One Quantifier Alternation in First-Order Logic with Modular Predicates

Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison $x<y$ and predicates for $x \equiv i \mod n$ has been investigated by Barrington, Compton, Straubing and Therien. The study of FO[<,MOD]-fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two-variable fragment FO2[<,MOD] is decidable. In this paper we continue this line of work. We give an effective algebraic characterization of the word languages in Sigma2[<,MOD]. The fragment Sigma2 consists of first-order formulas in prenex normal form with two blocks of quantifiers starting with an existential block. In addition we show that Delta2[<,MOD], the largest subclass of Sigma2[<,MOD] which is closed under negation, has the same expressive power as two-variable logic FO2[<,MOD]. This generalizes the result FO2[<] = Delta2[<] of Therien and Wilke to modular predicates. As a byproduct, we obtain another decidable characterization of FO2[<,MOD]

Beyond Rainbow-Ladder in bound state equations

In this work we devise a new method to study quark anti-quark interactions beyond simple ladder-exchange that yield massless pions in the chiral limit. The method is based on the requirement to have a representation of the quark-gluon vertex that is explicitly given in terms of quark dressings functions. We outline a general procedure to generate the Bethe-Salpeter kernel for a given vertex representation. Our method allows not only the identification of the mesons' masses but also the extraction of their Bethe-Salpeter wave functions exposing their internal structure. We exemplify our method with vertex models that are of phenomenological interest.Comment: 13 pages, 6 figures; v2: typos corrected, colors improve

Zur Kenntnis der Rädertierfauna des Kinda-Stausees in Zentral-Burma (Aschelminthes: Rotatoria) : mit 1 Tabelle

Erstmals wird die Rädertierfauna des 1985 neu entstandenen Kinda-Stausees im Einzugsgebiet des Panlaung-Flusses in Burma (Myanmar) beschrieben und im verbreitungsgeschichtlichen Zusammenhang diskutiert. Die Arbeit ist zugleich die bislang umfassendste Untersuchung von Rotatorien aus dieser tiergeographisch interessanten asiatischen Region. Die Plankton- und Aufwuchsproben wurden auf mehreren Exkursionen 1987-89 gesammelt. Insgesamt konnten 94 monogononte und 5 bdelloide Rädertier-Arten nachgewiesen werden; davon ist Wulfertia kindensis neu für die Wissenschaft. Die überwiegende Zahl der Spezies sind Kosmopoliten.The fauna of rotifers (Rotatoria) from the newly built Kinda-Reservoir (1985) is described. The man-made lake is located in central Myanmar (formerly Burma) on the Panlaung Chaung, the left hand tributary to the Irrawaddy River. The impoundment serves the power generation and irrigation purposes. Since 1987 to 1989 plankton and periphyton sampies were collected which yielded 94 monogonont and 5 bdelloid species; only 7 belong to the tropical and subtropical fauna the remaining have cosmopolitan distribution. The communication provides the first comprehensive record of the rotifer fauna of Burma, one species Wulfertia kiruiensis was first described

The beta-relaxation dynamics of a simple liquid

We present a detailed analysis of the beta-relaxation dynamics of a simple glass former, a Lennard-Jones system with a stochastic dynamics. By testing the various predictions of mode-coupling theory, including the recently proposed corrections to the asymptotic scaling laws, we come to the conclusion that in this time regime the dynamics is described very well by this theory.Comment: 9 pages of Latex, 4 figure

Characterizing classes of regular languages using prefix codes of bounded synchronization delay

In this paper we continue a classical work of Sch\"utzenberger on codes with bounded synchronization delay. He was interested to characterize those regular languages where the groups in the syntactic monoid belong to a variety $H$. He allowed operations on the language side which are union, intersection, concatenation and modified Kleene-star involving a mapping of a prefix code of bounded synchronization delay to a group $G\in H$, but no complementation. In our notation this leads to the language classes $SD_G(A^\infty)$ and $SD_H(A^\infty$). Our main result shows that $SD_H(A^\infty)$ always corresponds to the languages having syntactic monoids where all subgroups are in $H$. Sch\"utzenberger showed this for a variety $H$ if $H$ contains Abelian groups, only. Our method shows the general result for all $H$ directly on finite and infinite words. Furthermore, we introduce the notion of local Rees products which refers to a simple type of classical Rees extensions. We give a decomposition of a monoid in terms of its groups and local Rees products. This gives a somewhat similar, but simpler decomposition than in Rhodes' synthesis theorem. Moreover, we need a singly exponential number of operations, only. Finally, our decomposition yields an answer to a question in a recent paper of Almeida and Kl\'ima about varieties that are closed under Rees products