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991.
A Steiner triple system of order v, STS(v), may be called equivalent to another STS(v) if one can be converted to the other by a sequence of three simple operations involving Pasch trades with a single negative block. It is conjectured that any two STS(v)s on the same base set are equivalent in this sense. We prove that the equivalence class containing a given system S on a base set V contains all the systems that can be obtained from S by any sequence of well over one hundred distinct trades, and that this equivalence class contains all isomorphic copies of S on V. We also show that there are trades which cannot be effected by means of Pasch trades with a single negative block. 相似文献
992.
A 6-cycle system of a graph G is an edge-disjoint decomposition of G into 6-cycles. Graphs G, for which necessary and sufficient conditions for existence of a 6-cycle system have been found, include complete graphs and complete equipartite graphs. A 6-cycle system of G is said to be 2-perfect if the graph formed by joining all vertices distance 2 apart in the 6-cycles is again an edge-disjoint decomposition of G, this time into 3-cycles, since the distance 2 graph in any 6-cycle is a pair of disjoint 3-cycles.Necessary and sufficient conditions for existence of 2-perfect 6-cycle systems of both complete graphs and complete equipartite graphs are known, and also of λ-fold complete graphs. In this paper, we complete the problem, giving necessary and sufficient conditions for existence of λ-fold 2-perfect 6-cycle systems of complete equipartite graphs. 相似文献
993.
A connected graph Γ with at least 2n+2 vertices is said to be n-extendable if every matching of size n in Γ can be extended to a perfect matching. The aim of this paper is to study the 1-extendability and 2-extendability of certain semi-Cayley graphs of finite abelian groups, and the classification of connected 2-extendable semi-Cayley graphs of finite abelian groups is given. Thus the 1-extendability and 2-extendability of Cayley graphs of non-abelian groups which can be realized as such semi-Cayley graphs of abelian groups can be deduced. In particular, the 1-extendability and 2-extendability of connected Cayley graphs of generalized dicyclic groups and generalized dihedral groups are characterized. 相似文献
994.
Yanyuan Ma Marc G. Genton Emanuel Parzen 《Annals of the Institute of Statistical Mathematics》2011,63(2):227-243
The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous
distributions. However, this is no longer true for discrete distributions or samples with ties. We show that the definition
of sample quantiles based on mid-distribution functions resolves this issue and provides a unified framework for asymptotic
properties of sample quantiles from absolutely continuous and from discrete distributions. We demonstrate that the same asymptotic
normal distribution result as for the classical sample quantiles holds at differentiable points, whereas a more general form
arises for distributions whose cumulative distribution function has only one-sided differentiability. For discrete distributions
with finite support, the same type of asymptotics holds and the sample quantiles based on mid-distribution functions either
follow a normal or a two-piece normal distribution. We also calculate the exact distribution of these sample quantiles for
the binomial and Poisson distributions. We illustrate the asymptotic results with simulations. 相似文献
995.
Li-Ping Zhu Lin-Yi Qian Jin-Guan Lin 《Annals of the Institute of Statistical Mathematics》2011,63(6):1277-1293
In this paper we discuss variable selection in a class of single-index models in which we do not assume the error term as
additive. Following the idea of sufficient dimension reduction, we first propose a unified method to recover the direction,
then reformulate it under the least square framework. Differing from many other existing results associated with nonparametric
smoothing methods for density function, the bandwidth selection in our proposed kernel function essentially has no impact
on its root-n consistency or asymptotic normality. To select the important predictors, we suggest using the adaptive lasso method which
is computationally efficient. Under some regularity conditions, the adaptive lasso method enjoys the oracle property in a
general class of single-index models. In addition, the resulting estimation is shown to be asymptotically normal, which enables
us to construct a confidence region for the estimated direction. The asymptotic results are augmented through comprehensive
simulations, and illustrated by an analysis of air pollution data. 相似文献
996.
We study three different problems in the area of Toeplitz operators on the Segal-Bargmann space in Cn. Extending results obtained previously by the first author and Y.L. Lee, and by the second author, we first determine the commutant of a given Toeplitz operator with a radial symbol belonging to the class Sym>0(Cn) of symbols having certain growth at infinity. We then provide explicit examples of zero-products of non-trivial Toeplitz operators. These examples show the essential difference between Toeplitz operators on the Segal-Bargmann space and on the Bergman space over the unit ball. Finally, we discuss the “finite rank problem”. We show that there are no non-trivial rank one Toeplitz operators Tf for f∈Sym>0(Cn). In all these problems, the growth at infinity of the symbols plays a crucial role. 相似文献
997.
The blow-up solutions of the Cauchy problem for the Davey-Stewartson system, which is a model equation in the theory of shallow water waves, are investigated. Firstly, the existence of the ground state for the system derives the best constant of a Gagliardo-Nirenberg type inequality and the variational character of the ground state. Secondly, the blow-up threshold of the Davey-Stewartson system is developed in R3. Thirdly, the mass concentration is established for all the blow-up solutions of the system in R2. Finally, the existence of the minimal blow-up solutions in R2 is constructed by using the pseudo-conformal invariance. The profile of the minimal blow-up solutions as t→T (blow-up time) is in detail investigated in terms of the ground state. 相似文献
998.
In this paper, we prove a blow-up criterion in terms of the upper bound of the liquid mass for the strong solution to the two-dimensional (2D) viscous liquid-gas two-phase flow model in a smooth bounded domain. The result also applies to three-dimensional (3D) case. 相似文献
999.
Dharmanand Baboolal 《Czechoslovak Mathematical Journal》2011,61(3):845-861
Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such
a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another
example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to
be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification
for spaces, as well as the Freudenthal-Morita Theorem for spaces, can be obtained from our frame constructions. 相似文献
1000.
Xiaoying Han 《Journal of Mathematical Analysis and Applications》2011,376(2):481-493
We study the asymptotic behavior of solutions to the stochastic sine-Gordon lattice equations with multiplicative white noise. We first prove the existence and uniqueness of solutions, and then establish the existence of tempered random bounded absorbing sets and global random attractors. 相似文献