Continuous series of symmetric peak profile functions determined by standard deviation and kurtosis

A mathematical system for modeling the effects of symmetrized instrumental aberrations has been developed. The system is composed of the truncated Gaussian, sheared Gaussian, and Rosin-Rammler-type functions. The shape of the function can uniquely be determined by the standard deviation and kurtosis. A practical method to evaluate the convolution with the Lorentzian function and results of application to the analysis of experimental powder diffraction data are briefly described.

Modified Variable Step Size FLOM-CMA Based on Lorentzian Function under Impulse Noise

Aiming at the problem that the traditional equalization algorithm under impulse noise is difficult to suppress impulse noise and achieve equalization, a new modified variable step size FLOM-CMA algorithm based on Lorentzian function is proposed in this paper. The proposed algorithm has modified the cost function to made full use of the phase information of signal to correct the phase rotation. Also, by adjusting the FLOM of cost function, that impulse noise is restrained effectively. Furthermore, the Lorentzian function is use to update the step size to make sure it is is appropriate for each equalization point. Simulation experiments show that, compared with FLOM-CMA and VS-FLOM-CMA, the proposed algorithm that the proposed algorithm achieves higher convergence accuracy with similar convergence speed. And under different impulse noise conditions, the robustness of the algorithm is better.

DEVELOPMENT OF A LORENTZIAN-FUNCTION APPROXIMATION UTILIZING IN THE CHARGED- PARTICLE-INDUCED NONRESONANT REACTION RATE

A development has been made for the charged-particle-induced nonresonant reaction-rate equations. The forms of reaction-rate equations for nonresonant and resonant reactions have been united in a frame of Lorentzian-Function Approximation (LFA) mathematically. In the frame of LFA, the nonresonant reaction taken place within the Gamow window can be considered, in form, as a "resonance" reaction with a full width at half maximum (FWHM, Γ nr ) equal to the 1/e width (Δ) in a well-known Gaussian-Function Approximation (GFA).

Comparison the Gain Characteristic of AlInGaAs/AlGaAs and GaAs/AlGaAs Quantum Wells

According to the Harrison’s model, the level change of conduction and valence bands caused by the strain of AlInGaAs/AlGaAs quantum well (QW) was analyzed firstly. The energy level of the electron and hole in the AlInGaAs/AlGaAs strained and GaAs/AlGaAs unstrained QW were calculated, respectively. In addition, taking the lorentzian function, the linear gain of the two QWs were calculated and discussed. Contrast the gain performance of GaAs/AlGaAs QW with that of AlyInxGa1-x-yAs/AlGaAs QW, it can be found that the strained AlyInxGa1-x-yAs/AlGaAs QW material has more promising optical gain than that of the GaAs/AlGaAs QW.

Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 1 — Thermal Damping

Mathematical modeling of thermal effects on steady state dynamics of microresonators, utilizing an analytical approach is studied. Thermal phenomena has two distinct effects, which in this report are called, thermal damping and temperature relaxation. In this part of a two-part report we investigate the thermal damping and its effects on microresonator dynamics. To do this, first the reduced order mathematical model of the system is introduced as a forced mass-spring-damper system, and then a linearized model of electric actuated microbeam resonator is employed. The effect of thermal damping is modeled as an increase in damping rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. The developed analytic equation describing the frequency response of the system around resonance can be utilized to explain the dynamics of the system, as well as design of dynamic parameters. However, we have focused on exploration of thermal damping.

Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 2 — Temperature Relaxation

Thermal phenomena have two distinct effects, which are called, in this report, “thermal damping” and “temperature relaxation”. In this second part of a two-part report we (only) model and investigate the temperature relaxation and its effects on microresonator dynamics. A reduced order mathematical model of the system is introduced as a mass-spring-damper system actuated by a linearized electrostatic force. Temperature relaxation is the thermal stiffness softening and is modeled as a decrease in stiffness rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. Analytic equation describing the frequency response of the system near resonance which can be utilized to explain the dynamics of the system, as well as design of involved dynamic parameters is developed.