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.     

Analysis of G/D/1 Queueing Systems with Inputs Satisfying Large Deviation Principle under Weak* Topology

The large deviation principle (LDP) which has been effectively used in queueing analysis is the sample path LDP, the LDP in a function space endowed with the uniform topology. Chang [5] has shown that in the discrete-time G/D/1 queueing system under the FIFO discipline, the departure process satisfies the sample path LDP if so does the arrival process. In this paper, we consider arrival processes satisfying the LDP in a space of measures endowed with the weak^* topology (Lynch and Sethuraman [12]) which holds under a weaker condition. It is shown that in the queueing system mentioned above, the departure processes still satisfies the sample path LDP. Our result thus covers arrival processes which can be ruled out in the work of Chang [5]. The result is then applied to obtain the exponential decay rate of the queue length probability in an intree network as was obtained by Chang [5], who considered the arrival process satisfying the sample path LDP.     

On the option valuation and decomposition of exchange option

In this paper, we shall find the uniquerational price associated with the exchange option. Also, we find the decomposition of Snell envelope and value function of the American exchange option.     

Observation of the Bc meson in the exclusive decay Bc-->J/psipi

A fully reconstructed Bc-->J/psipi signal is observed with the D0 detector at the Fermilab Tevatron pp[over] collider using 1.3 fb(-1) of integrated luminosity. The signal consists of 54+/-12 candidates with a significance that exceeds 5 standard deviations, and confirms earlier observations of this decay. The measured mass of the Bc meson is 6300+/-14(stat)+/-5(syst) MeV/c2.     

Measurement of the forward-backward charge asymmetry in top-quark pair production

We present the first measurement of the integrated forward-backward charge asymmetry in top-quark-top-antiquark pair (tt) production in proton-antiproton (pp) collisions in the lepton+jets final state. Using a b-jet tagging algorithm and kinematic reconstruction assuming tt + X production and decay, a sample of 0.9 fb(-1) of data, collected by the D0 experiment at the Fermilab Tevatron Collider, is used to measure the asymmetry for different jet multiplicities. The result is also used to set upper limits on tt+X production via a Z' resonance.     

Structural and functional stabilities of artificially designed DNA ultra-thin films grown by silica Assistance

We report the structural and functional stabilities of artificially synthesized DNA ultra-thin films. Fully covered DNA ultra-thin films on a silica substrate were fabricated by the silica-assisted growth method and those samples were then incubated in various chemicals and physical conditions. The DNA ultra-thin films showed high maintainability under those harsh conditions and these results would aid to facilitate the use of artificial DNA ultra-thin films in advanced research areas such as biophotonics and bioelectronics.