Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

Phylogeographic Analysis Elucidates the Influence of the Ice Ages on the Disjunct Distribution of Relict Dragonflies in Asia

Unusual biogeographic patterns of closely related groups reflect events in the past, and molecular analyses can help to elucidate these events. While ample research on the origin of disjunct distributions of different organism groups in the Western Paleartic has been conducted, such studies are rare for Eastern Palearctic organisms. In this paper we present a phylogeographic analysis of the disjunct distribution pattern of the extant species of the strongly cool-adapted Epiophlebia dragonflies from Asia. We investigated sequences of the usually more conserved 18 S rDNA and 28 S rDNA genes and the more variable sequences of ITS1, ITS2 and CO2 of all three currently recognised Epiophlebia species and of a sample of other odonatan species. In all genes investigated the degrees of similarity between species of Epiophlebia are very high and resemble those otherwise found between different populations of the same species in Odonata. This indicates that substantial gene transfer between these populations occurred in the comparatively recent past. Our analyses imply a wide distribution of the ancestor of extant Epiophlebia in Southeast Asia during the last ice age, when suitable habitats were more common. During the following warming phase, its range contracted, resulting in the current disjunct distribution. Given the strong sensitivity of these species to climatic parameters, the current trend to increasing global temperatures will further reduce acceptable habitats and seriously threaten the existences of these last representatives of an ancient group of Odonata

Morphological re-examination of <b><i>Epiophlebia laidlawi</i></b> (Insecta: Odonata) including remarks on taxonomy

<p><i>Epiophlebia</i> is the only known taxon of Odonata that is neither part of the damselflies (Zygoptera) nor dragonflies (Anisoptera). Previously, two species of <i>Epiophlebia</i> were recognized, restricted to areas in Japan (<i>Epiophlebia superstes</i>) and the Himalayas (<i>Epiophlebia laidlawi</i>). Recently, the group gained attention with the description of new species from China – <i>Epiophlebia sinensis</i> and <i>Epiophlebia diana –</i> while a subsequent genetic study suggested only one species of <i>Epiophlebia</i>. To clarify these conflicting hypotheses this study focused on the under-recorded <i>Epiophlebia laidlawi.</i> This study elucidated the morphology of this species in comparison to <i>Epiophlebia superstes</i>, representing the first comparative study of <i>Epiophlebia</i> species. Furthermore, it presents notes on the taxonomic conditions of this group. With this study, a first step is made to resolve the confusion regarding the taxonomic status of the described <i>Epiophlebia</i> species. A number of anatomical characters – for example the different shape of the vertex of the head, the distinct colour patterns of the head, thorax and the abdomen or the differences in the shape of the hamulus anterior and posterior in the secondary male genitalia – confirmed the species status of <i>E. laidlawi</i> and underlined its distinctness from <i>E. superstes</i>. However, in the Chinese species <i>E. sinensis</i> and <i>E. diana</i> a re-examination is advised; especially in <i>E. diana</i> the species status is questionable.</p

Bio-inspired design and movement generation of dung beetle-like legs

African ball-rolling dung beetles can use their front legs for multiple purposes that include walking, manipulating or forming a dung ball, and also transporting it. Their multifunctional legs can be used as inspiration for the design of a multifunctional robot leg. Thus, in this paper, we present the development of real robot legs based on the study of the front legs of the beetle. The leg movements of the beetle, during walking as well as manipulating and transporting a dung ball, were observed and reproduced on the robot leg. Each robot leg consists of three main segments which were built using 3D printing. The segments were combined with four active joints in total (i.e., 4 degrees of freedom) to mimic the leg movements of the beetle for locomotion as well as object manipulation and transportation. Kinematics analysis of the leg was also performed to identify its workspace. The results show that the robot leg is able to perform all the movements with trajectories comparable to the beetle leg. To this end, the study contributes not only to the design of novel multifunctional robot legs but also to the methodology for bio-inspired leg design

The head morphology of Pyrrhosoma nymphula larvae (Odonata: Zygoptera) focusing on functional aspects of the mouthparts

BACKGROUND: The understanding of concerted movements and its underlying biomechanics is often complex and elusive. Functional principles and hypothetical functions of these complex movements can provide a solid basis for biomechanical experiments and modelling. Here a description of the cephalic anatomy of Pyrrhosoma nymphula (Zygoptera, Coenagrionidae) focusing on functional aspects of the mouthparts using micro computed tomography (μCT) is presented. RESULTS: We compared six different instars of the damselfly P. nymphula as well as one instar of the dragonfly Aeshna cyanea and Epiophlebia superstes each. In total 42 head muscles were described with only minor differences of the attachment points between the examined species and the absence of antennal muscle M. scapopedicellaris medialis (0an7) in Epiophlebia as a probable apomorphy of this group. Furthermore, the ontogenetic differences between the six larval instars are minor; the only considerable finding is the change of M. submentopraementalis (0la8), which is dichotomous in the early instars (I1,I2 and I3) with a second point of origin at the postero-lateral base of the submentum. This dichotomy is not present in any of the older instars studied (I6, middle-late and pen-ultimate). CONCLUSION: However, the main focus of the study herein, is to use these detailed morphological descriptions as basis for hypothetic functional models of the odonatan mouthparts. We present blueprint like description of the mouthparts and their musculature, highlighting the caused direction of motion for every single muscle. This data will help to elucidate the complex concerted movements of the mouthparts and will contribute to the understanding of its biomechanics not in Odonata only