An optimal service rate in a Poisson arrival queue with two-stage service policy*

We consider a two-stage service policy for a Poisson arrival queueing system. The idle server starts to work with ordinary service rate when a customer arrives. If the number of customers in the system reaches N, the service rate gets faster and continues until the system becomes empty. Otherwise, the server finishes the busy period with ordinary service rate. After assigning various operating costs to the system, we show that there exists a unique fast service rate minimizing the long-run average cost per unit time.This work was supported by Korea Research Foundation Grant(KRF-2002-070-C00021).     

Ideals and Subalgebras in BCI-Algebras

We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal.AMS Subject Classification (1991): 06F35, 03G25.The second author was supported by the LG Yonam Foundation (1995).     

Free vibration analysis of a hanged clamped-free cylindrical shell partially submerged in fluid: The effect of external wall,internal shaft,and flat bottom

The free flexural vibration of a hanged clamped-free cylindrical shell with various boundary conditions partially submerged in a fluid is investigated. Specifically, the effects of the boundary conditions such as the existence of the external wall, internal shaft, and bottom on the natural vibration characteristics of the partially submerged cylindrical shell are investigated both theoretically and experimentally. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion. The theoretical predictions were in good agreement with the experimental results validating the theoretical approach developed in this study. The effects of the external wall, internal shaft, and bottom on the natural vibration characteristics can be neglected when its boundaries are not very close to the shell structure.     

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.     

Monolayer assembly and striped architecture of Co nanoparticles on organic functionalized Si surfaces

We present a new strategy to fabricate a monolayer assembly of Br-terminated Co nanoparticles on functionalized Si surfaces by using chemical covalent bonding and microcontact printing method. Self-assembled monolayers (SAMs) of the Co nanoparticles formed on the hydroxyl-terminated Si surface exhibit two-dimensional island networks with locally ordered arrays via covalent linkage between nanoparticles and surface. On the other hand, SAMs of the nanoparticles on the aminopropyl-terminated Si surface show an individual and random distribution over an entire surface. Furthermore, we have fabricated striped architectures of Co nanoparticles using a combination of microcontact printing and covalent linkage. Microcontact printing of octadecyltrichlorosilane and selective covalent linkage between nanoparticles and functionalized Si surfaces lead to a hybrid nanostructure with selectively assembled nanoparticles stripes on the patterned functionalized Si surfaces. PACS 81.07.Ta; 61.46.+w; 81.16.Dn; 81.16.Be; 68.37.Hk; 82.80.Pv     

Nonane droplet combustion with and without buoyant convection: Flame structure, burning rate and extinction in air and helium

The burning and extinction characteristics of isolated small nonane droplets are examined in a buoyant convective environment and in an environment with no external axial convection (as created by doing experiments at low gravity) to promote spherical droplet flames. The ambience is air and a mixture of 30%O₂/70%He to assess the influence of soot formation. The initial droplet diameter (D_o) ranges from 0.4 to 0.95 mm. Measurements are reported of the extinction diameter and time to extinction, and of the evolution of droplet diameter, flame diameter, soot shell diameter, burning rate, and broadband radiative emissions.In a buoyancy-free environment for air larger droplets burn slower than smaller droplets for the range of D_o examined, which is attributed to the influence of soot. In the presence of a buoyant flow in air, no influence of D_o is observed on the burning rate while the buoyant flames are still heavily sooting. The effect of D_o is believed to be due to a combination of dominance of the nonluminous, nonsooting, portion of the buoyant flame around the forward half of the droplet on heat transport and the secondary role of the luminous wake portion of the flame. In a non-sooting helium inert at low gravity, no effect of D_o is found on the evolution of droplet diameter.Flame extinction is observed only in the 30%O₂/70%He ambience. For all of the observations, extinction appears to occur before the disappearance of the droplet which is then followed by a period of evaporation. The extinction diameter and time to extinction increases with D_o and an empirical correlation is presented for these two variables.     

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.     

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.     

Isocassiaoccidentalin B,A New C‐Glycosyl Flavone Containing a 3‐Keto Sugar,and Other Constituents from Cassia nomame

A new C‐glycosyl flavone containing a 3‐keto sugar, isocassiaoccidentalin B ( 1 ), was isolated from whole Cassia nomame (Sieber ) Honda plants, along with eleven known compounds, including two flavonoids ( 2 and 3 ), five flavonoid glycosides ( 4  –  8 ), two chalcones ( 9 and 10 ), and two phenylpropanoids ( 11 and 12 ). The chemical structures of all compounds were determined via 1D‐ and 2D‐NMR, and ESI‐MS. Among these, compounds 2 , 3 , 7 , and 8 were found to be the most potent in inhibiting nitric oxide release. Compounds 1 , 2 , 4 , 8 , 9 , and 10 showed significant free‐radical scavenging activity.     

Anisotropic assembly of Ag nanoprisms

The Ag nanoprisms with controlled arrangements show distinct optical, crystallographic, and surface-enhanced Raman scattering properties depending on their orientation in the assemblies, demonstrating that the controlled assembly of anisotropic nanostructures can be utilized as a powerful tool for studying their physicochemical properties and for the creation of new classes of functional materials.