Embedding a quantum rank three quadric in a quantum P3

We continue the classification, begun in [11], [14] and [12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadric hypersurfcice in P³. In this paper, we consider those cases where the quadric has rank 3. We also give sufficient conditions for the point scheme of any quadratic regular algebra of global dimension 4 to be the graph of an automorphism.     

On improper interval edge colourings

We study improper interval edge colourings, defined by the requirement that the edge colours around each vertex form an integer interval. For the corresponding chromatic invariant (being the maximum number of colours in such a colouring), we present upper and lower bounds and discuss their qualities; also, we determine its values and estimates for graphs of various families, like wheels, prisms or complete graphs. The study of this parameter was inspired by the interval colouring, introduced by Asratian, Kamalian (1987). The difference is that we relax the requirement on the original colouring to be proper.     

Radon Measure-Valued Solutions for a Class of Quasilinear Parabolic Equations

Initial value problems for quasilinear parabolic equations having Radon measures as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. In contrast, it is the purpose of this paper to define and investigate solutions that for positive times take values in the space of the Radon measures of the initial data. We call such solutions measure-valued, in contrast to function-valued solutionspreviously considered in the literature. We first show that there is a natural notion of measure-valued solution of problem (P) below, in spite of its nonlinear character. A major consequence of our definition is that, if the space dimension is greater than one, the concentrated part of the solution with respect to the Newtonian capacity is constant in time. Subsequently, we prove that there exists exactly one solution of the problem, such that the diffuse part with respect to the Newtonian capacity of the singular part of the solution (with respect to the Lebesgue measure) is concentrated for almost every positive time on the set where “the regular part (with respect to the Lebesgue measure) is large”. Moreover, using a family of entropy inequalities we demonstrate that the singular part of the solution is nonincreasing in time. Finally, the regularity problem is addressed, as we give conditions (depending on the space dimension, the initial data and the rate of convergence at infinity of the nonlinearity ψ) to ensure that the measure-valued solution of problem (P) is, in fact, function-valued.     

Multi-objective decision analysis for competence-oriented project portfolio selection

This paper develops a multi-objective optimization model for project portfolio selection taking employee competencies and their evolution into account. The objectives can include economic gains as well as gains expressed in terms of aggregated competence increments according to pre-defined profiles. In order to determine Pareto-optimal solutions, the overall problem is decomposed into a master problem addressing the portfolio selection itself, and a slave problem dealing with a suitable assignment of personnel to the work packages of the selected projects over time. We provide an asymptotic approximation of the problem by a linearized formulation, which allows an efficient and exact solution of the slave problem. For the solution of the master problem, we compare the multi-objective metaheuristics NSGA-II and P-ACO. Experimental results both for synthetically generated test instances and for real-world test instances, based on an application case from the E-Commerce Competence Center Austria, are presented.     

Benchmarking culture in Europe: A data envelopment analysis approach to identify city-specific strengths

Culture is an integral part of a city's quality of life, a driver of urban change, and a genuine economic sector. To support benchmarking of urban culture and facilitate peer learning amongst policymakers, the European Commission has recently created the ‘Cultural and Creative Cities Index’. While this index builds on a standardised method to aggregate 29 indicators for the 155 selected cities, it is explicitly acknowledged that a ‘gold standard’ for a ‘Cultural and Creative City’ does not exist. Instead, different approaches should be allowed for in capturing cities’ cultural and creative vitality. This is the point of departure for this paper, which employs a Benefit-of-the-Doubt (BoD) modelling approach to allow cities to combine such respect for performance diversity with peer learning and benchmarking. Expert-based weights are used to provide expert-consistent bounds for the shares of key dimensions in a city's final BoD index value. We identify three city clusters, amongst which there are large performance differences. Accordingly, we focus on the within-group identification of peer cities and target values, which we illustrate in more detail for Bilbao, Krak?w and Umeå, towards the formulation of fit-for-purpose policy measures that can support culture-led development.     

Preparation and structural characterisation of methoxybis(trimethylsilyl)silyl potassium and its condensation product

Depending on the conditions the reaction of tris(trimethylsilyl)methoxysilane (1) with potassium tert-butoxide either in benzene and in the presence of 18-crown-6 or in THF gives either the crown ether adduct of potassium-methoxybis(trimethylsilyl)silane (2), or 2-methoxytetrakis(trimethylsilyl)disilanyl potassium (3).     

Synthesis of unique cagelike thiacalix[4]arene derivatives in a 1,3-alternate conformation

A novel type of doubly bridged thiacalix[4]arenes in the 1,3-alternate conformation has been prepared by direct aminolysis reaction of easily accessible thiacalix[4]arene tetraacetates with alpha,omega-diamines. Despite the high excess of diamine, both sites of a 1,3-alternate conformer can be intramolecularly bridged to form the cagelike structures in high yields. Optimum results were obtained using 1,2-ethanediamine as bridging units. X-ray analysis of the novel cagelike molecules revealed a highly preorganized array of -C(O)-NH- bonds pointing to the interior of the cavity.     

Antimicrobial and Anticancer Application of Silver(I) Dipeptide Complexes

Three silver(I) dipeptide complexes [Ag(GlyGly)]_n(NO₃)_n (AgGlyGly), [Ag₂(GlyAla)(NO₃)₂]_n (AgGlyAla) and [Ag₂(HGlyAsp)(NO₃)]_n (AgGlyAsp) were prepared, investigated and characterized by vibrational spectroscopy (mid-IR), elemental and thermogravimetric analysis and mass spectrometry. For AgGlyGly, X-ray crystallography was also performed. Their stability in biological testing media was verified by time-dependent NMR measurements. Their in vitro antimicrobial activity was evaluated against selected pathogenic microorganisms. Moreover, the influence of silver(I) dipeptide complexes on microbial film formation was described. Further, the cytotoxicity of the complexes against selected cancer cells (BLM, MDA-MB-231, HeLa, HCT116, MCF-7 and Jurkat) and fibroblasts (BJ-5ta) using a colorimetric MTS assay was tested, and the selectivity index (SI) was identified. The mechanism of action of Ag(I) dipeptide complexes was elucidated and discussed by the study in terms of their binding affinity toward the CT DNA, the ability to cleave the DNA and the ability to influence numbers of cells within each cell cycle phase. The new silver(I) dipeptide complexes are able to bind into DNA by noncovalent interaction, and the topoisomerase I inhibition study showed that the studied complexes inhibit its activity at a concentration of 15 μM.