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1.
Walter L. Baily 《Proceedings Mathematical Sciences》1987,97(1-3):21-30
Earlier we obtained a new proof of Shimura’s reciprocity law for the special values of arithmetic Hilbert modular functions.
In this note we show how from this result one may derive Shimura’s reciprocity law for special values of arithmetic Siegel
modular functions. To achieve this we use Shimura’s classification of the special points of the Siegel space, Satake’s classification
of the equivariant holomorphic imbeddings of Hilbert-Siegel modular spaces into a larger Siegel space, and, finally, a corrected
version of some of Karel’s results giving an action of the Galois group Gal(Qab/Q) on arithmetic Siegel modular forms.
Research supported in part by the NSF Grant No. DMS-8601130. 相似文献
2.
Ze-shui Xu 《佛山科学技术学院》2009,1(1):79-89
An intuitionistic preference relation is a powerful means to express decision makers’information of intuitionistic preference
over criteria in the process of multi-criteria decision making. In this paper, we first define the concept of its consistence
and give the equivalent interval fuzzy preference relation of it. Then we develop a method for estimating criteria weights
from it, and then extend the method to accommodate group decision making based on them And finally, we use some numerical
examples to illustrate the feasibility and validity of the developed method. 相似文献
3.
The paper aims to provide precise proof theoretic characterizations of Myhill–Friedman-style “weak” constructive extensional set theories and Aczel–Rathjen analogous constructive set theories both enriched by Mostowski-style collapsing axioms and/or related anti-foundation axioms. The main results include full intuitionistic conservations over the corresponding purely arithmetical formalisms that are well known in the reverse mathematics – which strengthens analogous results obtained by the author in the 80s. The present research was inspired by the more recent Sato-style “weak weak” classical extensional set theories whose proof theoretic strengths are shown to strongly exceed the ones of the intuitionistic counterparts in the presence of the collapsing axioms. 相似文献
4.
L. Q. Anh P. Q. Khanh D. T. M. Van 《Journal of Optimization Theory and Applications》2012,153(1):42-59
Bilevel equilibrium and optimization problems with equilibrium constraints are considered. We propose a relaxed level closedness
and use it together with pseudocontinuity assumptions to establish sufficient conditions for well-posedness and unique well-posedness.
These conditions are new even for problems in one-dimensional spaces, but we try to prove them in general settings. For problems
in topological spaces, we use convergence analysis while for problems in metric cases we argue on diameters and Kuratowski’s,
Hausdorff’s, or Istrǎtescu’s measures of noncompactness of approximate solution sets. Besides some new results, we also improve
or generalize several recent ones in the literature. Numerous examples are provided to explain that all the assumptions we
impose are very relaxed and cannot be dropped. 相似文献
5.
In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce
the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining
Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic
fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic
fuzzy set theory and L-fuzzy set theory. 相似文献
6.
Using a slight generalization, due to Palmgren, of sheaf semantics, we present a term-model construction that assigns a model
to any first-order intuitionistic theory. A modification of this construction then assigns a nonstandard model to any theory
of arithmetic, enabling us to reproduce conservation results of Moerdijk and Palmgren for nonstandard Heyting arithmetic.
Internalizing the construction allows us to strengthen these results with additional transfer rules; we then show that even
trivial transfer axioms or minor strengthenings of these rules destroy conservativity over HA. The analysis also shows that nonstandard HA has neither the disjunction property nor the explicit definability property. Finally, careful attention to the complexity
of our definitions allows us to show that a certain weak fragment of intuitionistic nonstandard arithmetic is conservative
over primitive recursive arithmetic.
Received: 7 January 2000 / Revised version: 26 March 2001 / Published online: 12 July 2002 相似文献
7.
Alex Gamburd 《Israel Journal of Mathematics》2002,127(1):157-200
A celebrated theorem of Selberg states that for congruence subgroups of SL2(Z) there are no exceptional eigenvalues below 3/16. Extending the work of Sarnak and Xue for cocompact arithmetic lattices,
we prove a generalization of Selberg’s theorem for infinite index “congruence” subgroups of SL2(Z). For such subgroups with a high enough Hausdorff dimension of the limit set we establish a spectral gap property and consequently
solve a problem of Lubotzky pertaining to expander graphs.
The author was supported in part by the NSF graduate fellowship. 相似文献
8.
Dominique Schneider 《Israel Journal of Mathematics》1997,101(1):157-178
We obtain results on almost sure convergence of ergodic averages along arithmetic subsequences perturbed by independent identically
distributed random variables having ap
th
finite moment for somep>0. To prove these results, we use methods based on the harmonic analysis and the theory of Gaussian processes. In fact that
will express the stability of Bourgain’s results concerning convergence of ergodic averages for certain arithmetic subsequences.
相似文献
9.
A key tool in recent advances in understanding arithmetic progressions and other patterns in subsets of the integers is certain
norms or seminorms. One example is the norms on ℤ/Nℤ introduced by Gowers in his proof of Szemerédi’s Theorem, used to detect uniformity of subsets of the integers. Another
example is the seminorms on bounded functions in a measure preserving system (associated to the averages in Furstenberg’s
proof of Szemerédi’s Theorem) defined by the authors. For each integer k ≥ 1, we define seminorms on ℓ∞(ℤ) analogous to these norms and seminorms. We study the correlation of these norms with certain algebraically defined sequences,
which arise from evaluating a continuous function on the homogeneous space of a nilpotent Lie group on a orbit (the nilsequences).
Using these seminorms, we define a dual norm that acts as an upper bound for the correlation of a bounded sequence with a
nilsequence. We also prove an inverse theorem for the seminorms, showing how a bounded sequence correlates with a nilsequence.
As applications, we derive several ergodic theoretic results, including a nilsequence version of the Wiener-Wintner ergodic
theorem, a nil version of a corollary to the spectral theorem, and a weighted multiple ergodic convergence theorem. 相似文献
10.
Atsushi Moriwaki 《Inventiones Mathematicae》2000,140(1):101-142
In this paper, we propose a new height function for a variety defined over a finitely generated field over ℚ. For this height
function, we prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s
conjecture).
Oblatum 7-VI-1999 & 21-IX-1999 / Published online: 24 January 2000 相似文献
11.
A. B. Gordienko 《Algebra and Logic》2007,46(5):289-296
We deal with Sylvan’s logic CCω. It is proved that this logic is a conservative extension of positive intuitionistic logic. Moreover, a paraconsistent extension
of Sylvan’s logic is constructed, which is also a conservative extension of positive intuitionistic logic and has the property
of being decidable. The constructed logic, in which negation is defined via a total accessibility relation, is a natural intuitionistic
analog of the modal system S5. For this logic, an axiomatization is given and the completeness theorem is proved.
Supported by RFBR grant No. 06-01-00358 and by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 5, pp. 533–547, September–October, 2007. 相似文献
12.
Xue Gong Sun 《数学学报(英文版)》2010,26(1):155-160
Consider all the arithmetic progressions of odd numbers, no term of which is of the form 2^k + p, where k is a positive integer and p is an odd prime. ErdSs ever asked whether all these progressions can be obtained from covering congruences. In this paper, we characterize all arithmetic progressions in which there are positive proportion natural numbers that can be expressed in the form 2^k + p, and give a quantitative form of Romanoff's theorem on arithmetic progressions. As a corollary, we prove that the answer to the above Erdos problem is affirmative. 相似文献
13.
Morteza Moniri 《Archive for Mathematical Logic》2007,46(1):9-14
In this paper we naturally define when a theory has bounded quantifier elimination, or is bounded model complete. We give
several equivalent conditions for a theory to have each of these properties. These results provide simple proofs for some
known results in the model theory of the bounded arithmetic theories like CPV and PV1. We use the mentioned results to obtain some independence results in the context of intuitionistic bounded arithmetic. We
show that, if the intuitionistic theory of polynomial induction on strict
formulas proves decidability of
formulas, then P=NP. We also prove that, if the mentioned intuitionistic theory proves
, then P=NP. 相似文献
14.
We study general zero range processes with different types
of particles on a d-dimensional lattice with periodic
boundary conditions. A necessary and sufficient condition on the
jump rates for the existence of stationary product measures is
established. For translation invariant jump rates we prove the
hydrodynamic limit on the Euler scale using Yaus relative
entropy method. The limit equation is a system of conservation
laws, which is hyperbolic and has a globally convex entropy. We
analyze this system in terms of entropy variables. In addition
we obtain stationary density profiles for open
boundaries. 相似文献
15.
I. D. Zaslavsky 《Journal of Mathematical Sciences》2005,130(2):4578-4597
Formal axiomatic theories based on the three-valued logic of Lukasiewicz are considered. Main notions related to these theories, in particular, those of Luk-model, Luk-consistent theory, and Luk-complete theory are introduced. Logical calculuses that describe such theories are defined; counterparts of the classical compactness and completeness theorems are proved. Theories of arithmetic based on Lukasiewicz’s logic and on its constructive (intuitionistic) variant are investigated; the theorem on effective Luk-incompleteness is proved for a large class of arithmetic systems. This theorem is a three-valued counterpart of the famous Godel theorem on incompleteness of formal theories. Three-valued counterparts of Presburger’s arithmetic system are defined and proved to be Luk-complete but incomplete in the classical sense. Bibliography: 29 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 304, 2002, pp. 19–74. 相似文献
16.
In this paper, we investigate the closure of a large class of Teichmüller discs in the stratum Q(1, 1, 1, 1){\mathcal{Q}(1, 1, 1, 1)} or equivalently, in a
GL+2(\mathbbR){{\rm GL}^+_2(\mathbb{R})} -invariant locus L{\mathcal{L}} of translation surfaces of genus three. We describe a systematic way to prove that the
GL+2(\mathbbR){{\rm GL}^+_2(\mathbb{R})} -orbit closure of a translation surface in L{\mathcal{L}} is the whole locus L{\mathcal{L}} . The strategy of the proof is an analysis of completely periodic directions on such a surface and an iterated application
of Ratner’s theorem to unipotent subgroups acting on an “adequate” splitting. This analysis applies for example to all Teichmüller
discs obtained by the Thurston–Veech’s construction with a trace field of degree three which are moreover “obviously not Veech”.
We produce an infinite series of such examples and show moreover that the favourable splitting situation does not arise everywhere
on L{\mathcal{L}} , contrary to the situation in genus two. We also study completely periodic directions on translation surfaces in L{\mathcal{L}} . For instance, we prove that completely periodic directions are dense on surfaces obtained by the Thurston–Veech’s construction. 相似文献
17.
We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon’s product
formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of these weights
that are related to orthogonal polynomials; they form three 2-D families. For distributions from these families, we prove
two types of results. First, we construct explicit Markov chains that preserve these distributions. In particular, this leads
to a relatively simple exact sampling algorithm. Second, we consider a limit when all dimensions of the box grow and plane
partitions become large and prove that the local correlations converge to those of ergodic translation invariant Gibbs measures.
For fixed proportions of the box, the slopes of the limiting Gibbs measures (that can also be viewed as slopes of tangent
planes to the hypothetical limit shape) are encoded by a single quadratic polynomial. 相似文献
18.
This note explores the common core of constructive, intuitionistic, recursive and classical analysis from an axiomatic standpoint. In addition to clarifying the relation between Kleene’s and Troelstra’s minimal formal theories of numbers and number-theoretic sequences, we propose some modified choice principles and other function existence axioms which may be of use in reverse constructive analysis. Specifically, we consider the function comprehension principles assumed by the two minimal theories EL and M, introduce an axiom schema CFd asserting that every decidable property of numbers has a characteristic function, and use it to describe a precise relationship between the minimal theories. We show that the axiom schema AC00 of countable choice can be decomposed into a monotone choice schema AC 00 m (which guarantees that every Cauchy sequence has a modulus) and a bounded choice schema BC00. We relate various (classically correct) axiom schemas of continuous choice to versions of the bar and fan theorems, suggest a constructive choice schema AC1/2,0 (which incidentally guarantees that every continuous function has a modulus of continuity), and observe a constructive equivalence between restricted versions of the fan theorem and correspondingly restricted bounding axioms ${AB_{1/2,0}^{2^{\mathbb{N}}}}$ . We also introduce a version WKL!! of Weak K?nig’s Lemma with uniqueness which is intermediate in strength between WKL and the decidable fan theorem FTd. 相似文献
19.
We consider arithmetic varieties endowed with an action of the group scheme of n-th roots of unity and we define equivariant arithmetic K
0-theory for these varieties. We use the equivariant analytic torsion to define direct image maps in this context and we prove
a Riemann-Roch theorem for the natural transformation of equivariant arithmetic K
0-theory induced by the restriction to the fixed point scheme; this theorem can be viewed as an analog, in the context of Arakelov
geometry, of the regular case of the theorem proved by P. Baum, W. Fulton and G. Quart in [BaFQ]. We show that it implies
an equivariant refinement of the arithmetic Riemann-Roch theorem, in a form conjectured by J.-M. Bismut (cf. [B2, Par. (l),
p. 353] and also Ch. Soulé’s question in [SABK, 1.5, p. 162]).
Oblatum 22-I-1999 & 20-II-2001?Published online: 4 May 2001 相似文献
20.
Corentin Pontreau 《Monatshefte für Mathematik》2009,342(2):267-281
We prove a sharper so-called Mordell-Lang plus Bogomolov type result for curves lying in the two-dimensional linear torus.
We mainly follow the approach of Rémond in (Comp Math 134:337–366, 2002), using Vojta and Mumford type inequalities. In the
special case we consider, we improve Rémond’s main result using a better Bogomolov property and an elementary arithmetic Bézout
theorem. 相似文献