Spreading primitive groups of diagonal type do not exist

The synchronisation hierarchy of finite permutation groups consists of classes of groups lying between 2-transitive groups and primitive groups. This includes the class of spreading groups, which are defined in terms of sets and multisets of permuted points, and which are known to be primitive of almost simple, affine or diagonal type. In this paper, we prove that in fact no spreading group of diagonal type exists. As part of our proof, we show that all non-abelian finite simple groups, other than six sporadic groups, have a transitive action in which a proper normal subgroup of a point stabiliser is supplemented by all corresponding two-point stabilisers.Comment: 10 pages. Version 2 resolves the Monster group case of Theorem 1.3, with the aid of a result drawn to our attention by Prof. Tim Burnes

Fractional Quantum Hall Effect in a Diluted Magnetic Semiconductor

We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor Cd(1-x)Mn(x)Te. The presence of magnetic impurities results in a giant Zeeman splitting leading to an unusual ordering of composite fermion Landau levels. In experiment, this results in an unconventional opening and closing of fractional gaps around filling factor v = 3/2 as a function of an in-plane magnetic field, i.e. of the Zeeman energy. By including the s-d exchange energy into the composite Landau level spectrum the opening and closing of the gap at filling factor 5/3 can be modeled quantitatively. The widely tunable spin-splitting in a diluted magnetic 2DES provides a novel means to manipulate fractional states

Contrasting non-dynamic and dynamic models of the water-energy nexus in small, off-grid Mediterranean islands

Water and energy supply in small Mediterranean islands are strictly interrelated and face a large number of challenging issues, mainly caused by the distance from the mainland, the lack of accessible and safe potable water sources, and the high seasonal variability of the water and energy demands driven by touristic fluxes. The energy system generally relies on carbon intensive, expensive stand-alone diesel generators, while potable water supply is provided by tank vessels. Although this combination provides essential services for local communities, it is often economically and environmentally unsustainable due to high operational costs and greenhouse gas (GHG) emissions. A traditional approach to improve the sustainability and the efficiency of the water and energy systems is to couple renewable energy sources (RES) with water supply technologies (e.g., desalination), in order to obtain efficient planning solutions (i.e. RES capacity, desalination plant capacity) in a least-cost fashion. However, this approach is generally non-dynamic and optimizes the power allocation using fixed electricity loads as a surrogate of the actual water demand supplied by the desalination plant through the water distribution network. Although this load reflects the actual water demand on the long-term (i.e. monthly or annual time scale), it could strongly deviate from the real water demand if we consider shorter time scales (i.e. daily or hourly), over which the water distribution network is able to store and move water in space and time. In this work, we comparatively analyse this traditional non-dynamic model of the water-energy nexus with a novel dynamic modelling approach, where the operation of both the nexus components (i.e. power allocation and operations of the water distribution network) is conjunctively optimized with respect to multiple economic and sustainability indicators (e.g., net present costs, GHG emissions, water supply deficit, RES penetration). This comparative analysis is performed over the real case study of the Italian Ustica island in the Mediterranean Sea. Preliminary results show the effectiveness of the dynamic approach in improving the static solution with respect to almost all the system performance metrics considered

Starsat: A space astronomy facility

Preliminary design and analyses of a versatile telescope for Spacelab missions are presented. The system is an all-reflective Korsch three-mirror telescope with excellent performance characteristics over a wide field and a broad spectral range, making it particularly suited for ultraviolet observations. The system concept is evolved around the utilization of existing hardware and designs which were developed for other astronomy space projects

Identifying the hydraulic transmissivity of an aquifer with noisy hydraulic head data: a comparison study using three direct inversion methods

The parameters required to set up an hydrological model are often obtained by solving an inverse problem, using indirect or direct solution methods. Indirect methods are widely used, in particular when the state variable (here the hydraulic head h) is known at sparse locations only. Despite their flexibility, when the number of parameters rises, their computational requirements can become a challenging issue, together with problems related to non-uniqueness and instability. On the other side, direct methods have other limitations, including a more exhaustive knowledge of the state variables, but are less demanding in terms of computational resources. In this work three direct inversion methods are compared: the Comparison Model Method (CMM), the Double Constraint Method (DCM) and the Differential System Method (DSM). The three methods are compared on a two-dimensional synthetic aquifer, whose geometry, boundary conditions and h measurements are realistic and extracted from a data set collected for the aquifer of Weiach, north of Switzerland. Sequential-Gaussian simulation (SGS) was used to generate a transmissivity field (T ) for the aquifer, which was then used to obtain the h data required by the three methods. A noise of increasing magnitude was added to h to verify the stability of the methods with respect to noisy input data. For a small noise on the input h, the results obtained with the three methods are comparable. However, for more noisy data, the DCM is more robust, whereas the DSM is very sensitive to the position of the starting point for integration and to the T value assigned there

Diagonally Neighbour Transitive Codes and Frequency Permutation Arrays

Constant composition codes have been proposed as suitable coding schemes to solve the narrow band and impulse noise problems associated with powerline communication. In particular, a certain class of constant composition codes called frequency permutation arrays have been suggested as ideal, in some sense, for these purposes. In this paper we characterise a family of neighbour transitive codes in Hamming graphs in which frequency permutation arrays play a central rode. We also classify all the permutation codes generated by groups in this family

Stability of the Excitonic Phase in Bilayer Quantum Hall Systems at Total Filling One -- Effects of Finite Well Width and Pseudopotentials --

The ground state of a bilayer quantum Hall system at $\nu_{\rm T}=1$ with model pseudopotential is investigated by the DMRG method. Firstly, pseudopotential parameters appropriate for the system with finite layer thickness are derived, and it is found that the finite thickness makes the excitonic phase more stable. Secondly, a model, where only a few pseudopotentials with small relative angular momentum have finite values, is studied, and it is clarified how the excitonic phase is destroyed as intra-layer pseudopotential becomes larger. The importance of the intra-layer repulsive interaction at distance twice of the magnetic length for the destruction of the excitonic phase is found.Comment: 7 pages, 7 figure