Cauchy-like Integral Theorems for Quaternion and Biquaternion Functions

It is well known that there is an integral theorem for quaternion-valued functions analogous to Cauchys Theorem for complex-valued functions, namely Fueters Theorem. The class of quaternionic functions for which this applies are generally referred to as regular functions, and these provide the most productive means of generalising the class of holomorphic complex functions. This paper derives a second integral theorem, also analogous to Cauchys Theorem, and which is believed to be quite distinct from that of Fueter, despite appearances. The paper takes the opportunity to present the basis of the derivation of both theorems, and also their extension to the associated classes of right-regular and conjugate regular functions. Both theorems can also be extended into the biquaternionic domain in which the four quaternion coordinates may be complex valued. This is of interest in physics as the Hermitian biquaternions have a natural norm which is Minkowskian and provide an elegant formalism for Lorentz transformations.Comment: 20 pages, 1 Figur

COMPARING MANAGEMENT SYSTEMS FOR BEEF CATTLE BACKGROUNDING: A MULTIDISCIPLINARY APPROACH

Livestock Production/Industries,

Extraction of the Axial Nucleon Form Factor from Neutrino Experiments on Deuterium

We present new parameterizations of vector and axial nucleon form factors. We maintain an excellent descriptions of the form factors at low momentum transfers ($Q^2$), where the spatial structure of the nucleon is important, and use the Nachtman scaling variable $\xi$ to relate elastic and inelastic form factors and impose quark-hadron duality constraints at high $Q^2$ where the quark structure dominates. We use the new vector form factors to re-extract updated values of the axial form factor from \numu experiments on deuterium. We obtain an updated world average value from \numud, \numubarH and pion electroproduction experiments of $M_{A}$ = $1.014 \pm 0.014 GeV/c^2$. Our parameterizations are useful in modeling $\nu$ interactions at low energies (e.g. for \numu oscillations experiments). The predictions for high $Q^2$ can be tested in the next generation electron and \numu scattering experiments.Comment: Presented by A. Bodek at the European Physical Society Meeting, EPS2007, Manchester, England, July 2007, 4 pages, 2 figure

New atlas of IR solar spectra

Over 4500 absorption lines have been marked on the spectra and the corresponding line positions tabulated. The associated absorbing telluric or solar species for more than 90% of these lines have been identified and only a fraction of the unidentified lines have peak absorptions greater than a few percent. The high resolution and the low Sun spectra greatly enhance the sensitivity limits for identification of trace constituents

Formation of the oxygen torus in the inner magnetosphere: Van Allen Probes observations

We study the formation process of an oxygen torus during the 12–15 November 2012 magnetic storm, using the magnetic field and plasma wave data obtained by Van Allen Probes. We estimate the local plasma mass density (ρL) and the local electron number density (neL) from the resonant frequencies of standing Alfvén waves and the upper hybrid resonance band. The average ion mass (M) can be calculated by M ∼ ρL/neL under the assumption of quasi-neutrality of plasma. During the storm recovery phase, both Probe A and Probe B observe the oxygen torus at L = 3.0–4.0 and L = 3.7–4.5, respectively, on the morning side. The oxygen torus has M = 4.5–8 amu and extends around the plasmapause that is identified at L∼3.2–3.9. We find that during the initial phase, M is 4–7 amu throughout the plasma trough and remains at ∼1 amu in the plasmasphere, implying that ionospheric O+ ions are supplied into the inner magnetosphere already in the initial phase of the magnetic storm. Numerical calculation under a decrease of the convection electric field reveals that some of thermal O+ ions distributed throughout the plasma trough are trapped within the expanded plasmasphere, whereas some of them drift around the plasmapause on the dawnside. This creates the oxygen torus spreading near the plasmapause, which is consistent with the Van Allen Probes observations. We conclude that the oxygen torus identified in this study favors the formation scenario of supplying O+ in the inner magnetosphere during the initial phase and subsequent drift during the recovery phase

Excitation of EMIC waves detected by the Van Allen Probes on 28 April 2013

Abstract We report the wave observations, associated plasma measurements, and linear theory testing of electromagnetic ion cyclotron (EMIC) wave events observed by the Van Allen Probes on 28 April 2013. The wave events are detected in their generation regions as three individual events in two consecutive orbits of Van Allen Probe-A, while the other spacecraft, B, does not detect any significant EMIC wave activity during this period. Three overlapping H+ populations are observed around the plasmapause when the waves are excited. The difference between the observational EMIC wave growth parameter (Eh) and the theoretical EMIC instability parameter (Sh) is significantly raised, on average, to 0.10 ± 0.01, 0.15 ± 0.02, and 0.07 ± 0.02 during the three wave events, respectively. On Van Allen Probe-B, this difference never exceeds 0. Compared to linear theory (Eh\u3eSh), the waves are only excited for elevated thresholds

Cystatins as calpain inhibitors: Engineered chicken cystatin- and stefin B-kininogen domain 2 hybrids support a cystatin-like mode of interaction with the catalytic subunit of μ-calpain

Within the cystatin superfamily, only kininogen domain 2 (KD2) is able to inhibit μ- and m-calpain. In an attempt to elucidate the structural requirements of cystatins for calpain inhibition, we constructed recombinant hybrids of human stefin B (an intracellular family 1 cystatin) with KD2 and Delta L110 deletion mutants of chicken cystatin-KD2 hybrids. Substitution of the N-terminal contact region of stefin B by the corresponding KD2 sequence resulted in a calpain inhibitor of K-i = 188 nM. Deletion of L110, which forms a beta -bulge in family 1 and 2 cystatins but is lacking in KD2, improved inhibition of mu -calpain 4- to 8-fold. All engineered cystatins were temporary inhibitors of calpain due to slow substrate-like cleavage of a single peptide bond corresponding to Gly9-Ala10 in chicken cystatin. Biomolecular interaction analysis revealed that, unlike calpastatin, the cystatin-type inhibitors do not bind to the calmodulin-like domain of the small subunit of calpain, and their interaction with the mu -calpain heterodimer is completely prevented by a synthetic peptide comprising subdomain B of calpastatin domain 1. Based on these results we propose that (i) cystatin-type calpain inhibitors interact with the active site of the catalytic domain of calpain in a similar cystatin-like mode as with papain and (ii) the potential for calpain inhibition is due to specific subsites within the papain-binding regions of the general cystatin fold

Frequency-Dependent Attenuation Analysis of Ground-Penetrating Radar Data

In the early 1990s, it was established empirically that, in many materials, ground-penetrating radar (GPR) attenuation is approximately linear with frequency over the bandwidth of a typical pulse. Further, a frequency-independent Q* parameter characterizes the slope of the band-limited attenuation versus frequency curve. Here, I derive the band-limited Q* function from a first-order Taylor expansion of the attenuation coefficient. This approach provides a basis for computing Q* from any arbitrary dielectric permittivity model. For Cole-Cole relaxation, I find good correlation between the first-order Q* approximation and Q* computed from linear fits to the attenuation coefficient curve over two-octave bands. The correlation holds over the primary relaxation frequency. For some materials, this relaxation occurs between 10 and 200 MHz, a typical frequency range for many GPR applications. Frequency-dependent losses caused by scattering and by the commonly overlooked problem of frequency-dependent reflection make it difficult or impossible to measure Q* from reflection data without a priori understanding of the materials. Despite these complications, frequency-dependent attenuation analysis of reflection data can provide valuable subsurface information. At two field sites, I find well-defined frequency-dependent attenuation anomalies associated with nonaqueous-phase liquid contaminants