Generalized Weighted Morrey Estimates for Marcinkiewicz Integrals with Rough Kernel Associated with Schrödinger Operator and Their Commutators

Let L =-?+V(x) be a Schr?dinger operator, where ? is the Laplacian on ■~n,while nonnegative potential V(x) belonging to the reverse H?lder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schr?dinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schr?dinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.     

Initial systematic investigations of the landscape of low layer NAHE extensions

The discovery that the number of physically consistent string vacua is on the order of 10⁵⁰⁰ has prompted several statistical studies of string phenomenology. Contained here is one such study that focuses on the Weakly Coupled Free Fermionic Heterotic String (WCFFHS) formalism. Presented are systematic extensions of the well-known NAHE (Nanopoulos, Antoniadis, Hagelin, Ellis) set of basis vectors, which have been shown to produce phenomenologically realistic models. Statistics related to the number of U(1)’s, the specific gauge groups and their factors, non-Abelian singlets, and spacetime supersymmetries (ST SUSYs) are discussed for the full range of models produced. These findings are compared with prior results of other large-scale investigations. Statistical coupling between the gauge groups and the number of ST SUSYs is also discussed. In particular, for order-3 extensions there is a correlation between the appearance of exceptional groups and enhanced ST SUSY. Also discussed are some three-generation GUT models found among the data sets. These models are unique because they come from basis vectors which still have a geometric interpretation—there are no “rank cuts” in these models.     

Rapid analysis of phentolamine by high-performance liquid chromatography

A rapid liquid chromatographic method is validated for the quantitative analysis of phentolamine. Phentolamine exists in three forms for this investigation: as a mesylate salt, hydrochloride salt, and free base. In solution, phentolamine dissociates from its salt and is chromatographed as free phentolamine. This validation confirms the analysis of each form, which is simply based upon molar mass differences encountered in weighing. As such, both the United States Pharmacopeia hydrochloride and mesylate standards are used throughout this validation to demonstrate this equivalency. The validation demonstrates that this method may be used to quantitate phentolamine, regardless of its salt form.     

Observation of anomalous momentum transport in tokamak plasmas with no momentum input

Anomalous momentum transport has been observed in Alcator C-Mod tokamak plasmas through analysis of the time evolution of core impurity toroidal rotation velocity profiles. Following the L-mode to EDA (enhanced D(alpha)) H-mode transition, the ensuing cocurrent toroidal rotation velocity, which is generated in the absence of any external momentum source, is observed to propagate in from the edge plasma to the core. The steady state toroidal rotation velocity profiles are relatively flat and the momentum transport can be simulated with a simple diffusion model. Velocity profiles during edge localized mode free (ELM-free) H-modes are centrally peaked, which suggests the addition of inward momentum convection. In all operating regimes the observed momentum diffusivities are much larger than the neoclassical values.     

On the theory of homogeneous Lipschitz spaces and mean oscillation spaces

In this paper the equivalence between the mean oscillation spaces and the homogeneous Lipschitz spaces will be shown through the use of elementary and constructive means. The mean oscillation spaces have been previously defined by Ricci and Taibleson for the case where the dimensionn=1. These spaces are extended here in a natural way to IR ⁿ .     

The OH-initiated oxidation of 1,3-butadiene in the presence of O2 and NO: a photolytic route to study isomeric selective reactivity

We report the study of the isomeric selective OH-initiated oxidation of 1,3-butadiene in the presence of O2 and NO using the LP/LIF technique. The photolysis of monodeuterated 1-iodo-3-buten-2-ol provides only one of the possible OD-butadiene adducts, the minor addition channel product, simplifying the oxidation mechanism. We find, based on analysis of OD time-dependent traces that prompt rearrangement of initial beta-hydroxyalkyl radicals to alpha-hydroxyalkyl radicals occurs in agreement with RRKM/ME theoretical predictions. We report a rate constant of (3.3+/-1.0) x 10(-11) cm3 molecules(-1) s(-1) for deuterium abstraction from the alpha-hydroxyalkyl radical at 298 +/-2 K. Our approach demonstrates the feasibility of isomeric selective kinetic studies of the OH-initiated oxidation of unsaturated hydrocarbons.     

A new form of kinetic isotope effect. Dynamic effects on isotopic selectivity and regioselectivity

The intramolecular H/D kinetic isotope effect in the ene reaction of singlet oxygen with tetramethylethylene is studied using quasiclassical direct dynamics calculations on a B3LYP/6-31G* potential energy surface. Starting from the area of the energy surface around a valley-ridge inflection point, random trajectories lead to predominantly H abstraction over D abstraction, despite the symmetry of the surface and the absence of a barrier to either reaction. This demonstrates a new form of kinetic isotope effect, unrelated to the usual effect of zero-point energies on barriers. Dynamics calculations on the reaction of cis-2-pentene predict the experimentally observed mixture of regioisomeric products, while the minimum-energy path leads to only one product. For energy surfaces containing two adjacent saddle points, dynamics effects are important for understanding both product and isotopic selectivity, and this should be considered in the interpretation of experimental results.