The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence

Grant No. SRF-PRG-2557-02.A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.authorsversionpublishe

Presentations for three remarkable submonoids of the dihedral inverse monoid on a finite set

In this paper we consider the submonoids $\mathcal{OPDI}_n$, $\mathcal{MDI}_n$ and $\mathcal{ODI}_n$ of the dihedral inverse monoid $\mathcal{DI}_n$ of all orientation-preserving, monotone and order-preserving transformations, respectively. Our goal is to exhibit presentations for each of these three monoids.Comment: arXiv admin note: text overlap with arXiv:2205.0219

On monoids of endomorphisms of a cycle graph

In this paper we consider endomorphisms of an undirected cycle graph from Semigroup Theory perspective. Our main aim is to present a process to determine sets of generators with minimal cardinality for the monoids $wEnd(C_n)$ and $End(C_n)$ of all weak endomorphisms and all endomorphisms of an undirected cycle graph $C_n$ with $n$ vertices. We also describe Green's relations and regularity of these monoids and calculate their cardinalities

The use of mobile phones for skin tumor screening

A lot of importance is attributed to mobile telemedicine these days, a topic that encompasses a wide and ever growing range of applications. Small, handheld devices such as camera mobile phones have come into every day use providing technically sophisticated tasks on a user-friendly level and can therefore be easily used in various fields of telemedicine. Dermatology is a perfect candidate for the use of telemedicine tools in general, as well as mobile devices in particular. The unique aspect of mobile teledermatology is that this system represents a filtering, or triage system, allowing a sensitive approach for the management of patients with emergent skin diseases. In order to investigate the feasibility of teleconsultation using a new generation of cellular phones, a clinical study to evaluate the accuracy of online diagnosis of skin tumours was conducted. Teledermoscopy represents a recent development of teledermatology that might add up additional information in the diagnosis of pigmented skin lesions. Teledermatology, mobile as well as stationary, can advance the reliability of diagnosis by expert consultations without expensive and time-consuming relocations. Consequently, the quality of patient's care can be raised and the costs of the health care system can be reduced

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

Zusammenfassung: 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 8Dimensionen definiert. Es wurde ein Fragebogen mit 42Fragen aus 12validierten Messinstrumenten entwickelt. Der Originalfragebogen wurde mit 320Mitarbeitern aus 15Alteneinrichtungen getestet. Die Daten wurden mithilfe einer Faktorenanalyse und Cronbachsα untersucht und auf 3Faktoren und 16Fragen reduziert. Das revidierte Instrument wurde in einer weiteren Studie mit 136Mitarbeitern auf seine Anwendbarkeit überprüft. Ergebnisse: Als Ergebnis der Faktorenanalyse konnten 16Items mit einer 3-Faktoren-Struktur, d.h. soziale Teilhabe, emotionales Wohlbefinden und Selbstbestimmung, identifiziert werden. Diese 3Faktoren erklären 51,2% der Gesamtvarianz. Die Reliabilität der Gesamtskala beträgt 0,87, die der 3Subskalen 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 3Abstufungen 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 vergleiche

Momentum constraint relaxation

Full relativistic simulations in three dimensions invariably develop runaway modes that grow exponentially and are accompanied by violations of the Hamiltonian and momentum constraints. Recently, we introduced a numerical method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint violation and helps improve the quality of the numerical model. We present here a method that controls the violation of the momentum constraint. The method is based on the addition of a longitudinal component to the traceless extrinsic curvature generated by a vector potential w_i, as outlined by York. The components of w_i are relaxed to solve approximately the momentum constraint equations, pushing slowly the evolution toward the space of solutions of the constraint equations. We test this method with simulations of binary neutron stars in circular orbits and show that effectively controls the growth of the aforementioned violations. We also show that a full numerical enforcement of the constraints, as opposed to the gentle correction of the momentum relaxation scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More detailed description of the algorithms are provided. Final published versio

Towards absorbing outer boundaries in General Relativity

We construct exact solutions to the Bianchi equations on a flat spacetime background. When the constraints are satisfied, these solutions represent in- and outgoing linearized gravitational radiation. We then consider the Bianchi equations on a subset of flat spacetime of the form [0,T] x B_R, where B_R is a ball of radius R, and analyze different kinds of boundary conditions on \partial B_R. Our main results are: i) We give an explicit analytic example showing that boundary conditions obtained from freezing the incoming characteristic fields to their initial values are not compatible with the constraints. ii) With the help of the exact solutions constructed, we determine the amount of artificial reflection of gravitational radiation from constraint-preserving boundary conditions which freeze the Weyl scalar Psi_0 to its initial value. For monochromatic radiation with wave number k and arbitrary angular momentum number l >= 2, the amount of reflection decays as 1/(kR)^4 for large kR. iii) For each L >= 2, we construct new local constraint-preserving boundary conditions which perfectly absorb linearized radiation with l <= L. (iv) We generalize our analysis to a weakly curved background of mass M, and compute first order corrections in M/R to the reflection coefficients for quadrupolar odd-parity radiation. For our new boundary condition with L=2, the reflection coefficient is smaller than the one for the freezing Psi_0 boundary condition by a factor of M/R for kR > 1.04. Implications of these results for numerical simulations of binary black holes on finite domains are discussed.Comment: minor revisions, 30 pages, 6 figure

Beam Test of Silicon Strip Sensors for the ZEUS Micro Vertex Detector

For the HERA upgrade, the ZEUS experiment has designed and installed a high precision Micro Vertex Detector (MVD) using single sided micro-strip sensors with capacitive charge division. The sensors have a readout pitch of 120 microns, with five intermediate strips (20 micron strip pitch). An extensive test program has been carried out at the DESY-II testbeam facility. In this paper we describe the setup developed to test the ZEUS MVD sensors and the results obtained on both irradiated and non-irradiated single sided micro-strip detectors with rectangular and trapezoidal geometries. The performances of the sensors coupled to the readout electronics (HELIX chip, version 2.2) have been studied in detail, achieving a good description by a Monte Carlo simulation. Measurements of the position resolution as a function of the angle of incidence are presented, focusing in particular on the comparison between standard and newly developed reconstruction algorithms.Comment: 41 pages, 21 figures, 2 tables, accepted for publication in NIM