the first such subcategory was also shown by them to be the epireflective hull of Q inBTOP0. We show here that almost a perfectly analogous programme can be carried out within the categoryBFTS0of 2T0-fuzzy bitopological spaces after identifying a key cogenerator inBFTS0.

ISSN:1607-3606    

DOI:10.2989/16073600009485965

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The r-asymptotically quasi finite rank operators on Banach lattices are examples of regular Riesz operators. We characterise Riesz elements in a subalgebra of a Banach algebra in terms of Riesz elements in the Banach algebra. This enables us to characterize r-asymptotically quasi finite rank operators in terms of adjoint operators. The r-asymptotically quasi finite rank operators are also employed to study the following problem: Suppose operatorsSandTon a Banach latticeEsatisfy 0 ≤S≤T. IfTis a Riesz operator, when is it true thatSis a Riesz operator?

ISSN:1607-3606    

DOI:10.2989/16073600009485966

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Using an operator-theoretical approach we show that the famous Bishop-Phelps theorem cannot be extended to general complex Banach spaces.

ISSN:1607-3606    

DOI:10.2989/16073600009485967

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In [6] Freniche proved that any weakly null martingale difference sequence inL1[0, 1] has arithmetic means that converge in norm to 0. We show any weakly null martingale difference sequence in an Orlicz space whose N-function belongs to ∇3has arithmetic means that converge in norm to 0. Then based on a theorem in Stout [13, Theorem 3.3.9 (i) and (iii)], we give necessary and sufficient conditions for a bounded martingale difference sequence in an Orlicz space whose N-function belongs to a large class of ∇2functions to have means that converge to 0 a.s. Finally, we conclude with some expository comments including an easy proof of Komlos' theorem [9] forLp[0, 1], 1 < p < ∞.

ISSN:1607-3606    

DOI:10.2989/16073600009485968

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In [3] we defined a notion of compactness in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. In their paper the latter also introduced a fuzzy convergence structure c-lim for fuzzy function spaces thus proving that FCS is a topological quasitopos. In this paper we start the investigation of compactness criteria of the Arzelà-Ascoli type in these fuzzy function spaces. To this aim we first give a coarser fuzzy convergence structure p-lim of pointwise convergence, for which compactness is easily established (via the Tychonoff theorem) and then secondly introduce a notion of evenly continuous fuzzy subsets on which p-lim and c-lim coincide.

ISSN:1607-3606    

DOI:10.2989/16073600009485969

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this note we consider to what extent the functional calculus and the spectral theory in von Neumann algebras are preserved by the taking of quotients relative to two-sided ideals of the von Neumann algebra.

ISSN:1607-3606    

DOI:10.2989/16073600009485970

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

LetXbe a real and infinite dimensional Banach space. ByλXwe denote the vector space of all sequences (αn) of real numbers such that (αnxn) lies inside the range of someX-valued measure with bounded variation for every null sequence (xn) inX. Among other results we prove: (i)λXis the largest normal sequence spaceμsatisfying that every sequence (xn) ∈μ{X} lies inside the range of someX**-valued measure with bounded variation, and (ii)λXis a perfect space for whichl1⊂λX⊂l2. We also determinate the sequence spaceλXwhenXis anLp?space (1 ≤p≤ +∞).

ISSN:1607-3606    

DOI:10.2989/16073600009485971

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We give various constructions of which the most significant is a continuous scalar-valued 2-polynomialWon the separable Hilbert spacel2and an unbounded setR⊂l2such that (i)Wis bounded on anε-neighbourhood ofR; (ii)Wis unbounded on ½R; (iii)Wdoes not factor through any (continuous or not) 1-polynomial mapping froml2to a normed space and sendingRto a bounded set. This answers in the negative two 1935 questions asked by Mazur (Problems 55 and 75 in the Scottish Book). The construction is valid both over the real and complex fields. (In finite dimensions, the questions were answered in the positive by Auerbach soon after being asked.)

ISSN:1607-3606    

DOI:10.2989/16073600009485972

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor