L-Functions for Symmetric Products of Kloosterman Sums

The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and $\infty$. We study the local monodromy of this representation at $\infty$ using $l$-adic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of the $L$-functions of the symmetric products of the above representation. Our results generalize some results of Robba obtained through $p$-adic method.Comment: 25 page

A Class of Incomplete Character Sums

Using $\ell$-adic cohomology of tensor inductions of lisse $\overline{\mathbb Q}_\ell$-sheaves, we study a class of incomplete character sums.Comment: Following the suggestion of the referee, we use tensor induction to study a class of incomplete character sums. Originally we use transfer, which is a special case of tensor induction, and which only works for rank one sheaves. The paper is to appear in Quarterly Journal of Mathematic

Cosmology of the Spinor Emergent Universe and Scale-invariant Perturbations

A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation in the frame of spinor emergent universe cosmology. Particularly, we introduce a light scalar field of which the kinetic term couples to the bilinear of the spinor field. This kinetic coupling can give rise to an effective "Hubble radius" for primordial fluctuations from the scalar field to squeeze at large length scales as well as to form a nearly scale-invariant power spectrum. We study the stability of the backreaction and constrain the forms of the coupling terms. These almost scale-independent fluctuations are able to be transferred into curvature perturbation after the epoch of emergent universe through a generalized curvaton mechanism and thus can explain cosmological observations.Comment: 11 pages, 4 figure

Galectin-12 in Cellular Differentiation, Apoptosis and Polarization.

Galectin-12 is a member of a family of mammalian lectins characterized by their affinity for β-galactosides and consensus amino acid sequences. The protein structure consists of a single polypeptide chain containing two carbohydrate-recognition domains joined by a linker region. Galectin-12 is predominantly expressed in adipose tissue, but is also detected in macrophages and other leukocytes. Downregulation of galectin-12 in mouse 3T3-L1 cells impairs their differentiation into adipocytes. Conversely, overexpression of galectin-12 in vitro induces cell cycle arrest in G1 and apoptosis. Upregulation of galectin-12 and initiation of G1 cell cycle arrest are associated with driving pre-adipocytes toward terminal differentiation. Galectin-12 deficiency increases insulin sensitivity and glucose tolerance in obese animals. Galectin-12 inhibits macrophage polarization to the M2 population, enhancing inflammation and decreasing insulin sensitivity in adipocytes. Galectin-12 also affects myeloid differentiation, which is associated with chemotherapy resistance. In addition to highlighting the above-mentioned aspects, this review also discusses the potential clinical applications of modulating the function of galectin-12

A High speed 16-bit RISC processor chip

The goal of this thesis is to design and simulate a high speed 16-bit processor chip by using RISC architecture. The high computing speed is achieved by employing a more effective four-stage pipeline. This processor executes every instruction in one clock cycle, and it won\u27t have any delay of executing instructions when it executes Jump, Condition Jump, Call, and Return instructions. Its computing speed is 4 times faster than the speed of the Berkeley RISC II\u27s for the 8-MHz clock. The design includes the main architectural features of the RISC: the 4-stage pipeline, the thirty-two 8-bit register bank, the 16-bit address and data paths, the internal timer, the input port, and the two output ports. The chip is designed using 2u. CMOS N well two metal layer technology. The processor runs at a clock rate of 16 MHz. The size of the chip is 10535fim by 14677um. It consists of 24,982 transistors and consumes 200mw

Polygonal vortex beams in quasi-frequency-degenerate states

We originally demonstrate the vortex beams with patterns of closed polygons [namely polygonal vortex beams (PVBs)] generated by a quasi-frequency-degenerate (QFD) Yb:CALGO laser resonator with astigmatic transformation. The PVBs with peculiar patterns of triangular, square, and parallelogram shapes carrying large orbital angular momentums (OAMs) are theoretically investigated and experimentally obtained in the vicinity of the SU(2) degenerate states of laser resonator. The PVBs in QFD states are compared with the vortex beams with patterns of isolated spots arrays located on the triangle-, square-, and parallelogram-shaped routes [namely polygonalspots-array vortex beams (PSA-VBs)] under normal SU(2) degenerate states. Beam profile shape of PVB or PSA-VB and OAM can be controlled by adjusting the cavity length and the position of pump spot. The simulated and experimental results validate the performance of our method to generate PVB, which is of great potential for promoting novel technologies in particle trapping and beam shaping