Measurement and transformation of continuously modulated fields using a short-time measurement approach

Near-field measurements, which are performed in-situ, may suffer from the fact that the antenna under test (AUT) cannot be accessed to transmit or receive a specifically tailored test signal. In some scenarios, it might also be desired to test the AUT during its real operation state, especially when it comes to the verification of antenna systems. Therefore, the need to handle time- and space-modulated fields in combination with a time-harmonic near-field to far-field transformation (NFFFT) arises. For the case where unmanned aerial vehicles (UAVs) carry the field probe in in-situ measurement scenarios, long observation times, required for the resolution of the frequency spectra of modulated fields, are detrimental due to the UAV movement resulting in blurred measurement positions. The short-time measurement (STM) approach, presented in this article, offers a way to transform the measured field data using a time-harmonic NFFFT with short observation times for the collection of the individual field samples. Measurements are shown which demonstrate the applicability of the STM approach for the measurement and transformation of continuously time-modulated fields in different measurement scenarios.</p

Irrationale und rationale Kognitionen als Determinanten positiver Emotionen

Der Rational-Emotiven-Theorie (RET) von Ellis zufolge, sind irrationale (d.h. rigide, übersteigerte) Gedanken Ursache maladaptiver Emotionen (z.B. Schuld, Angst). Positive Emotionen wurden hierbei bislang kaum empirisch untersucht. Eine erste experimentelle Szenariostudie überprüft daher, ob zentrale positive Emotionen (Dankbarkeit, Freude, Stolz, Überraschung, Zuversicht) in ihrer Intensität von der Rationalität der erlebenden Person abhängen. Alle Emotionen werden dann intensiver erlebt, wenn Rationalität bei der Stimulusperson vorlag. Für Freude und Stolz wird dieser Unterschied nicht signifikant. In einer zweiten experimentellen Szenariostudie sollten daher Freude und Stolz mittels forced-choice Antwortalternativen rationalen oder irrationalen Gedanken zugeordnet werden. Zudem wurden die über Kognition oder Emotion charakterisierten Stimuluspersonen hinsichtlich Selbstwertkonzept und Problemverarbeitungsfähigkeit eingeschätzt. Irrationale Gedanken werden signifikant häufiger mit Stolz verbunden, Selbstwertkonzept und Problemverarbeitungsfähigkeit wird bei Personen, die durch Irrationalität und Stolz charakterisiert sind, dysfunktionaler eingeschätzt. Zusätzlich erhobene emotionstheoretische Variablen (Typizität, Einflussweite, Funktionalität,(Un-)Lust, Aktivation, Dauer) bestätigen eine Klassifikation von Stolz als maladaptive und Freude als adaptive Emotion

λ -Semidirect products of inverse monoids are weakly Schreier extensions

Funder: University of CambridgeAbstract: A split extension of monoids with kernel k:N→G, cokernel e:G→H and splitting s:H→G is weakly Schreier if each element g∈G can be written g=k(n)se(g) for some n∈N. The characterization of weakly Schreier extensions allows them to be viewed as something akin to a weak semidirect product. The motivating examples of such extensions are the Artin glueings of topological spaces and, of course, the Schreier extensions of monoids which they generalise. In this paper we show that the λ-semidirect products of inverse monoids are also examples of weakly Schreier extensions. The characterization of weakly Schreier extensions sheds some light on the structure of λ-semidirect products. The set of weakly Schreier extensions between two monoids comes equipped with a natural poset structure, which induces an order on the set of λ-semidirect products between two inverse monoids. We show that Artin glueings are in fact λ-semidirect products and inspired by this identify a class of Artin-like λ-semidirect products. We show that joins exist for this special class of λ-semidirect product in the aforementioned order

λ\lambda -Semidirect products of inverse monoids are weakly Schreier extensions

Funder: University of CambridgeAbstractA split extension of monoids with kernel $$k :N \rightarrow G$$ k : N → G , cokernel $$e :G \rightarrow H$$ e : G → H and splitting $$s :H \rightarrow G$$ s : H → G is weakly Schreier if each element $$g \in G$$ g ∈ G can be written $$g = k(n)se(g)$$ g = k ( n ) s e ( g ) for some $$n \in N$$ n ∈ N . The characterization of weakly Schreier extensions allows them to be viewed as something akin to a weak semidirect product. The motivating examples of such extensions are the Artin glueings of topological spaces and, of course, the Schreier extensions of monoids which they generalise. In this paper we show that the $$\lambda$$ λ -semidirect products of inverse monoids are also examples of weakly Schreier extensions. The characterization of weakly Schreier extensions sheds some light on the structure of $$\lambda$$ λ -semidirect products. The set of weakly Schreier extensions between two monoids comes equipped with a natural poset structure, which induces an order on the set of $$\lambda$$ λ -semidirect products between two inverse monoids. We show that Artin glueings are in fact $$\lambda$$ λ -semidirect products and inspired by this identify a class of Artin-like $$\lambda$$ λ -semidirect products. We show that joins exist for this special class of $$\lambda$$ λ -semidirect product in the aforementioned order.</jats:p

Baer sums for a natural class of monoid extensions

AbstractIt is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of extensions to a natural class of extensions of monoids, the cosetal extensions. An extension "Equation missing" is cosetal if for all $$g,g' \in G$$ g , g ′ ∈ G in which $$e(g) = e(g')$$ e ( g ) = e ( g ′ ) , there exists a (not necessarily unique) $$n \in N$$ n ∈ N such that $$g = k(n)g'$$ g = k ( n ) g ′ . These extensions generalise the notion of special Schreier extensions, which are themselves examples of Schreier extensions. Just as in the group case where a semidirect product could be associated to each extension with abelian kernel, we show that to each cosetal extension (with abelian group kernel), we can uniquely associate a weakly Schreier split extension. The characterization of weakly Schreier split extensions is combined with a suitable notion of a factor set to provide a cohomology group granting a full characterization of cosetal extensions, as well as supplying a Baer sum.</jats:p