One of the simple approaches to handle the measurement error in the regression analysis is the geometric **mean** (GM) functional relationship, initially proposed by Teissier (1948) and later by Barker et al. (1988) (cf Draper and Yang, 1997). This estimator has frequently been mentioned in the literature for two reasons. First, when there is no basis for distinguishing between the response and explanatory variables. Second, to handle the measurement error when no prior information is available. The geometric **mean** **method** has received much attention from the experts, and some have suggested that it is more useful than the ordinary least squares **method** (see Sprent and Dolby, 1980).

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The moving-**mean** **method** is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present ar- ticle is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-**mean**, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordi- nary global **mean**. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-**mean** and global-**mean** criteria hold. Among these three criteria, the lo- cal-**mean** one has the strongest adaptability, which is suggested for your usage.

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[5] Eman Abdul-Jabar Saad “Speeding Up Fractal Image Compression by Reducing Image Size” Electronic Computer Center, Mustansiriyah University, Baghdad, Iraq, Diyala Journal for pure sciences , Vol: 6 No: 4, October 2010 ISSN: 1992-0784 [6] George, L., "IFS Coding for Zero-**Mean** Image Blocks", Iraqi

The guarantee that the test packages are equal can be confirmed both theoretically and empirically. This confirmation is related to the concept equating or concordance of test score [5]. The equating can be performed using the classical approach (classical test theory approach) and the modern approach (item response theory approach) [6, 7]. The equating using the modern approach basically calculates the students’ ablities and level of difficulty into certain scores with a linear equation [2, 8]. In order to perform this calculation, parameter of index discriminant (a), level of difficulty (b), and pseudo-guessing (c) should be estimated first. The estimation that involves these parameters in the item response theory is known as the 3PL Model. On the other hand, several methods that can be implemented in order to perform equating are namely **mean** and **mean** **method**, **mean** and sigma **method**, and item characteristics curve **method** which includes the Stocking and Lord **method** [9, 10].

Abstract— Estimation of missing data is essential in the meteorological, climatologically and hydrology analyses. This study employed the arithmetic **mean** **method**, normal ratio **method**, the modified normal ratio **method**, and correlation coefficient weighting **method**. The performance of these methods are then compared using correlation coefficient, the S-index, the root **mean** squared error and **mean** absolute error methods. The objective of this study is to determine the best estimation **method** for missing data for four precipitation stations in Makassar city. The results show that the modified usual ratio **method** is suitable to estimate the missing precipitation data in Makassar city. This study result could be useful information for climate research to complete the missing precipitation data, especially for rain gauge stations in Makassar city.

Due to the complexity of algorithms and the large dif- ferences between the segmentation results and the real- ity, the current image segmentation research results limit the application of image segmentation results. The main reason is that there is a large loss of information between the continuous expression of the image and the discrete expression of the segmentation. This loss is often due to the generation of boundary information during the classification process. As a clustering **method**, K-**mean** has been successfully applied to the classifica- tion research of many studies. For example, Kang S H [13] and others proposed a data clustering model based on a variational approach. This model is an extension of the classical K-**mean** **method**, a regularized K-**mean** **method**, by selecting a parameter that automatically gives a reasonable number of clusters. The Walvoort D J J [14] team chose the **mean** squared shortest distance (MSSD) as an objective function to minimize it using K-**mean** clustering. The results describe two K-**mean** methods: one for unequal areas and the other for equal-area-segmentation; the results of simulation exper- iments on soil samples show that the algorithm gives satisfactory results within reasonable calculations. Frigg- stad Z [15] described how to solve better worst-case ap- proximation guarantee problem in the results. Friggstad Z and others settle this problem by showing that a sim- ple local search algorithm provides a polynomial time approximation scheme (PTAS) for K-means for a Euclid- ean space for any fixed point. Due to the advantage of K-**mean** in clustering, clustering studies in many fields today use K-**mean** as a classification tool and achieved good results [16 – 20].

Implementing the clustering methods to the gene data of chromosome1 we conclude that the 8 clusters (see sheet 2) which has been obtained after implementing the statistical approach through STATISTICA in which Cluster no.3 having many gene involved which can be concluded in it as on the basis of %coverage 0.97, number of cases 246, Centroids percentage % 77.35, also graph frequencies (see figure1) of cluster confirms the information of cluster 3, also chi square test gave the confirmation 1673.41 (see figure 2), also confirmation done by the normal distribution(figure3), frequency (figure4), Dendogram (figure5).In this paper goal was to find out the some interesting mathematical and important clusters in chromosome1 gene data which has been achieved. Conclusion is pulled that mathematical equations algorithms are helpful to find out the interesting information of data, and can implement those methods to smaller and larger scale for analysis. In future plan is to proceed to check the functions and structure of each cluster and this k-**mean** **method** can be implemented to get the clusters on large scale data of complete genome of Homo sapiens and other organisms.

Turbocharging an engine boosts its power by increasing the amount of input air. This task is accomplished by using the exhaust gas to power a turbine which is engaged with a compressor. The Variable Geometry Turbocharger, VGT is a unique turbocharger that the diffuser vane angle can be changed over a wide range of positions. The mathematics of turbomachinery flow analysis is intensive and uses iterative methods. Most of the flow analyses in the area of turbochargers are either experimental or numerical. Three-dimensional Computational Fluid Dynamics (CFD), two- dimensional multiple streamline and one dimensional **mean** line is the three primary numerically available methods. In this paper a **mean** line **method** has been used for predicting the performance of a centrifugal compressor with variable diffuser vane angle position at subcritical Mach numbers. The calculation is based on common thermodynamic and aerodynamic principles, and empirical correlations for losses in a **mean** line analyses. The model calculates the velocities, pressures, temperatures, pressure losses, work consumption, and efficiencies for a specified set of turbocharger geometry, atmospheric conditions, rotational speed, and fluid mass flow rate. The obtained numerical results are validated with the in house measured experimental data and good agreement observed. The purpose for compressor model analysis is to generate overall characteristic map and identify the impact of the diffuser vane angles on the performance. The overall characteristic map is generated by this **method** demonstrate very good agreement and the effect of variable vane angle in pressure ratio and operating range observed.

The dimension of image feature vector is too high, the data volume is large, and there is a large amount of information redundancy between the features. Principal Component Analysis (PCA) is one of the common and effective **method** of dimensionality reduction of feature level data. By means of principal component, the **method** presented in this paper not only eliminates the redundant information between features, but also reduces the dimension of feature space, and retains the required identification information [5]. PCA is a well-known algorithm for data dimensionality reduction and feature extraction which can transform high- dimensional original data vector into a low dimensional vector with uncorrelated components. It is an unsupervised **method** based on statistical analysis without prior knowledge. [6]

Figure 4 shows the segmentation results of four histological images selected from the dataset by using k-Means++, GMM-EM, KGC, HMRF-EM, **Mean** Shift and our proposed FMShift respectively. Fibrosis, vessels (including sinusoids) and other tissues are represented in light blue, white and lavender respectively. Table 1 illustrates the average accuracies with standard deviation over segmentation results obtained from twenty histological images using different methods. The perform- ance of six segmentation methods is quantified by Rand Index and Variation of Information for global evaluations. And the segmentation results of fibrosis and vessels are also measured by Dice Index independently at the same time. Table 2 summaries the average computation times for each **method**. All the above results are obtained with a standard Windows computer equipped with a 2.4 GHz Intel Core i5 processor and 8 GB RAM.

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Abstract :- Smart CCTV (Closed-Circuit Television) technology has increasingly been developed in the last few years to judge the situation and notify the administer or take immediate action for security and surveillance motives. Earlier, the Difference **Method** (FDM),Background Subtraction **Method** (BSM), and Adaptive Background Subtraction **Method** (ABSM) is used for motion object detection but these methods could not recognize rapid scene changes or an object does not move relatively for a long time. To solve such problem , we proposed a novel moving object detection **method** which showed high performance with regard to the MSE(**Mean** Squared Error ) and the accuracy of detecting the moving object contours compared to other existing methods. It also reduces the time complexity and provides the accuracy .It is also good for observation of many places at the same time with only a single CCTV system.

The rest of this paper is organized as follows. In Section 2, an iterative formula for computing matrix sign and its acceleration through a com- bination with Newton’s iteration (see e.g. [14] and the references therein) are presented. We also provide some discussions and illustrate how the new scheme could be constructed and imple- mented. An error analysis for computing ma- trix sign function is brought forward in Section 3. Note that the idea of computing the geometric **mean** using the sign function can also be found in [9, page 131] and has recently been revived in [18]. In Section 4, we show the numerical results and highlight the benefit of the technique. Fi- nally, several concluding comments are collected in Section 5.

range corresponding to 98% positive internal T-cells was used as the threshold marker. The threshold for positivity for ZAP-70 was 20%. 2) The geometric **mean** fluorescence intensity (geo MFI) index **method**: this approach was based on the evaluation of ZAP-70 expression levels in terms of geo MFI index. A two-tube **method** was used to calculate the ZAP-70 geo MFI index obtained from T-lymphocytes, CLL cells, and PE-conjugated isotype controls from CLL cells. Each program permits the analysis of ZAP-70 or PE- conjugated isotype control histograms with 256-channel resolution. Nonspecific staining was evaluated on gated CLL cells in a CD19/PE-isotype control plot, setting the electric voltage and compensation so that the geo **mean** of CLL cells was 10 ± 1 (tube 2). Subsequently, ZAP-70 was measured on a histogram, utilizing the “geo **mean**” parameter, on gated T-lymphocytes (T-geo **mean**), or CLL cells (B-geo **mean**) as defined in the CD3/CD5 or CD5/CD19 dot plot (tube 1). Values of the isotype control and CLL cells were determined from the CD5 + CD19 + gate and a minimum of 20,000 cells

so that the equation (2) is also known as the third order Runge-Kutta **method** based on arithmetic **mean**. Many reseachers follow this idea see [1, 4, 7] for examples. Wazwaz [7] replaces the arithmetic **mean** in equation (3) with contra-harmonic **mean**. Then Abadneh and Rosita [1] proposed a weighted third order Runge-Kutta **method** based on contra-harmonic **mean**.

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Abstract: This paper aims at presenting a new voting function which is obtained in Balinski- Laraki's framework and benefits **mean** and median advantages. The so-called **Mean**-Median Comprise **Method** (MMCM) has fulfilled criteria such as unanimity, neutrality, anonymity, monotonicity, and Arrow's independence of irrelevant alternatives. It also generalizes approval voting system.

Background Information on Side Weirs ROWLINGS (2010) Muslu (2001) conducted a numerical analysis of side weirs which examined them by using a variation of De Marchi‟s (1934) integral solution **method**. This slight alteration takes the stance that the weir coefficient and discharge angle are not in fact constant, as De Marchi assumed, but functions of several parameters. Doing this complicated the problem to such an extent that it could only be solved using an iterative process.

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Keywords Harmonic **Mean**, Runge-Kutta **method**, stability, error control. Abstrak Dalam kertas ini kami rumuskan satu kaedah terbenam berperingkat 4 yang berasaskan min harmonik dan min aritmetik. Kaedah ini berserta de- ngan skema RK-Harmonik boleh digunakan bagi menganggarkan penyelesaian kepada masalah nilai awal. Rantau kestabilan untuk skema ini juga dikaji dan kita simpulkan dapatan ini dengan satu contoh masalah sebagai mengesahkan keberkesanan kaedah ini.

C ), contra-harmonic **mean** Newton’s **method** ( ), cen- troidal **mean** Newton’s **method** ( ), logarithmic **mean** Newton’s **method** (LMNM) respectively to com- pute the extrememum of the function given in Table 1. We use the same functions as Kahya [6, 7]. The results are summarized in Table 2. We use as toler- ance. Computations have been performed using

In most cases the region of significance is split into two parts: The upper part ( μ is large) describes the region where a huge RTM effect is expected, larger than the actual difference of means, and a negative treatment effect ( τ < 0) can be confirmed. For example, assuming a correlation of r = 0.5 in Provencher's trial the region of significance includes all values above 481 meters, saying that Bosentan has a significantly (p < 0.05) negative effect on the patient's 6MWD if only the true **mean** 6MWD is above this value in the population of interest. This part of the region is of no further interest in our example, because here we are only interested in the one-sided hypothesis whether Bosentan can increase the patient's 6MWD. In other situations however a two-sided hypothesis might be more appropriate.

When we are using Min –Max and **Mean**-**Mean** algorithm there is a lack of clarity when we view the image, where as when we are using fuzzy logic which gives clarity of image which aids radiologist to diagnose the disease accurately. This technique gives the high quality image. In the fused image, the relative position of the functional information with respect to the anatomic landmarks is clearly displayed. This information may be very useful for physicians in medical diagnosis.