Finite symmetric functions with non-trivial arity gap

Given an $n$-ary $k-$valued function $f$, $gap(f)$ denotes the essential arity gap of $f$ which is the minimal number of essential variables in $f$ which become fictive when identifying any two distinct essential variables in $f$. In the present paper we study the properties of the symmetric function with non-trivial arity gap ($2\leq gap(f)$). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable.Comment: 12 page

M-Solid Subvarieties of some Varieties of Commutative Semigroups

∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.The basic concepts are M -hyperidentities, where M is a monoid of hypersubstitutions. The set of all M -solid varieties of semigroups forms a complete sublattice of the lattice of all varieties of semigroups. We fix some specific varieties V of commutative semigroups and study the set of all M -solid subvarieties of V , in particular, if V is nilpotent

Binary black hole late inspiral: Simulations for gravitational wave observations

Coalescing binary black hole mergers are expected to be the strongest gravitational wave sources for ground-based interferometers, such as the LIGO, VIRGO, and GEO600, as well as the space-based interferometer LISA. Until recently it has been impossible to reliably derive the predictions of General Relativity for the final merger stage, which takes place in the strong-field regime. Recent progress in numerical relativity simulations is, however, revolutionizing our understanding of these systems. We examine here the specific case of merging equal-mass Schwarzschild black holes in detail, presenting new simulations in which the black holes start in the late inspiral stage on orbits with very low eccentricity and evolve for ~1200M through ~7 orbits before merging. We study the accuracy and consistency of our simulations and the resulting gravitational waveforms, which encompass ~14 cycles before merger, and highlight the importance of using frequency (rather than time) to set the physical reference when comparing models. Matching our results to PN calculations for the earlier parts of the inspiral provides a combined waveform with less than half a cycle of accumulated phase error through the entire coalescence. Using this waveform, we calculate signal-to-noise ratios (SNRs) for iLIGO, adLIGO, and LISA, highlighting the contributions from the late-inspiral and merger-ringdown parts of the waveform which can now be simulated numerically. Contour plots of SNR as a function of z and M show that adLIGO can achieve SNR >~ 10 for some intermediate-mass binary black holes (IMBBHs) out to z ~ 1, and that LISA can see massive binary black holes (MBBHs) in the range 3x10^4 100 out to the earliest epochs of structure formation at z > 15.Comment: 17 pages, 20 figures. Final published versio

Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole

Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favorable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice stretching can be avoided by using excision and/or shift

Betreuungsindex in Pflegeheimen : Entwicklung und Validierung eines neuen Instruments zur Beurteilung von Betreuungsqualität in Pflegeheimen

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)Hintergrund: Derzeit gibt es in der Literatur kein geeignetes Instrument zur Beurteilung der Betreuungsqualität in Pflegeheimen. Die Autoren haben deshalb ein neues Instrument, den Betreuungsindex in Pflegeheimen (Nursing Home Care Index, NCI), konzipiert und getestet. Material und Methode: Betreuungsqualität wird in der Literatur in 8 Dimensionen definiert. Es wurde ein Fragebogen mit 42 Fragen aus 12 validierten Messinstrumenten entwickelt. Der Originalfragebogen wurde mit 320 Mitarbeitern aus 15 Alteneinrichtungen getestet. Die Daten wurden mithilfe einer Faktorenanalyse und Cronbachs α untersucht und auf 3 Faktoren und 16 Fragen reduziert. Das revidierte Instrument wurde in einer weiteren Studie mit 136 Mitarbeitern auf seine Anwendbarkeit überprüft. Ergebnisse: Als Ergebnis der Faktorenanalyse konnten 16 Items mit einer 3-Faktoren-Struktur, d. h. soziale Teilhabe, emotionales Wohlbefinden und Selbstbestimmung, identifiziert werden. Diese 3 Faktoren erklären 51,2% der Gesamtvarianz. Die Reliabilität der Gesamtskala beträgt 0,87, die der 3 Subskalen Selbstbestimmung 0,86, emotionales Wohlbefinden 0,71 und soziale Beziehungen bzw. Teilhabe 0,78. Die Gesamtpunktezahl des NCI erlaubt eine Kategorisierung der Betreuungsqualität in den 3 Abstufungen gut, ausreichend und dringender Verbesserungsbedarf. Schlussfolgerungen: Der NCI hat eine doppelte Funktion. Einerseits dient er Mitarbeitern und dem Heimmanagement als internes Qualitätssicherungsinstrument. Andererseits könnte es zukünftig Angehörigen von potenziellen Heimbewohnern die Möglichkeit bieten, die Betreuungsqualität verschiedener Pflegeheime zu vergleichen. Background: There is currently no adequate tool in the literature for assessing the quality of care in nursing homes. Therefore, we developed and tested a new instrument the Nursing Home Care Index (NCI). Methods: Quality of care is defined in the literature by 8 dimensions. An instrument with 42 questions of 12 validated scales was implemented. The new instrument was tested on 320 staff members in 15 nursing homes. The data were examined with the help of factor analysis and Cronbach’s α, which reduced the factors to 3 and the questions to 16. Finally the revised scale was tested in a further pilot study with 136 staff members. Results: The revised scale consists of 16 items. Based on the factor analysis, a 3-factor structure, namely social relationships, personal well-being, and self-determination were identified. These 3 factors explained 51.2% of total variance. Overall Cronbach’s α was 0.87. The α reliability for the subscales was 0.86 (self-determination), 71 personal well-being, and 0.78 social relationship, respectively. Based on the NCI score, quality of care can be categorized into 3 classes: good, adequate, and urgent need for action. Conclusions: The NCI has a double function. Nursing staff and management can now use the NCI to conduct internal quality assurance regarding their caring efforts. In the future, the NCI can become a useful tool for families and residents to compare the quality of care in different nursing homes

Representations of ordered doppelsemigroups by binary relations

We extend the study of doppelsemigroups and introduce the notion of an ordered doppelsemigroup. We construct the ordered doppelsemigroup of binary relations on an arbitrary set and prove that every ordered doppelsemigroup is isomorphic to some ordered doppelsemigroup of binary relations. In particular, we obtain an analogue of Cayley’s theorem for semigroups in the class of doppelsemigroups. We also describe the representations of ordered doppelsemigroups by binary transitive relations

On mappings of terms determined by hypersubstitutions

The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions forms a monoid. On the other hand, one can modify each hypersubstitution to any mapping on the set of terms. For this we can consider mappings ρ from the set of all hypersubstitutions into the set of all mappings on the set of all terms. If for each hypersubstitution σ the application of ρ(σ) to any identity in a given variety V is again an identity in V , so that variety is called ρ-solid. The concept of a ρ-solid variety generalizes the concept of a solid variety. In the present paper, we determine all ρ-solid varieties of semigroups for particular mappings ρ