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:
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 $m=3$.

Abstract:
Into a differential geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We construct a one-dimensional (mathematical) quantum field theory of AKSZ type in the BV formalism. Its quantization requires quantum corrections for classical local functionals at all loops, which are solved exactly by Fedosov's Abelian connections on Weyl bundles over symplectic manifolds. By consideration of the observables in our effective BV theory, we extend Fedosov's Abelian connections on Weyl bundles to a flat structure on a bundle of BV algebras. This allows us to utilize the tool of BV integration to obtain the trace map associated to the deformation quantization. This leads to a simple proof of the algebraic index theorem which corresponds to the one-loop computation in topological quantum mechanics.

Abstract:
Observations where additive noise is present can for many models be grouped into a compound observation matrix, adhering to the same type of model. There are many ways the observations can be stacked, for instance vertically, horizontally, or quadratically. An estimator for the spectrum of the underlying model can be formulated for each stacking scenario in the case of Gaussian noise. We compare these spectrum estimators for the different stacking scenarios, and show that all kinds of stacking actually decreases the variance when compared to just taking an average of the observations. We show that, regardless of the number of observations, the variance of the estimator is smallest when the compound observation matrix is made as square as possible. When the number of observations grow, however, it is shown that the difference between the estimators is marginal: Two stacking scenarios where the number of columns and rows grow to infinity are shown to have the same variance asymptotically, even if the asymptotic matrix aspect ratios differ. Only the cases of vertical and horizontal stackings display different behaviour, giving a higher variance asymptotically. Models where not all kinds of stackings are possible are also discussed.

Abstract:
Core-shell germanium nanowire (GeNW) is formed with a single-crystalline Ge core and concentric shells of nitride and silicon passivation layer by chemical vapor deposition (CVD), an Al2O3 gate dielectric layer by atomic layer deposition (ALD) and an Al metal surround-gate (SG) shell by isotropic magnetron sputter deposition. Surround gate nanowire field effect transistors (FETs) are then constructed using a novel self-aligned fabrication approach. Individual SG GeNW FETs show improved switching over GeNW FETs with planar gate stacks owing to improved electrostatics. FET devices comprised of multiple quasi-aligned SG GeNWs in parallel are also constructed. Collectively, tens of SG GeNWs afford on-currents exceeding 0.1mA at low source-drain bias voltages. The self-aligned surround gate scheme can be generalized to various semiconductor nanowire materials.

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:
The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai [FK96] seeks to relate two fundamental measures of Boolean function complexity: it states that $H[f] \leq C Inf[f]$ holds for every Boolean function $f$, where $H[f]$ denotes the spectral entropy of $f$, $Inf[f]$ is its total influence, and $C > 0$ is a universal constant. Despite significant interest in the conjecture it has only been shown to hold for a few classes of Boolean functions. Our main result is a composition theorem for the FEI conjecture. We show that if $g_1,...,g_k$ are functions over disjoint sets of variables satisfying the conjecture, and if the Fourier transform of $F$ taken with respect to the product distribution with biases $E[g_1],...,E[g_k]$ satisfies the conjecture, then their composition $F(g_1(x^1),...,g_k(x^k))$ satisfies the conjecture. As an application we show that the FEI conjecture holds for read-once formulas over arbitrary gates of bounded arity, extending a recent result [OWZ11] which proved it for read-once decision trees. Our techniques also yield an explicit function with the largest known ratio of $C \geq 6.278$ between $H[f]$ and $Inf[f]$, improving on the previous lower bound of 4.615.

Abstract:
Type II-plateau supernovae (SNe IIP) are the results of the explosions of red supergiants and are the most common subclass of core-collapse supernovae. Past observations have shown that the outer layers of the ejecta of SNe IIP are largely spherical, but the degree of asphericity increases toward the core. We present evidence for high degrees of asphericity in the inner cores of three recent SNe IIP (SNe 2006my, 2006ov, and 2007aa), as revealed by late-time optical spectropolarimetry. The three objects were all selected to have very low interstellar polarization (ISP), which minimizes the uncertainties in ISP removal and allows us to use the continuum polarization as a tracer of asphericity. The three objects have intrinsic continuum polarizations in the range of 0.83-1.56% in observations taken after the end of the photometric plateau, with the polarization dropping to almost zero at the wavelengths of strong emission lines. Our observations of SN 2007aa at earlier times, taken on the photometric plateau, show contrastingly smaller continuum polarizations (~0.1%). The late-time H-alpha and [O I] line profiles of SN 2006ov provide further evidence for asphericities in the inner ejecta. Such high core polarizations in very ordinary core-collapse supernovae provide further evidence that essentially all core-collapse supernova explosions are highly aspherical, even if the outer parts of the ejecta show only small deviations from spherical symmetry.