Abstract. It is very important for superior performance beam in flip chip of LED to realize its work efficiently and accurate positioning. To obtain the superior performance of beam, its dynamic mode is built and carried out by **Rayleigh** **method**, and it is explored to find out the change trend of the natural frequency and deflection of the beam with its structural parameters. Based on the dynamic modeling of beam, optimization model of beam is built and its optimization solution is obtained by genetic algorithm. The results provide a theoretical basis on the further design and dynamic analysis of flip chip of LED.

Show more
Based on the thrust generated from the propeller, was determined natural frequency of the rotor-arm part by **Rayleigh** **method**. The risk of resonance verified with the frequency of rotor rotation speed of propeller. Compared with the experimental results in the experimental device, it was confirmed that the resonance point and the calculated values are consistent. The authors can predict the risk of specific resonance frequency calculations using the **Rayleigh** **method**. Design to understand the natural frequency of aircraft parts, it is important to avoid the resonance. It is necessary to design to avoid resonance at near hovering number of revolutions.

Show more
Furthermore, dust particles have complex or irregular shapes. They are not like hydrometeor (such as rain) with clearly deﬁned and relatively known shapes. However, ellipsoidal shape is often applied as an approximate dust particle [7]. This means that in a medium with ellipsoidal dust particles, the attenuation and the phase rotation can be determined if the ellipsoid axes ratios are given. This paper, therefore, tackles the problems associated with attenuation and phase rotation of ellipsoidal particles. Mathematical models of dust induced complex scattering, in form of attenuation and phase rotation, are proposed using the **Rayleigh** **method**. The paper also presents an expression for the relation between visibility and dust concentration. The report of this work is organized such that introduction is given in Section 1. The relation between visibility and particle concentration is presented in Section 2. Formulation of the scattering coeﬃcients’ models, i.e., attenuation and phase rotation, in diﬀerent media using ellipsoid shape is detailed in Section 3. In Section 4, the attenuation and the phase rotation during SDS are determined using the proposed models. The results are analysed and benchmarked with some existing results. Conclusions are drawn in Section 5.

Show more
As the decay time of the impact sound was similar for computed true time domain and provided magnitude of the complex temporal acoustic pressure, the latter was used to check for the impact sound duration predicted by the different models. Decay time depended on the mesh density of the plate independently of whether the BEM or **Rayleigh** **method** was used. The fine model produced an impact sound which decayed in ~0.25 s, in better agreement with the experiment. Furthermore, the acoustic pressure was not fully damped when the simulation completed, so the termination time should be increased to capture the entire impact sound.

Show more
In order to modify the **Rayleigh** **method**, the point equivalent moment of inertia must be used in order calculate the natural frequency. The idea of point equivalent moment of inertia is concentrated on equation (2) and equation (3). In these equations, the parameters, affect on the value of equivalent moment of inertia, are the length of steps and the dimensions of cross section area of the steps. The length of small part can be expressed as a function of distance along the beam. Now if the beam is only large part then the equivalent moment of inertia will be (I 2 ). But if the beam

Show more
10 Read more

Microwave propagation suffers attenuation and phase rotation by suspended dust particles where occurrence of sand and dust storms (SDS) is predominant especially in arid and semi-arid regions. The SDS phenomenon has received considerable interest in recent times with emphasis on signal attenuation and phase rotation effects. To this end, mathematical models of dust induced complex scattering are developed and proposed using **Rayleigh** **method** to compute attenuation and phase rotation of electromagnetic waves by considering dust particle shapes and best fit ellipsoids. This part II of Microwave Attenuation and Phase Rotation in SDS also presents a new expression for the relation between visibility and dust concentration. The expression was included in the proposed models whose simulated results, when compared with some published results, show close agreement. Attenuation and phase rotation in dry dust are found to be significant only when visibility becomes severe or at increased microwave bands.

Show more
Table 2 shows yearly mean wind speed and corresponding standard deviation. Maximum mean wind speed & minimum mean wind speed was calculated to be 7.35 m/s and 5.07 m/s respectively. Yearly mean wind speed for 2014 was almost same as for 2011. The general trend in yearly mean wind speed seems to be decreasing gradually from 2004 to 2014. Especially, mean wind speed in December/January seems to be sharply decreasing as year progresses which lead to decrease in yearly mean wind speed. In other words, drop of wind speed on cold season is more severe than warm season. Several Processes on local, regional and global scales are likely contributing to this decrease. Increasing forest density can’t alone explain this phenomenon described by Iacono [33]. On other hand, several researches have shown using both climate model simulations [34] and surface ob- servations [35] [36] that the positions of the main storm tracks that cross North America, which are generally associated with the jet stream, have moved northwards. This may be impacting the wind speed pattern in nearby areas. Although, similar research is not found in sub-continent region, it can be predicted from their analysis, the global climate change has played a major role in this declining wind speed. The severe decrease of speed in cold season is also explained by increasing temperature in Mountainous region. The region which otherwise would be much colder, air with higher density would move to replace hotter air in lower belts. This pattern is affected. 3.2. Weibull and **Rayleigh** Distribution

Show more
13 Read more

Background: Ultrasound imaging plays an important role in computer diagnosis since it is non-invasive and cost-effective. However, ultrasound images are inevitably contaminated by noise and speckle during acquisition. Noise and speckle directly impact the physician to interpret the images and decrease the accuracy in clinical diagnosis. Denoising **method** is an important component to enhance the quality of ultrasound images; however, several limitations discourage the results because current denoising methods can remove noise while ignoring the statistical characteristics of speckle and thus undermining the effectiveness of despeckling, or vice versa. In addi- tion, most existing algorithms do not identify noise, speckle or edge before removing noise or speckle, and thus they reduce noise and speckle while blurring edge details. Therefore, it is a challenging issue for the traditional methods to effectively remove noise and speckle in ultrasound images while preserving edge details.

Show more
22 Read more

In this paper, we study an inverse source problem for the **Rayleigh**–Stokes problem for a generalized second-grade ﬂuid with a fractional derivative model. The problem is severely ill-posed in the sense of Hadamard. To regularize the unstable solution, we apply the Tikhonov **method** regularization solution and obtain an a priori error estimate between the exact solution and regularized solutions. We also propose methods for both a priori and a posteriori parameter choice rules. In addition, we verify the proposed regularized methods by numerical experiments to estimate the errors between the regularized and exact solutions.

Show more
20 Read more

The physical problem is illustrated by Figure 1. The acoustic domain is the cavity and the half-space beyond the mouth. The baﬄe is rigid and perfectly reﬂecting. This model can be applied to a range of acoustic cavity problems. In any practical problem the baﬄe must be ﬁnite. Even if there is no baﬄe, at least the continuity in the acoustic ﬁeld is maintained across the mouth and the model can still be applied with due care. The BERIM **method** can be applied in the usual two dimensional, three dimensional and axisymmetric domains. BERIM3 is an implementation of the methods required for general three dimensional problem.

Show more
Conventional MIMO is another **method** which is also in existence for solving this problem, here the use of multiple antennas at the transmitter and receiver introduces spatial degree of freedom that can increase the capacity and reduce the bit error rates [10, 11 and 12]. This technique is good but didn’t make use of channel state information to completely eliminate the effect of fading [4].

Abstract. The paper presents a **method** for a short-term tsunami forecast based on sea level data from remote sites. This **method** is based on Green’s function for the wave equa- tion possessing the fundamental property of symmetry. This property is well known in acoustics and seismology as the reciprocity principle. Some applications of this principle on tsunami research are considered in the current study. Simple relationships and estimated transfer functions enabled us to simulate tsunami waveforms for any selected oceanic point based only on the source location and sea level data from a re- mote reference site. The important advantage of this **method** is that it is irrespective of the actual source mechanism (seis- mic, submarine landslide or other phenomena). The **method** was successfully applied to hindcast several recent tsunamis observed in the Northwest Pacific. The locations of the earth- quake epicenters and the tsunami records from one of the NOAA DART sites were used as inputs for the modelling, while tsunami observations at other DART sites were used to verify the model. Tsunami waveforms for the 2006, 2007 and 2009 earthquake events near Simushir Island were simulated and found to be in good agreement with the observations. The correlation coefficients between the predicted and ob- served tsunami waveforms were from 0.50 to 0.85. Thus, the proposed **method** can be effectively used to simulate tsunami waveforms for the entire ocean and also for both regional and local tsunami warning services, assuming that they have ac- cess to the real-time sea level data from DART stations.

Show more
11 Read more

S t b c S t S t is 0 -cut of fuzzy reliability of a unit. In this **method**, for any particular level of 0 , upper and lower bound of S t b c ( , , , )[ 0 ] are two functions in terms of t . So, in this case reliability curve is like a band with upper and lower bound whose width depends on the ambiguity parameter (See Baloui Jamkhaneh, 2011). Fig. 1 shows cut of fuzzy reliability with 0 and 1. Fig. 2 shows that by increasing of the value of c , when t is small, we may find higher reliability band and for large value of t, we may find lower reliability band.

Show more
12 Read more

Frame length sizes and are assumed for PSAM LMMSE and cubic estimators. Two normalized Doppler frequencies ( ) are considered in this work: and . Fig. 6 and Fig. 7 show the CER performance of the proposed DM **method** in comparison to the conventional DM **method** analysed in [6–8] for these normalized Doppler frequencies. From the figures, the proposed DM **method** of extracting soft reliability information exhibits superior CER performance in comparison to the conventional DM **method**. As also shown in the figures, the CER performance of both methods of extracting reliability information over fading channels drop with increase in the normalized Doppler ; nevertheless, the proposed DM **method** displays superior CER performance to the conventional DM **method**. The CSI is difficult to obtain as the fading rate ( ) of the channel increases; therefore, the reliability information metric derived in Eqn. (23) and Eqn. (29) using the conventional and proposed DM methods respectively are not accurate. This resulted in the noticeable reduction in the CER performance as the fading rate increases from to . Furthermore, as the frame length size increases from , the CER performance of both DM methods degrade but the proposed DM **method** displays significant improvement in CER performance compared to the conventional DM **method**. More so, as shown in Fig. 6 and Fig. 7, irrespective of the channel estimation technique used, the proposed DM **method** offers significant improvement in CER performance ( ) in comparison with the conventional DM **method**. As a note, the performance of the PSAM LMMSE and cubic channel estimators depend on the frame length . The smaller the frame length size, the better the performance of the estimators.

Show more
10 Read more

The **Rayleigh**–Stokes equation (1) is a principal part in the description of dynamic ﬂu- ids [10]. More applications for such an equation can be found in [10, 11]. The initial and boundary value problems for the **Rayleigh**–Stokes problem, called direct problems, have already been researched in [10]. In some previous papers, Dehghan et al. [12–15] consid- ered some numeral solutions of the **Rayleigh**–Stokes problem. The initial value problem for the **Rayleigh**–Stokes equation has been studied by applying plenty of numeral methods such as the ﬁnite element **method**, etc. [10, 16].

Show more
16 Read more

Body waves (P and S) and surface waves (**Rayleigh**, Love, etc.) propagate when seismic waves are generated at or near the earth's surface. Wave bodies propagate through the entire body of the earth, while surface waves propagate along (or near) the surface of the earth. If the seismic source is vertical (impulsive or swept), then the surface wave type generated is **Rayleigh** wave, or more commonly called ground roll. Ground roll occurs more than two-thirds (2/3) of the generated seismic energy and is usually most dominant on multichannel recordings. Ground roll is the most effective type of surface wave in a surface seismic survey [14]. Therefore, most surface wave methods use active source by measuring **Rayleigh** wave phase velocity as a function of frequency [8]. The MASW measures **Rayleigh** waves and provides information throughout the depth range of the investigation. This leads to an evaluation of near surface velocity profiles.

Show more
14 Read more

F x = − + λ x − θ x > θ λ > , (2) In other hand, the **method** of L-moment estimators have been recently appeared in Hosking [8]. He used L-moment estimators for estimating the unknown parameters of log-normal, gamma, and generalized extreme value distribution. Next, several estimations had been proposed to follow the work carried by Hosking [8]. L-moment estimators for generalized **Rayleigh** distribution was introduced by Kundu and Raqab [10]. Karvanen [9] applied the **method** of L- moment estimators to estimate the parameters of polynomial quintile mixture. He introduced two parametric families, the normal-polynomial quintile mixture and Cauchy-polynomial quintile mixture. Abdul-Moniem [1,2,3] applied the **method** of L-moment estimators to estimate the parameters of exponential distribution, **Rayleigh** distribution and Wiebull distribution, respectively also the estimate of unknown parameters for generalized Pareto distribution are discussed by Abdul-Moniem and Selim [4]. The standard **method** to compute the L-moment estimators is to equate the sample L-moments with the corresponding population L-moments.

Show more
In this paper, a new hybrid approach is presented based on the combination of the power series expansions and the **Rayleigh**-Ritz **method** for stability and free vibration analyses of axially functionally graded non-uniform beams resting on constant Winkler-Pasternak elastic foundation. In the proposed novel technique, the power series approximation is first adopted to solve the motion equation. Regarding this numerical methodology, the transverse displacement and all mechanical properties are expanded in terms of power series of a known degree. By solving the eigenvalue problem, one can acquire the fundamental natural frequencies. According to aforementioned **method**, the expression of vibrational mode shape is also determined. Based on the similarities existing between the vibrational and buckling deformation shapes, **Rayleigh**-Ritz **method** is finally employed to construct eigenvalue problem for obtaining the critical loads. In order to illustrate the correctness and convergence of the **method**, several numerical examples of axially non-homogeneous and homogeneous beams are conducted. The obtained outcomes are compared to the results of Finite Element Analysis in terms of ANSYS software and those of other available numerical and analytical solutions. The accuracy of the **method** is then remarked.

Show more
25 Read more

telligent Machines, CAS, they all use thin plate as the elastomer to detect the outside force information. Thus, the knowledge of its free vibration is significant to the structural designers [8]. The free vibration characteristic of a elastic thin plate is the basis and has great significance for the follow-up studies of the forced vibration. Since the introduction of the small deflection theory of plate bending, people are interested in vibration problems of the elastic thin plate. The free vibration analysis of rectangular and circular plates is important for the design of plate-type structures. Consequently, a great many of research reports have been conducted on the dynamic behavior of such structures. Leissa offered comprehensive sets of research data for the free vibration of elastic thin plates based on Kirchhoff’s thin plate theory [9]. As closed form solutions for plate vibration problems are known only for certain special cases in which at least a pair of opposite sides is simply supported. One has to use approximate **method**. As a result, a large number of useful methods have been developed to get solutions for some practical problems. The **Rayleigh**-Ritz **method** is one of the most popular methods to obtain the approximate solutions for the natural frequencies of rectangular and annular plates [10-12]. **Rayleigh**-Ritz **method** uses a linear combination of some assumed basic functions to express the mode shape. Finite element methods often divide the elastic body into a number of smaller elements and approximate the solution by using local piecewise continuous shape functions [13,14]. And there are some other approximate methods including the differential quadrature (DQ) **method** [15], the least squares techniques [16], the Meshless methods [17], and the spline finite strip **method** by G. Akhras and W. Li [18].

Show more
It may not be reasonable that start testing at the third observation. However there are cases where the process shift occurs at third observation. In practice the particular should gather a modest number of observations to get an initial verification that the **Rayleigh** distribution was a reasonable fit. Then only the formal change point can be applied. In view of this our main simulation is based on assumption of 9 readings without testing, with testing starting at the 10th observation, however 9 readings itself is hard to believe in a HLRD for the Quality variable. Perhaps it is making reasonable compromise between the conflicting desires.

Show more