A formulation of the Jacobi coefficients clj(a,b)via Bell polynomials

The Jacobi polynomials ( , ) are deeply intertwined with the Laplacian on compact rank one symmetric spaces. They represent the spherical or zonal functions and as such constitute the main ingredients in describing the spectral measures and spectral projections associated with the Laplacian on these spaces. In this note we strengthen this connection by showing that a set of spectral and geometric quantities associated with Jacobi operator fully describe the Maclaurin coefficients associated with the heat and other related Schwartzian kernels and present an explicit formulation of these quantities using the Bell polynomials

Semigroup asymptotics, Funk-Hecke identity and the Gegenbauer coefficients associated with the spherical Laplacian

A trace formulation of the Maclaurin spectral coefficients of the Schwartzian kernel of functions of the spherical Laplacian is given. A class of polynomials Pv/l (X) (l >_ 0, v > −1/2) linking to the classical Gegenbauer polynomials through a differential-spectral identity is introduced and its connection to the above spectral coefficients and their asymptotics analysed. The paper discusses some applications of these ideas combined with the Funk-Hecke identity and semigroup techniques to geometric and variational-energy inequalities on the sphere and presents some examples

Temperature and horizontal wind measurements on the ER-2 aircraft during the 1987 airborne Antarctic ozone experiment

The NASA ER-2 aircraft is equipped with special instrumentation to provide accurate in situ measurement of the atmospheric state variables during flight. The Meteorological Measurement System (MMS) on the ER-2 aircraft is described. Since the meteorological parameters (temperature, pressure, and wind vector) are extensively used by other ER-2 experimenters for data processing and interpretation, the accuracy and resolution of each of these parameters are assessed and discussed. During the 1987 Airborne Antarctic Ozone Experiment (AAOE) mission, the ER-2 aircraft was stationed at Punta Arenas, Chile (53 S, 72 W), and successfully flew over Antarctica on 12 occasions between August 17 and September 22, 1987. On each of the 12 flights, the ER-2 aircraft flight plan was to take off at approximately the same local time, fly southward at a near constant potential temperature surface, descend and ascend at the southernmost terminus at about 72 S over Antarctica and return northward at either the same or a different constant potential temperature surface. The measurements of the MMS experiment during the AAOE mission are presented. MMS data are organized to provide a composite view of the polar atmosphere, which is characterized by frigid temperatures and high zonal winds. Altitudinal variations of the temperature measurement (during takeoff/landing at Punta Arenas and during descent/ascent at the southern terminus) and latitudinal variations of the zonal wind (on near constant potential temperature surfaces) are emphasized and discussed

Theories of developmental dyslexia: Insights from a multiple case study of dyslexic adults

A multiple case study was conducted in order to assess three leading theories of developmental dyslexia: the phonological, the magnocellular (auditory and visual) and the cerebellar theories. Sixteen dyslexic and 16 control university students were administered a full battery of psychometric, phonological, auditory, visual and cerebellar tests. Individual data reveal that all 16 dyslexics suffer from a phonological deficit, 10 from an auditory deficit, 4 from a motor deficit, and 2 from a visual magnocellular deficit. Results suggest that a phonological deficit can appear in the absence of any other sensory or motor disorder, and is sufficient to cause a literacy impairment, as demonstrated by 5 of the dyslexics. Auditory disorders, when present, aggravate the phonological deficit, hence the literacy impairment. However, auditory deficits cannot be characterised simply as rapid auditory processing problems, as would be predicted by the magnocellular theory. Nor are they restricted to speech. Contrary to the cerebellar theory, we find little support for the notion that motor impairments, when found, have a cerebellar origin, or reflect an automaticity deficit. Overall, the present data support the phonological theory of dyslexia, while acknowledging the presence of additional sensory and motor disorders in certain individuals

Applications of the ER-2 meteorological measurement system

The NASA ER-2 aircraft is used as a platform for high altitude atmospheric missions. The Meteorological Measurement System (MMS) was developed specifically for atmospheric research to provide accurate high resolution measurements of pressure, temperature, and the 3-D wind vector with a sampling rate of 5/s. The MMS consist of three subsystems: (1) an air motion sensing system to measure the velocity of the air with respect to the aircraft; (2) a high resolution inertial navigation system (INS) to measure the velocity of the aircraft with respect to the earth; and (3) a data acquisition system to sample, process, and record the measurement quantities. MMS data have been used extensively by ER-2 investigators in elucidating the polar ozone chemistry. Herein, applications on atmospheric dynamics are emphasized. Large scale (polar vortex, potential vorticity, model atmosphere), mesoscale (gravity waves, mountain waves) and microscale (heat fluxes) atmospheric phenomena are investigated and discussed

Amino acid changes in the spike protein of feline coronavirus correlate with systemic spread of virus from the intestine and not with feline infectious peritonitis

Recent evidence suggests that a mutation in the spike protein gene of feline coronavirus (FCoV), which results in an amino acid change from methionine to leucine at position 1058, may be associated with feline infectious peritonitis (FIP). Tissue and faecal samples collected post mortem from cats diagnosed with or without FIP were subjected to RNA extraction and quantitative reverse-transcriptase polymerase chain reaction (qRT-PCR) to detect FCoV RNA. In cats with FIP, 95% of tissue, and 81% of faecal samples were PCR-positive, as opposed to 22% of tissue, and 60% of faecal samples in cats without FIP. Relative FCoV copy numbers were significantly higher in the cats with FIP, both in tissues (P < 0.001) and faeces (P = 0.02). PCR-positive samples underwent pyrosequencing encompassing position 1058 of the FCoV spike protein. This identified a methionine codon at position 1058, consistent with the shedding of an enteric form of FCoV, in 77% of the faecal samples from cats with FIP, and in 100% of the samples from cats without FIP. In contrast, 91% of the tissue samples from cats with FIP and 89% from cats without FIP had a leucine codon at position 1058, consistent with a systemic form of FCoV. These results suggest that the methionine to leucine substitution at position 1058 in the FCoV spike protein is indicative of systemic spread of FCoV from the intestine, rather than a virus with the potential to cause FIP