Mathematical Proceedings of the Cambridge Philosophical Society - Tập 119 Số 1 - Trang 113-118 - 1996
Kanji Morimoto, Masashi Sakuma, Yoshiyuki Yokota
Let K be a knot in the 3-sphere S3, N(K) the regular neighbourhood of K and E(K)
= cl(S3−N(K)) the exterior of K. The tunnel number t(K) is the minimum number of
mutually disjoint arcs properly embedded in E(K) such that the complementary
space of a regular neighbourhood of the arcs is a handlebody. We call the family
of arcs satisfying this condition an unknotting tunnel system for K. In
particul... hiện toàn bộ
Mathematical Proceedings of the Cambridge Philosophical Society - Tập 31 Số 4 - Trang 520-524 - 1935
H. O. Hirschfeld
Let us consider a discontinuous bivariate distribution. That is, let us consider
N × Q non-negative values pνq (ν = 1, 2, …, N; q = 1, 2, …, Q), being the
theoretical probabilities of the νth value of a variate Xμ (μ = 1, 2, …, N)
concurring with the qth value of a second variate Ys (s = 1, 2, …, Q).
Mathematical Proceedings of the Cambridge Philosophical Society - Tập 44 Số 1 - Trang 50-57 - 1948
C. Radhakrishna Rao
If the probability differential of a set of stochastic variates contains k
unknown parameters, the statistical hypotheses concerning them may be simple or
composite. The hypothesis leading to a complete specification of the values of
the k parameters is called a simple hypothesis, and the one leading to a
collection of admissible sets a composite hypothesis. In this paper we shall be
concerned wit... hiện toàn bộ
Mathematical Proceedings of the Cambridge Philosophical Society - Tập 60 Số 4 - Trang 787-800 - 1964
John H. Conway, H. T. Croft
1. Mikusiński ((2), Problem 84) asks: can we express the surface of a sphere (in
Euclidean 3-space) as the union of non-overlapping congruent great-circle arcs?
We give a partial answer to this question.
Mathematical Proceedings of the Cambridge Philosophical Society - Tập 24 Số 1 - Trang 89-110 - 1928
D. R. Hartree
The paper is concerned with the practical determination of the characteristic
values and functions of the wave equation of Schrodinger for a non-Coulomb
central field, for which the potential is given as a function of the distance r
from the nucleus.The method used is to integrate a modification of the equation
outwards from initial conditions corresponding to a solution finite at r = 0,
and inwar... hiện toàn bộ
Mathematical Proceedings of the Cambridge Philosophical Society - Tập 121 Số 1 - Trang 101-113 - 1997
Pei‐de Chen, Richard L. Tweedie
For a general state space Markov chain on a space (X, [Bscr ](X)), the existence
of a Doeblin decomposition, implying the state space can be written as a
countable union of absorbing ‘recurrent’ sets and a transient set, is known to
be a consequence of several different conditions all implying in some way that
there is not an uncountable collection of absorbing sets. These include([Mscr ])
there e... hiện toàn bộ
Mathematical Proceedings of the Cambridge Philosophical Society - Tập 79 Số 1 - Trang 129-134 - 1976
Israel Berstein
This note contains a partial generalization of the results of (3). We extend to
arbitrary n and k the complete determination of the cases in which cup length is
strictly less than the maximum possible value dim Gn, k(R) = nk. We also show
that the Lusternik–Schnirelmann category cat Gn, k(R) < nk in the same cases.