The Garden Hose Complexity for the Equality Function

The garden hose complexity is a new communication complexity introduced by H. Buhrman, S. Fehr, C. Schaffner and F. Speelman [BFSS13] to analyze position-based cryptography protocols in the quantum setting. We focus on the garden hose complexity of the equality function, and improve on the bounds of O. Margalit and A. Matsliah[MM12] with the help of a new approach and of our handmade simulated annealing based solver. We have also found beautiful symmetries of the solutions that have lead us to develop the notion of garden hose permutation groups. Then, exploiting this new concept, we get even further, although several interesting open problems remain.Comment: 16 page

Robust and real-time control of magnetic bearings for space engines

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small

Dealing with dichotomies: Economic and innovative capacity on Bornholm

This paper aims to characterise the interplay between regional development and economic and innovative capacity on the Danish island community of Bornholm. Drawing on studies of institutions, innovative capacity is highlighted as knowledge resources, relational resources and mobilisation capacity. Building on these concepts, the institutions of regional development on Bornholm are examined in terms of how traditional core competencies in agriculture and the fishing industries are being utilised and are in the process of change towards a new core competency. The study shows how knowledge resources on Bornholm appear to be sufficient for fostering regional development in new endeavours. Bornholm is also working hard to facilitate new relationships and social capital to build innovative capacity. But the mobilisation of visions and goals towards a new core competency is being hindered by to the social and institutional dichotomies on the island. These dichotomies are examined in the paper and examples are presented of how Bornholm is currently dealing with this situation

Airport Level of Service: A Model according to Departing Passenger’s Perceptions at a Small-sized Airport

Purpose: This study proposes a conceptual model of level of service evaluation to a small-sized airport with a focus on departing passengers. Design/methodology: The variables selected to compose the model were chosen according to their adequacy to departing passengers and the airport’s characteristics. A survey was conducted, and, posteriorly, exploratory factor analysis was used in order to verify the adequacy of the conceptual model proposed and also to improve it according to the results obtained. Findings: The results show that the level of service of the airport is composed of three dimensions: airport characteristics, passenger processing, and prices. The relative importance of the dimensions according to their contribution to the composition of the airport’s overall level of service was also determined. Originality/value: The paper combines theoretical and practical findings in a model for level of service evaluation to a small-sized airport from an air transportation management perspective.Peer Reviewe

Interplay between structure and magnetism in the low-dimensional spin system K(C8H16O4)2CuCl3∗H2OK(C_8H_{16}O_4)_2CuCl_3{*}H_2O

Materials based on a crown ether complex together with magnetic ions, especially Cu(II), can be used to synthesize new low dimesional quantum spin systems. We have prepared the new crown ether complex Di-\mu-chloro-bis(12-crown-4)-aquqdichloro-copper(II)-potassium, $K(C_8H_{16}O_4)_2CuCl_3{*}H_2O$ (1), determined its structure, and analyzed its magnetic properties. Complex (1) has a monoclinic structure and crystallizes in space group $P2_1/n$ with the lattice parameters of $a=9.5976(5)\r{A}$, $b=11.9814\r{A}, c=21.8713\r{A}$ and $\beta=100.945(4)\deg$. The magnetic properties of this compound have been investigated in the temperature range 1.8 K - 300 K. The magnetic susceptibility shows a maximum at 23 K, but no 3-D long range magnetic order down to 1.8 K. The S=1/2 Cu(II) ions form antiferromagnetically coupled dimers with Cu-Cl distances of $2.2554(8)\r{A}$ and $4.683(6)\r{A}$, and a Cu-Cl-Cu angle of $115.12(2)\deg$ with $2J_{dimer}=-2.96meV (-23.78 cm^{-1})$. The influence of $H_2O$ on the Cl-Cu-Cl exchange path is analyzed. Our results show that the values of the singlet-triplet splitting are increasing considering $H_2O$ molecules in the bridging interaction. This is supported by Density functional theory (DFT) calculations of coupling constants with Perdew and Wang (PWC), Perdew, Burke and Ernzenrhof (PBE) and strongly constrained and appropriately normed (SCAN) exchange-correlation function show excellent agreement for the studied compound