共查询到20条相似文献,搜索用时 31 毫秒
1.
We study Lebesgue and Atsuji spaces within subsystems of second order arithmetic. The former spaces are those such that every
open covering has a Lebesgue number, while the latter are those such that every continuous function defined on them is uniformly
continuous. The main results we obtain are the following: the statement “every compact space is Lebesgue” is equivalent to
; the statements “every perfect Lebesgue space is compact” and “every perfect Atsuji space is compact” are equivalent to ; the statement “every Lebesgue space is Atsuji” is provable in ; the statement “every Atsuji space is Lebesgue” is provable in . We also prove that the statement “the distance from a closed set is a continuous function” is equivalent to .
Received: February 2, 1996 相似文献
2.
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
3.
David Carlton 《manuscripta mathematica》2001,105(2):201-234
We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a “determinant” map from this moduli surface to (Z/N
Z)*; its fibers are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences
between them, and study how those spaces of modular forms behave as modules for the Hecke algebra. We discover that the component
with determinant −1 is somehow the “dominant” one; we characterize the difference between its spaces of modular forms and
the spaces of modular forms on the other components using forms with complex multiplication. In addition, we prove Atkin–Lehner-style
results about these spaces of modular forms. Finally, we show some simplifications that arise when N is prime, including a complete determination of such CM-forms, and give numerical examples.
Received: 20 September 2000 / Revised version: 7 February 2001 相似文献
4.
The external Cayley transform is used for the conversion between the linear dynamical systems in scattering form and in impedance
form. We use this transform to define a class of formal impedance conservative boundary control systems (colligations), without
assuming a priori that the associated Cauchy problems are solvable. We give sufficient and necessary conditions when impedance
conservative colligations are internally well-posed boundary nodes; i.e., when the associated Cauchy problems are solvable
and governed by C
0 semigroups. We define a “strong” variant of such colligations, and we show that “strong” impedance conservative boundary
colligation is a slight generalization of the “abstract boundary space” construction for a symmetric operator in the Russian
literature. Many aspects of the theory is illustated by examples involving the transmission line and the wave equations.
Received: August 21, 2006. Accepted: October 22, 2006. 相似文献
5.
Licun Xue 《International Journal of Game Theory》2000,29(3):339-357
This paper defines “negotiation-proof Nash equilibrium', a notion that applies to environments where players can negotiate
openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested
players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections;
moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof
Nash equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of
coalition-proof Nash equilibrium. (2) The negotiation process is formalized by a “graph”, which serves as a natural extension to the approach that models
preplay communication by an extensive game.
Received: October 1998/Final version: May 2000 相似文献
6.
Andreas Gathmann 《Mathematische Annalen》2003,325(2):393-412
Let X be a smooth complex projective variety, and let be a smooth very ample hypersurface such that is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of)
the “mirror formula”, i.e. we show that the generating function of the genus zero 1-point Gromov-Witten invariants of Y can be obtained from that of X by a certain change of variables (the so-called “mirror transformation”). Moreover, we use the same techniques to give a
similar expression for the (virtual) numbers of degree-d plane rational curves meeting a smooth cubic at one point with multiplicity 3d, which play a role in local mirror symmetry.
Received: 11 July 2001 / Published online: 4 February 2003
Funded by the DFG scholarships Ga 636/1–1 and Ga 636/1–2. 相似文献
7.
8.
Yuriy A. Drozd 《manuscripta mathematica》2001,104(2):239-256
9.
J.-L. Waldspurger 《Mathematische Annalen》2009,343(1):103-174
In order to use the trace formula of Arthur–Selberg in the twisted case, we need to prove the “twisted weighted fundamental
lemma”, that is a sophisticated version of the fundamental lemma. Here, we prove that this twisted weighted fundamental lemma
follows from two others lemmas, where the torsion has disappeared: the weighted fundamental lemma for Lie algebras and a “non-standard
weighted fundamental lemma”, concerning Lie algebras too. 相似文献
10.
Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy
of symbols. The symbolic structure is responsible for ellipticity and for the nature of parametrices within an algebra of
“edge-degenerate” pseudo-differential operators. The edge symbolic component of that hierarchy takes values in boundary value
problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in
this theory, in particular, the contribution with holomorphic operator-valued Mellin symbols. We establish a calculus in a
framework of “twisted homogeneity” that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces.
We then derive an equivalent representation with a particularly transparent composition behaviour. 相似文献
11.
We prove a preservation theorem for limit steps of countable support iterations of proper forcing notions whose particular
cases are preservations of the following properties on limit steps: “no random reals are added”, “μ(Random(V))≠1”, “no dominating reals are added”, “Cohen(V) is not comeager”. Consequently, countable support iterations of σ-centered forcing notions do not add random reals.
The work was supported by BRF of Israel Academy of Sciences and by grant GA SAV 365 of Slovak Academy of Sciences. 相似文献
12.
Yu. G. Dutkevich 《Journal of Mathematical Sciences》2005,131(1):5278-5285
The dependence of the complete upper angle in the sense of A. D. Aleksandrov about a point on the Minkowski plane on the form
of the “unit circle” (the centrally symmetric convex curve Φ determining the Minkowski metric ρΦ) is studied.The complete upper angle is computed in three cases: if Φ is a square, a “cut circle,” or a “rounded rhombus.”
Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 42–53. 相似文献
13.
Vittorio Martino Annamaria Montanari 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(3-4):377-390
We prove interior gradient estimates of viscosity solutions of the prescribed Levi mean curvature equation.
The second author was partially supported by Indam, within the interdisciplinary project “Nonlinear subelliptic equations
of variational origin in contact geometry”. 相似文献
14.
The Generalized Riemann Problem (GRP) for a nonlinear hyperbolic system of m balance laws (or alternatively “quasi-conservative” laws) in one space dimension is now well-known and can be formulated
as follows: Given initial-data which are analytic on two sides of a discontinuity, determine the time evolution of the solution
at the discontinuity. In particular, the GRP numerical scheme (second-order high resolution) is based on an analytical evaluation
of the first time derivative. It turns out that this derivative depends only on the first-order spatial derivatives, hence
the initial data can be taken as piecewise linear. The analytical solution is readily obtained for a single equation (m = 1) and, more generally, if the system is endowed with a complete (coordinate) set of Riemann invariants. In this case it
can be “diagonalized” and reduced to the scalar case. However, most systems with m > 2 do not admit such a set of Riemann invariants. This paper introduces a generalization of this concept: weakly coupled
systems (WCS). Such systems have only “partial set” of Riemann invariants, but these sets are weakly coupled in a way which
enables a “diagonalized” treatment of the GRP. An important example of a WCS is the Euler system of compressible, nonisentropic
fluid flow (m = 3). The solution of the GRP discussed here is based on a careful analysis of rarefaction waves. A “propagation of singularities”
argument is applied to appropriate Riemann invariants across the rarefaction fan. It serves to “rotate” initial spatial slopes
into “time derivative”. In particular, the case of a “sonic point” is incorporated easily into the general treatment. A GRP
scheme based on this solution is derived, and several numerical examples are presented. Special attention is given to the
“acoustic approximation” of the analytical solution. It can be viewed as a proper linearization (different from the approach
of Roe) of the nonlinear system. The resulting numerical scheme is the simplest (second-order, high-resolution) generalization
of the Godunov scheme. 相似文献
15.
B. Anchouche 《manuscripta mathematica》1999,100(4):423-436
We show that over some smooth projective varieties every semistable Higgs logarithmic vector bundle is semistable in the ordinary
sense, hence satisfies Bogomolov inequality. More generaly, we prove that semistable Higgs parabolic vector bundles of rank
two over smooth projective varieties of dimension ≥ 2 satisfy the “parabolic” 'Bogomolov inequality
Received: 1 March 1999 / Revised version: 11 June 1999 相似文献
16.
Xingwei Hu 《International Journal of Game Theory》2006,34(2):229-240
This paper extends the traditional “pivoting” and “swing” schemes in the Shapley–Shubik (S-S) power index and the Banzhaf index to the case of “blocking”. Voters are divided into two groups: those who vote for the bill and those against the bill. The uncertainty of the division is described by a probability distribution. We derive the S-S power index, based on a priori ignorance about the random bipartition. 相似文献
17.
Marko Uršič 《Acta Analytica》2002,17(1):53-67
This paper deals with one of the basic philosophical questions in modern cosmology: can the so-called “Anthropic Principle”,
considered as an alternative to the classical teleology of creation, be an adequate explanation of the evidence that our universe
is “fine-tuned” for the emergence of life and consciousness. The main problem with this principle is not its presumed teleology,
as it is sometimes wrongly supposed, but quite the contrary: its intention to avoid teleological explanations by including
the existence of many universes (“multiverse”) into extended cosmological models. After having compared logical and cosmological
many-worlds concepts, this paper reaches the conclusion that the ontological reality of the “multiverse” is an even more problematic
presupposition than some properly revised version of teleological causality. This in itself does not imply the classical theistic
explanation of creation, since it also yields a pantheistic explanation of the emergence of life and consciousness in our
universe. 相似文献
18.
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
19.
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
20.
This paper explicitly describes the procedure of associating an automorphic representation of PGSp(2n,?) with a Siegel modular form of degree n for the full modular group Γ
n
=Sp(2n,ℤ), generalizing the well-known procedure for n=1. This will show that the so-called “standard” and ldquo;spinor”L-functions associated with such forms are obtained as Langlands L-functions. The theory of Euler products, developed by Langlands, applied to a Levi subgroup of the exceptional group of type
F
<4, is then used to establish meromorphic continuation for the spinor L-function when n=3.
Received: 28 March 2000 / Revised version: 25 October 2000 相似文献