On a Riemann hypothesis analogue for selfdual weight enumerators of genus less than 3

In this contribution the Riemann hypothesis analogue presented by Iwan Duursma is considered. Whether the analogue for a given selfdual code holds depends on its Hamming weight enumerator. A necessary and sufficient condition is provided in the case of genus less than 3 for the homogeneous polynomials in two variables invariant under the MacWilliams transform. Also the case of half integral genus is studied and similar results are obtained.     

Differential Forms in Synthetic Differential Supergeometry

We present a basic theory of differential formsin synthetic differential supergeometry. Exteriordifferential calculus is developed, and Cartan's threemagic formulas as well as a variant of de Rham's theorem are established.     

A new glycosylation method part 3: study of microwave effects at low temperatures to control reaction pathways and reduce byproducts

The efficiency of microwave irradiation at low temperature for glycosylations is described. Although oligosaccharide synthesis usually requires reactive donors for glycosylations, which have leaving groups on the anomer positions, i.e., trichloroacetoimidates, halogenates, thioalkyl glycosides, etc., the suitable donors in our microwave supported synthesis of Lewis X oligosaccharide were very stable acetate derivatives. Regarding glycosylation with a fucosyl acetate donor and a glucosamine acceptor, microwave irradiation with simultaneous cooling improved yields. Moreover, further synthesis to Lewis X derivatives was achieved only with microwave irradiation at low temperatures. Without microwave irradiation, we could only obtain byproducts and none of the designed product at any reaction temperature.     

Interfacial structure of oxidized inner pores in precursor-derived Si–C–N ceramics

Inner pore channels were commonly found in precursor-derived Si–C–N ceramics. After annealing in air at 1420 °C, their oxidation structures were investigated by analytical TEM. A carbon-rich ring was frequently observed under the silica layer inside the pore channels, which consisted of graphite-like clusters in size of 20–30 nm. Origin of such interfacial structure is due to the excessive free-carbon in the amorphous Si–C–N matrix that had survived the oxidation process. This graphitic interface could further improve the oxidation resistance of the SiO₂ over-layer. This novel interfacial structure was also found by annealing in N₂, reaffirming the effect of composition of Si–C–N matrix.     

Control of high-k/germanium interface properties through selection of high-k materials and suppression of GeO volatilization

Two approaches to control high-k/Ge interface qualities were investigated. The first approach was using high-k materials that are intimate with Ge. These Ge-intimate high-k materials should have moderate reactivity with Ge to form an amorphized interface that will reduce the interface defects and will suppress the GeO desorption at the interface. The second approach was modifying the annealing processes by using a cap layer to block GeO out-diffusion. We found that Si works as the cap layer very efficiently. By combining those two approaches, we achieved fairly good high-k/Ge metal-insulator-semiconductor (MIS) characteristics with LaYO₃ as the Ge-intimate high-k material, and a NiSi_X electrode as the cap layer. These results provide us an important guide for controlling the high-k/Ge interface properties.