On the Exponential Bound of the Cutoff Resolvent

A simpler proof of a result of Burq [1] is presented.

On the Uniform Decay of the Local Energy

It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. We extend this to even dimensional spaces and to more general perturbations (including the transmission problem) showing that any uniform decay of the local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time and n being the space dimension.

Validity of currently used cutoff values of body mass index as a measure of obesity in Sri Lankan children

The aim of the study was to determine the reliability of body mass index based (BMI) cutoff values in diagnosing obesity among Sri Lankan children. Height, weight, waist circumference (WC) and hip circumference (HC) in 282 children were measured. Total body water was determined by deuterium dilution and fat mass (FM) derived using age and gender specific constants. A percentage FM of 30% for girls and 25% for boys were considered as cutoff levels for obesity. Two hundred and eighty two children (M/F: 158/124) were studied and 99 (80%) girls and 72 (45.5%) boys were obese based on % body fat. Eight (6.4%) girls and nine (5.7%) boys were obese based on International Obesity Task Force (IOTF) cutoff values. Percentage FM and WC centile charts were able to diagnose a significant proportion of children as true obese children. The FM and BMI were closely associated in both girls (r = 0.82, p < 0.001) and boys (r = 0.87, p < 0.001). Percentage FM and BMI had a very low but significant association; girls (r = 0.32, p < 0.001) and boys (r = 0.68, p < 0.001). FM had a significant association with WC and HC. BMI based cutoff values had a specificity of 100% but a very low sensitivity, varying between 8% and 23.6%. BMI is a poor indicator of the percentage fat and the commonly used cutoff values were not sensitive to detect cases of childhood obesity in Sri Lankan children.

Cement bentonite cutoff walls for polluted sites

Cement-bentonite (CB) cutoff walls have long been used to control ground water flow and contaminant migration at polluted sites. Hydraulic conductivity and unconfined compressive strength are two short-term properties often used by industry and owners in CB specification and are important parameters discussed in this paper. For polluted sites, long-term compatibility is also an important issue. These properties are coupled to a number of external factors including the mix design, construction sequence, presence/absence of contaminants at the site. Additional short-term properties for engineering assessment include the stressstrain characteristics in both drained and undrained shear in both with and without confinement as well as one-dimensional consolidation properties. Long term CB properties are affected by aging, reaction chemistry, drying, in situ stress state, and interaction with the polluted environment. © 2013 Taylor & Francis Group.

Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.

Feller transition functions, Resolvent Decomposition Theorems, and their application in unstable denumerable Markov processes

This paper surveys the recent progresses made in the field of unstable denumerable Markov processes. Emphases are laid upon methodology and applications. The important tools of Feller transition functions and Resolvent Decomposition Theorems are highlighted. Their applications particularly in unstable denumerable Markov processes with a single instantaneous state and Markov branching processes are illustrated.

High-energy cutoff in the spectrum of strong-field nonsequential double ionization

Electron energy distributions of singly and doubly ionized helium in an intense 390 nm laser field have been measured at two intensities (0.8 PW/cm(2) and 1.1 PW/cm(2), where PW equivalent to 10(15) W/cm(2)). Numerical solutions of the full-dimensional time-dependent helium Schrodinger equation show excellent agreement with the experimental measurements. The high-energy portion of the two-electron energy distributions reveals an unexpected 5U(p) cutoff for the double ionization (DI) process and leads to a proposed model for DI below the quasiclassical threshold.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Comment on "Dynamics in a Multicomponent Plasma Near the Low-Frequency Cutoff"

A Comment on the Letter by Gurudas Ganguli and Leonid Rudakov, Phys. Rev. Lett. 93 135001 (2004). The authors of the Letter offer a Reply.

Propagation Characteristics of Groove Gap Waveguide Below and Above Cutoff

Recently, gap waveguides have been shown as a potential alternative to conventional waveguides in the millimeterwave band. Until now, Groove Gap Waveguide (GGW) has been studied through direct correspondence with rectangular waveguide with the same physical dimensions. However there have been observed differences in the above cutoff propagation characteristics between these two waveguide types. Furthermore, the behavior of GGW below cutoff remains unknown. This work presents a discussion of both below and above cutoff propagation characteristics of GGW, and introduces a simple model that explains the observed GGW behavior and establishes well its propagation characteristics. Two TRL calibration kits have been manufactured, and the measurements have good agreement with the proposed analysis model results.

Multipole Theory Analysis of Cutoff Wavenumbers of Waveguides Partially Filled with Dielectric

A new approach, the multipole theory (MT) method, is presented for the computation of cutoff wavenumbers of waveguides partially filled with dielectric. The MT formulation of the eigenvalue problem of an inhomogeneous waveguide is derived. Representative computational examples, including dielectric-rod-loaded rectangular and double-ridged waveguides, are given to validate the theory, and to demonstrate the degree of its efficiency