Electronic and Vibrational Spectroscopy of 1‐Methylthymine and its Water Clusters: The Dark State Survives Hydration

Electronic and vibrational gas phase spectra of 1‐methylthymine (1MT) and 1‐methyluracil (1MU) and their clusters with water are presented. Mass selective IR/UV double resonance spectra confirm the formation of pyrimidine‐water clusters and are compared to calculated vibrational spectra obtained from ab initio calculations. In contrast to Y. He, C. Wu, W. Kong; J. Phys. Chem. A, 2004 , 108, 94 we are able to detect 1MT/1MU and their water clusters via resonant two‐photon delayed ionization under careful control of the applied water‐vapor pressure. The long‐living dark electronic state of 1MT and 1MU detected by delayed ionization, survives hydration and the photostability of 1MT/1MU cannot be attributed solely to hydration. Oxygen coexpansions and crossed‐beam experiments indicate that the triplet state population is probably small compared to the ¹nπ* and/or hot electronic ground state population. Ab initio theory shows that solvation of 1MT by water does not lead to a substantial modification of the electronic relaxation and quenching of the ¹nπ* state. Relaxation pathways via ¹ππ*¹–nπ*¹ and ¹ππ *–S₀ conical intersections and barriers have been identified, but are not significantly altered by hydration.     

Active Molybdenum‐Based Anode for Dehydrogenative Coupling Reactions

A new and powerful active anode system that can be operated in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) has been discovered. In HFIP the molybdenum anode forms a compact, conductive, and electroactive layer of higher‐valent molybdenum species. This system can replace powerful but stoichiometrically required Mo^V reagents for the dehydrogenative coupling of aryls. This electrolytic reaction is more sustainable and allows the conversion of a broad scope of activated arenes.     

An Experimental Study of the Kinetics of the Reactions of Isopropyl,sec‐Butyl,and tert‐Butyl Radicals with Molecular Chlorine at Low Pressures (0.5–7.0 Torr) in the Temperature Range 190–480 K

In this work, we have measured the rate coefficients of the reactions of isopropyl (propan‐2‐yl), sec‐butyl (butan‐2‐yl), and tert‐butyl (2‐methylpropan‐2‐yl) radicals with molecular chlorine as a function of temperature (190–480 K). The experiments were done in a tubular laminar flow reactor coupled to a photoionization quadrupole mass spectrometer employing a gas‐discharge lamp for ionization. The radicals were homogeneously produced in the reactor by photolyzing suitable precursor molecules with 193‐nm pulsed exciplex laser radiation. The bimolecular rate coefficients were obtained by monitoring the radical decay signals in real time under pseudo–first‐order conditions. The rate coefficients of all three reactions showed negative temperature dependence. The bath gas used in the experiments was helium, and the rate coefficients appeared to be independent of the helium concentrations employed ([2.4–14] × 10¹⁶ cm^?3) for all three reactions. The rate coefficients of the reactions can be approximated in the studied temperature range by the following parameterizations: We estimate that the overall uncertainties of the measured rate coefficients are ±20%. We were able to observe 2‐chloropropane (i‐C₃H₇Cl) product for the i‐C₃H₇^● + Cl₂ reaction. No products were observed for the other two reactions, and the reasons for this are briefly discussed in the text.     

The Random Average Process and Random Walk in a Space-Time Random Environment in One Dimension

We study space-time fluctuations around a characteristic line for a one-dimensional interacting system known as the random average process. The state of this system is a real-valued function on the integers. New values of the function are created by averaging previous values with random weights. The fluctuations analyzed occur on the scale n ^1/4, where n is the ratio of macroscopic and microscopic scales in the system. The limits of the fluctuations are described by a family of Gaussian processes. In cases of known product-form invariant distributions, this limit is a two-parameter process whose time marginals are fractional Brownian motions with Hurst parameter 1/4. Along the way we study the limits of quenched mean processes for a random walk in a space-time random environment. These limits also happen at scale n ^1/4 and are described by certain Gaussian processes that we identify. In particular, when we look at a backward quenched mean process, the limit process is the solution of a stochastic heat equation.     

Singlet versus triplet dynamics of β-carotene studied by quantum control spectroscopy

Biomolecules very often present complex energy deactivation networks with overlapping electronic absorption bands, making their study a difficult task. This can be especially true in transient absorption spectroscopy when signals from bleach, excited state absorption and stimulated emission contribute to the signal. However, quantum control spectroscopy can be used to discriminate specific electronic states of interest by applying specifically designed laser pulses. Recently, we have shown the control of energy flow in bacterial light-harvesting using shaped pump pulses in the visible and the selective population of pathways in carotenoids using an additional depletion pulse in the transient absorption technique. Here, we apply a closed-loop optimization approach to β-carotene using a spatial light modulator to decipher the energy flow network after a multiphoton excitation with a shaped ultrashort pulse in the near-IR. After excitation, two overlapping bands were detected and identified as the S₁ state and the first triplet state T₁. Using the transient absorption signal at a specific probe delay as feedback, the triplet signal could be optimized over the singlet contribution.     

Parametric multiple sequence alignment and phylogeny construction

Bounds are given on the size of the parameter-space decomposition induced by multiple sequence alignment problems where phylogenetic information may be given or inferred. It is shown that many of the usual formulations of these problems fall within the same integer parametric framework, implying that the number of distinct optima obtained as the parameters are varied across their ranges is polynomially bounded in the length and number of sequences.     

Comparing adult mathematical literacy with PISA students: results of a pilot study

In Germany, very little empirical data about the mathematical competence of adults is available. The aim of this study is to test the level of mathematical competence in an adult sample. For this purpose, a mathematics test was constructed using the PISA mathematics framework as a guideline. The test consisted of fourteen public items from the mathematics test in PISA 2000. The study was implemented by carrying out house visits (Germany). The sample was comprised of 64 adults (90% women, age: 41 years). The test results were scaled in the metric of PISA 2000. Compared with the average German student competencies in PISA 2000, the average competency in the adult sample was on the same level as the fifteen-year-old comprehensive secondary school student (at a German Gymnasium). Further analysis shows that the mathematics competency level in the adult sample is positively connected to the individual vocational education degree.     

Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

The Limit Distribution of the Largest Interpoint Distance from a Symmetric Kotz Sample

Generalizing recent work of P. C. Matthews and A. L. Rukhin (Ann. Appl. Probab.3(1993), 454–466), we obtain the limit law of the largest interpoint Euclidean distance for a spherically symmetric multivariate sample of the Kotz distribution. While going through the proof, some errors in the reasoning given by Matthews and Rukhin are pointed out and corrected.