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1.
Inna Bumagina 《Geometriae Dedicata》2004,106(1):211-230
A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology
35 (2) 1999, 301–321). 相似文献
2.
We investigate function spaces of generalised smoothness of Besov and Triebel–Lizorkin type. Equivalent quasi-norms in terms
of maximal functions and local means are given. An atomic decomposition theorem for this type of spaces is proved.
Mathematics Subject Classification (2000) 46E35 相似文献
3.
Banach frames and atomic decompositions are sequences that have basis-like properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove several functional — analytic properties of these decompositions, and show how these properties apply to Gabor and wavelet systems. We first prove that frames and atomic decompositions are stable under small perturbations. This is inspired by corresponding classical perturbation results for bases, including the Paley — Wiener basis stability criteria and the perturbation theorem el kato. We introduce new and weaker conditions which ensure the desired stability. We then prove quality properties of atomic decompositions and consider some consequences for Hilbert frames. Finally, we demonstrate how our results apply in the practical case of Gabor systems in weighted L2 spaces. Such systems can form atomic decompositions for L2w(IR), but cannot form Hilbert frames but L2w(IR) unless the weight is trivial. 相似文献
4.
We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ3, with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona
occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2. The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions. 相似文献
5.
Robert W. Baddeley Cheryl E. Praeger Csaba Schneider 《Transactions of the American Mathematical Society》2006,358(4):1619-1641
A permutation group is innately transitive if it has a transitive minimal normal subgroup, which is referred to as a plinth. We study the class of finite, innately transitive permutation groups that can be embedded into wreath products in product action. This investigation is carried out by observing that such a wreath product preserves a natural Cartesian decomposition of the underlying set. Previously we classified the possible embeddings in the case where the plinth is simple. Here we extend that classification and identify several different types of Cartesian decompositions that can be preserved by an innately transitive group with a non-abelian plinth. These different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action. We also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products.
6.
A comparative investigation has been made of the nonisothermal, solid-state thermal decompositions of the oxalates of six divalent transition metals (cations: manganese, iron, cobalt, nickel, copper and zinc) in alternative flowing atmospheres, inert (N2, CO2), reducing (H2) and oxidizing (air). Derivative thermogravimetry (DTG) and differential scanning calorimetry (DSC) response peak maxima, providing a measure of reaction temperatures, have been used to determine salt reactivities and thus to characterize the factors that control the relative stabilities of this set of chemically related reactants. Two trends were identified. Trend (1): in the inert and reducing atmospheres, the decomposition temperature (salt stability) increased with rise in enthalpy of formation of the divalent transition metal oxide, MO. It is concluded that the rupture of the cation-oxygen (oxalate) bond is the parameter that determines the stability of salts within this set. Trend (2): the diminution of decomposition temperatures from values for reactions in inert/reducing atmosphere to those for reactions in an oxidizing atmosphere increased with the difference in formation enthalpy between MO and the other participating oxide (MO3/2 or MO1/2). The change of cation valence tended to promote reaction, most decompositions in O2 occurred at lower temperatures, but the magnitude of the effect varied considerably within this set of reactants. Observed variations in stoichiometric and kinetic characteristics with reaction conditions are discussed, together with the mechanisms of thermal decompositions of these solid oxalates.This approach to the elucidation of crystolysis reaction mechanisms emphasizes the value of comparative investigations within the group of chemically related reactants. Previous isothermal kinetic studies had been made for each of the reactants selected here. From these, much has been learned about the form of the (isothermal) solid-state yield-time curves, often interpreted to provide information about the geometry of interface development for the individual rate processes. However, identification of the controls of reactivity, reaction initiation (nucleation) and advance (nucleus growth), is much more difficult to characterize and less progress has been made towards elucidation of the interface chemistry. The trends of reactivity changes with salt compositions, identified here, offer a complementary approach to that provided by the study of single salts. Much of the recent literature on thermal decompositions of solids has been concerned with individual reactants, but many results and conclusions are not presented in the widest possible perspective. Comparisons between systematically related reactants are identified here as providing a chemical context for the elucidation of the chemical steps that participate in interface reactions. The article advocates the use of a more chemical approach in investigations of crystolysis (solid-state chemical) reactions. 相似文献
7.
A. K. Galwey 《Journal of Thermal Analysis and Calorimetry》2006,86(1):267-286
This critical
survey argues that the theory, conventionally used to interpret kinetic data
measured for thermal reactions of initially solid reactants, is not always
suitable for elucidating reaction chemistry and mechanisms or for identifying
reactivity controls. Studies of solid-state decompositions published before
the 1960s usually portrayed the reaction rate as determined by Arrhenius type
models closely related to those formulated for homogeneous rate processes,
though scientific justifications for these parallels remained incompletely
established. Since the 1960s, when thermal analysis techniques were developed,
studies of solid-state decompositions contributed to establishment of the
new experimental techniques, but research interest became redirected towards
increasing the capabilities of automated equipment to collect, to store and
later to analyze rate changes for selected reactions. Subsequently, much less
attention has been directed towards chemical features of the rate processes
studied, which have included a range of reactants that is much more diverse
than the simple solid-state reactions with which early thermokinetic studies
were principally concerned. Moreover, the theory applied to these various
reactants does not recognize the possible complexities of behaviour that may
include mechanisms involving melting and/or concurrent/consecutive reactions,
etc. The situation that has arisen following, and attributable to, the eclipse
of solid-state decomposition studies by thermal analysis, is presented here
and the consequences critically discussed in a historical context. It is concluded
that methods currently used for kinetic and mechanistic investigations of
all types of thermal reactions indiscriminately considered by the same, but
inadequate theory, are unsatisfactory. Urgent and fundamental reappraisal
of the theoretical foundations of thermokinetic chemical studies is now necessary
and overdue.
While there are important, but hitherto unrecognized,
delusions in thermokinetic methods and theories, an alternative theoretical
explanation that accounts for many physical and chemical features of crystolysis
reactions has been proposed. However, this novel but general model for the
thermal behaviour and properties of solids has similarly remained ignored
by the thermoanalytical community. The objective of this article is to emphasize
the now pressing necessity for an open debate between these unreconciled opinions
of different groups of researchers. The ethos of science is that disagreement
between rival theories can be resolved by experiment and/or discussion, which
may also strengthen the foundations of the subject in the process. As pointed
out below, during recent years there has been no movement towards attempting
to resolve some fundamental differences of opinion in a field that lacks an
adequate theory. This should be unacceptable to all concerned. Here some criticisms
are made of specific features of the alternative reaction models available
with the stated intention of provoking a debate that might lead to identification
of the significant differences between the currently irreconciled views. This
could, of course, attract the displeasure of both sides, who will probably
criticise me severely. Because I intend to retire completely from this field
soon, it does not matter to me if I am considered to be ‘wrong’,
if it contributes to us all eventually agreeing to get the science ‘right’. 相似文献
8.
This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity . Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals. 相似文献
9.
David Mercier Éric Lefèvre François Delmotte 《International Journal of Approximate Reasoning》2012,53(2):146-158
In this article, the contextual discounting of a belief function, a classical discounting generalization, is extended and its particular link with the canonical disjunctive decomposition is highlighted. A general family of correction mechanisms allowing one to weaken the information provided by a source is then introduced, as well as the dual of this family allowing one to strengthen a belief function. 相似文献
10.
Hans Triebel 《Numerical Functional Analysis & Optimization》2013,34(1-2):307-317
Classical Taylor expansions of holomorphic functions in the complex plane are extended to distributions in Rnand in domains 相似文献