A chain theorem for internally 4-connected binary matroids

This is the post-print version of the Article - Copyright @ 2011 ElsevierLet M be a matroid. When M is 3-connected, Tutte’s Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M) − E(N)| = 1 unless M is a wheel or a whirl. This paper establishes a corresponding result for internally 4-connected binary matroids. In particular, we prove that if M is such a matroid, then M has an internally 4-connected proper minor N with |E(M) − E(N)| at most 3 unless M or its dual is the cycle matroid of a planar or Möbius quartic ladder, or a 16-element variant of such a planar ladder.This study was partially supported by the National Security Agency

Towards a splitter theorem for internally 4-connected binary matroids

This is the post-print version of the Article - Copyright @ 2012 ElsevierWe prove that if M is a 4-connected binary matroid and N is an internally 4-connected proper minor of M with at least 7 elements, then, unless M is a certain 16-element matroid, there is an element e of E(M) such that either M\e or M/e is internally 4-connected having an N-minor. This strengthens a result of Zhou and is a first step towards obtaining a splitter theorem for internally 4-connected binary matroids.This study is partially funded by Marsden Fund of New Zealand and the National Security Agency

A Simulation Analysis of the Relationship between Retail Sales and Shopping Center Rents

This article examines the variation in rents per square foot among regional shopping centers in the United States in response to variation in retail sales per square foot. The analysis breaks new ground by treating base and percentage rents as endogenous functions of retail sales. The analysis further distinguishes between de facto, if not de jure, fixed and percentage leases, and between new versus existing leases. Simulation results suggest that shopping center rents can easily increase in the short-run as retail sales decrease, or they can easily decrease as retail sales increase. In addition, the results suggest that shopping center rents per square foot generally react more aggressively to an increase in retail sales per square foot over time than to a decrease in retail sales per square foot, all else equal

The Effect of Firm Characteristics on the Use of Percentage Retail Leases

Choice of lease payments has been widely studied in the literature. There are three—not necessarily exclusive—explanations that have received attention. The first attributes the choice of fixed versus percentage lease payments to risk-sharing preferences. The second explanation views percentage-of-sales lease agreements as a way discriminating monopolists can appropriate economic rents. The third attributes percentage-of-sales lease agreements to a metering and bonding argument. This paper examines the proposition that the choice of percentage retail leases is driven in part by managements\u27 desire to circumvent the cost of violating debt covenant restrictions. The evidence presented here supports the prediction that retail firms with higher debt–asset ratios are more likely to adopt percentage lease agreements

Probing dipole-forbidden autoionizing states by isolated attosecond pulses

We propose a general technique to retrieve the information of dipole-forbidden resonances in the autoionizing region. In the simulation, a helium atom is pumped by an isolated attosecond pulse in the extreme ultraviolet (EUV) combined with a few-femtosecond laser pulse. The excited wave packet consists of the $^1S$, $^1P$, and $^1D$ states, including the background continua, near the $2s2p(^1P)$ doubly excited state. The resultant electron spectra with various laser intensities and time delays between the EUV and laser pulses are obtained by a multilevel model and an ab initio time-dependent Schr\"odinger equation calculation. By taking the ab initio calculation as a "virtual measurement", the dipole-forbidden resonances are characterized by the multilevel model. We found that in contrast to the common assumption, the nonresonant coupling between the continua plays a significant role in the time-delayed electron spectra, which shows the correlation effect between photoelectrons before they leave the core. This technique takes the advantages of ultrashort pulses uniquely and would be a timely test for the current attosecond technology.Comment: 10 pages, 6 figure

Large-angle slewing maneuvers for flexible spacecraft

A new class of closed-form solutions for finite-time linear-quadratic optimal control problems is presented. The solutions involve Potter's solution for the differential matrix Riccati equation, which assumes the form of a steady-state plus transient term. Illustrative examples are presented which show that the new solutions are more computationally efficient than alternative solutions based on the state transition matrix. As an application of the closed-form solutions, the neighboring extremal path problem is presented for a spacecraft retargeting maneuver where a perturbed plant with off-nominal boundary conditions now follows a neighboring optimal trajectory. The perturbation feedback approach is further applied to three-dimensional slewing maneuvers of large flexible spacecraft. For this problem, the nominal solution is the optimal three-dimensional rigid body slew. The perturbation feedback then limits the deviations from this nominal solution due to the flexible body effects. The use of frequency shaping in both the nominal and perturbation feedback formulations reduces the excitation of high-frequency unmodeled modes. A modified Kalman filter is presented for estimating the plant states

Transform methods for precision continuum and control models of flexible space structures

An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality