Continuous functions with universally divergent Fourier series on small subsets of the circle

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality properties.Comment: 6 page

The spectroscopic parameters of sodium cyanide, NaCN (X 1A'), revisited

The study of the rotational spectrum of NaCN (X $^1$A') has recently been extended in frequency and in quantum numbers. Difficulties have been encountered in fitting the transition frequencies within experimental uncertainties. Various trial fits traced the difficulties to the incomplete diagonalization of the Hamiltonian. Employing fewer spectroscopic parameters than before, the transition frequencies could be reproduced within experimental uncertainties on average. Predictions of $a$-type $R$-branch transitions with $K_a \le 7$ up to 570 GHz should be reliable to better than 1 MHz. In addition, modified spectroscopic parameters have been derived for the 13C isotopic species of NaCN.Comment: 5 pages, no figure, J. Mol. Spectrosc., appeared; CDMS links update

A Convenient Synthesis of 14C-Anthralin

Anthralin [1,8-dihydroxy-9(10H)-anthracenone] is among the most widely used drugs in the topical treatment of psoriasis1). However, not much is known concerning its mode of action at the molecular level, although a variety of cellular targets have been implicated both in the main and side effects of anthralin2 ). In particular, the interaction of anthralin with proteins has long been recognized to occur3 , 4 ) and there has been renewed interest in this topic, mostly directed toward the investigation whether enzyme inhibition by anthralin is related to oxygen radicalmediated damage of proteins5 ) . In order to gain a more profound understanding of the interaction between this drug and cellular targets, anthralin labelled with a non-exchangeable radioisotope in a suitable position was highly desirable. Furthermore, this labelled compound might serve as a useful starting material for the synthesis of analogues labelled in the anthrone nucleus. Since structural modification of anthralin has provided compounds with improved biological activity6 '7), labelled compounds are required for studies on skin penetration and metabolism of these future drugs. Although routes to 14C-anthralin have already been described8,9), each of these methods suffers from too many synthetic steps, or the use of hazardous 14C-sources1 ) . In this paper, we describe a short and efficient synthesis of l,8-dihydroxy-[10-14C]-9(10H)-anthracenone

Automated, unsupervised inversion of multiwavelength lidar data with TiARA : Assessment of retrieval performance of microphysical parameters using simulated data

We evaluate the retrieval performance of the automated, unsupervised inversion algorithm, Tikhonov Advanced Regularization Algorithm (TiARA), which is used for the autonomous retrieval of microphysical parameters of anthropogenic and natural pollution particles. TiARA (version 1.0) has been developed in the past 10 years and builds on the legacy of a data-operator-controlled inversion algorithm used since 1998 for the analysis of data from multiwavelength Raman lidar. The development of TiARA has been driven by the need to analyze in (near) real time large volumes of data collected with NASA Langley Research Center's high-spectral-resolution lidar (HSRL-2). HSRL-2 was envisioned as part of the NASA Aerosols-Clouds-Ecosystems mission in response to the National Academy of Sciences (NAS) Decadal Study mission recommendations 2007. TiARA could thus also serve as an inversion algorithm in the context of a future space-borne lidar. We summarize key properties of TiARA on the basis of simulations with monomodal logarithmic-normal particle size distributions that cover particle radii from approximately 0.05 μm to 10 μm. The real and imaginary parts of the complex refractive index cover the range from nonabsorbing to highly light-absorbing pollutants. Our simulations include up to 25% measurement uncertainty. The goal of our study is to provide guidance with respect to technical features of future space-borne lidars, if such lidars will be used for retrievals of microphysical data products, absorption coefficients, and single-scattering albedo. We investigate the impact of two different measurement-error models on the quality of the data products.We also obtain for the first time, to the best of our knowledge, a statistical view on systematic and statistical uncertainties, if a large volume of data is processed. Effective radius is retrieved to 50% accuracy for 58% of cases with an imaginary part up to 0.01i and up to 100% of cases with an imaginary part of 0.05i. Similarly, volume concentration, surface-area concentration, and number concentrations are retrieved to 50% accuracy in 56%-100% of cases, 99%-100% of cases, and 54%-87% of cases, respectively, depending on the imaginary part. The numbers represent measurement uncertainties of up to 15%. If we target 20% retrieval accuracy, the numbers of cases that fall within that threshold are 36%-76% for effective radius, 36%-73% for volume concentration, 98%-100% for surface-area concentration, and 37%-61% for number concentration. That range of numbers again represents a spread in results for different values of the imaginary part. At present, we obtain an accuracy of (on average) 0.1 for the real part. A case study from the ORCALES field campaign is used to illustrate data products obtained with TiARA.Peer reviewe

Human versus robots in the discovery and crystallization of gigantic polyoxometalates

The discovery of new gigantic molecules formed by self-assembly and crystal growth is challenging as it combines two contingent events; first is the formation of a new molecule, and second its crystallization. Herein, we construct a workflow that can be followed manually or by a robot to probe the envelope of both events and employ it for a new polyoxometalate cluster, Na6[Mo120Ce6O366H12(H2O)78]⋅200 H2O (1) which has a trigonal-ring type architecture (yield 4.3 % based on Mo). Its synthesis and crystallization was probed using an active machine-learning algorithm developed by us to explore the crystallization space, the algorithm results were compared with those obtained by human experimenters. The algorithm-based search is able to cover ca. 9 times more crystallization space than a random search and ca. 6 times more than humans and increases the crystallization prediction accuracy to 82.4±0.7 % over 77.1±0.9 % from human experimenters

Description of atomic excitations in heavy-ion reactions

Excitations of the atomic shell in heavy-ion collisions are influenced by the presence of a nuclear reaction. In the present Rapid Communication we point out the equivalence between a semiclassical description based on the nuclear autocorrelation function with an earlier model which employs a distribution of reaction times f(T). For the example of U+U collisions, results of coupled-channel calculations for positron creation and K-hole excitations are discussed for two schematic reaction models

Sit-and-Wait Strategies in Dynamic Visual Search

The role of memory in visual search has lately become a controversial issue. Horowitz and Wolfe (1998) observed that performance in a visual search task was little affected by whether the stimuli were static or randomly relocated every 111 ms. Because a memory-based mechanism, such as inhibition of return, would be of no use in the dynamic condition, Horowitz and Wolfe concluded that memory is likewise not involved in the static condition. However, Horowitz and Wolfe could not effectively rule out the possibility that observers adopted a different strategy in the dynamic condition than in the static condition. That is, in the dynamic condition observers may have attended to a subregion of the display and waited for the target to appear there (sit-and-wait strategy). This hypothesis is supported by experimental data showing that performance in their dynamic condition does not differ from performance in another dynamic condition in which observers are forced to adopt a sit-and-wait strategy by being presented with a limited region of the display only

Asymptotic flexibility of globally hyperbolic manifolds

In this short note, a question of patching together globally hyperbolic manifolds is adressed which appeared in the context of the construction of Hadamard states.Comment: 2 pages, submitted to 'Mathematische Zeitschrift