Double complex and gamma-monomials in global function fields

We investigate Γ-monomials of positive characteristic Γ-functions in the global function fields by using Anderson's double complex method. The results are the generalizations of those in the rational function field case.     

Aperture-Angle and Hausdorff-Approximation of Convex Figures

The aperture angle α(x,Q) of a point x ∉ Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q⊂C is the minimum aperture angle of any x∈C∖Q with respect to Q. We show that for any compact convex set C in the plane and any k>2, there is an inscribed convex k-gon Q⊂C with aperture angle approximation error . This bound is optimal, and settles a conjecture by Fekete from the early 1990s. The same proof technique can be used to prove a conjecture by Brass: If a polygon P admits no approximation by a sub-k-gon (the convex hull of k vertices of P) with Hausdorff distance σ, but all subpolygons of P (the convex hull of some vertices of P) admit such an approximation, then P is a (k+1)-gon. This implies the following result: For any k>2 and any convex polygon P of perimeter at most 1 there is a sub-k-gon Q of P such that the Hausdorff-distance of P and Q is at most  . This research was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-311-D00763). NICTA is funded through the Australian Government’s Backing Australia’s Ability initiative, in part through the Australian Research Council.     

Possible isolation number of a matrix over nonnegative integers

Let ?₊ be the semiring of all nonnegative integers and A an m × n matrix over ?₊. The rank of A is the smallest k such that A can be factored as an m × k matrix times a k×n matrix. The isolation number of A is the maximum number of nonzero entries in A such that no two are in any row or any column, and no two are in a 2 × 2 submatrix of all nonzero entries. We have that the isolation number of A is a lower bound of the rank of A. For A with isolation number k, we investigate the possible values of the rank of A and the Boolean rank of the support of A. So we obtain that the isolation number and the Boolean rank of the support of a given matrix are the same if and only if the isolation number is 1 or 2 only. We also determine a special type of m×n matrices whose isolation number is m. That is, those matrices are permutationally equivalent to a matrix A whose support contains a submatrix of a sum of the identity matrix and a tournament matrix.     

Misalignment tolerance analysis and fabrication for highly efficient parallel optical-electrical convertor module

A compact, highly efficient, and passively assembled parallel optical-electrical convertor module (POECM) for active optical cable application is proposed. This paper presents our POECM structure, optical design simulation results, fabrication process, and data transmission test results, in sequence. The POECM has a compact size of \(18.5\hbox {mm} \times 10\hbox {mm} \times 2.8\hbox {mm}\) . We confirm a data rate of total throughput at 21.6 Gbps ( \(5.4\hbox {Gbps} \times 4\) channels) with a bit error rate of less than \(10^{-12}\) .     

Multichannel transceiver dual-tuned RF coil for proton/sodium MR imaging of knee cartilage at 3 T

Sodium magnetic resonance (MR) imaging is a promising technique for detecting changes of proteoglycan (PG) content in cartilage associated with knee osteoarthritis. Despite its potential clinical benefit, sodium MR imaging in vivo is challenging because of intrinsically low sodium concentration and low MR signal sensitivity. Some of the challenges in sodium MR imaging may be eliminated by the use of a high-sensitivity radiofrequency (RF) coil, specifically, a dual-tuned (DT) proton/sodium RF coil which facilitates the co-registration of sodium and proton MR images and the evaluation of both physiochemical and structural properties of knee cartilage. Nevertheless, implementation of a DT proton/sodium RF coil is technically difficult because of the coupling effect between the coil elements (particularly at high field) and the required compact design with improved coil sensitivity. In this study, we applied a multitransceiver RF coil design to develop a DT proton/sodium coil for knee cartilage imaging at 3 T. With the new design, the size of the coil was minimized, and a high signal-to-noise ratio (SNR) was achieved. DT coil exhibited high levels of reflection S11 (～-21 dB) and transmission coefficient S12 (～-19 dB) for both the proton and sodium coils. High SNR (range 27-38) and contrast-to-noise ratio (CNR) (range 15-21) were achieved in sodium MR imaging of knee cartilage in vivo at 3-mm(3) isotropic resolution. This DT coil performance was comparable to that measured using a sodium-only birdcage coil (SNR of 28 and CNR of 20). Clinical evaluation of the DT coil on four normal subjects demonstrated a consistent acquisition of high-resolution proton images and measurement of relative sodium concentrations of knee cartilages without repositioning of the subjects during the same MR scanning session.     

Transparent p‐NiO/n‐ZnO diodes used in circuit rectifiers

We report on the fabrication of a transparent photostable cell circuit composed of drive and resistor diodes which are face‐to‐face connected to each other with different device area. The diodes consisted of e‐beam evaporated p‐NiO on sputter‐deposited n‐ZnO for p/n diode formation on indium‐tin‐oxide glass. Our transparent diodes show photostable rectifying behavior, about 10³ on/off current ratio and even dynamic rectification at a maximum frequency of 100 Hz AC input signal in ambient light. The noticeable photo‐responsivity of the circuit was obtained only under ultraviolet (UV) light. We conclude that our transparent diode circuit is promising in enriching the field of transparent device electronics. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of Morphological Homogeneity of Superspherical Gold Nanoparticles on Plasmonic Photothermal Heat Generation

The plasmonic photothermal (PPT) characteristics of gold nanostructures have been extensively investigated theoretically and experimentally due to their potential for use materials science and industry. The management of the size and shape of gold nanoparticles has been a key issue in the development of better solutions for PPT heat generation because their size and shape determine their resultant photothermal properties. However, the light absorption of gold nanostructures is mainly dependent on the wavelength and orientation of the incident light; hence, maintaining uniform size and shape is critical for achieving maximum photothermal energy. Morphologically homogeneous spherical gold nanoparticles, or super gold nanospheres prepared by slowly etching uniform octahedral gold nanoparticles, demonstrate better PPT heat generation compared with commercially available nonsmooth gold nanoparticles (GNSs). The PPT heating experiments show a maximum temperature difference of 5.7 °C between the super and ordinary GNSs with the same average maximum Feret's diameters, which result from the more efficient PPT heat power generation (20.6%) of the super GNSs. In an electromagnetic‐wave simulation, the super GNSs show lower polarization dependence and a 24.6% higher absorption cross‐section than ordinary GNSs.     

Synthesis of blue-light-emitting ZnGa2O4 nanowires using chemical vapor deposition

A high-density array of vertically aligned ZnGa(2)O(4) nanowires has been synthesized on Si substrates via CVD of ZnO-Ga at 1000 degrees C consisting of a single-crystalline cubic spinel structure grown in a [111] direction and exhibiting strong photoluminescence and cathodoluminescence in the blue wavelength region.