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1.
Malene Steen Nielsen Flagga Frank Antonsen 《International Journal of Theoretical Physics》2004,43(9):1917-1930
We show that stable causality is related to the vanishing of the top Stiefel–Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and sufficient condition. 相似文献
2.
H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds. 相似文献
3.
We consider context-free grammars of the form G = {f → fb1+b2+1ga1+a2, g → fb1 ga1+1},where ai and bi are integers sub ject to certain positivity conditions. Such a grammar G gives rise to triangular arrays {T(n, k)}0≤k≤n satisfying a three-term recurrence relation. Many combinatorial sequences can be generated in this way. Let Tn (x) =∑nk=0T(n, k)xk. Based on the differential operator with respect to G, we define a sequence of linear operators Pn such that Tn+1(x) = Pn(Tn(x)). Applying the characterization of real stability preserving linear operators on the multivariate polynomials due to Borcea and Br?ndén, we obtain a necessary and sufficient condition for the operator Pn to be real stability preserving for any n. As a consequence, we are led to a sufficient condition for the real-rootedness of the polynomials defined by certain triangular arrays, obtained by Wang and Yeh.Moreover, as special cases we obtain grammars that lead to identities involving the Whitney numbers and the Bessel numbers. 相似文献
4.
Abdelhafed Elkhadiri 《Bulletin of the Brazilian Mathematical Society》2000,31(1):45-71
Let be an open subset of
n
and
be a subalgebra of the algebra of analytic functions on . We suppose that
satisfies some weak conditions of noetherianity such that we can construct a finite stratification for each ideal of
. We also suppose that
satifies global £ojasiewicz's inequalities. We prove the following: Let
andf C
on
flat on ; if for eacha the Taylor's serie off ata, T
a
f, is in the ideal generated byT
a
f
1,...,T
a
f
p
in the ring of formal power series, then there exist
1,...,
p
,C
on
flat on such that
. This result extends the classic Hormander's theorem of division (for a polynomial) or the £ojasiewicz-Malgrange theorem in the local analytic case.Reherches menées dans le cadre du Programme d'Appui à la Recherche Scientifique (PARS MI 33) 相似文献
6.
Christian Bargetz 《Mathematische Nachrichten》2014,287(1):10-22
In this article, we show that the Valdivia–Vogt structure table—containing the sequence space representations of the most used spaces of smooth functions appearing in the theory of distributions—can be interpreted as a commutative diagram, i.e., there is an isomorphism between the space of infinitely differentiable functions and the space , where s is the space of rapidly decreasing sequences, such that its restriction to the other function spaces in the structure table yields an isomorphism between these spaces of smooth functions and their sequence space representation. This result answers the corresponding question of Prof. Dietmar Vogt formulated on the conference “Functional Analysis: Applications to Complex Analysis and Partial Differential Equations” held in B?dlewo in May 2012. 相似文献
7.
Thomas Zaslavsky 《Discrete and Computational Geometry》2002,27(3):303-351
For each pair (Q
i
,Q
j
) of reference points and each real number r there is a unique hyperplane h \perp Q
i
Q
j
such that d(P,Q
i
)
2
- d(P,Q
j
)
2
= r for points P in h . Take n reference points in d -space and for each pair (Q
i
,Q
j
) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure
of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real,
additive gain graph (this is a graph with an additive real number associated invertibly to each edge) whose set of balanced
flats has the same structure as the intersection semilattice. We examine the requirements for genericity, which are related
to behavior at infinity but remain mysterious; also, variations in the construction rules for perpendiculars. We investigate
several particular arrangements with a view to finding the exact numbers of faces of each dimension. The prototype, the arrangement
of all perpendicular bisectors, was studied by Good and Tideman, motivated by a geometric voting theory. Most of our particular
examples are suggested by extensions of that theory in which voters exercise finer discrimination. Throughout, we propose
many research problems.
Received July 20, 2000, and in revised form September 29, 2001, and October 12, 2001. Online publication March 4, 2002. 相似文献
8.
本文讨论一类(包括Koch曲线在内的)自相似曲线,证明了其上的简单曲线是Whitney型临界集,并在微小扰动下仍是简单曲线. 相似文献
9.
We study the asymptotic properties of both the horizontal and vertical shift functions based on independent ranked set samples
drawn from continuous distributions. Several tests derived from these shift processes are developed. We show that by using
balanced ranked set samples with bigger set sizes, one can decrease the width of the confidence band and hence increase the
power of these tests. These theoretical findings are validated through small-scale simulation studies. An application of the
proposed techniques to a cancer mortality data set is also provided.
Part of the research was conducted while Kaushik Ghosh was visiting Statistical Research and Applications Branch of the National
Cancer Institute on an Intergovernmental Personnel Assignment. 相似文献
10.