Search results for "Integer"
showing 10 items of 250 documents
Threshold expansion of the sunset diagram
1999
By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its threshold, i.e. in any given order in the difference between the external momentum squared and its threshold value, (m_1+m_2+m_3)^2. In particular, this algorithm includes an explicit recurrence procedure to analytically calculate sunset diagrams with arbitrary integer powers of propagators at the threshold.
Non-equivalent hyperbolic knots
2002
We construct, for each integer n 3, pairs of non-equivalent hyperbolic knots with the same 2fold and n-fold cyclic branched covers. We also discuss necessary conditions for such pairs of knots to exist. 2001 Elsevier Science B.V. All rights reserved. MSC: primary 57M25; secondary 57M12, 57M50
In the Shadows of a hypergraph: looking for associated primes of powers of squarefree monomial ideals
2018
The aim of this paper is to study the associated primes of powers of square-free monomial ideals. Each square-free monomial ideal corresponds uniquely to a finite simple hypergraph via the cover ideal construction, and vice versa. Let H be a finite simple hypergraph and J(H) the cover ideal of H. We define the shadows of hypergraph, H, described as a collection of smaller hypergraphs related to H under some conditions. We then investigate how the shadows of H preserve information about the associated primes of the powers of J(H). Finally, we apply our findings on shadows to study the persistence property of square-free monomial ideals and construct some examples exhibiting failure of contai…
Capacity and Energy-Consumption Optimization for the Cluster-Tree Topology in IEEE 802.15.4
2011
International audience; 802.15.4 proposes to use a cluster-tree hierar- chy to organize the transmissions in Wireless Sensor Networks. In this letter, we propose a framework to analyze formally the capacity and the energy consumption of this structure. We derive a Mixed Integer Linear Programming (MILP) formulation to obtain a topology compliant with the standard. This formulation provides the optimal solution for the network capacity: this con- stitutes an upper bound for any distributed algorithms permitting to construct a cluster-tree. This framework can also be used to evaluate the capacity and to compare quantitatively different cluster-tree algorithms.
Nurse Scheduling Problem: An Integer Programming Model with a Practical Application
2012
We use a binary integer programming model to formulate and solve a nurse scheduling problem (NSP) which maximally satisfies nurse preferences. In a practical application of a VA hospital, besides considering the scheduling of two types of nurses (registered nurses and licensed practical nurses), two other types of employees (nursing assistants and health care techs), one nurse manager, and a clinical nurse leader are also included in our model. Most of these employees are working full-time. In addition, we distinguish the schedule of weekdays and weekends with different requirements and different preferences for employees. Besides the requirements for each shift, we consider requirements fo…
The linear diophantine problem of Frobenius for subsets of arithmetic sequences
1997
Let A k = {a 1,. . . , a k } $ \subset \Bbb N $ with gcd (a 1,. . . , a k ) = 1. We shall say that a natural number n has a representation by a 1,. . . , a k if $ n =\sum \limits_{i=1}^{k}a_ix_i,\; x_i\in \Bbb N_0 $ . Let g = g (A k ) be the largest integer with no such representation. We then study the set A k = {a,ha + d,ha + 2d,..., ha + (k - 1) d} h,d > 0, gcd (a,d) = 1). If l k denotes the greatest number of elements which can be omitted without altering g (A k ), we show that ¶¶ $ 1-{4 \over \sqrt k} \le {l_k\over k} \le 1 - {3\over k}, $ ¶¶ provided a > k, or a = k with $ d \ge 2 h \sqrt {k} $ . The lower bound can be improved to 1 - 4 / k if we choose a > (k - 4) k + 3. Moreover, we…
Formulations for an inventory routing problem
2014
In this paper, we present and compare formulations for the inventory routing problem (IRP) where the demand of customers has to be served, over a discrete time horizon, by capacitated vehicles starting and ending their routes at a depot. The objective of the IRP is the minimization of the sum of inventory and transportation costs. The formulations include known and new mathematical programming formulations. Valid inequalities are also presented. The formulations are tested on a large set of benchmark instances. One of the most significant conclusions is that the formulations that use vehicle-indexed variables are superior to the more compact, aggregate formulations.
Potential predation pressure of littoral mysids on herring (Clupea harengus membras L.) eggs and yolk-sac larvae
2008
The predation potential of littoral mysid shrimps (Mysidacea) on Baltic herring (Clupea harengus membras L.) eggs and yolk-sac larvae was studied experimentally. The results showed that littoral mysids feed actively on both eggs and yolk-sac larvae. It was shown that Neomysis integer preys on eggs, which are not attached to the substrate. Alternative food (yolk-sac larvae or zooplankton) did not decrease feeding rate on eggs. Only gravel as a bottom material lowered the ingestion rate to nearly zero. The largest of the mysid species Praunus flexuosus ate yolk-sac larvae more than other mysids and most efficiently. Mysids switched to feed on eggs when larvae and eggs were offered simultaneou…
A characterization of the distribution of a weighted sum of gamma variables through multiple hypergeometric functions
2008
Applying the theory on multiple hypergeometric functions, the distribution of a weighted convolution of Gamma variables is characterized through explicit forms for the probability density function, the distribution function and the moments about the origin. The main results unify some previous contributions in the literature on nite convolution of Gamma distributions. We deal with computational aspects that arise from the representations in terms of multiple hypergeometric functions, introducing a new integral representation for the fourth Lauricella function F (n) D and its con uent form (n) 2 , suitable for numerical integration; some graphics of the probability density function and distr…
The shortest-path problem with resource constraints with -loop elimination and its application to the capacitated arc-routing problem
2014
Abstract In many branch-and-price algorithms, the column generation subproblem consists of computing feasible constrained paths. In the capacitated arc-routing problem (CARP), elementarity constraints concerning the edges to be serviced and additional constraints resulting from the branch-and-bound process together impose two types of loop-elimination constraints. To fulfill the former constraints, it is common practice to rely on a relaxation where loops are allowed. In a k-loop elimination approach all loops of length k and smaller are forbidden. Following Bode and Irnich (2012) for solving the CARP, branching on followers and non-followers is the only known approach to guarantee integer …