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Consider uncertain alternatives for which an event has two consequences (binary gambles, “gambles” for short) and over them
an operation of joint receipt which need not be closed and may be non-commutative. The two structures are linked by a distributivity
property called segregation and a preference order. Utility functions order nonnegative numbers to consequences and gambles.
Utility representations describe how the utility of a gamble depends on the utilities of consequences and on the “weight”
of the event (a number in [0,1], depending on the event). Functional characterizations give necessary and sufficient conditions,
often in form of functional equations, for certain properties of representations. We first give a functional characterization
of the often postulated event commutativity stating that two events can be interchanged in special composite gambles where
one outcome is a consequence but the other is itself a gamble. A utility representation is separable if it is multiplicative
for gambles with one consequence having 0 utility. We give three more specific characterizations of separable representations
by segregation, by homogeneity and event commutativity, and by homogeneity and segregation, and show that in the last case
event commutativity follows.
Received 10 August 2001; in revised form 6 November 2001 相似文献
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Attila Gilányi 《Aequationes Mathematicae》1997,54(1-2):289-307
Summary The aim of this paper is to give a characterization of monomial functions with the aid of an operator
introduced in Section 1. The present results were inspired by A. Dinghas [2] and A. Simon and P. Volkmann [5], who treated
the characterization of polynomial functions by the so called Dinghas interval-derivatives. 相似文献
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Dieter Pumplün 《manuscripta mathematica》1980,32(3-4):309-333
Initial cones are shown to be mono-cones for several important types of functors, namely those possessing a reducible generator or having a certain topological (1.7) resp. algebraic property (1.8). These results are useful for the computation of the universal initial completion of faithful, topologically algebraic functors, contain results of Börger-Tholen and Hoffmann for certain setbased functors as special cases and allow a complete characterization of the initial cones in quite a few categories. 相似文献
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Reinhold Hübl 《Mathematische Zeitschrift》2001,236(1):201-214
In this note we study injective local morphisms of local excellent domains. In particular we are interested in the problem when the –adic topology onS restricts to a topology on R that is linearly equivalent to the –adic topology. Using a valuative criterion, we prove this in case R is analytically irreducible and is essentially of finite type, and we recover and extend a weak version of Gabrielov's rank condition.
Received July 30, 1999; in final form November 16, 1999 / Published online December 8, 2000 相似文献
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For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podle is established. 相似文献
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Summary.
We study certain functional equations derived from the
definition of a Jordan *-derivation pair.
More precisely, if A is a complex
*-algebra and M is a
bimodule over A, having the structure of a complex vector space
compatible with the structure of A,
such that
implies
m = 0 and
implies m
= 0 and
if
are unknown additive mappings satisfying
then E and
F can be represented by double centralizers. The
obtained result implies that one of the equations in the
definition of a Jordan *-derivation pair is redundant.
Furthermore, a remark on the extension of this result to unknown
additive mappings
such that
is given in a special case. 相似文献
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Problems on associative functions 总被引:1,自引:0,他引:1
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Let S be a real interval with
, and
be a function satisfying
We show that if h is Lebesgue or Baire measurable, then there
exists
such that
That result is motivated by a question of E. Manstaviius.
Received: 11 February 2003 相似文献
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László Székelyhidi 《Aequationes Mathematicae》2005,70(1-2):122-130
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Laurence Barker 《Journal of Pure and Applied Algebra》2010,214(10):1759-1777
We introduce the lifted Tornehave morphism , an inflation Mackey morphism for finite groups, π being a set of primes, K the kernel of linearization, and B∗ the dual of the Burnside functor. For p-groups, is unique up to scalar multiples. It induces two morphisms of biset functors, one with a codomain associated with a subgroup of the Dade group, the other with a codomain associated with a quotient of the Burnside unit group. 相似文献
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Some functional equations in the spaces of generalized functions 总被引:1,自引:0,他引:1
Summary. Making use of the fundamental solution of the heat equation we find the solutions of some functional equations such as the Cauchy equations, Pexider equations, quadratic functional equations and dAlembert equations in the spaces of Schwartz distributions and Sato hyperfunctions. 相似文献