In a weakly coupled structural-acoustic problem, the boundary conditions may be composed by two conditions. One is a velocity boundary condition, which can be obtained from a dynamic structural analysis and the other is an acoustic impedance boundary condition. The acoustic impedance boundary condition is used for modeling acoustic absorbent behavior at boundaries proportional to the velocity d...

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this arti...

The highly sensitive nature of surface plasmon resonance (SPR) spectroscopy and surface plasmon field-enhanced fluorescence spectroscopy (SPFS) are governed by the strong surface plasmon resonance-generated evanescent field at the metal/dielectric interface. The greatest evanescent field amplitude at the interface and the maximum attenuation of the reflectance are observed when a nonabsorbing d...

In this paper we characterize the radical of an arbitrary‎ ‎submodule $N$ of a finitely generated free module $F$ over a‎ ‎commutatitve ring $R$ with identity‎. ‎Also we study submodules of‎ ‎$F$ which satisfy the radical formula‎. ‎Finally we derive‎ ‎necessary and sufficient conditions for $R$ to be a‎ ‎Pr$ddot{mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $Rbigopl...

Time series analysis is the statistical approach used to analyze a of data. most popular method for forecasting, which widely in several and economic applications. The wavelet transform powerful mathematical technique that converts an analyzed signal into time-frequency representation. provides information both time domain frequency domain. aims this study are propose function by derivation quo...

In this paper, we consider the problem of extending existing submodule construction techniques that have been developed for finite state models into more expressive and compact behavioral models that handle data through parameterized interactions, state variables and simple guards. We provide a behavioral model based on extended Input-Output Automata and describe an algorithm that provides the ...