Unravelling Mathieu moonshine

The D1–D5–KK–p system naturally provides an infinite-dimensional module graded by the dyonic charges whose dimensions are counted by the Igusa cusp form, _Φ10(Z)${\Phi }_{10}(\mathbf{Z})$. We show that the Mathieu group, _M24$M_{24}$, acts on this module by recovering the Siegel modular forms that count twisted dyons as a trace over this module. This is done by recovering Borcherds product formulae for these modular forms using the _M24$M_{24}$ action. This establishes the correspondence (‘moonshine’) proposed in arXiv:0907.1410 that relates conjugacy classes of _M24$M_{24}$ to Siegel modular forms. This also, in a sense that we make precise, subsumes existing moonshines for _M24$M_{24}$ that relates its conjugacy classes to eta-products and Jacobi forms.     

Patterning of antibodies using flexographic printing

Antibodies were patterned onto flexible plastic films using the flexographic printing process. An ink formulation was developed using high molecular weight polyvinyl alcohol in carbonate-bicarbonate buffer. In order to aid both antibody adhesion and the quality of definition in the printed features, a nitrocellulose coating was developed that was capable of being discretely patterned, thus increasing the signal-to-noise ratio of an antibody array. Printing antibody features such as dots, squares, text, and fine lines were reproduced effectively. Furthermore, this process could be easily adapted for printing of other biological materials, including, but not limited to, enzymes, DNA, proteins, aptamers, and cells.     

FT-IR, FT-Raman and UV spectral investigation; computed frequency estimation analysis and electronic structure calculations on 1-nitronaphthalene

In this work, the vibrational spectral analysis was carried out by using FT-Raman and FT-IR spectroscopy in the range 100-4000cm(-1) and 400-4000cm(-1) respectively, for 1-nitronaphthalene (C(10)H(7)NO(2)) molecule. The molecular structure, fundamental vibrational frequencies and intensity of the vibrational bands are interpreted with the aid of structure optimizations and normal coordinate force field calculations based density functional theory (DFT) and ab initio HF methods and different basis sets combination. The complete vibrational assignments of wavenumbers were made on the basis of total energy distribution (TED). The results of the calculations were applied to simulated spectra of the title compound, which show excellent agreement with observed spectra. The scaled B3LYP/6-311++G(d,p) results show the best agreement with the experimental values over the other methods. The energy and oscillator strength calculated by time-dependent density functional theory (TD-DFT) complements with the experimental findings. Thermodynamic properties of the title compound at different temperatures have been calculated. Besides, frontier molecular orbitals (FMO), molecular electrostatic potential (MEP) were performed.     

Process optimization of vapor phase pyridine synthesis using response surface methodology

The vapor phase pyridine synthesis from acetaldehyde, formaldehyde and ammonia over HZSM-5 catalyst was studied. The process parameters like temperature, aldehyde ratio, and Si/Al ratio in HZSM-5 was investigated and the process conditions were optimized using surface response methodology (RSM) based on Box-Behnken design. The influence of process parameters investigated using analysis of variance (ANOVA), to identify the significant parameters. The optimum conditions for high yield of pyridine were identified to be a reaction temperature 400°C, aldehyde ratio 1: 1 and Si/Al ratio 106.7. A maximum of 55% yield of pyridine formed under the optimum experimental conditions. The proposed model equation using RSM has shown good agreement with the experimental data, with a correlation coefficient R ² = 0.99.     

Student Outcomes in a Local Systemic Change Project

The Local Systemic Change initiative of the National Science Foundation supports projects focusing primarily on teacher enhancement through extensive professional development and the use of standards‐based curriculum materials. The underlying rationale is that the effective use of such materials will ultimately result in enhanced student learning. However, the research base regarding the impact of these efforts on student learning is rather lean. This paper describes the results of a curriculum‐aligned assessment comprising selected items from the Third International Mathematics and Science Study. The assessment was administered to fifth graders involved in a Local Systemic Change project to address the following questions: How does the performance of students involved in the project compare nationally and internationally? and Does length of involvement in the project make a difference in student performance? Additional evidence to relate student outcomes to the project's systemic change efforts are provided.     

H2, B−H,and Si−H Bond Activation and Facile Protonolysis Driven by Pt-Base Metal Cooperation

We report a series of heterobimetallic Pt/Zn and Pt/Ca complexes to study the effect of proximity of a dicationic base metal on the organometallic Pt species. Varying degrees of Pt⋅⋅⋅Zn and Zn interaction with the bridging Me group are achieved, showcasing snapshots of a hypothetical process of retrotransmetalation from Pt to Zn. In contrast, only weak interactions were observed for Ca with a Pt-bound Me group. Activation of H₂, B−H and Si−H bonds leads to the formation of hydride-bridged Pt−H−Zn complexes, which is not observed in the absence of Zn, pointing out the importance of metal-metal cooperation. Reactivity of PtMe₂/M²⁺ with terminal acetylene, water and methanol is also studied, leading to facile protonation of one of the Me groups at the Pt center only when Zn is present. This study sheds light on various ways in which the presence of a 2+ metal cation significantly affects the reactivity of a common organoplatinum complex.     

On stochastic games with additive reward and transition structure

In this paper, we introduce a new class of two-person stochastic games with nice properties. For games in this class, the payoffs as well as the transitions in each state consist of a part which depends only on the action of the first player and a part dependent only on the action of the second player.For the zero-sum games in this class, we prove that the orderfield property holds in the infinite-horizon case and that there exist optimal pure stationary strategies for the discounted as well as the undiscounted payoff criterion. For both criteria also, finite algorithms are given to solve the game. An example shows that, for nonzero sum games in this class, there are not necessarily pure stationary equilibria. But, if such a game possesses a stationary equilibrium point, then there also exists a stationary equilibrium point which uses in each state at most two pure actions for each player.     

Two-particle correlations in 360 GeV/cp p interactions

Two particle correlations of hadrons produced in 360 GeV/cpp interactions are investigated in the transverse plane and in rapidity. The data were obtained at the European hybrid spectrometer equipped with a rapid cycling bubble chamber. The observed transverse and rapidity correlations are compared with the one string LUND-and a two string dual parton-model. These models predict in general stronger correlations in the transverse plane and much weaker correlations in rapidity than found in the data. The LUND-FRITIOF-and multichain dual parton models provide a better reproduction of the data, although the agreement is not yet satisfactory. Only the UA5 cluster model GENCL shows agreement with the data.     

A short convergent synthesis of the [3.2.1]dioxabicyclooctane subunit of sorangicin A via regioselective epoxide opening

In this paper, we disclose the synthesis of the dioxabicyclo[3.2.1]octane subunit of the potent antibiotic sorangicin A. The synthesis was achieved in a convergent manner in 8 steps. Regio- and stereoselective intermolecular epoxide opening, ring-closing metathesis and iodo-etherification are key steps. cis-2-Butene diol has been employed as a common staring material.     

New two-color dimer models with critical ground states

We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.