Aperture-Angle and Hausdorff-Approximation of Convex Figures

The aperture angle alpha(x, Q) of a point x not in 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 of C is the minimum aperture angle of any x in 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 of C with aperture angle approximation error (1 - 2/(k+1)) pi. 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 sigma, 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 1/(k+1) * sin(pi/(k+1)).Comment: Fixed incorrect affiliatio

Anticancer effect of tectochrysin in colon cancer cell via suppression of NF-kappaB activity and enhancement of death receptor expression

BACKGROUND: Flavonoids are a diverse family of natural phenolic compounds commonly found in fruits and vegetables. Epidemiologic studies showed that flavonoids also reduce the risk of colon cancer. Tectochrysin is one of the major flavonoids of Alpinia oxyphylla Miquel. However, the anti-cancer effects and the molecular mechanisms of tectochrysin in colon cancer cells have not yet been reported. We investigated whether tectochrysin could inhibit colon cancer cell growth at 1, 5, 10 μg/ml. In in vivo study, we injected a tectochrysin treatment dose of 5 mg/kg to each mouse. RESULTS: Tectochrysin suppressed the growth of SW480 and HCT116 human colon cancer cells. The expression of DR3, DR4 and Fas were significantly increased, and pro-apoptotic proteins were also increased. Tectochrysin treatment also inhibited activity of NF-κB. A docking model indicated that tectochrysin binds directly to the p50 unit. In in vivo, tumor weights and volumes in mice were reduced when treated with tectochrysin. Tectochrysin leads to apoptotic cell death in colon cancer cells through activation of death receptors expression via the inhibition of NF-κB. CONCLUSIONS: Tectochrysin can be a useful agent for the treatment of colon cancer cell growth as well as an adjuvant agent for chemo-resistant cancer cells growth

Antifungal and antiaflatoxigenic methylenedioxy-containing compounds and piperine-like synthetic compounds

Twelve methylenedioxy-containing compounds including piperine and 10 piperine-like synthetic compounds were assessed to determine their antifungal and antiaflatoxigenic activities against Aspergillus flavus ATCC 22546 in terms of their structure-activity relationships. Piperonal and 1,3-benzodioxole had inhibitory effects against A. flavus mycelial growth and aflatoxin B1 production up to a concentration of 1000 mu g/mL. Ten piperine-like synthetic compounds were synthesized that differed in terms of the carbon length in the hydrocarbon backbone and the presence of the methylenedioxy moiety. In particular, 1-(2-methylpiperidin-1-yl)-3-phenylprop-2-en-1-one had potent antifungal and antiaflatoxigenic effects against A. flavus up to a concentration of 1 mu g/mL. This synthetic compound was remarkable because the positive control thiabendazole had no inhibitory effect at this concentration. Reverse transcription-PCR analysis showed that five genes involved in aflatoxin biosynthesis pathways were down-regulated in A. flavus, i.e., aflD, aflK, aflQ, aflR, and aflS; therefore, the synthetic compound inhibited aflatoxin production by down-regulating these genes.ope

Digital Workflow for Retrofitting a Surveyed Crown Using a Removable Partial Denture as an Antagonist

Digital workflow expedites the procedure of retrofitting a surveyed crown against an existing removable partial denture (RPD). This article describes a simple and straightforward technique of digital workflow where an existing RPD is scanned as an antagonist to design the rest seat, guide plane, and height of contour of a surveyed crown.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156192/2/jopr13187_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156192/1/jopr13187.pd

The First Very Long Baseline Interferometry Image of 44 GHz Methanol Maser with the KVN and VERA Array (KaVA)

We have carried out the first very long baseline interferometry (VLBI) imaging of 44 GHz class I methanol maser (7_{0}-6_{1}A^{+}) associated with a millimeter core MM2 in a massive star-forming region IRAS 18151-1208 with KaVA (KVN and VERA Array), which is a newly combined array of KVN (Korean VLBI Network) and VERA (VLBI Exploration of Radio Astrometry). We have succeeded in imaging compact maser features with a synthesized beam size of 2.7 milliarcseconds x 1.5 milliarcseconds (mas). These features are detected at a limited number of baselines within the length of shorter than approximately 650 km corresponding to 100 Mlambda in the uv-coverage. The central velocity and the velocity width of the 44 GHz methanol maser are consistent with those of the quiescent gas rather than the outflow traced by the SiO thermal line. The minimum component size among the maser features is ~ 5 mas x 2 mas, which corresponds to the linear size of ~ 15 AU x 6 AU assuming a distance of 3 kpc. The brightness temperatures of these features range from ~ 3.5 x 10^{8} to 1.0 x 10^{10} K, which are higher than estimated lower limit from a previous Very Large Array observation with the highest spatial resolution of ~ 50 mas. The 44 GHz class I methanol maser in IRAS 18151-1208 is found to be associated with the MM2 core, which is thought to be less evolved than another millimeter core MM1 associated with the 6.7 GHz class II methanol maser.Comment: 19 pages, 3 figure

Inscribing or Circumscribing a Histogon to a Convex Polygon

We consider two optimization problems of approximating a convex polygon, one by a largest inscribed histogon and the other by a smallest circumscribed histogon. An axis-aligned histogon is an axis-aligned rectilinear polygon such that every horizontal edge has an integer length. A histogon of orientation ? is a copy of an axis-aligned histogon rotated by ? in counterclockwise direction. The goal is to find a largest inscribed histogon and a smallest circumscribed histogon over all orientations in [0,?). Depending on whether the horizontal width of a histogon is predetermined or not, we consider several different versions of the problem and present exact algorithms. These optimization problems belong to shape analysis, classification, and simplification, and they have applications in various cost-optimization problems

Copper nanofiber-networked cobalt oxide composites for high performance Li-ion batteries

We prepared a composite electrode structure consisting of copper nanofiber-networked cobalt oxide (CuNFs@CoOx). The copper nanofibers (CuNFs) were fabricated on a substrate with formation of a network structure, which may have potential for improving electron percolation and retarding film deformation during the discharging/charging process over the electroactive cobalt oxide. Compared to bare CoOxthin-film (CoOxTF) electrodes, the CuNFs@CoOxelectrodes exhibited a significant enhancement of rate performance by at least six-fold at an input current density of 3C-rate. Such enhanced Li-ion storage performance may be associated with modified electrode structure at the nanoscale, improved charge transfer, and facile stress relaxation from the embedded CuNF network. Consequently, the CuNFs@CoOxcomposite structure demonstrated here can be used as a promising high-performance electrode for Li-ion batteries

Successful Hemostasis with Recombinant Activated Factor VII in a Patient with Massive Hepatic Subcapsular Hematoma

Recombinant activated coagulation factor VII (rFVIIa) is known to be effective in the management of acquired deficiencies of factor VII and platelet function defects. But recently, rFVIIa has been successfully used to treat ongoing bleeding in disseminated intravascular coagulopathy (DIC) condition. The patient reported here was suspected to be suffering from toxic hepatitis on admission. After percutaneous liver biopsy, bleeding occurred and did not stop even after right hepatic artery embolization. The patient developed a severe hemorrhage that resulted in hypovolemic shock, hemoperitoneum, and a massive subcapsular hematoma. The patient then developed DIC due to massive transfusion, as well as acute liver necrosis. The patient was given 400 μg/kg of rFVIIa. Recombinant factor VIIa was administered in an attempt to control the bleeding. This stabilized the hemoglobin levels of the patient. The patient gradually recovered in 4 months. In conclusion, this case suggests that rFVIIa can be successfully used for the hemostasis of uncontrolled bleeding in DIC