ABSTRACT:Problem: Surge is an instability that affects the entire compression system. Surge is characterized by a limit cycle oscillation that results in large amplitude fluctuations of the pressure and flow rate. In contrast to rotating stall, during surge the average mass flow is unsteady but circumferentially uniform. Approach: The attempt to find a simple model structure which can capture in some appropriate sense the key of the dynamical properties of the physical plant, we study the application possibilities of the anti-surge detection system by using **Gaussian** **curve** membership function to protect the centrifugal compressor from surge by using Neural fuzzy. Results: By testing the new Neural- Fuzzy system which has been created for demonstrate the validity of proposed control scheme, the new neural-fuzzy system get a good results compared by the used detection system. Conclusion: We can use Neural-Fuzzy system to detect the surge in centrifugal compressor Alternative to current detection system.

IR reflectance maxima of composite “rubber-carbon nanotube” in the spectral area of CH valence and deformation vibrations. The IR peak dependence on the carbon nanotube content corresponds to 1D **Gaussian** **curve** for the diffusion equation in the electric field between electrons of nanotubes and protons in polymer according to “semiconductor” model of the composite structuring. For our case of the long-acting hundreds nanometer interactions, the polymer crystallization depends on sp 3 C-C bonds organization in the intrinsic electric field according to the semiconductor n-p model. Tensile strength for polyamide-6 composites at 0.25% CNTs increases 1.7 times and tensile deformation – 2.3 times.

beam is different at different angle-of-arrival and moves correspondingly with the change in angle-of-arrival. The system works with the assumption that laser beam has a **Gaussian** intensity profile. Theoretically, the system is able to measure the angle-of-arrival with the very high angular resolution, depending upon the number of sampling instants in the **Gaussian** fitted **curve**. The resolution can be increased by increasing the sampling instants in the **Gaussian** fitted **curve**. With 261 sampling points the resolution of the system is 0.105°. Since minimum three detectors are to be illuminated for **Gaussian** **curve** fitting, total field of view achieved is 55°. This is less than other techniques mentioned in introduction section. The minimum SNR required for the operation of system is 30db as below this the errors in **curve** plotting increase drastically. This technique can be used as a simple approach for designing angle-of-arrival sensors for finding the direction of incoming laser radiation on combat vehicles.

The **curve** fitting tool is used to find a **curve** that best fits the data. Interpolation and smoothing are the two possible ways for **curve** fitting. There are several algorithms and method available that serves the purpose of **curve** fitting. Few of these methods are iterative method, nonlinear least square estimation, weighted least square estimation, and algorithms are Trust-Region algorithm, Caruana’s algorithm, Guos algorithm, and Levenberg-Marquardt algorithm. **Gaussian** **curve** fitting fits the **Gaussian** function on to the given data points. Out of all methods, the Guos algorithm is the most appropriate method as it is least sensitive to the random noise [10].

In the experiment, the tissue sample was completely submerged in degassed water and a 5 MHz single element 0.25 in elemental diameter; immersion transducer (Olympus- V310-SU, Band width 16–24 MHz at -6 dB) was used for scanning. Tissue samples were held stationary and the transducer was moved five-millimeter steps using a computer controlled micro position system. RF echo data was acquired at a sampling rate of 1GHz, using the same transducer. Readings were taken at fifteen distinct positions of the tissue sample and 32 echo signals at different time intervals were collected at each position. Real time signal acquisition was done by a PC oscilloscope (PicoScope 3204D). Settings were adjusted to acquire 100000 samples at a sampling interval of 1ns. Refer Figure 1 for a signal received from a single position of a bovine liver sample. One echo signal was selected per each position and a Hamming window was applied to the RF echo signal, followed by Fast Fourier Transformation (FFT). Average of all Fast Fourier transformed power spectra at fifteen different locations were calculated. A **Gaussian** **curve** was fitted on the averaged FFT data. This **Gaussian** **curve** was used to calculate full width at half maximum(FWHM). The data acquired by a chicken liver sample and a bovine liver sample and fitted **Gaussian** **curve** shown in Figure 2. Two **Gaussian** curves were normalized for visual comparison.

the first tunnel construction are shown to have good agreement with O’Reilly and New (1982). This is expected because the first tunnel is excavated in effectively a greenfield site and this behaviour was reflected in the first tunnel settlements for all tests. Three observations can be made from this procedure. First, the observed volume loss associated with the second tunnel is larger than that of the first. For the 3D tests presented here the additional volume loss was on average 14%. Second, the surface settlements generated by either tunnel construction on the side of the centre-line away from the other tunnel are fairly typical in shape (i.e. could be well represented as a **Gaussian** **curve** with values of i and K comparable with previous research and field data). The third observation is that the surface settlements gener- ated by either tunnel construction on the side of the centre-line towards the other tunnel do not appear to be as well represented by the **Gaussian** **curve**. This could potentially be a feature of the modelling technique, as both tunnels are pre-bored in the clay

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After underpassing, no movement of the up line was discernible in the data: therefore the volume loss must have been approximately 0.0%. The down line, on the other hand, did experience some settlement. The tilt sensors at each end of the string showed some rotation, so it was not known what the settlements at the ends of the string were. Precise levelling of the ends of the string showed that no significant movements occurred, but the repeatability, as discussed previously, was probably only 0.5 mm. A regression analysis varying both trough width and string end settlement showed that the best fit to the data was obtained with a string end settlement of 0.05 mm and a trough width of 7.0 m. The adjusted tilt sensor data are compared with the **Gaussian** **curve** fit in Figure 13. The tilt sensor data in Figure 13 have been resolved to take account of the 758 angle between the TWRM tunnel and the HS1 tunnel. The volume loss of the **Gaussian** **curve**, V l , was

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This paper considers a decomposition framework as a mechanism for information hiding for secure commu- nication via open network channels. Two varieties of this framework are provided: one is based on **Gaussian** arithmetic with complex modulus and another on an elliptic **curve** modular equation. The proposed algorithm is illustrated in a numerical example.

Figure 3. Top panel: Variation of airmass across the night. Sec- ond panel: Shift in the pixel positions in x (spatial direction) for the target trace (blue crosses) and comparison trace (red plusses). Third panel: Shift in the pixel positions in y (dispersion direc- tion) for the target trace (blue crosses) and comparison trace (red plusses). Fourth panel: The rotation of the target trace (blue crosses) and comparison trace (red plusses) shown as the differ- ence in x position at the bottom and top of the trace. Fifth panel: The raw white light light **curve** shown by red data points and gen- erated from summing up the bins shown in Fig. 2. Over plotted are the fits from the analytic transit light **curve** with a cubic in time polynomial (green line) and a **Gaussian** Process (GP, black line). Sixth panel: Residuals to the GP fit are given by the red points with the dark grey and light grey shaded regions indicating the 1 and 3 sigma confidence intervals respectively.

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from o u r num erical sim ulations of ro u g h surface scattering. Results are presented for **Gaussian** rough surfaces w ith m oderate to large slopes and a correlation-length of the sam e order as the electrom agnetic w avelength. We have com pared ou r num erical results for the average scattered pow er w ith the expected scattered pow er obtained w ith the K irchhoff m ethod. The results presented in C hapter 6 provide strong evidence th at the degree of shadow ing at the surface boundary is greater for horizontal polarization than for vertical polarization. This po in t is illustrated in the near-field of the surface w ith contour-plots of the electrom agnetic field in the vicinity of the surface boundary. In the far-field, w e have found th at the Kirchhoff m ethod can p ro v id e a qualitative d escrip tio n of the average scattered pow er, even w hen the surface correlation-length is com parable to the electrom agnetic w avelength. In the h o rizo n tal p o lariza tio n case, this description is obtained by using the K irchhoff ap proxim ation w ith the correction for sh ad o w in g deriv ed in (W agner, 1967). In th e vertical polarization case on the other hand, the Kirchhoff m eth o d often gives a b etter estim ate to the backw ard scattered p o w er w h en th e shad o w in g correction is not used.

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Practice shows that for elections without fraud, the distribution of voter turnout, as well as votes for candidates, in electoral precincts is close to a normal distribution; this is the "pure fair signal" (see Fig. 1). This is a critical assumption and its accurate test goes beyond the scope of this article. However, qualitatively and intuitively it can be assumed that elections should obey the law of large numbers. The vote of each citizen is an independent, random value with negligible effect on the final result. According to the central limit theorem, the mean of a large number of such random values should be normally distributed; all roads lead to a **Gaussian**. In the case of falsification of almost all types this distribution of votes is inevitably altered. In most cases the votes of "dead souls"

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Nonparametric models are data-driven but not protected against overfitting, and hence this issue needs particular attention. Cross- validation is being used here to protect against overfitting by partitioning the data set into folds and estimating the accuracy for each of these. The primary objective of the cross-validation (CV) analysis is to determine whether the developed model for **curve** estimation is appropriate for power **curve** prediction independently of the data set. This helps to estimate how accurately an estimated model will perform for independent SCADA data sets. Here, the monthly SCADA data is partitioned into approximately 20% and 80% for training and validation respectively. Fivefold cross- validation was found to give satisfactory results. The approach used in this study is similar to leave-p-out CV approach. These techniques applied to both nonparametric models for better results. The algorithms for power **curve** fitting using **Gaussian** Process and Regression Tree described as follows.

by powers of 2 and low-cost blocks for multiplication by normal elements of the binary field. Since the exponents are powers of 2, the modules are implemented by some simple cyclic shifts in the normal basis representation. As a result, the multiplier has a simple structure with a low critical path delay. The efficiency of the proposed structure is studied in terms of area and time complexity by using its implementation on Vertix-4 FPGA family and also its ASIC design in 180nm CMOS technology. Comparison results with other structures of the **Gaussian** normal basis multiplier verify that the proposed architecture has better performance in terms of speed and hardware utilization.

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Table 1 presents three estimation results, which differ with respect to the specification of the unemployment effects on wage formation. In column one the unemployment rate is linearly specified, like in the Freia-Kompas model of the Central Planning Bureau (1989). The estimation result shows that only the weak Phillips **curve** effect has a significant influence on wage growth, whereas the strong Phillips **curve** effect has not. In the second column the unemployment rate is logarithmicly specified. Now both the weak Phillips **curve** effect and the strong Phillips **curve** effect appear to have a significant negative influence on wage growth. However, the overall fit drops. The third column shows the estimation results if a reciprocal specification of the unemployment rate is used, as in Kuipers et al. (1988) and Brunia and Kuper (1990). Again the strong Phillips **curve** effect is found to be significant, but in comparison with column (1) the overall fit drops. With respect to the other explanatory variables the estimation results are quite

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Gompertz **curve** was proposed in 1825 by B. Gompertz, a British statistician and mathematician. Gompertz **curve** is similar to Logistic **curve**. As a common S-**curve**, it is often used to describe growth of some plants and economic rules. The significant difference between Gompertz **curve** and Logistic **curve** lies in that Gompertz has inflection point but no centrosymmetric point. The growth in the main growth area of Gompertz **curve** is noticeably more than that of Logistic **curve**. Therefore, Gompertz **curve** is more suitable for simulating urbanization process. Mathematical expression of Gompertz **curve** is:

In another coating run, 87.5 kg of uncoated tablet cores (Tablets B) were added to the coating pan at approximately 140 minutes into the coating process of an initial batch of the same size (Tablets A). Coating was applied to the combined batches for a further 80 minutes for a total coating time of 220 minutes. Figure 7 shows that the resulting changes to the coating thickness distributions. The emergence of two distinct coating thickness distributions representing the initial batch 'Tablets A' and the additional batch 'Tablets B' is clearly visible after 140 minutes. At the same time, there is a clear shift in the original single coating distribution implying continued increasing thickness in the coating of Tablets A. The width and CoV of the two separate **Gaussian** approximated distributions of Tablets A and Tablets B are plotted in Figure 8. The plot of CoV over the entire coating trial shows that that coating thickness variability increases sharply as a whole following the insertion of Tablets B until 160 minutes of the process, but gradually reduces thereafter, which is in good qualitative agreement with simulations 3 . During previous coating trials conducted under the same process conditions, the minimum resolvable coating thickness of 30 to 40 µm was detected after approximately 80 minutes of coating time. Since this corresponds to the total duration that Tablets B were coated for, we should not expect changes to the coating on those tablets. The coating thickness distribution during the first 80 minutes interval, nevertheless appears to take the form of **Gaussian** distribution centred around 40 to 50 µm. By introducing uncoated cores into an already coated batch of the same size, we speculate that it may take twice as long to reach the minimum 7

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Wind turbine rotor curves constructed together with error bars and compared with measured rotor curves shown in figure 7 and 8. The uncertainty of rotor curves based on binning assess via its error bars. The two standard deviations (i.e., 95% confidence intervals) of measured power values and measured rotor speed are used to calculate the error bars of rotor power **curve** and rotor speed **curve** respectively. This obtained error bar used to measure the uncertainty associated with a bin of the respective rotor curves. But, the accuracy of ‘method of bin’ is weaken due to the selection of bin width of 0.5 m/sec because within each bin the output (Power, rotor speed) will depend strongly and non-linearly on input (wind speed, rotor speed) and a wide bin would result in a systematic bias,

Figure 2. Multiwavelength light **curve** of QSO B0218+357 during the flaring state in July/August 2014. a) MAGIC (points) above 100 GeV with a **Gaussian** fit to the peak position (thick solid line). b) Fermi-LAT above 0.3 GeV with the average flux from the 3rd Fermi Catalog [19] showed as a dashed line. Notice that during the days where the trailing emission was expected Fermi-LAT was in pointing mode allowing to significantly detect lower flux levels. c) Swift-XRT count rate in the 0.3-10 keV range. d) KVA in R band (not corrected for the contribution of host/lens galaxies and the Galactic extinction). The two shaded regions are separated by 11.46 days.

A powerful and compelling **curve** fitting procedure known as a **Gaussian** Processes (GP) is a very general stochastic non-linear model. Due to improvements in desktop computing these models are now widely available and feasible for wind turbine power **curve** fitting. GP power **curve** fitting comes with intrinsic confidence intervals (that reflect the standard deviation of the model), and this has proved valuable for uncertainty assessment and fault detection analysis, [22]. GPs are also useful in estimating the power load probability density; for example, in [23] a **Gaussian** Process model based on quantile regression has been used for short-term probabilistic load forecasting which is useful in application areas like grid management and power dispatching. Accurate wind power estimation is vital for the safe and cost-effective use of wind energy, and here GPs have also started to find application; for example,[24], where a GP and a numerical weather prediction (NWP) model were used for power forecasting and found to give 9% to 14% improvement in forecasting accuracy over an artificial neural network model. Network integration costs associated with wind power can be significant but substantially reduced by accurate forecasting, and a practical GP application to this is demonstrated in [25].

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The fitness, or goal, function that defines the performance of the model is based on a simple least squares error approach comparing the **curve**(s) with the target on a point-by-point basis. An alternative goal function described by Wilson and Ross [12] has been implemented based on performance metrics such as initial permeability, saturation flux, and energy loss. By using weighting of metrics, the goal function is made appropriate for the ultimate application.