Spectral determinants and zeta functions of Schr\"odinger operators on metric graphs

A derivation of the spectral determinant of the Schr\"odinger operator on a metric graph is presented where the local matching conditions at the vertices are of the general form classified according to the scheme of Kostrykin and Schrader. To formulate the spectral determinant we first derive the spectral zeta function of the Schr\"odinger operator using an appropriate secular equation. The result obtained for the spectral determinant is along the lines of the recent conjecture.Comment: 16 pages, 2 figure

Rotational spectroscopy of the HCCO and DCCO radicals in the millimeter and submillimeter range

The ketenyl radical, HCCO, has recently been detected in the ISM for the first time. Further astronomical detections of HCCO will help us understand its gas-grain chemistry, and subsequently revise the oxygen-bearing chemistry towards dark clouds. Moreover, its deuterated counterpart, DCCO, has never been observed in the ISM. HCCO and DCCO still lack a broad spectroscopic investigation, although they exhibit a significant astrophysical relevance. In this work we aim to measure the pure rotational spectra of the ground state of HCCO and DCCO in the millimeter and submillimeter region, considerably extending the frequency range covered by previous studies. The spectral acquisition was performed using a frequency-modulation absorption spectrometer between 170 and 650 GHz. The radicals were produced in a low-density plasma generated from a select mixture of gaseous precursors. For each isotopologue we were able to detect and assign more than 100 rotational lines. The new lines have significantly enhanced the previous data set allowing the determination of highly precise rotational and centrifugal distortion parameters. In our analysis we have taken into account the interaction between the ground electronic state and a low-lying excited state (Renner-Teller pair) which enables the prediction and assignment of rotational transitions with $K_a$ up to 4. The present set of spectroscopic parameters provides highly accurate, millimeter and submillimeter rest-frequencies of HCCO and DCCO for future astronomical observations. We also show that towards the pre-stellar core L1544, ketenyl peaks in the region where $c$-$\mathrm{C_3H_2}$ peaks, suggesting that HCCO follows a predominant hydrocarbon chemistry, as already proposed by recent gas-grain chemical models

Adubos verdes de outono/inverno no Mato Grosso do sul.

Aspectos gerais de manejo da materia organica; Resultados obtidos entre 1986-1989, na regiao de Dourados; Resultados obtidos no periodo 1990-1992, na regiao de Dourados; Resultados obtidos em 1993, na regiao centro-norte do Mato Grosso do Sul; Conclusoes e sugestoes de pesquisa; Caracterizacao das principais especies selecionadas; Centeio; Nabo forrageiro; Aveia; Aveia-preta; Aveia-branca; Canola; Triticalebitstream/item/38988/1/DOC4-1995.pd

Codon-biased translation can be regulated by wobble-base tRNA modification systems during cellular stress responses

tRNA (tRNA) is a key molecule used for protein synthesis, with multiple points of stress-induced regulation that can include transcription, transcript processing, localization and ribonucleoside base modification. Enzyme-catalyzed modification of tRNA occurs at a number of base and sugar positions and has the potential to influence specific anticodon-codon interactions and regulate translation. Notably, altered tRNA modification has been linked to mitochondrial diseases and cancer progression. In this review, specific to Eukaryotic systems, we discuss how recent systems-level analyses using a bioanalytical platform have revealed that there is extensive reprogramming of tRNA modifications in response to cellular stress and during cell cycle progression. Combined with genome-wide codon bias analytics and gene expression studies, a model emerges in which stress-induced reprogramming of tRNA drives the translational regulation of critical response proteins whose transcripts display a distinct codon bias. Termed Modification Tunable Transcripts (MoTTs), we define them as (1) transcripts that use specific degenerate codons and codon biases to encode critical stress response proteins, and (2) transcripts whose translation is influenced by changes in wobble base tRNA modification. In this review we note that the MoTTs translational model is also applicable to the process of stop-codon recoding for selenocysteine incorporation, as stop-codon recoding involves a selective codon bias and modified tRNA to decode selenocysteine during the translation of a key subset of oxidative stress response proteins. Further, we discuss how in addition to RNA modification analytics, the comprehensive characterization of translational regulation of specific transcripts requires a variety of tools, including high coverage codon-reporters, ribosome profiling and linked genomic and proteomic approaches. Together these tools will yield important new insights into the role of translational elongation in cell stress response.National Science Foundation (U.S.) (CHE-1308839)Singapore. National Research Foundation (Singapore-MIT Alliance for Research and Technology Center. Infectious Disease Research Program

A new proof of the Vorono\"i summation formula

We present a short alternative proof of the Vorono\"i summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula for a Schr\"odinger operator on a non-compact quantum graph \mathfrak{G} [S. Egger n\'e Endres and F. Steiner, J. Phys. A: Math. Theor. 44 (2011) 185202 (44pp)]. As a byproduct we give a new proof of a non-trivial identity for a particular Lambert series which involves the divisor function d(n) and is identical with the trace of the Euclidean wave group of the Laplacian on the infinite graph \mathfrak{G}.Comment: Enlarged version of the published article J. Phys. A: Math. Theor. 44 (2011) 225302 (11pp

Improving Lifelong Learning by Fostering Students' Learning Strategies at University

The foundation of how students usually learn is laid early in their academic lives. However, many or even most students do not primarily rely on those learning strategies that are most favorable from a scientific point of view. To change students' learning behavior when they start their university education, we developed a computer-based adaptive learning environment to train favorable learning strategies and change students' habits using them. This learning environment pursues three main goals: acquiring declarative and conditional knowledge about learning strategies, consolidating that knowledge, and applying these learning strategies in practice. In this report, we describe four experimental studies conducted to optimize this learning environment (n = 336). With those studies, we improved the learning environment with respect to how motivating it is, investigated an efficient way to consolidate knowledge, and explored how to facilitate the formation of effective implementation intentions for applying learning strategies and changing learning habits. Our strategy-training module is implemented in the curriculum for freshman students at the Department of Psychology, University of Freiburg (Germany). Around 120 students take part in our program every year. An open version of this training intervention is freely available to everyone

Zeta functions of quantum graphs

In this article we construct zeta functions of quantum graphs using a contour integral technique based on the argument principle. We start by considering the special case of the star graph with Neumann matching conditions at the center of the star. We then extend the technique to allow any matching conditions at the center for which the Laplace operator is self-adjoint and finally obtain an expression for the zeta function of any graph with general vertex matching conditions. In the process it is convenient to work with new forms for the secular equation of a quantum graph that extend the well known secular equation of the Neumann star graph. In the second half of the article we apply the zeta function to obtain new results for the spectral determinant, vacuum energy and heat kernel coefficients of quantum graphs. These have all been topics of current research in their own right and in each case this unified approach significantly expands results in the literature.Comment: 32 pages, typos corrected, references adde

The CDMS view on molecular data needs of Herschel, SOFIA, and ALMA

The catalog section of the Cologne Database for Molecular Spectroscopy, CDMS, contains mostly rotational transition frequencies, with auxiliary information, of molecules observable in space. The frequency lists are generated mostly from critically evaluated laboratory data employing established Hamiltonian models. The CDMS has been online publicly for more than 12 years, e.g., via the short-cut http://www.cdms.de. Initially constructed as ascii tables, its inclusion into a database environment within the Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu) has begun in June 2008. A test version of the new CDMS is about to be released. The CDMS activities have been part of the extensive laboratory spectroscopic investigations in Cologne. Moreover, these activities have also benefit from collaborations with other laboratory spectroscopy groups as well as with astronomers. We will provide some basic information on the CDMS and its participation in the VAMDC project. In addition, some recent detections of molecules as well as spectroscopic studies will be discussed to evaluate the spectroscopic data needs of Herschel, SOFIA, and ALMA in particular in terms of light hydrides, complex molecules, and metal containing speciesComment: 14 pages, 1 figure; AIP Conf. Proc., accepted; Proceedings of the Eighths International Conference on Atomic and Molecular Data and Their Applicatio

Interleukin-1ß in human colostrum

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The Berry-Keating operator on L^2(\rz_>, x) and on compact quantum graphs with general self-adjoint realizations

The Berry-Keating operator H_{\mathrm{BK}}:= -\ui\hbar(x\frac{ \phantom{x}}{ x}+{1/2}) [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\"odinger dynamics is discussed in the Hilbert space L^2(\rz_>, x) and on compact quantum graphs. It is proved that the spectrum of $H_{\mathrm{BK}}$ defined on L^2(\rz_>, x) is purely continuous and thus this quantization of $H_{\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the "squared" Berry-Keating operator $H_{\mathrm{BK}}^2:= -x^2\frac{ ^2\phantom{x}}{ x^2}-2x\frac{ \phantom{x}}{ x}-{1/4}$ which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for $H_{\mathrm{BK}}^2$ on compact quantum graphs. While the spectra of both $H_{\mathrm{BK}}$ and $H_{\mathrm{BK}}^2$ on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither $H_{\mathrm{BK}}$ nor $H_{\mathrm{BK}}^2$ can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.Comment: 33p