639 research outputs found
Finite symmetric functions with non-trivial arity gap
Given an -ary
valued function , denotes the essential arity gap of
which is the minimal number of essential variables in which become fictive
when identifying any two distinct essential variables in . In the present
paper we study the properties of the symmetric function with non-trivial arity
gap (). 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
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
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
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
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