Displaying similar documents to “Semantics of MML Query”

Bertrand’s Ballot Theorem

Karol Pąk (2014)

Formalized Mathematics

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In this article we formalize the Bertrand’s Ballot Theorem based on [17]. Suppose that in an election we have two candidates: A that receives n votes and B that receives k votes, and additionally n ≥ k. Then this theorem states that the probability of the situation where A maintains more votes than B throughout the counting of the ballots is equal to (n − k)/(n + k). This theorem is item #30 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/. ...

On the homotopy category of Moore spaces and the cohomology of the category of abelian groups

Hans-Joachim Baues, Manfred Hartl (1996)

Fundamenta Mathematicae

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The homotopy category of Moore spaces in degree 2 represents a nontrivial cohomology class in the cohomology of the category of abelian groups. We describe various properties of this class. We use James-Hopf invariants to obtain explicitly the image category under the functor chain complex of the loop space.

A categorical concept of completion of objects

Guillaume C. L. Brümmer, Eraldo Giuli (1992)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.

Deformations of bimodule problems

Christof Geiß (1996)

Fundamenta Mathematicae

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We prove that deformations of tame Krull-Schmidt bimodule problems with trivial differential are again tame. Here we understand deformations via the structure constants of the projective realizations which may be considered as elements of a suitable variety. We also present some applications to the representation theory of vector space categories which are a special case of the above bimodule problems.

Fundamental pro-groupoids and covering projections

Luis Hernández-Paricio (1998)

Fundamenta Mathematicae

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We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent...

Splitting obstructions and properties of objects in the Nil categories

Tadeusz Koźniewski (1999)

Fundamenta Mathematicae

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We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Applications include a description of Cappell's special UNil group and reformulations of those splitting and fibering theorems which use the Nil groups.

Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology

Michael Slack (1999)

Fundamenta Mathematicae

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A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant...

Coherent and strong expansions of spaces coincide

Sibe Mardešić (1998)

Fundamenta Mathematicae

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In the existing literature there are several constructions of the strong shape category of topological spaces. In the one due to Yu. T. Lisitsa and S. Mardešić [LM1-3] an essential role is played by coherent polyhedral (ANR) expansions of spaces. Such expansions always exist, because every space admits a polyhedral resolution, resolutions are strong expansions and strong expansions are always coherent. The purpose of this paper is to prove that conversely, every coherent polyhedral (ANR)...

Loop spaces and homotopy operations

David Blanc (1997)

Fundamenta Mathematicae

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We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking values in π * X . These depend on first algebraically “delooping” the Π-algebras π * X , using the H-space structure on X, and then trying to realize the delooped Π-algebra.

Goldstern–Judah–Shelah preservation theorem for countable support iterations

Miroslav Repický (1994)

Fundamenta Mathematicae

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[1] T. Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. [2] T. Bartoszyński and H. Judah, Measure and Category, in preparation. [3] D. H. Fremlin, Cichoń’s diagram, Publ. Math. Univ. Pierre Marie Curie 66, Sém. Initiation Anal., 1983/84, Exp. 5, 13 pp. [4] M. Goldstern, Tools for your forcing construction, in: Set Theory of the Reals, Conference of Bar-Ilan University, H. Judah (ed.), Israel Math. Conf. Proc. 6, 1992, 307-362....