7‐Nitro­indazole

The title compound, C₇H₅N₃O₂, is an inhibitor of nitric oxide synthase and mono­amine oxidase. The N1H tautomer crystallized as a dimer and adopts a planar conformation assisted by intramolecular hydrogen bonding.     

On Dirichlet <Emphasis Type="Italic">L</Emphasis>-functions with periodic coefficients and Eisenstein series

We prove a Lipschitz type summation formula with periodic coefficients. Using this formula, representations of the values at positive integers of Dirichlet L-functions with periodic coefficients are obtained in terms of Bernoulli numbers and certain sums involving essentially the discrete Fourier transform of the periodic function forming the coefficients. The non-vanishing of these L-functions at s = 1 are then investigated. There are additional applications to the Fourier expansions of Eisenstein series over congruence subgroups of \({SL_2(\mathbb{Z})}\) and derivatives of such Eisenstein series. Examples of a family of Eisenstein series with a high frequency of vanishing Fourier coefficients are given.     

Highly effective activation of aryl chlorides for Suzuki coupling in aqueous media using a ferrocene-based Pd(II)–diimine catalyst

The Suzuki coupling of aryl chlorides with boronic acids using a ferrocene-containing Pd(II)–diimine complex as catalyst, in aqueous media, under microwave heating is reported. A small amount of the catalyst (0.1%) was found to be highly effective for coupling unactivated aryl chlorides with boronic acids to form sterically hindered ortho-substituted biaryls. The same catalyst also enabled the coupling of aryl bromides and iodides with various boronic acids in very high yields. The catalyst is air stable and the catalytic reaction can be completed in 15 min.     

A complex adaptive systems perspective of innovation diffusion: an integrated theory and validated virtual laboratory

In this paper we integrate the rich yet fragmented insights from the extensive literature on the diffusion of innovation into an elegant, coherent model. Using complex adaptive systems theory as the overarching framework, we integrate prior literature around three constructs: agents, interactions, and an environment. The integrated model is presented in both natural language and as an agent-based simulation model. A series of validation experiments instill confidence that our agent-based model (and similar others) can be used as a virtual research laboratory. We provide theoretical and methodological directions for future research.     

Ulrich bundles on quartic surfaces with Picard number 1

In this note, we prove that there exist stable Ulrich bundles of every even rank on a smooth quartic surface $X?{\mathbb{P}}^3$ with Picard number 1.     

Engineered 3D tissue models for cell-laden microfluidic channels

Delivery of nutrients and oxygen within three-dimensional (3D) tissue constructs is important to maintain cell viability. We built 3D cell-laden hydrogels to validate a new tissue perfusion model that takes into account nutrition consumption. The model system was analyzed by simulating theoretical nutrient diffusion into cell-laden hydrogels. We carried out a parametric study considering different microchannel sizes and inter-channel separation in the hydrogel. We hypothesized that nutrient consumption needs to be taken into account when optimizing the perfusion channel size and separation. We validated the hypothesis by experiments. We fabricated circular microchannels (r = 400 μm) in 3D cell-laden hydrogel constructs (R = 7.5 mm, volume = 5 ml). These channels were positioned either individually or in parallel within hydrogels to increase nutrient and oxygen transport as a way to improve cell viability. We quantified the spatial distribution of viable cells within 3D hydrogel scaffolds without channels and with single- and dual-perfusion microfluidic channels. We investigated quantitatively the cell viability as a function of radial distance from the channels using experimental data and mathematical modeling of diffusion profiles. Our simulations show that a large-channel radius as well as a large channel to channel distance diffuse nutrients farther through a 3D hydrogel. This is important since our results reveal that there is a close correlation between nutrient profiles and cell viability across the hydrogel. Young Seok Song and Richard L. Lin have contributed equally to this contribution     

Pair correlation of torsion points on elliptic curves

We prove the existence of the pair correlation measure associated to torsion points on the real locus E(R) of an elliptic curve E and provide an explicit formula for the limiting pair correlation function.