Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

A comparative Raman study of the interaction of electron donor and acceptor molecules with graphene prepared by different methods

Interaction of tetrathiafulvalene (TTF) and tetracyanoethylene (TCNE) with few-layer graphene samples prepared by the exfoliation of graphite oxide (EG), conversion of nanodiamond (DG) and arc-evaporation of graphite in hydrogen (HG) has been investigated by Raman spectroscopy to understand the role of the graphene surface. The position and full-width at half maximum of the Raman G-band are affected on interaction with TTF and TCNE and the effect is highest with EG and least with HG. The effect of TTF and TCNE on the 2D-band is also maximum with EG. The magnitude of interaction between the donor/acceptor molecules varies in the same order as the surface areas of the graphenes. (C) 2009 Published by Elsevier B. V.

Foot morphological difference between habitually shod and unshod runners

Foot morphology and function has received increasing attention from both biomechanics researchers and footwear manufacturers. In this study, 168 habitually unshod runners (90 males whose age, weight & height were 23 +/- 2.4years, 66 +/- 7.1kg & 1.68 +/- 0.13m and 78 females whose age, weight & height were 22 +/- 1.8years, 55 +/- 4.7kg & 1.6 +/- 0.11m) (Indians) and 196 shod runners (130 males whose age, weight & height were 24 +/- 2.6years, 66 +/- 8.2kg & 1.72 +/- 0.18m and 66 females whose age, weight & height were 23 +/- 1.5years, 54 +/- 5.6kg & 1.62 +/- 0.15m)(Chinese) participated in a foot scanning test using the easy-foot-scan (a three-dimensional foot scanning system) to obtain 3D foot surface data and 2D footprint imaging. Foot length, foot width, hallux angle and minimal distance from hallux to second toe were calculated to analyze foot morphological differences. This study found that significant differences exist between groups (shod Chinese and unshod Indians) for foot length (female p = 0.001), width (female p = 0.001), hallux angle (male and female p = 0.001) and the minimal distance (male and female p = 0.001) from hallux to second toe. This study suggests that significant differences in morphology between different ethnicities could be considered for future investigation of locomotion biomechanics characteristics between ethnicities and inform last shape and design so as to reduce injury risks and poor performance from mal-fit shoes.

Determination of the enthalpies of sublimation and evaporation from thermogravimetric data: Application to metalorganic complexes of Al and Cr

A series of bimetallic acetylacetonate (acac) complexes, AlxCr1-x(acac)(3), 0 <= x <= 1, have been synthesized for application as precursors for the CVD Of Substituted oxides, such as (AlxCr1-x)(2)O-3. Detailed thermal analysis has been carried out on these complexes, which are solids that begin subliming at low temperatures, followed by melting, and evaporation from the melt. By applying the Langmuir equation to differential thermogravimetry data, the vapour pressure of these complexes is estimated. From these vapour pressure data, the distinctly different enthalpies of sublimation and evaporation are calculated, using the Clausius-Clapeyron equation. Such a determination of both the enthalpies of sublimation and evaporation of complexes, which sublime and melt congruently, does not appear to have been reported in the literature to date.

Influence of non-stoichiometric defects on nonlinear absorption and refraction in Nd:Zn co-doped lithium niobate

Nonlinear absorption and refraction phenomena in stoichiometric lithium niobate (SLN) pure and co-doped with Zn and Nd, and congruent lithium niobate (CLN) were investigated using Z-scan technique. Femtosecond laser pulses from Ti:Sapphire laser (800 nm, 110 fs pulse width and 1 kHz repetition rate) were utilized for the experiment. The process responsible for nonlinear behavior of the samples was identified to be three photon absorption (3PA). This is in agreement with the band gap energies of the samples obtained from the linear absorption cut off and the slope of the plot of Ln(1 − TOA) vs. Ln(I0) using Sutherland’s theory (s = 2.1, for 3PA). The nonlinear refractive index (n2) of Zn doped samples was found to be lower than that of pure samples. Our experiments show that there exists a correlation between the nonlinear properties and the stoichiometry of the samples. The values of n2 fall into the same range as those obtained for the materials of similar band gap.

Practical Algorithms For Mean Velocity Estimation In Pulse Doppler Weather Radars Using A Small Number Of Samples

Doppler weather radars with fast scanning rates must estimate spectral moments based on a small number of echo samples. This paper concerns the estimation of mean Doppler velocity in a coherent radar using a short complex time series. Specific results are presented based on 16 samples. A wide range of signal-to-noise ratios are considered, and attention is given to ease of implementation. It is shown that FFT estimators fare poorly in low SNR and/or high spectrum-width situations. Several variants of a vector pulse-pair processor are postulated and an algorithm is developed for the resolution of phase angle ambiguity. This processor is found to be better than conventional processors at very low SNR values. A feasible approximation to the maximum entropy estimator is derived as well as a technique utilizing the maximization of the periodogram. It is found that a vector pulse-pair processor operating with four lags for clear air observation and a single lag (pulse-pair mode) for storm observation may be a good way to estimate Doppler velocities over the entire gamut of weather phenomena.

Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected

A simple circuit to aid direct measurement of capture cross sections of deep level impurities

An inexpensive and simple circuit to aid the direct measurement of majority carrier capture cross sections of impurity levels in the band gap of a semiconductor by the variable width filling pulse technique is presented. With proper synchronisation, during the period of application of the pulse, the device is disconnected from the capacitance meter to avoid distortion of the pulse and is reconnected again to the meter to record the emission transient. Modes of operation include manual triggering for long emission transients, repetitive triggering for isothermal and DLTS measurements and the DLTS mode which is to be used with signal analysers that already provide a synchronising pulse for disconnection.

Flow of metal into the flash gap in the last stages of a plane-strain closed-die forging operation

In closed-die forging the flash geometry should be such as to ensure that the cavity is completely filled just as the two dies come into contact at the parting plane. If metal is caused to extrude through the flash gap as the dies approach the point of contact — a practice generally resorted to as a means of ensuring complete filling — dies are unnecessarily stressed in a high-stress regime (as the flash is quite thin and possibly cooled by then), which reduces the die life and unnecessarily increases the energy requirement of the operation. It is therefore necessary to carefully determine the dimensions of the flash land and flash thickness — the two parameters, apart from friction at the land, which control the lateral flow. The dimensions should be such that the flow into the longitudinal cavity is controlled throughout the operation, ensuring complete filling just as the dies touch at the parting plane. The design of the flash must be related to the shape and size of the forging cavity as the control of flow has to be exercised throughout the operation: it is possible to do this if the mechanics of how the lateral extrusion into the flash takes place is understood for specific cavity shapes and sizes. The work reported here is part of an ongoing programme investigating flow in closed-die forging. A simple closed shape (no longitudinal flow) which may correspond to the last stages of a real forging operation is analysed using the stress equilibrium approach. Metal from the cavity (flange) flows into the flash by shearing in the cavity in one of the three modes considered here: for a given cavity the mode with the least energy requirement is assumed to be the most realistic. On this basis a map has been developed which, given the depth and width of the cavity as well as the flash thickness, will tell the designer of the most likely mode (of the three modes considered) in which metal in the cavity will shear and then flow into the flash gap. The results of limited set of experiments, reported herein, validate this method of selecting the optimum model of flow into the flash gap.

Kallikrein-related peptidases in prostate cancer: From molecular function to clinical application

Prostate cancer is a leading contributor to male cancer-related deaths worldwide. Kallikrein-related peptidases (KLKs) are serine proteases that exhibit deregulated expression in prostate cancer, with KLK3, or prostate specific antigen (PSA), being the widely-employed clinical biomarker for prostate cancer. Other KLKs, such as KLK2, show promise as prostate cancer biomarkers and, additionally, their altered expression has been utilised for the design of KLK-targeted therapies. There is also a large body of in vitro and in vivo evidence supporting their role in cancer-related processes. Here, we review the literature on studies to date investigating the potential of other KLKs, in addition to PSA, as biomarkers and in therapeutic options, as well as their current known functional roles in cancer progression. Increased knowledge of these KLK-mediated functions, including degradation of the extracellular matrix, local invasion, cancer cell proliferation, interactions with fibroblasts, angiogenesis, migration, bone metastasis and tumour growth in vivo, may help define new roles as prognostic biomarkers and novel therapeutic targets for this cancer.

Effect of a magnetic field on the flow and blood oxygenation in channels of variable cross-section

The effect of a magnetic field on the flow and oxygenation of an incompressible Newtonian conducting fluid in channels with irregular boundaries has been investigated. The geometric parameter δ, which is a ratio of the mean half width of the channel d to the characteristic length λ along the channel over which the significant changes in the flow quantities occur, has been used for perturbing the governing equations. Closed form solutions of the various order equations are presented for the stream function. The equations for oxygen partial pressure remain nonlinear even after perturbation, therefore a numerical solution is presented. The expressions for shear stress at a wall and pressure distributions are derived. Here the separation in the flow occurs at a higher Reynolds number than the corresponding non-magnetic case. It is found that the magnetic field has an effect on local oxygen concentration but has a little effect on the saturation length.

A H-1-NMR STUDY OF BILIRUBIN IX-ALPHA SOLUBILIZATION BY CHOLATE MICELLES - APPLICATION OF NUCLEAR OVERHAUSER EFFECTS

The solubilization of bilirubin IX-Alpha in aqueous solution by sodium cholate micelles has been examined by 270 MHz 1H-NMR spectroscopy. Incorporation of bilirubin into the micelles is accompanied by specific shifts of bilirubin vinyl and bridgehead protons and the C18 and C19 methyl groups of the steroid. The observed chemical shifts show a monotonic concentration dependence suggesting that changes in aggregation size are continuous. Nuclear Overhauser effects (NOE) have been shown to be a useful probe or micellization. A 4:1 cholate/bilirubin mixture has been investigated by difference NOE spectroscopy. The observation of intermolecular nuclear Overhauser effects between peripheral protons of bilirubin and cholate are diagnostic of spatially proximate groups. Inter-cholate nuclear Overhauser effects increase in magnitude upon bilirubin incorporation suggesting closer packing of steroid molecules on solubilization of the pigment. Intramolecular nuclear Overhauser effects observed for solubilized bilirubin are consistent with a compact intramolecularly hydrogen-bonded conformation resembling that determined for bilirubin in the solid state.

Simple new PWM patterns for thyristor three-phase AC/DC convertors

Thyristor forced commutated AC/DC convertors are useful for improving the power factor and waveform of AC-side line current. These are controlled through pulse-width modulation schemes for best performance. However, the 3-phase versions impose restrictions on the PWM strategies that can be implemented for excellent harmonic rejection. This paper presents new PWM control strategies for the 3-phase converters and compares them along with the conventional 4-pulse PWM strategy for harmonic elimination. Finally, two new PWM strategies are shown to be the best, for which oscillograms are presented from actual implementation.

Laboratory investigation on the effects of overburden pressure, water, and time on slaking induced material property degradation of coal mine spoil

In open-cut strip mining, waste material is placed in-pit to minimise operational mine costs. Slope failures in these spoil piles pose a significant safety risk to personnel, along with a financial risk from loss of equipment and scheduling delays. It has been observed that most spoil pile failures occur when the pit has been previously filled with water and then subsequently dewatered. The failures are often initiated at the base of spoil piles where the material can undergo significant slaking (disintegration) over time due to overburden pressure and water saturation. It is important to understand how the mechanical properties of base spoil material are affected by slaking when designing safe spoil pile slope angles, heights, and dewatering rates. In this study, fresh spoil material collected from a coal mine in Brown Basin Coalfield of Queensland, Australia was subjected to high overburden pressure (0 – 900 kPa) under saturated condition and maintained over a period of time (0 – 6 months) allowing the material to slake. To create the above conditions, laboratory designed pressure chambers were used. Once a spoil sample was slaked under certain overburden pressure over a period of time, it was tested for classification, permeability, and strength properties. Results of this testing program suggested that the slaking of saturated coal mine spoil increase with overburden pressure and the time duration over which the overburden pressure was maintained. Further, it was observed that shear strength and permeability of spoil decreased with increase in spoil slaking.