Every complex quadratic polynomial is conjugate by an affine transformation to one o f the form fc: z -* z2+ c where c e i . Douady and Hubbard , in [ D H l], undertake a rigorous analysis of this fam ily with the full proofs appearing in [ DH2 ] ( where more general polynomials are co n sid ered ) . For a polynomial f o f degree at least two the point oo is a super-attracting fixed point and its basin o f attraction is connected . The complement K(f) , the set o f z whose iterates rem ain bounded , is known as the "filled in Julia s e t" :- corresponding to the fact that its boundary is the Julia set J ( f ) . The dynamics o f f on components o f th e interior o f K(f) is governed by the general theory o f rational m aps . For a discussion o f rational m aps ( and a much more complete list o f references) the reader is directed to Blanchard's survey article [ B ].
Operated under the same conditions, the Single Frequency Method yields the lowest detection probability, while the Top Frequency Method performs significantly better as it considers the shift of the bottleneck signature in the spectrum across time. Both the Top-M Frequencies Method and All Frequen- cies Method improve the detection probability on the training set by considering more frequency information, but they do not produce significant gains on the detection probability on other sets, compared with the Top Frequency Method. This suggests that the top frequency captures most of the statistical difference that persists over the time. It is our future work to carry further investigation why these two multi-variate methods do not provide better performance and refine them for improvements.
The weight function used to curve fit the 70 Gaussian cases is (^(z) = z. This is based on the consideration th at, the high range cycle part of the PD F should be given more attention, but on the other hand, some emphasis should remain on keeping the PDF shape generally correct. The 70 sets of fitted param eters for the 70 Gaussian signals are listed in Table 8.4 and 8.5. The generally used “cost” (or residual) is not listed in this table, but instead, the fatigue damage rates of the fitted model curve compared with the damage counted directly from the tim e signals are listed. The listed here are the damage values obtained when inverse S-N curve slope b = 5.0 is used while are the values when 6 = 8.0 is used. Most of them meet well with the tim e history curves from the point of view of fatigue. The average absolute error is 7% for b = 5.0 and 18% for b = 8.0. The maximum error is 35% for 6 = 5.0 and 4 ^ ^ for b = 8.0. When the P D F ’s from both the tim e series and the curve fitting are plotted together, it was noted th at most of them meet quite well. Figure 8.10 shows the curve fitting results for spectrum 1. Figure 8.10(a) shows the rainflow cycle P D F ’s from the simulated tim e history and curve fitting. Figure 8.10(b) shows the correspondent damage density of the cycles when b=5.0 is used.
In this context, the level t should be considered as a resolution level for the data analysis. For instance, when the threshold t is taken equal to 0, the groups in the sense of Hartigan (1975) are the connected components of the support of the underlying distribution, while as t increases, the clusters concentrate in a neighborhood of the principal modes of the density f . Several clustering algorithms deriving from Hartigan’s definition have been introduced building. In Cuevas et al. (2000, 2001), and in the related work by Azzalini and Torelli (2007), clustering is performed by estimating the connected components of L (t). Hartigan’s definition is also used in Biau et al. (2007) to define an estimate of the number of clusters based on an approximation of the level set by a neighborhood graph.
The clustering analysis is an important and active re- search field in data mining, and the research is about the classification of data objects. In order to conveniently ex- pound and understand the data objects and extract inher- ent information or knowledge hidden in the data, it is necessary to use cluster analysis technology. Its main idea is to divide the data into several classes or clusters, so as to make the objects in same cluster become the most similar while objects in different clusters vary greatly. On the whole, the algorithm can be divided into partition method, hierarchical method, density method, and model method and so on . Generally, the traditional clustering algorithm has following drawbacks: low efficiency in clustering, long processing time in large data and difficulty in meeting the expected effect. For these problems, a popu- lar research idea is correspondingly formed: combining clustering analysis, parallel computing and cloud comput- ing, and designing an efficient parallel clustering algorithm [2,3]. This paper adopts the classical spectral clustering
The second part of the thesis is focused on the development of signal processing techniques to analyse signals on the sphere in joint spatio-spectral (spatial-spectral) domain. A transform analogous to short-time Fourier transform (STFT) in time- frequency analysis is formulated for signals defined on the sphere, in order to devise a spatio-spectral representation of a signal. The proposed transform is referred as the spatially localized spherical harmonic transform (SLSHT) and is defined as windowed spherical harmonic transform, resulting in the SLSHT distribution. The properties of the SLSHT distribution and its analysis in the spherical harmonic domain are also provided. Furthermore, examples are provided to demonstrate the capability of SLSHT to reveal spatially localized spectral contents in a signal that were not obtainable from traditional spherical harmonics analysis. With the consideration that data-sets on the sphere can be of considerable size and the SLSHT is intrinsically computationally demanding depending on the band-limits
The controlling function cos for value c exhibits new characteristics for the generating fractals. Here we have presented the geometric properties of fractals along different axis. The fractals generated depends on the parameter p. From above observation and analysis 2p image of mini Mandelbrot is generated for above cos controlling function. For p=1, two (2p) mirror image (similar faced) of mini Mandelbrot bulbs are obtained at an angle of 180 0 . For p=2, four mirror image of mini
The linear dependence of the current and the wave intensity in expression (18) allows us to reduce the spectral intensity and, thus, to comply the absorption depth of the waves with the depth of the registering environment. Under the conditions of the reduction of the solar spectrum for 1010 times, according to Lambert’s law, the spectral dependence of the absorption depth in the shortwave (Figure 6(a)) and the long wave (Figure 6(b)) ranges, reaches from 20 nm up to 16 μk. The most intensive growth of the depth is observed in the ranges higher than 400 nm (Figure 6 presents the range from 100 nm up to 16 μk). Thus, the contribution of the waves into the current in that range is relatively small.
In the case of the sound signals analysis we usually use logarithmic scale on the frequency axis. Computing of a sound signal spectrum by the Fourier transform does not bring ideal results in this case. WFB spectralanalysis is a new method which combines wavelet filter bank with the Fourier transform. This method brings good frequency resolution on the low frequencies together with a fast response on the high frequencies. This paper consists of a short introduction to the WFB spectralanalysis and a description of the Matlab GUI for the WFB spectralanalysis.
An optimized buck converter was designed by using Eq. (1 -5). The following values were obtained for Vin= 12VDC and VOUT = 5V: C1=10µ F, L=16µ F, C2=500µ F, f SW =300KHz and Rl=2.5Ω. The MOSFET used was IRF15003s with Rds(on)=3.3mΩ and Ggate=0.28nC. In order to obtain 5VDC at the output, a duty cycle of D = 0.416 was used. The following figure shows the MOSFET drain current spectral composition. Figures 3, 4 and 5 show the spectral composition of the current in the MOSFET, the diode current and the output voltage respectively.
The objective of Uncertainty Analysis (UA) is the evaluation and mitigation of such parameter uncertainties on the Quantities of Interest (QoI). Central part of this process is the uncertainty propagation by means of the mathematical model. Classical approaches contain First Order Second Moment (FOSM) methods and Monte Carlo sampling. However, the FOSM is limited by the fact that it linearizes the system equation (Cacuci et al. (2005)) and will produce symmetrical confidence interval (Vrachimis et al. (2016)). Monte Carlo sampling does not suffer from these limitations, but for models with many parameters it is constrained by the curse of dimensionality. This paper proposes an alternative approach to the uncertainty propagation with the Polynomial Chaos Expansion (PCE) (Smith (2013), Xiu (2010)) Depending on its application the PCE has the potential to greatly reduce or even eliminate the sampling by use of the mathematical model.
The most remarkable results of [15–18] are the characterization theorems for the spectral data of the matrix Sturm–Liouville operator, i.e. necessary and suﬃcient conditions for the solvability of the corresponding inverse problems. A crucial role in those conditions is played by asymptotic formulas for the eigenvalues and the weight matrices.
The spectral problems on graphs arise in the investigation of processes in various do- mains of natural science; from complex molecules to neuron systems. Methods developed by mathematicians make it possible to describe such problems in terms of the diﬀerential equations by constructing for these problems an exact analogue of the Sturm-Liouville theory.
Because the solar wind is a collisionless plasma, local ionic charge states reflect conditions of its source regions. Comparing the fluxes of the C+N emission below 500 eV, the O emission and the O emission yields a quantitative probe of the state of the wind. In accordance with our modelling, we found that spectral differences amongst the comets in our survey could be very well understood in terms of solar wind conditions. We are able to distinguish interactions with three different wind types, being the cold, fast wind (I), the warm, slow wind (II); and the hot, fast, disturbed wind (III). Based on our findings, we pre- dict the existence of even cooler cometary X-ray spectra when a comet interacts with the fast, cool high latitude wind from polar coronal holes. The upcoming solar minimum offers the perfect opportunity for such an observation.
movements were excluded. The EEG data was filtered using Finite Impulse Response (FIR) band-pass filter between 1.0 and 100 Hz with the number of coefficient is 4,000 and Hanning window with 50% overlap. Fast Fourier Transform (FFT) was then performed to the selected data for every 1 s segment and the power spectral density (PSD) data in (lv 2 ) was obtained. The PSD was segmented into
Table 3 shows the seasonal analysis of total column ozone (TCO) for the four ground based stations. It is clear that there is a considerable seasonal variation of TCO for each station, where the difference between mean TCO of spring and autumn in the northern station (Matrouh) is 24.8 DU while for the maximum values the difference is about 41.7 DU. Also, the maximum seasonal values of TCO appears in spring followed by summer while the minimum seasonal values of TCO occurs in autumn for the four stations. Table 3 illustrates also the coefficient of variation (COV) and the trend by least square method for the seasonal values of TCO of four stations. The maximum COV for each station appears in winter and spring respectively, while the minimum appears in summer of all stations except for Hurgada. The trend values illustrate that there is an increase of TCO for the seasons of the four stations except at the winter of Cairo.
the method is often referred to as power subtraction with oversubtraction. This ad hoc modification significantly de- creases the noise level and reduces the audible artifacts. In addition, it significantly distorts the output speech, which makes this modification (more or less) useless for high- quality speech enhancement. This fact is easily seen from (9) when δ 1. Thus for moderate and low speech-to-noise ra- tios (in the ν -domain), the expression under the root sign is very often negative and the rectifying device will therefore set it to zero (or any other predetermined small value), which in turn implies that only frequency bands where the local signal-to-noise ratio is high appear in the output. Due to the nonlinear rectifying device, the present analysis technique is not directly applicable in this case.