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1.
Algebroid functions, Wirsing's theorem and their relations 总被引:1,自引:0,他引:1
Min Ru 《Mathematische Zeitschrift》2000,233(1):137-148
In this paper, we first point out a relationship between the Second Main Theorem for algebriod functions in Nevanlinna theory
and Wirsing's theorem in Diophantine approximation. This motivates a unified proof for both theorems. The second part of this
paper deals with “moving targets” problem for holomorphic maps to Riemann surfaces. Its counterpart in Diophantine approximation
follows from a recent work of Thomas J. Tucker. In this paper, we point out Tucker's result in the special case of the approximation
by rational points could be obtained by doing a “translation” and applying the corresponding result with fixed target. However,
we could not completely recover Tucker's result concerning the approximation by algebraic points. In the last part of this
paper, cases in higher dimensions are studied. Some partial results in higher dimensions are obtained and some conjectures
are raised.
Received August 26, 1997; in final form June 30, 1998 相似文献
2.
Peter Heichelheim 《Arkiv f?r Matematik》1974,12(1):167-171
One of the theorems of Bengt Stolt’s article “On the Diophantine Equationu
2−Dv
2=4N” is not quite correct in its entirety. A counter-example will be given to show this. A modification of the theorem which
he was trying to prove will be given for certain special cases. 相似文献
3.
We introduce in this paper the concept of “impulse evolutionary game”. Examples of evolutionary games are usual differential
games, differentiable games with history (path-dependent differential games), mutational differential games, etc. Impulse
evolutionary systems and games cover in particular “hybrid systems” as well as “qualitative systems”. The conditional viability
kernel of a constrained set (with a target) is the set of initial states such that for all strategies (regarded as continuous
feedbacks) played by the second player, there exists a strategy of the first player such that the associated run starting
from this initial state satisfies the constraints until it hits the target. This paper characterizes the concept of conditional
viability kernel for “qualitative games” and of conditional valuation function for “qualitative games” maximinimizing an intertemporal
criterion. The theorems obtained so far about viability/capturability issues for evolutionary systems, conditional viability
for differential games and about impulse and hybrid systems are used to provide characterizations of conditional viability
under impulse evolutionary games. 相似文献
4.
MichaelFilippakis LeszekGasinskit NikolaosS.PapageorgiouI 《应用数学学报(英文版)》2004,20(2):179-190
We study the periodic problem for differential inclusions in R~N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem. 相似文献
5.
6.
Paolo Terenzi 《Israel Journal of Mathematics》1998,108(1):345-347
This complement includes stronger versions of the theorems of the paper “A positive answer to the basis problem”, practically
with the same proofs. 相似文献
7.
A definition of “Šipoš integral” is given, similarly to [3], [5], [10], for real-valued functions and with respect to Dedekind
complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental
properties and some convergence theorems for the Šipoš integral are proved.
This paper was supported by the cooperation project between Slovak Academy of Sciences (S.A.V.) and Italian National Council
of Researches (C.N.R.) 相似文献
8.
Flavia Ventriglia 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):203-212
We introduce asymptotically exhaustive functions defined on Vitali Spaces with values in a Hausdorff commutative topological
group and we prove for them some classical convergence theorems.
This article was supported by MURST, project “Analisi Reale” 相似文献
9.
We study the R-controllability (the controllability within the attainability set) and the R-observability of time-varying linear differential-algebraic equations (DAE). We analyze DAE under assumptions guaranteeing
the existence of a structural form (which is called “equivalent”) with separated “differential” and “algebraic” subsystems.
We prove that the existence of this form guarantees the solvability of the corresponding conjugate system, and construct the
corresponding “equivalent form” for the conjugate DAE. We obtain conditions for the R-controllability and R-observability, in particular, in terms of controllability and observability matrices. We prove theorems that establish certain
connections between these properties. 相似文献
10.
In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special
gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are
proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations.
The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations
with two and three lines of changing type.
相似文献
11.
Joseph Hersch 《Commentarii Mathematici Helvetici》1969,44(1):354-366
Summary The “harmonic transplantation” allows to extend some isoperimetric theorems, so far proved by conformal mapping, to higher
connectivity and to higher dimensions; for the first eigenvalue λ1 of a membrane, it again can give only upper bounds.—The “transplantation by moduli” is much more flexible; for example, it
leads to a simple one-dimensional interpretation of the Rayleigh-Faber-Krahn theorem.
相似文献
12.
Gino Tironi 《Mediterranean Journal of Mathematics》2006,3(2):313-325
In this paper it is given a survey of principal results (old and new) concerning the class of pseudoradial spaces. In this
class cardinal invariants and their inequalities are considered. The behaviour of pseudoradial spaces under the operations
of taking topological products and subspaces are examined and a typical proof is given. A particular attention is dedicated
to the so called “small cardinals” in connection with pseudoradiality. Pseudoradiality of 2ω 2 is also examined. It is proved that pseudoradiality can be ω1 productive for spaces of weight at most ω2. Finally, several open problems are presented.
This work was supported by the National Group “Real Analysis, Measure Theory with Applications to Economy” of the Italian
Ministery of Education, University and Research. 相似文献
13.
A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It
is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex
mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space
is confined to ℂn, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge. 相似文献
14.
Mechanical theorem proving in differential geometry 总被引:1,自引:0,他引:1
Hongbo Li 《中国科学A辑(英文版)》1997,40(4):350-356
An automated reasoning method, based on Wu’s method and calculus of differential forms, is proposed for mechanical theorem
proving in local theory of space surfaces in differential geometry. The method has been used to simplify one of Chem’s theorems:
“The non-trivial families of isometric surfaces having the same principal curvatures are W-surfaces.” Some other theorems
are also tested by this method. The proofs are generally simpler than those in differential geometry textbooks.
Project supported partially by the National Natural Science Foundation of China. 相似文献
15.
Carlo Sempi 《Mediterranean Journal of Mathematics》2006,3(2):283-300
This contribution aims at presenting a survey of a portion of the theory of Probabilistic Normed spaces. No result will be proved, so that the reader is referred to the original sources for the proofs. The theory of PN
spaces has many facets and touches on many branches of mathematics, for instance, geometry, functional analysis, topology,
probability. This justifies the adjective “partial” that appears in the title. Therefore, it is perhaps better to declare
from the start what one may expect from this survey. It is only natural to investigate which “classical”properties of normed
spaces are preserved in the new setting. But it is probably more interesting to look for those properties that pertain to
the new theory and which have no corresponding analogue in the classical theory. It must also be added that Probabilistic
Normed spaces may be approached from different standpoints: they may be studied for their own sake, as a special subject in
functional analysis or in topology that is worth investigating simply because it is there, or because it provides a tool to
approach open problems or, again, to shed light on topics that one thought had been thoroughly investigated. In this, one
thinks immediately of the possible applications in probability and statistics.
This paper was written as a part of the project “Metodi stocastici in finanza matematica” of the Italian M.I.U.R.. 相似文献
16.
This paper is devoted to some selected topics relating Combinatorial Optimization and Hierarchical Classification. It is oriented
toward extensions of the standard classification schemes (the hierarchies): pyramids, quasi-hierarchies, circular clustering,
rigid clustering and others. Bijection theorems between these models and dissimilarity models allow to state some clustering
problems as optimization problems. Within the galaxy of optimization we have especially discussed the following: NP-completeness
results and search for polynomial instances; problems solved in a polynomial time (e.g. subdominant theory); design, analysis
and applications of algorithms. In contrast with the orientation to “new” clustering problems, the last part discusses some
standard algorithmic approaches.
This article appeared in 4OR 2, 179–219, 2004. 相似文献
17.
D. V. Trushin 《Journal of Mathematical Sciences》2008,152(4):595-603
We obtained the criterion of existence of a quasi-linear polynomial in a differential ideal in the ordinary ring of differential
polynomials over a field of characteristic zero. We generalized the “going up” and “going down” theorems onto the case of
Ritt algebras. In particular, new finiteness criteria for differential standard bases and estimates that characterize calculation
complexity were obtained.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 1, pp. 215–227, 2007. 相似文献
18.
H. Gröflin 《Combinatorica》1987,7(2):193-204
A class of integer polyhedra with totally dual integral (tdi) systems is proposed, which generalizes and unifies the “Switching
Paths Polyhedra” of Hoffman (introduced in his generalization of Max Flow-Min Cut) and such polyhedra as the convex hull of
(the incidence vectors of) all “path-closed sets” of an acyclic digraph, or the convex hull of all sets partitionable intok path-closed sets. As an application, new min-max theorems concerning the mentioned sets are given. A general lemma on when
a tdi system of inequalities is box tdi is also given and used. 相似文献
19.
Extended formulations in combinatorial optimization 总被引:1,自引:0,他引:1
Michele Conforti Gérard Cornuéjols Giacomo Zambelli 《4OR: A Quarterly Journal of Operations Research》2010,8(1):1-48
This survey is concerned with the size of perfect formulations for combinatorial optimization problems. By “perfect formulation”,
we mean a system of linear inequalities that describes the convex hull of feasible solutions, viewed as vectors. Natural perfect
formulations often have a number of inequalities that is exponential in the size of the data needed to describe the problem.
Here we are particularly interested in situations where the addition of a polynomial number of extra variables allows a formulation
with a polynomial number of inequalities. Such formulations are called “compact extended formulations”. We survey various
tools for deriving and studying extended formulations, such as Fourier’s procedure for projection, Minkowski–Weyl’s theorem,
Balas’ theorem for the union of polyhedra, Yannakakis’ theorem on the size of an extended formulation, dynamic programming,
and variable discretization. For each tool that we introduce, we present one or several examples of how this tool is applied.
In particular, we present compact extended formulations for several graph problems involving cuts, trees, cycles and matchings,
and for the mixing set. We also present Bienstock’s approximate compact extended formulation for the knapsack problem, Goemans’
result on the size of an extended formulation for the permutahedron, and the Faenza-Kaibel extended formulation for orbitopes. 相似文献
20.
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