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1.
Colin Adams 《Mathematical Intelligencer》2000,22(3):37-38
Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal,
or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open
to Cohn Adam’s column.
Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be hannless. 相似文献
2.
Johann C. Marek 《Acta Analytica》2011,26(1):53-61
Experiences are interpreted as conscious mental occurrences that are of phenomenal character. There is already a kind of (weak)
intentionality involved with this phenomenal interpretation. A stricter conception of experiences distinguishes between purely
phenomenal experiences and intentional experiences in a narrow sense. Wittgenstein’s account of psychological (experiential)
verbs is taken over: Usually, expressing mental states verbally is not describing them. According to this, “I believe” can
be seen as an expression of one’s own belief, but not as an expression of a belief about one’s belief. Hence, the utterance
“I believe it is raining” shows that I believe that it is raining, although it is not said by these words that I believe that it is raining. Thinking thoughts such as “I believe it is raining, but it is not raining”
(a variant of Moore’s paradox) is an absurdity between what is already said by silently uttering “It is not raining” and what
is shown by silently uttering “I believe it is raining.” The paper agrees with a main result of Wittgenstein’s considerations
of Moore’s paradox, namely the view that logical structure, deducibility, and consistency cannot be reduced solely to propositions—besides
a logic of propositions, there is, for example, a logic of assertions and of imperatives, respectively. 相似文献
3.
Rémi Peyre 《Potential Analysis》2008,29(1):17-36
Carne’s bound is a sharp inequality controlling the transition probabilities for a discrete reversible Markov chain (Section 1).
Its ordinary proof uses spectral techniques which look as efficient as miraculous. Here we present a new proof, comparing
a “drift” for ways “out” and “back”, to get the gaussian part of the bound (Section 2), and using a conditioning technique
to get the flight factor (Section 4). Moreover we show how our proof is more “supple” than Carne’s one and may generalize
(Section 3.2).
相似文献
4.
We localize and strengthen Katona’s idea of an edge-toughness to a local topological toughness. We disprove a conjecture of
Katona concerning the conection between edge-toughness and factors. For the topological toughness we prove a theorem similar
to Katona’s 2k-factor-conjecture, which turned out to be false for his edge-toughness. We prove, that besides this the topological toughness
has nearly all known nice properties of Katona’s edge-toughness and therefore is worth to be considered.
Research supported by the “Mathematics in Information Society” project carried out by Alfréd Rényi Institute of Mathematics
- Hungarian Academy of Sciences, in the framework of the European Community’s “Confirming the International Role of Community
Research” programme.
Research supported by the Ministry of Education OTKA grant OTKA T 043520. 相似文献
5.
Yuri Gurevich 《Israel Journal of Mathematics》1977,27(3-4):299-319
We deal with the monadic theory of linearly ordered sets and topological spaces, disprove two of Shelah’s conjectures and
prove some more results. In particular, if the Continuum Hypothesis holds, then there exist monadic formulae expressing the
predicates “X is countable” and “X is meager” in the real line and in Cantor’s Discontinuum. 相似文献
6.
We are interested in the maximum possible number of facets that Dirichlet stereohedra for three-dimensional crystallographic
groups can have. In two previous papers, D. Bochiş and the second author studied the problem for noncubic groups. This paper
deals with “full” cubic groups, while “quarter” cubic groups are left for a subsequent paper. Here, “full” and “quarter” refers
to the recent classification of three-dimensional crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston.
This paper’s main result is that Dirichlet stereohedra for any of the 27 full groups cannot have more than 25 facets. We also
find stereohedra with 17 facets for one of these groups.
Research partially supported by the Spanish Ministry of Education and Science, grant number MTM2005-08618-C02-02. 相似文献
7.
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
8.
Martina Fürst 《Acta Analytica》2011,26(1):63-74
The aim of this paper is to reinforce anti-physicalism by extending the “hard problem” to a specific kind of intentional states.
For reaching this target, I investigate the mental content of the new intentional states of Jackson’s Mary. I proceed in the
following way: I start analyzing the knowledge argument, which highlights the “hard problem” tied to phenomenal consciousness.
In a second step, I investigate a powerful physicalist reply to this argument: the phenomenal concept strategy. In a third step, I propose a constitutional account of phenomenal concepts that captures the Mary scenario adequately, but
implies anti-physicalist referents. In a last step, I point at the ramifications constitutional phenomenal concepts have on
the constitution of Mary’s new intentional states. Therefore, by focusing the attention on phenomenal concepts, the so-called
“hard problem” of consciousness will be carried over to the alleged “easy problem” of intentional states as well. 相似文献
9.
Tullio Levi-Civita 《Regular and Chaotic Dynamics》2011,16(5):550-554
We bring to the reader’s attention a translation of Levi-Civita’s work “Sugli integrali algebrici delle equazioni dinamiche”
(1896). 相似文献
10.
Rodolphe Garbit 《Israel Journal of Mathematics》2011,182(1):333-336
This note gives a positive answer to an old question in elementary probability theory that arose in Furstenberg’s seminal
article “Disjointness in Ergodic Theory.” As a consequence, Furstenberg’s filtering theorem holds without any integrability
assumption. 相似文献
11.
Juan Carlos Martínez 《Israel Journal of Mathematics》2001,123(1):273-284
It was proved by Baumgartner and Shelah that Con (ZFC)→Con (ZFC + “there is a superatomic Boolean algebra of width ω and height
ω2”). In this paper we improve Baumgartner-Shelah’s theorem, showing that Con (ZFC)→Con (ZFC+“for every α<ω3 there is a superatomic Boolean algebra of width ω and height α”).
The preparation of this paper was supported by DGICYT Grant PB98-1231. 相似文献
12.
O. D. Frolkina 《Moscow University Mathematics Bulletin》2009,64(6):253-258
In 1998, Y. Benyamini published interesting results concerning interpolation of sequences using continuous functions ℝ → ℝ.
In particular, he proved that there exists a continuous function ℝ → ℝ which in some sense “interpolates” all sequences (x
n
)
n∈ℤ ∈ [0, 1]ℤ “simultaneously.” In 2005, M.R. Naulin and C. Uzcátegui unified and generalized Benyamini’s results. In this paper, the case
of topological spaces X and Y with an Abelian group acting on X is considered. A similar problem of “simultaneous interpolation” of all “generalized sequences” using continuous mappings
X → Y is posed. Further generalizations of Naulin-Uncátegui theorems, in particular, multidimensional analogues of Benyamini’s
results are obtained. 相似文献
13.
Acceptable moves for the “worthwhile-to-move” incremental principle are such that “advantages-to-move” are higher than some
fraction of “costs-to-move”. When combined with optimization, this principle gives raise to adaptive local search proximal
algorithms. Convergence results are given in two distinctive cases, namely low local costs-to-move and high local costs-to-move.
In this last case, one obtains a dynamic cognitive approach to Ekeland’s ϵ-variational principle. Introduction of costs-to-move in the algorithms yields robustness and stability properties. 相似文献
14.
Graph factors 总被引:1,自引:0,他引:1
W. T. Tutte 《Combinatorica》1981,1(1):79-97
This exposition is concerned with the main theorems of graph-factor theory, Hall’s and Ore’s Theorems in the bipartite case,
and in the general case Petersen’s Theorem, the 1-Factor Theorem and thef-Factor Theorem. Some published extensions of these theorems are discussed and are shown to be consequences rather than generalizations
of thef-Factor Theorem. The bipartite case is dealt with in Section 2. For the proper presentation of the general case a preliminary
theory of “G-triples” and “f-barriers” is needed, and this is set out in the next three Sections. Thef-Factor Theorem is then proved by an argument of T. Gallai in a generalized form. Gallai’s original proof derives the 1-Factor
Theorem from Hall’s Theorem. The generalization proceeds analogously from Ore’s Theorem to thef-Factor Theorem. 相似文献
15.
Michael Davis 《Mathematical Intelligencer》1994,16(4):21-28
The short answer to the question just posed seems to be, “Not much.” Since I have given “the long answer” elsewhere,12 I can summarize it here. Berg could see no point in writing Bromley. What could he write to someone he believed guilty of
plagiarism? What could such a letter accomplish? He did, however, write to New York University Press; to all the universities
involved, and to the Works’ English publisher (Pickering and Chatto), who said they passed the letter on to Campbell-Kelly
(30 June 1990); to a great many professional societies in Australia, England, and the United States; to a great many governmental
agencies and some politicians in those countries; to some publications, both academic and popular; to the Pope and several
cardinals; and to a miscellany of other individuals. Generally, those in the best position to do something—for example, the
three universities involved —did not even answer Berg’s letter. Others often did answer, but their answer was generally that
they were in no position to do anything.
That was how matters stood when I published my first article on “the Berg Affair”.12 Its publication finally roused those best positioned to answer. Late in 1993, Galler, Bromley, and Campbell-Kelly wrote letters
to the editor of Accountability in Research criticizing me for not getting their side of the story before I published Berg’s.
Campbell-Kelly threatened the journal’s publisher with a lawsuit if I (or it) did not retract. The three also provided some
insight into what their explanation of events might be. Bromley, though listed prominently in ads for the Works, claimed to
have had only a small part, merely advising Campbell-Kelly on selection and arrangement of the papers printed in Volumes 2
and 3. Campbell-Kelly confirmed that Bromley took no part in the detailed editing or in the provision of documents. That work
was performed by one C.J.D. (“Jim”) Roberts, a “London-based independent scholar” who was “editorial consultant to the Works”
(and, apparently, worked directly under Campbell-Kelly). Roberts seems to deserve more public credit than he has so far received.
According to Campbell-Kelly, it was Roberts who, making a systematic search for unknown holdings of Babbage, turned up the
original of the letter to Quetelet by writing the Royal Library (one “tiny triumph” among many). Campbell-Kelly also claimed
that neither he nor Roberts knew of Berg’s prior discovery. 相似文献
16.
Dina Friedland 《Israel Journal of Mathematics》1970,8(1):30-33
It is shown that irreflexive Banach spaces are imperfect: thus the “perfect” spaces are exactly the reflexive Banach spaces
and “mixed” spaces do not exist.
This paper is part of the author’s M.Sc. dissertation, performed under guidance of Dr. D. Amir at the Technion — Israel Institute
of Technology. The author wishes to thank Dr. Amir for his help. 相似文献
17.
Semën S. Podkorytov 《Central European Journal of Mathematics》2011,9(6):1232-1241
Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain
complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce
the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra. 相似文献
18.
Francesco Costantino 《Geometriae Dedicata》2006,121(1):89-111
We provide sufficient conditions assuring that a suitably decorated 2-polyhedron can be thickened to a compact four-dimensional
Stein domain. We also study a class of flat polyhedra in 4-manifolds and find conditions assuring that they admit Stein, compact
neighborhoods. We base our calculations on Turaev’s shadows suitably “smoothed”; the conditions we find are purely algebraic
and combinatorial. Applying our results, we provide examples of hyperbolic 3-manifolds admitting “many” positive and negative
Stein fillable contact structures, and prove a four-dimensional analog of Oertel’s result on incompressibility of surfaces
carried by branched polyhedra.
相似文献
19.
The comprehensive model with “weighted-objective nearness degree” is introduced in the process of multi-objective decision-making,
by which a reduction problem of inference antecedents is studied in traditional fuzzy inference method. Moreover, based on
the comprehensive model with “weighted-objective nearness degree”, SMTT fuzzy inference algorithm is proposed. This algorithm
not only shows the relative importance of every antecedent component in fuzzy inference, but also considers the influence
of nearness degree between every antecedent component’s evaluation and inference objective on inference conclusions. The enactment
of inference objective reflects the preference degree of decision maker to every antecedent component’s evaluation. Therefore,
it is much fitter for the demands of practical inference. 相似文献
20.
Eugene Mills 《Acta Analytica》2006,21(4):50-61
Any satisfactory account of freedom must capture, or at least permit, the mysteriousness of freedom—a “sweet” mystery involving a certain kind of ignorance rather than a “sour” mystery of unintelligibility, incoherence,
or unjustifiedness. I argue that compatibilism can capture the sweet mystery of freedom. I argue first that an action is free
if and only if a certain “rationality constraint” is satisfied, and that nothing in standard libertarian accounts of freedom
entails its satisfaction. Satisfaction of this constraint is consistent with the universal causal predetermination of action
(UCP). If UCP is true and the rationality constraint satisfied, there’s a sense in which our actions are explanatorily (though
not necessarily causally) overdetermined. While it seems plausible (given UCP) that our actions are so overdetermined, it seems utterly mysterious why they should be so overdetermined. Compatibilism’s capacity to accommodate this mystery is a mark in its favor. 相似文献