On Higher Dimensional Point Sets in General Position

A finite point set in ?^d is in general position if no d + 1 points lie on a common hyperplane. Let ?_d(N) be the largest integer such that any set of N points in ?^d with no d + 2 members on a common hyperplane, contains a subset of size ?_d(N) in general position. Using the method of hypergraph containers, Balogh and Solymosi showed that ??(N) < N^{5/6 + o(1)}. In this paper, we also use the container method to obtain new upper bounds for ?_d(N) when d ? 3. More precisely, we show that if d is odd, then ?_d(N) < N^{1/2 + 1/(2d) + o(1)}, and if d is even, we have ?_d(N) < N^{1/2 + 1/(d-1) + o(1)}. We also study the classical problem of determining the maximum number a(d,k,n) of points selected from the grid [n]^d such that no k + 2 members lie on a k-flat. For fixed d and k, we show that a(d,k,n)? O(n^{d/{2?(k+2)/4?}(1- 1/{2?(k+2)/4?d+1})}), which improves the previously best known bound of O(n^{d/?(k + 2)/2?}) due to Lefmann when k+2 is congruent to 0 or 1 mod 4

Unavoidable patterns in complete simple topological graphs

In this paper, we show that every complete $n$-vertex simple topological graph contains a topological subgraph on at least $(\log n)^{1/4 - o(1)}$ vertices that is weakly isomorphic to the complete convex geometric graph or the complete twisted graph. This improves the previously known bound of $\Omega(\log^{1/8}n)$ due to Pach, Solymosi, and T\'oth. We also show that every complete $n$-vertex simple topological graph contains a planar path of length at least $(\log n)^{1 - o(1)}$

Water absorption and maintenance of nanofiber cellulose production by Gluconacetobacter rhaeticus TL-2C

Physiochemical properties of bacterial cellulose producing by Gluconacetobacter rhaeticus TL-2C was investigated for confirming its possibility as wound care dressing material. Scanning electron micrograph showed that the diameter of bacterial cellulose fiber was 40 to 50 nm. Solid state 13C nuclear magnetic resonance (NMR) data showed that the bacterial cellulose had amorphous peak of C-4 and C-6 and the crystallinity index of bacterial cellulose was 75.4. Water absorption ability of bacterial cellulose was 19-fold higher than α-cellulose. Bacterial cellulose had 2-fold higher water maintenance ability than α-cellulose.Key words: Bacterial cellulose, Gluconacetobacter rhaeticus, nanofiber, water absorption

Infrared-Mediated Drug Elution Activity of Gold Nanorod-Grafted TiO 2

The purpose of this research was to prepare gold nanorod- (GNR-) grafted TiO2 nanotubes by thiolactic acid treatment and evaluate remote-controlled drug elution and antibacterial activity by infrared (IR) light irradiation. Tetracycline used as an antibiotic was loaded into GNR-grafted TiO2 nanotubes by using 2 w/v% polylactic acid solutions. A near-IR laser (830 nm) was used for remote-controlled IR light irradiation. Results of SEM, TEM, XRD, and EDX revealed that GNR chemically bonded to the whole surface of the TiO2 nanotubes. An antibiotic release test revealed that on-off drug elution was triggered effectively by the photothermal effect of GNR grafted on TiO2 nanotubes. Furthermore, an antibacterial agar zone test indicated that the annihilated zone of Streptococcus mutans in the experimental group with IR light irradiation was significantly larger than that of the corresponding group without IR light irradiation (P<0.05). Therefore, GNR-grafted TiO2 nanotubes would be expected to extend the limited usage of TiO2, which show photocatalytic activity only within the ultraviolet (UV) to IR region, thereby allowing the development of novel fusion technologies in the field of implant materials