Abstract:
Here we define Rarita-Schwinger operators on cylinders and construct their fundamental solutions. Further the fundamental solutions to the cylindrical Rarita-Schwinger type operators are achieved by applying translation groups. In turn, a Borel-Pompeiu Formula, Cauchy Integral Formula and a Cauchy Transform are presented for the cylinders. Moreover we show a construction of a number of conformally inequivalent spinor bundles on these cylinders. Again we construct Rarita-Schwinger operators and their fundamental solutions in this setting. Finally we study the remaining Rarita-Schwinger type operators on cylinders.

Abstract:
In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.

Abstract:
A correlation is observed between the diameter (d) distribution of single walled carbon nanotubes and the percentages of metallic and semiconducting tubes in materials synthesized at low temperature (600 C) by plasma-assisted chemical vapor deposition. Small diameter nanotubes (average d~1.1 nm) show semiconducting-tube percentage much higher than expected for random chirality distribution. Density functional theory calculations reveal discernable differences in the cohesive energies and heat of formation energies for similar-diameter metallic, quasi-metallic and semiconducting nanotubes. Semiconducting nanotubes exhibit the lowest energies and the stabilization effect scales with ~1/d2. This is a likely thermodynamic factor in preferential growth of small diameter semiconducting nanotubes.

Abstract:
We present optical photometric and spectral data of the peculiar Type Ic SN 2002ap. Photometric coverage includes UBVRI bands from 2002 January 30, the day after discovery, through 2002 December 12. There are 5 early-time spectra and 8 in the nebular phase. We determine that SN 2002ap is similar to SN 1997ef and the GRB-associated SN 1998bw with respect to spectral and photometric characteristics. The nebular spectra of SN 2002ap present the largest Mg I] \lambda 4571 to [O I] \lambda \lambda 6300, 6364 ratio of any supernova spectra yet published, suggesting that the progenitor of SN 2002ap was a highly stripped star. Comparing the nebular spectra of SN 1985F and SN 2002ap, we notice several similar features, casting the classification of SN 1985F as a normal Type Ib supernova in doubt. We also present nebular modeling of SN 2002ap and find that the object ejected >~ 1.5 M_{sun} of material within the outer velocity shell of the nebula (~5500 km/s) and synthesized ~0.09 M_{sun} of 56Ni.

Abstract:
SN 2002es is a peculiar subluminous Type Ia supernova (SN Ia) with a combination of observed characteristics never before seen in a SN Ia. At maximum light, SN 2002es shares spectroscopic properties with the underluminous SN 1991bg subclass of SNe Ia, but with substantially lower expansion velocities (~6000 km/s) more typical of the SN 2002cx subclass. Photometrically, SN 2002es differs from both SN 1991bg-like and SN 2002cx-like supernovae. Although at maximum light it is subluminous (M_B=-17.78 mag), SN 2002es has a relatively broad light curve (Dm15(B)=1.28 +/- 0.04 mag), making it a significant outlier in the light-curve width vs. luminosity relationship. We estimate a 56Ni mass of 0.17 +/- 0.05 M_sun synthesized in the explosion, relatively low for a SN Ia. One month after maximum light, we find an unexpected plummet in the bolometric luminosity. The late-time decay of the light curves is inconsistent with our estimated 56Ni mass, indicating that either the light curve was not completely powered by 56Ni decay or the ejecta became optically thin to gamma-rays within a month after maximum light. The host galaxy is classified as an S0 galaxy with little to no star formation, indicating the progenitor of SN 2002es is likely from an old stellar population. We also present a less extensive dataset for SN 1999bh, an object which shares similar observed properties. Both objects were found as part of the Lick Observatory Supernova Search, allowing us to estimate that these objects should account for ~2.5% of SNe Ia within a fixed volume. We find that current theoretical models are unable to explain the observed of characteristics of SN 2002es.

Abstract:
This is the second paper of a series in which we present new measurements of the observed rates of supernovae (SNe) in the local Universe, determined from the Lick Observatory Supernova Search (LOSS). In this paper, a complete SN sample is constructed, and the observed (uncorrected for host-galaxy extinction) luminosity functions (LFs) of SNe are derived. These LFs solve two issues that have plagued previous rate calculations for nearby SNe: the luminosity distribution of SNe and the host-galaxy extinction. We select a volume-limited sample of 175 SNe, collect photometry for every object, and fit a family of light curves to constrain the peak magnitudes and light-curve shapes. The volume-limited LFs show that they are not well represented by a Gaussian distribution. There are notable differences in the LFs for galaxies of different Hubble types (especially for SNe Ia). We derive the observed fractions for the different subclasses in a complete SN sample, and find significant fractions of SNe II-L (10%), IIb (12%), and IIn (9%) in the SN II sample. Furthermore, we derive the LFs and the observed fractions of different SN subclasses in a magnitude-limited survey with different observation intervals, and find that the LFs are enhanced at the high-luminosity end and appear more "standard" with smaller scatter, and that the LFs and fractions of SNe do not change significantly when the observation interval is shorter than 10 days. We also discuss the LFs in different galaxy sizes and inclinations, and for different SN subclasses. Some notable results are ... (abridged).

Abstract:
This paper concerns migrant identity construction in an ESOL course. Taking a poststructuralist perspective, identity is viewed a fluid process of ongoing struggle between different subject positions that individuals take in a variety of social sites. In this study, five migrant ESOL learners were interviewed to talk about the concept of self to investigate the process of identity construction. The purpose of this study was also toidentify the role of learning English for migrant workers in relation to imagined community and self. The study showed how these migrant ESOL learners conceptualize self in relation to two aspects: learning English and investment, gaining social and cultural capitals and access to imagine community, and being transmigrants. This paper highlights the implications in language education.

Abstract:
Acetylcholine-based neurotransmission is regulated by cationic, ligand-gated ion channels called nicotinic acetylcholine receptors (nAChRs). These receptors have been linked to numerous neurological diseases and disorders such as Alzheimer's disease, Parkinson's disease, and nicotine addiction. Recently, a class of compounds has been discovered that antagonize nAChR function in an allosteric fashion. Models of human α4β2 and α3β4 nicotinic acetylcholine receptor (nAChR) extracellular domains have been developed to computationally explore the binding of these compounds, including the dynamics and free energy changes associated with ligand binding. Through a blind docking study to multiple receptor conformations, the models were used to determine a putative binding mode for the negative allosteric modulators. This mode, in close proximity to the agonist binding site, is presented in addition to a hypothetical mode of antagonism that involves obstruction of C loop closure. Molecular dynamics simulations and MM-PBSA free energy of binding calculations were used as computational validation of the predicted binding mode, while functional assays on wild-type and mutated receptors provided experimental support. Based on the proposed binding mode, two residues on the β2 subunit were independently mutated to the corresponding residues found on the β4 subunit. The T58K mutation resulted in an eight-fold decrease in the potency of KAB-18, a compound that exhibits preferential antagonism for human α4β2 over α3β4 nAChRs, while the F118L mutation resulted in a loss of inhibitory activity for KAB-18 at concentrations up to 100 μM. These results demonstrate the selectivity of KAB-18 for human α4β2 nAChRs and validate the methods used for identifying the nAChR modulator binding site. Exploitation of this site may lead to the development of more potent and subtype-selective nAChR antagonists which may be used in the treatment of a number of neurological diseases and disorders.

Abstract:
In this paper we study some operators associated to the Rarita-Schwinger operators. They arise from the difference between the Dirac operator and the Rarita-Schwinger operators. These operators are called remaining operators. They are based on the Dirac operator and projection operators $I-P_k.$ The fundamental solutions of these operators are harmonic polynomials, homogeneous of degree $k$. First we study the remaining operators and their representation theory in Euclidean space. Second, we can extend the remaining operators in Euclidean space to the sphere under the Cayley transformation.

Abstract:
We introduce a new statistic, skip, on rational $(3,n)$-Dyck paths and define a marked rank word for each path when $n$ is not a multiple of 3. If a triple of valid statistics (area,skip,dinv) are given, we have an algorithm to construct the marked rank word corresponding to the triple. By considering all valid triples we give an explicit formula for the $(m,n)$-rational $q,t$-Catalan polynomials when $m=3$. Then there is a natural bijection on the triples of statistics (area,skips,dinv) which exchanges the statistics area and dinv while fixing the skip. Thus we prove the $q,t$-symmetry of $(m,n)$-rational $q, t$-Catalan polynomials for $m=3$.