Properties of reflected sunlight derived from a Green's function method

The inference of optical depth and particle size of clouds and aerosols using remotely sensed reflected radiance at solar wavelengths has received much attention recently. The information these measurements provide is path integrated. However, very little is known about the vertical distribution of this weighting. To characterize it, we first solve the radiative transfer equation (RTE) by a Green's function approach, and then investigate the sensitivity of the weighting to vertical inhomogeneities in the extinction by introducing a function that is closely related to the Green's function, herein called the contribution function. This function calculates the contributions to the radiance at the upper boundary of the medium by underlying layers. Three hypothetical clouds of identical optical depth but exhibiting different extinction profiles were used in this study. The contribution function was found very sensitive to the extinction profile. The global reflection and transmission matrices used to construct the Green's function, derived using an eigenmatrix method, resulted in an efficient, stable, and accurate method for calculating the emerging radiances that can be extended to multi-layered media.     

On similarity and scaling of the radiative transfer equation

The present paper shows how the well-known similarity and scaling concepts are properties of the radiative transfer equation and not specifically of the degree of anisotropy of the phase function. It is shown that the key assumption regarding the angular dependence of the radiative field is essential in determining both the value for the parameter used to scale the radiative transfer, as well as the number of streams used in calculating the radiances for various atmospheric problems. Simulations performed on realistic type of cirrus clouds, characterized by strongly anisotropic functions, demonstrates the superior computational advantage for accurately simulating radiances. A new approach for determining the scaling parameter is introduced.     

Potential Benefits and Barriers to Integration

The rhetoric surrounding integration of mathematics and science abounds. Professional organizations’ standards and recommendations for reform in mathematics and science education each point out the need to make connections among various disciplines. However, some remain unconvinced, citing a lack of research supporting the assertion that integration improves student achievement. This article examines the current situation, discusses the growing body of related research, and examines the implementation issues related to integrated curriculum projects. The conclusion calls for mathematics and science educators to work collaboratively to address implementation issues surrounding reform of any kind and to explore further the possibilities of integration.     

Numerical methods for reaction-diffusion problems with non-differentiable kinetics

Summary We consider a class of steady-state semilinear reaction-diffusion problems with non-differentiable kinetics. The analytical properties of these problems have received considerable attention in the literature. We take a first step in analyzing their numerical approximation. We present a finite element method and establish error bounds which are optimal for some of the problems. In addition, we also discuss a finite difference approach. Numerical experiments for one- and two-dimensional problems are reported.Dedicated to Ivo Babuka on his sixtieth birthdayResearch partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF under Grant Number AFOSR 85-0322     

Rearrangements in cobaltic fluoride fluorinations of cycloalkanes with seven or more ring carbons

Cyclo-heptane, -octane, -decane, -dodecane and -octadecane have been fluorinated in the vapour phase with cobaltic fluoride. The perfluorocarbons obtained revealed varying degrees of skeletal rearrangements. Thus, cycloheptane gave perfluoro-cycloheptane and -methylcyclohexane; cyclooctane gave at least eight fluorocarbons including-bicyclo(3,3,0)octane and -cyclooctane; cyclodecane gave a complex mixture from which were isolated perfluoro cis- and trans-bicyclo(4,4,0)decanes but no perfluorocyclodecane; cyclododecane and cyclooctadecane gave complex fluorocarbon mixtures in which none of the fluorocarbons with the original cycloalkene skeleton could be detected.Tetradecafluorobicyclo(3,3,0)octane gave dodecafluorobicyclo (3,3,0)oct-1(5)-ene and decafluorobicyclo(3,3,0)octa-di-1(5), 2-ene when pyrolysed over iron gauze.The fluorination of cyclooctane also afforded 1$\text{H}$-pentadecafluorocyclooctane which was dehydrofluorinated to tetradecafluorocyclooctene. This was converted to a range of derivatives including dodecafluorosuberic acid, 1,2-dichlorotetradecafluorocyclooctane, 1-methoxy tridecafluorocyclooctene and tetradecafluorocyclooctanone.     

The binding selectivity of ADAR2's dsRBMs contributes to RNA-editing selectivity

ADAR2 is an RNA editing enzyme that deaminates adenosines in certain duplex structures. Here, we describe the role of its RNA binding domain, consisting of two copies of a common dsRNA binding motif (dsRBM), in editing site selectivity. ADAR2's dsRBMs bind selectively on a duplex RNA that mimics the Q/R editing site in the glutamate receptor B-subunit pre-mRNA. This selectivity is different from that of PKR's dsRBM I, indicating that dsRBMs from different proteins possess intrinsic binding selectivity. Using directed hydroxyl radical cleavage data, molecular models were developed that predict important recognition surfaces on the RNA for identified dsRBM binding sites. Blocking these surfaces by benzyl modification of guanosine 2-amino groups impeded RNA-editing, demonstrating a correlation between deamination efficiency by ADAR2 and selective binding by its dsRBMs. In addition, the editing activity of a mutant of ADAR2 lacking dsRBM I on N(2)-benzylguanosine-modified RNA suggests the location of the dsRBM I binding site that leads to editing at the GluR-B Q/R site.