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991.
992.
Kevin Leckey Ralph Neininger Henning Sulzbach 《Stochastic Processes and their Applications》2019,129(2):507-538
A fundamental algorithm for selecting ranks from a finite subset of an ordered set is Radix Selection. This algorithm requires the data to be given as strings of symbols over an ordered alphabet, e.g., binary expansions of real numbers. Its complexity is measured by the number of symbols that have to be read. In this paper the model of independent data identically generated from a Markov chain is considered.The complexity is studied as a stochastic process indexed by the set of infinite strings over the given alphabet. The orders of mean and variance of the complexity and, after normalization, a limit theorem with a centered Gaussian process as limit are derived. This implies an analysis for two standard models for the ranks: uniformly chosen ranks, also called grand averages, and the worst case rank complexities which are of interest in computer science.For uniform data and the asymmetric Bernoulli model (i.e. memoryless sources), we also find weak convergence for the normalized process of complexities when indexed by the ranks while for more general Markov sources these processes are not tight under the standard normalizations. 相似文献
993.
Consider a system into which units of random type enter at fixed points in time. Suppose each unit is endowed with a lifetime whose distribution is specific to its type, during which it is active (present in the system), and after which it is inactive (deleted from the system). Some unit types may tend to remain active for longer periods than others, and thus the limiting proportion of a given type within the active population may differ from the probability that an entering unit is of that type. The relation between the probabilities of types and the limiting proportion of types is shown to depend on the life distributions in a manner determined by the arrival time sequence. 相似文献
994.
Patricia E. Simmons Tom Albers Debbie Barco Michelle Barker Ron Beer Cassandra Belton Betty Burris Hal Donovan Pili Dressel Ron Giesler Terri Gipson Neal Gleditsch Marian Heimbouch Lea Heintz Linda Kalinowski Kathy Ketterer Kit Klein Lebee Meehan Diane Miller Donna Northcott Barb Pollman Tom Potter Jeffrey Powell Dan Prater Doug Raney Chris Roman Beryl Rosenthal Brian Schaffer Joe Seidler Laura Sturmfels Mary Stewart Carey Tisdal Carol Valenta Suzanne Walton Ralph Wilke 《School science and mathematics》1998,98(7):354-356
995.
Ralph J. Faudree Ronald J. Gould Michael S. Jacobson Linda Lesniak Akira Saito 《Discrete Mathematics》2005,300(1-3):218-224
In this note, we consider a minimum degree condition for a hamiltonian graph to have a 2-factor with two components. Let G be a graph of order n3. Dirac's theorem says that if the minimum degree of G is at least , then G has a hamiltonian cycle. Furthermore, Brandt et al. [J. Graph Theory 24 (1997) 165–173] proved that if n8, then G has a 2-factor with two components. Both theorems are sharp and there are infinitely many graphs G of odd order and minimum degree which have no 2-factor. However, if hamiltonicity is assumed, we can relax the minimum degree condition for the existence of a 2-factor with two components. We prove in this note that a hamiltonian graph of order n6 and minimum degree at least has a 2-factor with two components. 相似文献
996.
Given integers k,s,t with 0≤s≤t and k≥0, a (k,t,s)-linear forest F is a graph that is the vertex disjoint union of t paths with a total of k edges and with s of the paths being single vertices. If the number of single vertex paths is not critical, the forest F will simply be called a (k,t)-linear forest. A graph G of order n≥k+t is (k,t)-hamiltonian if for any (k,t)-linear forest F there is a hamiltonian cycle containing F. More generally, given integers m and n with k+t≤m≤n, a graph G of order n is (k,t,s,m)-pancyclic if for any (k,t,s)-linear forest F and for each integer r with m≤r≤n, there is a cycle of length r containing the linear forest F. Minimum degree conditions and minimum sum of degree conditions of nonadjacent vertices that imply that a graph is (k,t,s,m)-pancyclic (or just (k,t,m)-pancyclic) are proved. 相似文献
997.
Edward Hult Houyuan Jiang Daniel Ralph 《Computational Optimization and Applications》2014,59(1-2):185-200
The stochastic uncapacitated single allocation p-hub center problem is an extension of the deterministic version which aims to minimize the longest origin-destination path in a hub and spoke network. Considering the stochastic nature of travel times on links is important when designing a network to guarantee the quality of service measured by a maximum delivery time for a proportion of all deliveries. We propose an efficient reformulation for a stochastic p-hub center problem and develop exact solution approaches based on variable reduction and a separation algorithm. We report numerical results to show effectiveness of our new reformulations and approaches by finding global solutions of small-medium sized problems. The combination of model reformulation and a separation algorithm is particularly noteworthy in terms of computational speed. 相似文献
998.
Ralph deLaubenfels 《Israel Journal of Mathematics》1993,81(1-2):227-255
We show that, whenA generates aC-semigroup, then there existsY such that [M(C)] →Y →X, andA|
Y
, the restriction ofA toY, generates a strongly continuous semigroup, where ↪ means “is continuously embedded in” and ‖x‖[Im(C)]≡‖C
−1
x‖. There also existsW such that [C(W)] →X →W, and an operatorB such thatA=B|
X
andB generates a strongly continuous semigroup onW. If theC-semigroup is exponentially bounded, thenY andW may be chosen to be Banach spaces; in general,Y andW are Frechet spaces. If ρ(A) is nonempty, the converse is also true.
We construct fractional powers of generators of boundedC-semigroups.
We would like to thank R. Bürger for sending preprints, and the referee for pointing out reference [37]. This research was
supported by an Ohio University Research Grant. 相似文献
999.
Using standard nonlinear programming (NLP) theory, we establish formulas for first and second order directional derivatives
of optimal value functions of parametric mathematical programs with complementarity constraints (MPCCs). The main point is
that under a linear independence condition on the active constraint gradients, optimal value sensitivity of MPCCs is essentially
the same as for nonlinear programs, in spite of the combinatorial nature of the MPCC feasible set. Unlike NLP however, second
order directional derivatives of the MPCC optimal value function show combinatorial structure.
Received: October 31, 2000 / Accepted: March 8, 2002?Published online June 25, 2002 相似文献
1000.
Ralph J. Faudree Evelyne Flandrin Michael S. Jacobson Jenő Lehel Richard H. Schelp 《Graphs and Combinatorics》2000,16(4):399-410
It will be shown that if G is a graph of order n which contains a triangle, a cycle of length n or n−1 and at least cn odd cycles of different lengths for some positive constant c, then there exists some positive constant k=k(c) such that G contains at least kn
1/6 even cycles of different lengths. Other results on the number of even cycle lengths which appear in graphs with many different
odd length cycles will be given.
Received: October 15, 1997 相似文献