All degree six local unitary invariants of k qudits

We give explicit index-free formulae for all the degree six (and also degree four and two) algebraically independent local unitary invariant polynomials for finite dimensional k-partite pure and mixed quantum states. We carry out this by the use of graph-technical methods, which provides illustrations for this abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom

The Forum of European Geological Surveys Geochemistry Task Group 1994-1996 inventory

The Forum of European Geological Surveys (FOREGS) includes representatives from 33 European countries and is responsible for co-ordinating Geological Survey activities in Europe. The FOREGS Geochemistry Task Group was established in 1994 to develop a strategy for the preparation of European geochemical maps following the recommendations of the International Geological Correlation Programme (IGCP) Project 259 ‘International Geochemical Mapping’ (now the International Union of Geological Sciences (IUGS) /International Association of Geochemistry and Cosmochemistry (IAGC) Working Group on Global Geochemical Baselines). The FOREGS geochemistry programme is aimed at preparing a standardised European geochemical baseline to IGCP-259 standards. The principal aims of this dataset will be for environmental purposes, as a baseline for the assessment of the extent and distribution of contaminated land in the context of variations in the natural geochemical background, but it will also have applications in resource assessment and for the development of policy for the sustainable management of metalliferous mineral and other resources. The first phase of the programme was the compilation of an inventory of geochemical data based on the results of a questionnaire completed by Geological Surveys and related organisations throughout the FOREGS community. The results show that the sample types which have been used most extensively are stream sediment (26% coverage), surface water (19% coverage) and soil (11% coverage). Stream sediments have been collected using a narrow range of mesh sizes (< 150–< 200 μm), but soil samples have been collected according to two different conventions: some surveys used a similar mesh size range to that used for stream sediments while others employed the < 1000 or < 2000 μm fractions traditionally used by soil surveys. Sample densities range from 1 sample per 0.5 km2 to 1 per 3500 km2. Various analytical methods have been used, but most of the available data have been calibrated using international reference materials, and data for the most important of the potentially harmful elements (PHEs) are available for most datasets. Systematic radiometric data are available for only a small proportion of Europe, a situation which compares very unfavourably with that in Australia, North America, the former Soviet Union and many developing countries. Recommendations are made for increasing the compatibility of geochemical methods between national geochemical surveys as a basis for the preparation of a series of European geochemical maps. The next stage of the FOREGS Geochemistry Task Group will be the collection of the Global Reference Network of samples against which to standardise national datasets according to the methods recommended in the final report of the IGCP 259 programme

Analysis of Surface Runoff

A mathematical model of surface runoff is presented which is of use in building a model of erosion processes. The method used for deriving the conceptual model of surface runoff is based on the mathematical expression of the basic laws of movement of water -- the equation of continuity and the equation of motion. Both equations form a system of nonlinear partial differential equations with two unknown functions expressing the depth and velocity of the movement of water along the slope, in dependence on their location on the slope, and time. The input variables of the model are the intensity and direction of the impinging raindrops, the intensity of infiltration and the physical characteristics of the slope (gradient, length and properties of soil surface). Extensive laboratory experiments have been carried out to determine the functional dependence of tangential stress on the depth and rate of runoff from different types of soil surfaces. Further, the conceptual model of surface runoff has been simplified to a kinematic one by using a simple relation between depth and rate of surface runoff instead of the equation of motion. Two empirical parameters of this relation have been determined by using data from the above mentioned laboratory experiments during calibration of the kinematic model. The kinematic model is recommended because of its simplicity with regard to simulation of the surface runoff formation from individual slopes within the watershed. The model is a multipurpose one. It may be used either for hydrological purposes (simulation of surface runoff characteristics) or for soil conservation purposes. The model outputs are surface characteristics (depth, velocity, rate). It is possible by comparing the surface runoff velocity with the critical nonscouring velocity for given field conditions to determine the critical slope length which is the basis for planning efficient soil conservation measures

Erosion and Water Quality as Modeled by Creams: A Case Study of the Sedlicky Catchment

In the process of verifying and validating the models of agricultural nonpoint source pollution at IIASA, a study was made of the Sedlicky brook (Bohemia, Czechoslovakia) case. The CREAMS model, verified at the Samsin research area (Czechoslovakia) has been used as the mathematical instrument. The validation results of the CREAMS model for the boundary conditions between the field level and the watershed level seem to show that under certain conditions, it can be applied to small watersheds. For large watersheds, modification of the hydrology submodel is necessary in order to describe the comprehensive hydrologic phenomena, particularly, the interflow and some of the subsurface flow

Procedures, Numerical Parameters and Coefficients of the Creams Model: Application and Verification in Czechoslovakia

Problems of agricultural nonpoint source pollution have been investigated by the Resources and Environment Area (Task 2) at IIASA. The CREAMS model has been used as a mathematical aid to arrive at an in-depth understanding of erosion and to predict its influence on agriculture. The CREAMS model was created using data from North America. Investigations of its general use and verification under various conditions were useful. This paper summarizes the results of the verification of this model in a research area in Czechoslovakia and focuses attention on certain points which must be carefully considered during application of this model

Three fermions with six single particle states can be entangled in two inequivalent ways

Using a generalization of Cayley's hyperdeterminant as a new measure of tripartite fermionic entanglement we obtain the SLOCC classification of three-fermion systems with six single particle states. A special subclass of such three-fermion systems is shown to have the same properties as the well-known three-qubit ones. Our results can be presented in a unified way using Freudenthal triple systems based on cubic Jordan algebras. For systems with an arbitrary number of fermions and single particle states we propose the Pl\"ucker relations as a sufficient and necessary condition of separability.Comment: 23 pages LATE

On the algebra of local unitary invariants of pure and mixed quantum states

We study the structure of the inverse limit of the graded algebras of local unitary invariant polynomials using its Hilbert series. For k subsystems, we conjecture that the inverse limit is a free algebra and the number of algebraically independent generators with homogenous degree 2m equals the number of conjugacy classes of index m subgroups in a free group on k-1 generators. Similarly, we conjecture that the inverse limit in the case of k-partite mixed state invariants is free and the number of algebraically independent generators with homogenous degree m equals the number of conjugacy classes of index m subgroups in a free group on k generators. The two conjectures are shown to be equivalent. To illustrate the equivalence, using the representation theory of the unitary groups, we obtain all invariants in the m=2 graded parts and express them in a simple form both in the case of mixed and pure states. The transformation between the two forms is also derived. Analogous invariants of higher degree are also introduced.Comment: 14 pages, no figure

Factors affecting hotel selection: Greek customers' perception

Selection of hotel is of high priority and significance for tourists and entails a complicated decision-making process. The paper aims at identifying the most significant hotel selection factors taken into account by Greek customers. An empirical research study was conducted using an online survey. Ten factors identified by literature review included in the investigation. The findings indicate that Cleanliness is the most important factor in the selection of accommodation, followed by Price and Staff. Considering the priorities of tourists, hotel managers may design more effectively their segmentation, targeting and positioning strategy to ensure that their offerings match the needs and wants of their guests

Factors affecting hotel selection: Greek customers' perception

Selection of hotel is of high priority and significance for tourists and entails a complicated decision-making process. The paper aims at identifying the most significant hotel selection factors taken into account by Greek customers. An empirical research study was conducted using an online survey. Ten factors identified by literature review included in the investigation. The findings indicate that Cleanliness is the most important factor in the selection of accommodation, followed by Price and Staff. Considering the priorities of tourists, hotel managers may design more effectively their segmentation, targeting and positioning strategy to ensure that their offerings match the needs and wants of their guests