Contraharmonic Mean Research Articles

Radio Contra Harmonic Mean Number of Graphs

Objectives: To explore the least upper bound of graphs by radio contra harmonic labeling. Methods: Contra harmonic mean function or , radio mean labeling condition and radio harmonic mean labeling are used. Findings: Here we introduce radio contra harmonic mean labeling and its least upper bound, designated as radio contra harmonic mean number, by formulating the constraints. Novelty: Based on radio mean labeling and contra harmonic mean labeling, the new concept of radio contra harmonic mean labeling was established. The bounds of some special graphs are encountered here. This kind of labeling is employed in secure communication networks and is also applicable in X-rays, crystallography, coding theory, computing etc. Keywords: Radio contra harmonic mean labeling, rchmn (G), Order, Diameter, Smallest span

A novel adaptive contextual information-based 2D-histogram for image thresholding

This paper proposes a new two-dimensional (2D) histogram containing an image's adaptive local spatial contextual information. The correlation information between pixels is essential to achieve the optimal thresholds for image segmentation purposes. But it is an arduous task to find adaptive spatial information efficiently. So, an innovative adaptive local spatial information technique is proposed here to compute a novel 2D histogram. An adaptive contraharmonic mean (ACM) filter-based 2D-histogram is designed that contains contextual information by a unique proposed logical pseudo-energy (LPE) function. The order of contraharmonic filter Q is adaptively obtained using LPE, and the 2D Tsallis-Havrda-Charvat entropy is utilized to obtain the segmented results. Setting the Q value of the contraharmonic mean filter is tedious, and the proposed LPE function solves this problem. For the result assessments, the presented framework is compared with other maximum sum entropy-based methods, which are 2D-Kapur, 2D-Renyi, 2D-Tsallis, 2D-Masi and Parzen-window-based Kapur entropies-based image segmentation approaches. The proposed ACM-based Tsallis-Havrda-Charvat (Tsallis) entropy (ACM-Tsallis) shows excellent segmented results above local mean-based 2D-entropies methods and the latest Parzen-based Kapur entropy approach.

Modifikasi metode iterasi berorde tiga dengan orde konvergensi optimal

Weerakoon-Fernando’s and Homeier’s methods are a third-order iterative method to solve nonlinear equations. A new third-order iterative method is constructed by sum of Weerakoon-Fernandon’s and Homeier’s method. This paper discusses the modification of the third-order iterative method using contra harmonic mean with involving one real parameter q. The aim of this modification is to improve the convergence order of the method and keep the number of function evaluations. Based on the result of study shows that the method has a third-order of convergence for and a fourth-order of convergence for with three evaluation of functions. Furthermore, numerical simulation is given to exam the perfomance of the methods. The measurement of performance of the methods, such as : number of iterations, number of function evaluations, numerical convergence order, and value of function, are compared with Newton’s, Weerakoon-Fernando’s, and Homeier’s methods. Generally, the result of numerical simulation shows that the new method for has better performance than others.
 Keywords: Weerakoon-Fernando’s method, Homeier’smethod, order of convergence, contra harmonic mean, evaluation of functionMSC2020: 41A25, 41A58, 65H05

Stable Computer Method for Solving Initial Value Problems with Engineering Applications

Engineering and applied mathematics disciplines that involve differential equations in general, and initial value problems in particular, include classical mechanics, thermodynamics, electromagnetism, and the general theory of relativity. A reliable, stable, efficient, and consistent numerical scheme is frequently required for modelling and simulation of a wide range of real-world problems using differential equations. In this study, the tangent slope is assumed to be the contra-harmonic mean, in which the arithmetic mean is used as a correction instead of Euler’s method to improve the efficiency of the improved Euler’s technique for solving ordinary differential equations with initial conditions. The stability, consistency, and efficiency of the system were evaluated, and the conclusions were supported by the presentation of numerical test applications in engineering. According to the stability analysis, the proposed method has a wider stability region than other well-known methods that are currently used in the literature for solving initial-value problems. To validate the rate convergence of the numerical technique, a few initial value problems of both scalar and vector valued types were examined. The proposed method, modified Euler explicit method, and other methods known in the literature have all been used to calculate the absolute maximum error, absolute error at the last grid point of the integration interval under consideration, and computational time in seconds to test the performance. The Lorentz system was used as an example to illustrate the validity of the solution provided by the newly developed method. The method is determined to be more reliable than the commonly existing methods with the same order of convergence, as mentioned in the literature for numerical calculations and visualization of the results produced by all the methods discussed, Mat Lab-R2011b has been used.

Dynamic Comparison of Variations of Newton’s Methods with Different Types of Means for Solving Nonlinear Equations

This article discusses dynamic comparison of variations of Newton’s methods with different types of means for solving nonlinear equations. There are two factors that are considered to affect the shape of the basin of attraction of a method namely the size of the determined convergence area and number of partitions. The computation results of some functions show that harmonic mean Newton’s method (HMN) has small divergence area. On the other hand, contra harmonic mean Newton’s method (CMN) has the largest divergence area and is considered to be the least effective method

Perbandingan Algoritma untuk Mereduksi Noise pada Citra Digital

Image restoration is one of the stages in the field of Digital Image Processing. Image restoration is objective, in the sense that restoration techniques tend to be based on mathematical or probabillistic models of image degradation. The mathematical algorithm to reduce noise in digital images in this study uses 8 filtering algorithm methods. The purpose of this study is to compare 8 filtering algorithm and conclude which algorithm is the best for reducing noise in digital images. The method for generating noise uses Rayleigh Noise and Erlang (Gamma) Noise. The algorithm for reducing noise is Arithmetic Mean Filter, Geometric Mean Filter, Harmonic Mean Filter, Contraharmonic Mean Filter, Geometric Mean Filter, Harmonic Mean Filter, Contraharmonic Mean Filter, Median Filter, Maximum Filter, Minimum Filter, and Midpoint Filter. The measurement to determine which algorithm is the best using Root Mean Square Error (RMSE). Tests were carried out on 15 digital images by testing 1200 times. The conclusion of this study is that the best algorithm for noise reduction is Median Filter by resulting the smallest RMSE value of 6.0860942.

Mean-Based Efficient Hybrid Numerical Method For Solving First-Order Ordinary Differential Equations

The center of interest of this work is to introduce a mean-based efficient hybrid numerical method for solving first-order ordinary differential equations with initial conditions. This method is generated by the mean of the modified slope of modified Euler’s method and the mean of main incremental functions of RK-2 method and a second-order contra harmonic mean method. The factors related to the numerical method have been analyzed to observe its performance and found that the method satisfies all its factors. It also performs with better accuracy than modified Euler’s methods, a second stage second-order contra harmonic mean method, and RK-2 method. The proposed method performed with better accuracy than the existing methods, but it is also better workable on some other second-order well-known methods.

Harmonic Mean and Contra-Harmonic Mean Derivative-Based Closed Newton-Cotes Quadrature

In this paper, the Harmonic mean and Contra-harmonic mean of two endpoints [a,b] are applied at the derivative of the error term in the existing CNC formulas. This modified error term is included as an additional function to the existing formula. The new error terms are derived using the method of precision for the proposed formulas. Comparisons are made between the existing CNC formulas and the proposed CNC formulas by using numerical examples. The proposed Harmonic mean derivate-based (HMD) and the Contra-harmonic mean derivative-based (CHMD). CNC formulas give better results for definite integrals. Another two of its statistical means are discussed and derived for the existing CNC formulas in the subsequent paper.

Analisis Perbandingan Metode Harmonic Mean Filter dan Contraharmonic Mean Filter untuk mengurangi noise pada Citra Digital

The results of digital camera recordings to take digital images, there are often some disturbances that appear in the digital image called noise. The noise that is often found in digital images is Salt-Pepper Noise and Speckle Noise. An image that has noise usually occurs due to an error in image retrieval techniques. Noise that usually appears is spots on the image, it is necessary to reduce noise by using the right filter method so that the resulting image matches the original. One of the filter methods to reduce noise is the harmonic mean-filter and contra-harmonic mean filter methods. From the calculation results of the average Mean Square Error (MSE) and Peak Signal to Noise Ratio (PSNR), it can be concluded that the Harmonic Mean Filter method is better at reducing salt & pepper noise. While the Contra-Harmonic Mean Filter method is better at reducing speckle noise.

A New Modified Algorithm Based Upon Exponential and Polynomial Functions for Solving Initial Value Problems

The main focus of this paper is to propose a fourth-order convergent modified numerical algorithm by using an exponential and polynomial type function for getting the approximate solution of initial value problems (IVPs) in ordinary differential equations (ODEs). The proposed algorithm has been tested and analyzed for the convergence, stability, consistency, of several numerical experiments that proved the superiority of the proposed algorithm against algorithms including the fourth-order arithmetic mean (AM), the fourth-order harmonic mean (HM), and the fourth-order Contra harmonic mean( ). Keywords: Modified numerical algorithm, Ordinary differential equation, Order of convergence, Initial value problems, Stability, and Consistency. DOI: 10.7176/MTM/11-6-01 Publication date: December 31 st 2021

Nakagami-m Fading Detection with Eigen Value Spectrum Algorithms

One of the most crucial roles of the cognitive radio (CR) is detection of spectrum ‘holes’. The ‘no a-priori knowledge required’ prospective of blind detection techniques has attracted the attention of researchers and industries, using simple Eigen values. Over the years, a number of study and research has been carried out to determine the impact of thermal noise in the performance of the detector. However, there has not been much work on the impact of man-made noise, which also hinders the performance of the detector. As a result, both man-made impulse noise and thermal Gaussian noise are examined in this proposed study to determine the performance of blind Eigen value-based spectrum sensing. Many studies have been conducted over long sample length by oversampling or increasing the duration of sensing. As a result, a research progress has been made on shorter sample lengths by using a novel algorithm. The proposed system utilizes three algorithms; they are contra-harmonic-mean minimum Eigen value, contra-harmonic mean Maximum Eigen value and maximum Eigenvalue harmonic mean. For smaller sample lengths, there is a substantial rise in the number of cooperative secondary users, as well as a low signal-to-noise ratio when employing the maximum Eigen value Harmonic mean. The experimental analysis of the proposed work with respect to impulse noise and Gaussian signal using Nakagami-m fading channel is observed and the results identified are tabulated.

A new method using the Forward Backward technique with Contra Harmonic mean formula

We introduce a new method for solving Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), by making a mixing between the Forward (Predictor) – Backward (Corrector) technique and used it in the Contra Harmonic mean formula, this new method give us a parallelism in numerical calculations and it is more accurate than the old classical Runge – Kutta formula of the same order.

Sharp contra-harmonic mean bounds for the Sandor-Yang means

In this paper, we present the best possible two Sandor-Yang means bounds by the one-parameter contra-harmonic mean. As applications, we find new bounds for the second Seiffert and Neuman-Sandor means.

New Modification on Heun’s Method Based on Contraharmonic Mean for Solving Initial Value Problems with High Efficiency

In this paper, small modification on Improved Euler’s method (Heun’s method) is proposed to improve the efficiency so as to solve ordinary differential equations with initial condition by assuming the tangent slope as an average of the arithmetic mean and contra-harmonic mean. In order to validate the conclusion, the stability, consistency, and accuracy of the system were evaluated and numerical results were presented, and it was recognized that the proposed method is more stable, consistent, and accurate with high performance.

A Computationally Efficient Skull Scraping Approach for Brain MR Image

Background: In the process of volumetric evaluation of the damaged region in the human brain from a MR image it is very crucial to remove the non-brain tissue from the acquainted image. At times there is a chance during the process of assessing the damaged region through automated approaches might misinterpret the non-brain tissues like skull as damaged region due to their similar intensity features. So in order to address such issues all such artefacts. Objective: In order to mechanize an efficient approach that can effectively address the issue of removing the non-brain tissues with minimal computation effort and precise accuracy. It is very essential to keep the computational time to be as minimal as possible because the processes of skull removal is used in conjunction with segmentation algorithm, and if the skull scrapping approach has consumed a considerable amount of time, they it would impact the over segmentation and volume assessment time which is not advisable. Methods: In this paper a completely novel approach named Structural Augmentation has been proposed, that could efficiently remove the skull region from the MR image. The proposed approach has several phases that include applying of Hybridized Contra harmonic and Otsu AWBF filtering for noise removal and threshold approximation through Otsu based approach and constructing the bit map based on the approximated threshold. Morphological close operation followed by morphological open operation with reference to a structural element through the generated bitmap image. Results: The experiment are carry forwarded on a real time MR images of the patient at KGH hospital, Visakhapatnam and the images from open sources repositories like fmri. The experiment is conducted on the images of varied noise variance that are tabulated in the results and implementation section of the article. The accuracy of the proposed method has been evaluated through metrics like Accuracy, Sensitivity, Specificity through true positive, true negative, False Positive and False negative evaluations. And it is observed that the performance of the proposed algorithm seems to be reasonable good. Conclusion: The skull scrapping through structural Augmentation is computationally efficient when compared with other conventional approaches concerning both computational complexity and the accuracy that could be observed on experimentation. The Adaptive Weighted Bilateral Filter that acquire the weight value from the approximated contra harmonic mean will assist in efficient removal of poison noised by preserving the edge information and Otsu algorithm is used to determine the appropriate threshold value for constructing the bitmap image of the original MRI image which is efficient over the earlier mean based approach for estimating the threshold. Moreover, the efficiency of the proposed approach could be further improved by using customized structural elements and incorporating the fuzzy based assignments among the pixels that belong to brain tissue and skull effectively.

Perbandingan Algoritma Contraharmonic Mean Filter dan Arithmetic Mean Filter untuk Mereduksi Exponential Noise

Noise in the image caused a decrease in image quality, so that the image will look dirty and spots appear on the resulting image. Noise also results in reduced information on the resulting image so that noise limits valuable information when image analysis is performed. Filtering technique is one way to overcome noise. The filtering technique used in this study is using the Contraharmonic Mean Filter algorithm and the Arithmetic Mean Filter algorithm with the type of noise used to reduce the Exponential Noise. The results of the two algorithms show that the Arithmetic Mean Filter algorithm is a better algorithm to reduce the Exponential Noise compared to the Contraharmonic Mean Filter algorithm which is proven based on the value of MSE (Mean Square Error) and PSNR (Peak Signal-to-Noise Ratio).

Numerical Solutions of Fuzzy Differential Equation under Generalized Differentiability concept using a Third Order Runge - Kutta Method with Contra Harmonic Mean

Numerical Solutions of Fuzzy Differential Equation under Generalized Differentiability concept using a Third Order Runge - Kutta Method with Contra Harmonic Mean

A 2-Stage Implicit Runge-Kutta Method Based on Heronian Mean for Solving Ordinary Differential Equations

In recent times, the use of different types of mean in the derivation of explicit Runge-Kutta methods had been on increase. Researchers have explored explicit Runge-Kutta methods derivation by using different types of mean such as geometric mean, harmonic mean, contra-harmonic mean, heronian mean to name but a few; as against the conventional explicit Runge-Kutta methods which was viewed as arithmetic mean. However, despite efforts to improve the derivation of explicit Runge-Kutta methods with use of other types of mean, none has deemed it fit to extend this notion to implicit Runge-Kutta methods. In this article, we present the use of heronian mean as a basis for the construction of implicit Runge-Kutta method in a way of improving the conventional method which is arithmetic mean based. Numerical results was conducted on ordinary differential equations which was compared with the conventional two-stage fourth order implicit Runge-Kutta (IRK4) method and two-stage third order diagonally implicit Runge-Kutta (DIRK3) method. The results presented confirmed that the new scheme performs better than these numerical methods. A better Qualitative properties using Dalquist test equation were established.

Sharps Bounds for Power Mean in Terms of Contraharmonic Mean

In this research work, we consider the below inequalities: (1.1). The researchers attempt to find an answer as to what are the best possible parameters α, β that (1.1) can be held? The main tool is the optimization of some suitable functions that we seek to find out. Without loss of generality, we have assumed that a > b and let for 1) and a b, (t small) for 2) to determine the condition for α and β to become f(t) ≤ 0 and g(t) ≥ 0.

Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean

In the article, we prove that lambda _{1}=1/2+sqrt{ [ (sqrt{2}+ log (1+sqrt{2}) )/2 ]^{1/nu }-1}/2, mu _{1}=1/2+sqrt{6 nu }/(12nu ), lambda _{2}=1/2+sqrt{ [(pi +2)/4 ] ^{1/nu }-1}/2 and mu _{2}=1/2+sqrt{3nu }/(6nu ) are the best possible parameters on the interval [1/2, 1] such that the double inequalities \t\t\tCν[λ1x+(1−λ1)y,λ1y+(1−λ1)x]A1−ν(x,y)<RQA(x,y)<Cν[μ1x+(1−μ1)y,μ1y+(1−μ1)x]A1−ν(x,y),Cν[λ2x+(1−λ2)y,λ2y+(1−λ2)x]A1−ν(x,y)<RAQ(x,y)<Cν[μ2x+(1−μ2)y,μ2y+(1−μ2)x]A1−ν(x,y)\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document} $$\\begin{aligned}& C^{\\nu }\\bigl[\\lambda _{1}x+(1-\\lambda _{1})y, \\lambda _{1}y+(1-\\lambda _{1})x\\bigr]A ^{1-\\nu }(x, y) \\\\& \\quad < \\mathcal{R}_{QA}(x, y)< C^{\\nu }\\bigl[\\mu _{1}x+(1-\\mu _{1})y, \\mu _{1}y+(1-\\mu _{1})x\\bigr]A^{1-\\nu }(x, y), \\\\& C^{\\nu }\\bigl[\\lambda _{2}x+(1-\\lambda _{2})y, \\lambda _{2}y+(1-\\lambda _{2})x\\bigr]A ^{1-\\nu }(x, y) \\\\& \\quad < \\mathcal{R}_{AQ}(x, y)< C^{\\nu }\\bigl[\\mu _{2}x+(1-\\mu _{2})y, \\mu _{2}y+(1-\\mu _{2})x\\bigr]A^{1-\\nu }(x, y) \\end{aligned}$$ \\end{document} hold for all x, y>0 with xneq y and nu in [1/2, infty ), where A(x, y) is the arithmetic mean, C(x, y) is the contraharmonic mean, and mathcal{R}_{QA}(x, y) and mathcal{R}_{AQ}(x, y) are two Neuman means.