this paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. after a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. using doublet mechanics, the relation between natural f...

The Helmholtz equation, ∆u(x) + n(x)ωu(x) = f(x), x ∈ R, (1) is a time-independent linear partial differential equation. The interpretation of the unknown u(x) and the parameters n(x), ω and f(x) depends on what the equation models. The most common areas are wave propagation problems and quantum mechanics, in which case u(x) is the amplitude of a time-harmonic wave and the orbitals for an energ...

26 It is well documented that capacitance-based soil moisture sensor measurements are particularly influ27 enced by particle size distribution, density, salinity, and temperature of a soil, in addition to its moisture 28 content. Moreover, the equations provided by manufacturers of soil moisture sensors are often only 29 applicable to a limited number of soil types, thus yielding significant er...

Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R2. In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Fréchet differentiability of the scattering map is examined. A new continuati...

The method of estimating age frequency from length frequency via the von Bertalanffy growth equation is deterministic and yields biased results. Most of the biascan be removed by incorporating a stochastic element in the von Bertalanffy relationship. The stochastic element is based on estimated probabilities of lengths by intervals at age. the probabilities being estimated from variances in len...

We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low frequencies, independent of the geometry of the compact part of the manifold. We further prove a new type of Morawetz estimate in this context, with both hypothese...

High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic markets with limit order books. We use NASDAQ ITCH data to identify significa...

an active antenna for transmitter application in s frequency band is designed and analyzed using harmonic balance technique which is based on the nonlinear model of active devices. in this active antenna, the amplifier is integrated with the radiator which is a rectangular patch antenna. this patch antenna is analyzed employing full-wave momentum method. by applying nonlinear model of transisto...

We consider the high-frequency Helmholtz equation with a given source term, and a small absorption parameter α > 0. The high-frequency (or: