Normal forms of ordinary linear differential equations in arbitrary characteristic

Fuchs' Theorem on the solutions of ordinary linear differential equations with regular singularities is extended to positive characteristic by proving a normal form theorem for the respective linear differential operators. This yields an explicit algorithm to compute a basis of solutions in characteristic p.Comment: 40 page

Learning to trade in an unbalanced market

We study the evolution of trading strategies in double auctions as the size of the market gets larger. When the number of buyers and sellers is balanced, Fano et al. (2011) show that the choice of the order-clearing rule (simultaneous or asynchronous) steers the emergence of fundamentally different strategic behavior. We extend their work to unbalanced markets, confirming their main result as well as that allocative inefficiency tends to zero. On the other hand, we discover that convergence to the competitive outcome takes place only when the market is large and that the long side of the market is more effective at improving its disadvantaged terms of trade under asynchronous order-clearing.Trading protocols; Market design; Allocative efficiency; Genetic Programming

The Archetypal Homoleptic Lanthanide Quadruple-Decker—Synthesis, Mechanistic Studies, and Quantum Chemical Investigations

The synthesis of the first well-defined neutral and homoleptic (same metal, same ligand) all-carbon-based quadruple-decker complexes [Sm$^{III/II/III}$$_{3}$(COT$^{1,4-SiiPr3}$)$_{4}$] (COT$^{1,4-SiiPr3}$=1,4-($^{i}$Pr$_{3}$Si)$_{3}$C$_{8}$H$_{6}$)) along with other unique sandwich complexes is shown. Reduction of [Sm$^{III}$(COT$^{1,4-SiiPr3}(BH$$_{4}$)(thf)] (COT$^{1,4-SiiPr3}$=1,4-($^{i}$Pr$_{3}$Si)$_{3}$C$_{8}$H$_{6}$) with KC$_{8}$ resulted in [Sm$^{III/II/III}$$_{3}$(COT$^{1,4-SiiPr3}$)$_{4}$] the first example of a homoleptic lanthanide quadruple-decker. As indicated by an analysis of the bond metrics in the solid-state, the inner Sm ion is present in the divalent oxidation state, while the outer ones are trivalent. This observation could be confirmed by quantum chemical calculations. Mechanistic studies revealed not only insight into possible formation pathways of [Sm$^{III/II/III}$$_{3}$(COT$^{1,4-SiiPr3}$)$_{4}$] but also resulted in the transformation to other mixed metal sandwich complexes with unique structural properties. These are the 1D-polymeric chain structured [KSm$^{III}$(COT$^{1,4-SiiPr3}$)$_{4}$]$_{n}$ and the hexametallic species [(tol)K(COT$^{1,4-SiiPr3}$)Sm$^{II}$COT$^{1,4-SiiPr3}$)K]$_{2}$ which were initially envisioned as possible building blocks as part of different retrosynthetically guided pathways that we developed

Using Augmented Reality in Software Engineering Education? First insights to a comparative study of 2D and AR UML modeling

Although there has been much speculation about the potential of Augmented Reality (AR) in teaching for learning material, there is a significant lack of empirical proof about its effectiveness and implementation in higher education. We describe a software to integrate AR using the Microsoft Hololens into UML (Unified Modeling Language) teaching. Its user interface is laid out to overcome problems of existing software. We discuss the design of the tool and report a first evaluation study. The study is based upon effectiveness as a metric for students performance and components of motivation. The study was designed as control group experiment with two groups. The experimental group had to solve tasks with the help of the AR modeling tool and the control group used a classic PC software. We identified tendencies that participants of the experimental group showed more motivation than the control group. Both groups performed equally well

A Survey on Data Plane Programming with P4: Fundamentals, Advances, and Applied Research

With traditional networking, users can configure control plane protocols to match the specific network configuration, but without the ability to fundamentally change the underlying algorithms. With SDN, the users may provide their own control plane, that can control network devices through their data plane APIs. Programmable data planes allow users to define their own data plane algorithms for network devices including appropriate data plane APIs which may be leveraged by user-defined SDN control. Thus, programmable data planes and SDN offer great flexibility for network customization, be it for specialized, commercial appliances, e.g., in 5G or data center networks, or for rapid prototyping in industrial and academic research. Programming protocol-independent packet processors (P4) has emerged as the currently most widespread abstraction, programming language, and concept for data plane programming. It is developed and standardized by an open community and it is supported by various software and hardware platforms. In this paper, we survey the literature from 2015 to 2020 on data plane programming with P4. Our survey covers 497 references of which 367 are scientific publications. We organize our work into two parts. In the first part, we give an overview of data plane programming models, the programming language, architectures, compilers, targets, and data plane APIs. We also consider research efforts to advance P4 technology. In the second part, we analyze a large body of literature considering P4-based applied research. We categorize 241 research papers into different application domains, summarize their contributions, and extract prototypes, target platforms, and source code availability.Comment: Submitted to IEEE Communications Surveys and Tutorials (COMS) on 2021-01-2

Wahlbörsen als interdisziplinäres Instrument der Sozialforschung: Erfahrungen aus Wahlen in Österreich

'Wahlbörsen sind ein Instrument der Meinungsforschung, um Wahlergebnisse vorherzusagen, leisten aber aufgrund der ihnen zuteil werdenden öffentlichen Aufmerksamkeit auch Funktionen der politischen Bildungsarbeit. Struktur und Methodik von Wahlbörsen, aber auch ihre Möglichkeiten und Grenzen werden ausführlich dargestellt. Detailanalysen beschäftigen sich insbesondere mit dem Kursverlauf und der Dateninterpretation einer von den Autorinnen betreuten Wahlbörse vor der österreichischen Nationalratswahl 2002 sowie mit neuen Erkenntnissen über Handelsentscheidungen und das politische Informationsverhalten der Händlerinnen. Die Schlussfolgerung ist, dass Wahlbörsen in Zukunft regelmäßig stattfinden werden, aber mit steigender Öffentlichkeit vermehrt Konflikte zwischen wissenschaftlichen Interessen und den Anliegen von medialen Veranstaltern entstehen, die den spielerischen Charakter in den Mittelpunkt stellen. Dementsprechend werden konkrete Empfehlungen für die zukünftige Gestaltung von Wahlbörsen gegeben.' (Autorenreferat)'Political Stock Markets (PSMs) are an instrument of opinion research to predict the outcome of elections and other uncertain events. Due to the high degree of public awareness they can further be considered a means of civic education. In this article the structure and methodology of PSMs, as well as their strengths and weaknesses, are explored in depth. Detailed analyses are done on the chart and trading data of a recent PSM of the Austrian parliamentary election in 2002, which was supervised by the authors. We present new insights on trading decisions and political information behaviour of traders. Our conclusion is that PSMs will be conducted regularly in the future, but with increasing publicity the conflicts between the interests of involved scientists and hosting media, who tend to stress the entertainment character of PSMs, could increase. Therefore, we include a number of precise suggestions to possibly improve the design of future PSMs.' (author's abstract)

Introduction of plumbole to f-element chemistry

Herein, we present the synthesis and characterization of heteroleptic lanthanide complexes bearing a dianionic η5-plumbole ligand in their coordination sphere. The reaction proceeds via a salt elimination reaction between the dilithioplumbole ([Li(thf)]$_2$[1,4-bis-tert-butyl-dimethylsilyl-2,3-bis-phenyl-plumbolyl] = [Li$_2$(thf)$_2$(η$^5$-L$^Pb$)]) and specifically designed [Ln(η$^8$-COT$^TIPS$)BH$_4$] precursors (Ln = lanthanide, La, Ce, Sm, Er; COT$^TIPS$ = 1,4-bis-triisopropylsilyl-cyclooctatetraenyl), that are capable of stabilizing a planar plumbole moiety in the coordination sphere of different trivalent lanthanide ions. In-depth ab initio calculations show that the aromaticity of the dianionic plumbole is retained upon coordination. Electron delocalization occurs from the plumbole HOMO to an orbital of mainly d-character at the lanthanide ion. The magnetic properties of the erbium congener were investigated in detail, leading to the observation of magnetic hysteresis up to 5 K (200 Oe s$^−1$), an unequivocal proof for single molecule magnet behavior in this system. The magnetic behavior of the erbium species can be modulated by manipulating the position of the lithium cation in the complex, which directly influences the bonding metrics in the central [(η$^5$-L$^Pb$)Er(η$^8$-COT$^TIPS$)]− fragment. This allowed us to assess a fundamental magneto-structural correlation in an otherwise identical inner coordination sphere

Hypothesis That Urethral Bulb (Corpus Spongiosum) Plays an Active Role in Male Urinary Continence

The proximal urethral bulb in men is enlarged, surrounds the bulbous urethra, and extends dorsally towards the perineum. During intercourse engorgement takes place due to increased blood flow through the corpus spongiosum. Antegrade ejaculation is facilitated by contraction of the bulbospongiosus muscles during climax. Micturition during sexual stimulation is functionally inhibited. Supporting the bulb may indirectly facilitate continence in a certain subset of patients with postprostatectomy incontinence. During physical activity with increased abdominal pressure, reflex contraction of the pelvic floor muscles as well as the bulbospongiosus muscles occurs to support sphincter function and limit urinary incontinence. Operations to the prostate may weaken urinary sphincter function. It is hypothesized that the distal urinary sphincter may be supported indirectly by placing a hammock underneath the urethral bulb. During moments of physical stress the “cushion” of blood within the supported corpus spongiosum helps to increase the zone of coaptation within the sphincteric (membranous) urethra. This may lead to urinary continence in patients treated by a transobturator repositioning sling in patients with postprostatectomy incontinence. This paper describes the possible role of the urethral bulb in male urinary continence, including its function after retroluminal sling placement (AdVance, AdVance XP® Male Sling System, Minnetonka, USA)