COMMUTATION PROPERTIES OF THE FORM SUM OF POSITIVE, SYMMETRIC OPERATORS

A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation properties of the form sum extension are observed

Positive forms on Banach spaces

The first representation theorem establishes a correspondence between positive, self-adjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying space is a reflexive Banach space. In particular, the construction of the Friedrichs extension and the form sum of positive operators can be carried over to this case

On Fuglede’s conjecture and the existence of universal spectra

Recent methods developed by, Too [18], Kolountzakis and Matolcsi [7] have led to counterexamples to Fugelde's Spectral Set Conjecture in both directions. Namely, in R(5) Tao produced a spectral set which is not a tile, while Kolountzakis and Matolcsi showed all example of a nonspectral tile. In search of lower dimensional nonspectral tiles we were led to investigate the Universal Spectrum Conjecture (USC) of Lagarias and Wang [14]. In particular, we prove here that the USC and the "tile --> spectral " direction of Fuglede's conjecture are equivalent in any dimensions. Also, we show by an example that the sufficient condition of Lagarias and Szabo [13] for the existence of universal spectra is not necessary. This fact causes considerable difficulties in producing lower dimensional examples of tiles which have no spectra. We overcome these difficulties by invoking some ideas of Revesz and Farkas [2], and obtain nonspectral tiles in R(3)

Kelet-Közép-Európa térszerkezeti képe = The spatial structure of East-Central Europe

The aim of this paper is to explore and analyze the main characteristics of East- Central Europe’s spatial structure and its changes during the recent years. In the first section we summarize the theoretical foundations of the notion and the elements of spatial structure, mainly based on our previous research. We discuss the complex way of the description of spatial structure (the regional development inequalities and the differences of socio-economic concentration), and analyze its three main elements (node, axis, zone). The next part reviews some recent and older literature about the changing ideas and approaches of spatial structure of Europe. We also describe the macroregion’s position in the spatial structure of Europe. The main difference between the point of views is whether the continent shows a polycentric spatial structure or a centre-periphery model, and whether East-Central Europe is a semi-periphery of the continent or a potential economic centre. Finally, based on the literature synthesis and our own calculations based on regional data provided by Eurostat, we trace the spatial structure of the macroregion. The more and less developed zones show a West–East contrast with some segregated, more developed regions in the Eastern part, but there isn’t a large socio-economic central area. The nodes are not concentrated, they have different social and economic weights, and the axes are probably the Pan-European corridors. The main change of the spatial structure in the 2000s is that the Southern part of the macroregion has become more homogeneous (a less developed zone)

Characterizing and quantifying the incompatibility of quantum instruments

Incompatibility of quantum devices is one of the cornerstones of quantum theory, and the incompatibility of quantum measurements and channels has been linked to quantum advantage in certain information theoretic tasks. In this work, we focus on the less well-explored question of the incompatibility of quantum instruments, that is, devices that describe the measurement process in its entirety, accounting for both the classical measurement outcome and the quantum post-measurement state. In particular, we focus on the recently introduced notion of parallel compatibility of instruments, which has been argued to be a natural notion of instrument compatibility. We introduce -- similarly to the case of measurements and channels -- the incompatibility robustness of quantum instruments and derive universal bounds on it. We then prove that post-processing of quantum instruments is a free operation for parallel compatibility. Last, we provide families of instruments for which our bounds are tight, and families of compatible indecomposable instruments.Comment: 10 pages, typos fixed, minor issues fixe

An invertible map between Bell non-local and contextuality scenarios

We present an invertible map between correlations in any bipartite Bell scenario and behaviours in an indexed family of contextuality scenarios. The map takes local, quantum and non-signalling correlations to non-contextual, quantum and contextual behaviours, respectively. Consequently, we find that the membership problem of set of quantum behaviours in a contextuality scenario is undecidable and the set cannot be fully realised using finite dimensional quantum systems. Finally, we find that neither this set, nor its closure, can be the limit of any sequence of computable supersets, due to the result MIP*=RE. In particular, the semidefinite programming hierarchies in the literature cannot converge to the quantum set of behaviours nor its closure.Comment: Comments welcome

The effect of different substrates on morphological characteristics of acclimatized Bowiea volubilis

Before acclimatization of Bowiea volubilis, in vitro propagated bulbs were cleaned and separated into four sizes (from 6 to 15 mm). We formed a total of 10 groups with 30-30 individuals, distributing the sizes evenly. Four types of substrate (peat, perlite, coconut fiber, sand) and their mixtures of 50-50% were used. Previously we examined three parameters: length, diameter and weight of the bulbs; later the weight of the successfully acclimatized plants, the number and length of roots and leaves were measured. The acclimatization was done in one of the greenhouses of the Buda Arboretum, where the plants were grown with fleece covering till one month, irrigated every three days, without the use of nutrient replenishment and artificial lighting. After 3 month period, survived plants developed effectively on peat + perlite, sand + perlite and sand + peat mixtures. In these cases, we achieved the largest increases in roots, green parts, bulbs and total weight