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1.
Shmuel Rosset 《Israel Journal of Mathematics》1981,39(3):255-258
We prove that the Brauer class of a crossed product is a sum of symbols iff its “local” components are. Analogously we show
that a solution of the “Goldie rank conjecture” would follow from the “local” statements; an extension of a result of Cliff-Sehgal
is an easy corollary. 相似文献
2.
Nikola Kompa 《Acta Analytica》2005,20(1):16-28
The basic idea of conversational contextualism is that knowledge attributions are context sensitive in that a given knowledge
attribution may be true if made in one context but false if made in another, owing to differences in the attributors’ conversational
contexts. Moreover, the context sensitivity involved is traced back to the context sensitivity of the word “know,” which,
in turn, is commonly modelled on the case either of genuine indexicals such as “I” or “here” or of comparative adjectives
such as “tall” or “rich.” But contextualism faces various problems. I argue that in order to solve these problems we need
to look for another account of the context sensitivity involved in knowledge attributions and I sketch an alternative proposal. 相似文献
3.
Christof Külske 《Probability Theory and Related Fields》2001,119(1):1-30
Can the joint measures of quenched disordered lattice spin models (with finite range) on the product of spin-space and disorder-space
be represented as (suitably generalized) Gibbs measures of an “annealed system”? - We prove that there is always a potential
(depending on both spin and disorder variables) that converges absolutely on a set of full measure w.r.t. the joint measure
(“weak Gibbsianness”). This “positive” result is surprising when contrasted with the results of a previous paper [K6], where
we investigated the measure of the set of discontinuity points of the conditional expectations (investigation of “a.s. Gibbsianness”).
In particular we gave natural “negative” examples where this set is even of measure one (including the random field Ising
model). Further we discuss conditions giving the convergence of vacuum potentials and conditions for the decay of the joint
potential in terms of the decay of the disorder average over certain quenched correlations. We apply them to various examples.
From this one typically expects the existence of a potential that decays superpolynomially outside a set of measure zero.
Our proof uses a martingale argument that allows to cut (an infinite-volume analogue of) the quenched free energy into local
pieces, along with generalizations of Kozlov's constructions.
Received: 11 November 1999 / Revised version: 18 April 2000 / Published online: 22 November 2000
RID="*"
ID="*" Work supported by the DFG Schwerpunkt `Wechselwirkende stochastische Systeme hoher Komplexit?t' 相似文献
4.
Michel Talagrand 《Publications Mathématiques de L'IHéS》1995,81(1):73-205
The concentration of measure phenomenon in product spaces roughly states that, if a set A in a product ΩN of probability spaces has measure at least one half, “most” of the points of Ωn are “close” to A. We proceed to a systematic exploration of this phenomenon. The meaning of the word “most” is made rigorous
by isoperimetrictype inequalities that bound the measure of the exceptional sets. The meaning of the work “close” is defined
in three main ways, each of them giving rise to related, but different inequalities. The inequalities are all proved through
a common scheme of proof. Remarkably, this simple approach not only yields qualitatively optimal results, but, in many cases,
captures near optimal numerical constants. A large number of applications are given, in particular to Percolation, Geometric
Probability, Probability in Banach Spaces, to demonstrate in concrete situations the extremely wide range of application of
the abstract tools.
Dedicated to Vitali Milman 相似文献
5.
Various statistics on wreath products are defined via canonical words, “colored” right to left minima and “colored” descents.
It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type.
These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial
realizations within the wreath product. The above setting also gives rise to a MacMahon-type equi-distribution theorem over
subsets with prescribed statistics.
Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network “Algebraic
Combinatorics in Europe”, grant HPRN-CT-2001-00272.
Partially supported by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant
HPRN-CT-2001-00272. 相似文献
6.
We introduce the wedge product of two polytopes. The wedge product is described in terms of inequality systems, in terms of
vertex coordinates as well as purely combinatorially, from the corresponding data of its constituents. The wedge product construction
can be described as an iterated “subdirect product” as introduced by McMullen (Discrete Math 14:347–358, 1976); it is dual
to the “wreath product” construction of Joswig and Lutz (J Combinatorial Theor A 110:193–216, 2005). One particular instance
of the wedge product construction turns out to be especially interesting: The wedge products of polygons with simplices contain
certain combinatorially regular polyhedral surfaces as subcomplexes. These generalize known classes of surfaces “of unusually
large genus” that first appeared in works by Coxeter (Proc London Math Soc 43:33–62, 1937), Ringel (Abh Math Seminar Univ
Hamburg 20:10–19, 1956), and McMullen et al. (Israel J Math 46:127–144, 1983). Via “projections of deformed wedge products”
we obtain realizations of some of the surfaces in the boundary complexes of 4-polytopes, and thus in
\mathbb R3{{\mathbb R}^3} . As additional benefits our construction also yields polyhedral subdivisions for the interior and the exterior, as well
as a great number of local deformations (“moduli”) for the surfaces in
\mathbb R3{{\mathbb R}^3} . In order to prove that there are many moduli, we introduce the concept of “affine support sets” in simple polytopes. Finally,
we explain how duality theory for 4-dimensional polytopes can be exploited in order to also realize combinatorially dual surfaces
in
\mathbb R3{{\mathbb R}^3} via dual 4-polytopes. 相似文献
7.
T. V. Panchapagesan 《Rendiconti del Circolo Matematico di Palermo》1995,44(3):417-440
The concept of an orthogonal spectral representation (OTSR) of a Hilbert spaceH relative to a spectral measureE(.) is introduced and it is shown that every Hilbert space admits an OTSR relative to a given spectral measure. Apart from
the various results obtained about OTSRs, the principal result of Allan Brown (1974) is deduced as an easy consequence of
this study. A new complete system of unitary invariants called the “equivalence of OTSRs”, is given for spectral measures.
Two special types of OTSRs called “BOTSR” and “COBOTSR” are introduced and characterized respectively in terms of the “GCGS-property”
and “CGS-property” of the associated spectral measure. Various complete systems of unitary invariants are given for spectral
measures with the GCGS-property. Finally, the Wecken-Plesner-Rohlin theorem on hermitian operators with simple spectra is
generalized to arbitrary spectral measures. 相似文献
8.
Various demands of different patients over both medical resource and time domains in health care systems raise requests of
strategies for balanced system capacity from an operations perspective. In this paper, a quantitative modeling technique with
both patient arrival and associated treatment process integrated are used to characterize health care system performance and
evaluate system efficiency. The patient arrival process is described as a dynamic random Poisson process and patient treatments
are characterized as consumption processes of various health care resources over time with a view of the “product line” used.
The waiting time of patients and usage of health care resources are proposed as system performance measures based on their
means, variances, and confidence intervals. A simulation considering patients with several various diseases is given to find
a mechanism of conflicting factors in decisions of balanced system capacity, and an operation scheme of “evenly balanced load
for bottlenecks” is obtained based on analysis of simulation outputs. Simul8 provides the software environment for the simulation. 相似文献
9.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
10.
Florin Panaite 《Czechoslovak Mathematical Journal》2012,62(1):187-195
The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with
a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor
product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from
Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are
particular cases of invariance under twisting, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery
duality theorem. 相似文献
11.
Direct product rings have received relatively little attention, perhaps because they are sometimes labeled “trivial” [8, p.6].
Nevertheless, the 2-dimensional direct product ring of the reals, when expressed in the “hyperbolic basis”, is analogous in
many ways to the system of complex numbers and also has a physical interpretation. This prompted an exploratory foray into
the world ofn-dimensional direct product rings of the reals to see how much can be extended from the 2-dimensional case (see, e.g. [3,4,5]).
Section 1 provides algebraic notation, up to the point of defining polar coordinates. Section 2 uses analysis to explore differentiability
and conformality. 相似文献
12.
Li Zunxian 《数学学报(英文版)》1992,8(2):177-183
In this paper the “residual complex” is defined when a group and its subgroups act on a complex. With its aid a homological
spectral sequence of group products is given. And the author makes a concentrated study of the structure of the residual complex
and proves that it becomes a clear “step complex” if the group can be expressed as an amalgamated free product of its subgroups.
Project supported by the National Natural Science Foundation of China 相似文献
13.
We show the equivalence of categories of model-theoretic imaginaries (of various kinds) with categories of “small” (finitely
generated, finitely presented, coherent) functors. We do this first for certain locally finitely presented categories and
then, by localising, for much more general “definable categories” (categories of models of coherent theories). We also investigate
the corresponding notion of interpretation. 相似文献
14.
This study concerns the equilibrium behavior of a general class of Markov network processes that includes a variety of queueing
networks and networks with interacting components or populations. The focus is on determining when these processes have product
form stationary distributions. The approach is to relate the marginal distributions of the process to the stationary distributions
of “node transition functions” that represent the nodes in isolation operating under certain fictitious environments. The
main result gives necessary and sufficient conditions on the node transition functions for the network process to have a product
form stationary distribution. This result yields a procedure for checking for a product form distribution and obtaining such
a distribution when it exits. An important subclass of networks are those in which the node transition rates have Poisson
arrival components. In this setting, we show that the network process has a product form distribution and is “biased locally
balanced” if and only if the network is “quasi-reversible” and certain traffic equations are satisfied. Another subclass of
networks are those with reversible routing. We weaken the known sufficient condition for such networks to be product form.
We also discuss modeling issues related to queueing networks including time reversals and reversals of the roles of arrivals
and departures. The study ends by describing how the results extend to networks with multi-class transitions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
We prove two related results. The first is an “earthquake theorem” for closed hyperbolic surfaces with cone singularities
where the total angle is less than π: any two such metrics in are connected by a unique left earthquake. The second result
is that the space of “globally hyperbolic” AdS manifolds with “particles” – cone singularities (of given angle) along time-like
lines – is parametrized by the product of two copies of the Teichmüller space with some marked points (corresponding to the
cone singularities). The two statements are proved together.
F.B. was partially supported by the A.N.R. project GEODYCOS. J.-M.S. was partially supported by the A.N.R. programs RepSurf,
2006-09, ANR-06-BLAN-0311, GeomEinstein, 2006-09, 06-BLAN-0154, and FOG, 2007-10, ANR-07-BLAN-0251-01. 相似文献
16.
Yu. V. Matiyasevich 《Proceedings of the Steklov Institute of Mathematics》2011,275(1):118-132
This survey presents various theorems (obtained mainly by specialists in mathematical logic and computability theory) stating
the impossibility of algorithms for solving certain Diophantine problems. Often the technique developed for obtaining such
“negative” results also allows one to prove many “positive” theorems on the possibility of formulating Diophantine problems
with special properties. This survey also lists a number of questions that remain open. 相似文献
17.
Adam B. Levy 《Journal of Optimization Theory and Applications》2012,153(3):633-649
We introduce and study decompositions of finite sets as well as coverings of their convex hulls, and use these objects to
develop various estimates of and formulas for the “hull-volume” of the sets (i.e., the volume of their convex hull). We apply
our results to the convergence analysis of the “iterate-sets” associated with each iteration of a reduce-or-retreat optimization
method (including pattern-search methods like Nelder–Mead as well as model-based methods). 相似文献
18.
K. A. Volosov 《Journal of Mathematical Sciences》2008,151(1):2639-2650
We propose a new method for solving the “shallow-water” equations. We show that from the equations of “shallow water” one
obtains nonlinear Liouville-type equations, Helmholtz equations, etc. This allows one to construct eigenfunctions of various
structures that appear in the flow in the two-dimensional case. We obtain exact and asymptotic solutions in an elliptic domain
with singularities.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 17–32, 2006. 相似文献
19.
Gábor Czédli 《Mathematica Slovaca》2011,61(6):859-870
For each of the relations “less than or equal to”, “less than”, “covered by”, and “covered by or equal to”, we characterize
finite orders (also called posets) with the property that the pair of Galois closure operators induced by the relation in
question coincides with the pair of closure operators introduced and applied in our previous paper in 2007. We also consider
the “less than or equal to” relation between the set of join-irreducible elements and the set of meet-irreducible elements,
and we show that the above-mentioned pairs of closure operators coincide for finite modular lattices. 相似文献
20.
Ahlswede Rudolf Khachatrian Levon H. Mauduit C. Sárközy A. 《Periodica Mathematica Hungarica》2003,46(2):107-118
In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were
introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography)
it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if
it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences
constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献