The B(E2↑) and Rtr of 21+ states in90Zr and60Ni

The ground state transition probabilities for the 2₁⁺ states in⁹⁰Zr and⁶⁰Ni as determined by resonance fluorescence and reorientation effect methods are used as constraints to deduce transition densities from inelastic electron scattering data. The (e, e') cross sections for the ⁹⁰Zr, 2₁⁺ state at 2.186 MeV were measured at the Kelvin Laboratory, while for the 2₁⁺ state at 1.333 MeV in⁶⁰Ni, the existing (e, e') data of Yale and Sendai were used. The discrepancy between the model independent (e, e') result of Yale for⁹⁰Zr and the (γ, γ') measurement is explained. The importance of an accurate knowledge of the ground state charge distribution for analysis of (e, e') data is emphasized. For⁹⁰Zr, the B(E2↑) is 674 ± 60 e²· fm⁴ and ^R_tr is 5.74 ± 0.11 fm. For the 1.333 MeV state in⁶⁰Ni, these values are 918 ± 26 e²· fm⁴ and 5.33 ± 0.03 fm respectively.     

Bidentate carbenoid ester coordination in ruthenium(II) Schiff-base complexes leading to excellent levels of diastereo- and enantioselectivity in catalytic alkene cyclopropanation

Exceptionally high stereoselectivity (ee < or = 98%, dr < or = 99:1) in the cyclopropanation of alkenes with ethyl diazoacetate using a non-planar ruthenium(II) Schiff-base precatalyst is a result of eta 2C,O binding of the carbenoid ester intermediate, according to DFT calculations.     

Heat and mass-transfer modeling of an angled gas-jet LCVD system

Laser chemical vapor deposition (LCVD) is a new manufacturing process that holds great potential for the production of small and complex metallic, ceramic and composite parts. Since LCVD is a thermally activated process, the most important process variable is temperature. Therefore, a thermal model was developed for a gas-jet LCVD system, accounting for Gaussian-beam laser heating and gas-jet convection cooling. The forced convection cooling imposed by the gas-jet reagent delivery system was significant, accounting for a 15 to 20% change in the substrate temperature. The deposition rate for a given material is not only affected by temperature, but also by the mass transport of reagent gases. An angled gas-jet reagent supply was designed to aid mass transport, but the need and impact of such a system has been debated. Therefore, a two-dimensional mass-transport model was developed to estimate the effects of a gas jet with respect to local reagent concentration variations and reaction rates. Across all deposition regimes, the gas jet was found to be an effective tool for increasing the concentration of reagent gases at the surface of the substrate. The gas jet also generated higher deposition rates and increased deposit resolution for those processes severely limited by diffusion. PACS 05.60.-k; 44.27+g; 44.05+e     

Harmonic analysis associated with a discrete Laplacian

It is well known that the fundamental solution of

$${u_t}\left( {n,t} \right) = u\left( {n + 1,t} \right) - 2u\left( {n,t} \right) + u\left( {n - 1,t} \right),n \in \mathbb{Z},$$

with u(n, 0) = δ _nm for every fixed m ∈ Z is given by u(n, t) = e ^?2t I _n?m (2t), where I _k (t) is the Bessel function of imaginary argument. In other words, the heat semigroup of the discrete Laplacian is described by the formal series W _t f(n) = Σ _m∈Z e ^?2t I _n?m (2t)f(m). This formula allows us to analyze some operators associated with the discrete Laplacian using semigroup theory. In particular, we obtain the maximum principle for the discrete fractional Laplacian, weighted ? ^p (Z)-boundedness of conjugate harmonic functions, Riesz transforms and square functions of Littlewood-Paley. We also show that the Riesz transforms essentially coincide with the so-called discrete Hilbert transform defined by D. Hilbert at the beginning of the twentieth century. We also see that these Riesz transforms are limits of the conjugate harmonic functions. The results rely on a careful use of several properties of Bessel functions.

     

Models for homotopy categories of injectives and Gorenstein injectives

A natural generalization of locally noetherian and locally coherent categories leads us to define locally type FP_∞ categories. They include not just all categories of modules over a ring, but also the category of sheaves over any concentrated scheme. In this setting we generalize and study the absolutely clean objects recently introduced in [5 Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring (arXiv:1405.5768). [Google Scholar]]. We show that 𝒟(𝒜𝒞), the derived category of absolutely clean objects, is always compactly generated and that it is embedded in K(Inj), the chain homotopy category of injectives, as a full subcategory containing the DG-injectives. Assuming the ground category 𝒢 has a set of generators satisfying a certain vanishing property, we also show that there is a recollement relating 𝒟(𝒜𝒞) to the (also compactly generated) derived category 𝒟(𝒢). Finally, we generalize the Gorenstein AC-injectives of [5 Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring (arXiv:1405.5768). [Google Scholar]], showing that they are the fibrant objects of a cofibrantly generated model structure on 𝒢.     

Kaplansky classes and derived categories

We put a monoidal model category structure on the category of chain complexes of quasi-coherent sheaves over a quasi-compact and semi-separated scheme X. The approach generalizes and simplifies the method used by the author in (Trans Am Math Soc 356(8) 3369–3390, 2004) and (Trans Am Math Soc 358(7), 2855–2874, 2006) to build monoidal model structures on the category of chain complexes of modules over a ring and chain complexes of sheaves over a ringed space. Indeed, much of the paper is dedicated to showing that in any Grothendieck category , any nice enough class of objects induces a model structure on the category Ch() of chain complexes. The main technical requirement on is the existence of a regular cardinal κ such that every object satisfies the following property: Each κ-generated subobject of F is contained in another κ-generated subobject S for which . Such a class is called a Kaplansky class. Kaplansky classes first appeared in Enochs and López-Ramos (Rend Sem Mat Univ Padova 107, 67–79, 2002) in the context of modules over a ring R. We study in detail the connection between Kaplansky classes and model categories. We also find simple conditions to put on which will guarantee that our model structure is monoidal. We will see that in several categories the class of flat objects form such Kaplansky classes, and hence induce monoidal model structures on the associated chain complex categories. We will also see that in any Grothendieck category , the class of all objects is a Kaplansky class which induces the usual (non-monoidal) injective model structure on Ch().     

Adaptive explicit-implicit tau-leaping method with automatic tau selection

The existing tau-selection strategy, which was designed for explicit tau leaping, is here modified to apply to implicit tau leaping, allowing for longer steps when the system is stiff. Further, an adaptive strategy that identifies stiffness and automatically chooses between the explicit and the (new) implicit tau-selection methods to achieve better efficiency is proposed. Numerical testing demonstrates the advantages of the adaptive method for stiff systems.     

Effect of reactant size on discrete stochastic chemical kinetics

This paper is aimed at understanding what happens to the propensity functions (rates) of bimolecular chemical reactions when the volume occupied by the reactant molecules is not negligible compared to the containing volume of the system. For simplicity our analysis focuses on a one-dimensional gas of N hard-rod molecules, each of length l. Assuming these molecules are distributed randomly and uniformly inside the real interval [0,L] in a nonoverlapping way, and that they have Maxwellian distributed velocities, the authors derive an expression for the probability that two rods will collide in the next infinitesimal time dt. This probability controls the rate of any chemical reaction whose occurrence is initiated by such a collision. The result turns out to be a simple generalization of the well-known result for the point molecule case l=0: the system volume L in the formula for the propensity function in the point molecule case gets replaced by the "free volume" L-Nl. They confirm the result in a series of one-dimensional molecular dynamics simulations. Some possible wider implications of this result are discussed.     

Stereoselective catalytic tishchenko reduction of β-hydroxyketones using scandium triflate

A number of aliphatic and aromatic β-hydroxyketones were reduced to 1,3-diol monoesters by aldehydes in the presence of a catalytic amount of scandium triflate. Chiral substrates were reduced with high 1,3-anti diastereoselectivity.