False Position Research Articles

Reconstruction of the genesis of a Renaissance algorithm to calculate sine tables

AbstractRecently, a manuscript has been discovered in which Jost Bürgi (1552–1632) presented an algorithm to calculate sine tables of high precision with only a modest amount of numerical effort [1], [2]. Several modern proofs for the correctness of this algorithm have been given, all of which, however, use methods that were not at hand at Bürgi's time. This raises the question how Bürgi had found his algorithm.Building on [5], an educated guess is presented how Bürgi may have found his algorithm and also collected enough evidence for its correctness. For this, only methods are needed which were known at Bürgi's time, like prosthaphaeresis and the method of false position.

Estimation of optimum sample size allocation: An illustration with body mass index for evaluating the effect of a dietetic supplement

In many medical researches, it is needed to determine the optimal sample size allocation in a heterogeneous population. This paper proposes the algorithm for optimal sample size allocation. We consider the optimal allocation problem as an optimization problem and the solution is obtained by using Bisection, Secant, Regula–Falsi and other numerical methods. The performance of the algorithm for different numerical methods are analyzed and evaluated in terms of computing time, number of iterations and gain in accuracy using stratification. The efficacy of algorithm is evaluated for the response in terms of body mass index (BMI) to the dietetic supplement with diabetes mellitus, HIV/AIDS and cancer post-operatory recovery patients.

Implementations of Open and Closed Method Numerically: A Non-linear Equations Solution Convergence Test

Non-linear equations are one of the studies in mathematics. Root search in complex non-linear equations can be solved by numerical methods. Many methods to solve the equation. Therefore, the purpose of this research is to conduct simulation of closed and open methods such as Newton Raphson method, Secant method, Regula Falsi, Fixet Point, and Bisection. This is done as a form of comparative research to see the accuracy, number of iterations, and errors of each method in resolving the non-linear equations. As for the case being resolved is the roots of the exponential equation, trigonometry, logarithmic and polynomial degrees of three. The results of this study resulted in different levels of convergence in resolving each case

Research on Minimum Time Interception Problem with a Tangent Impulse under Relative Motion Models

The minimum time interception problem with a tangent impulse whose direction is the same as the satellite’s velocity direction is studied based on the relative motion equations of elliptical orbits by the combination of analytical, numerical, and optimization methods. Firstly, the feasible domain of the true anomaly of the target under the fixed impulse point is given, and the interception solution is transformed into a univariate function only with respect to the target true anomaly by using the relative motion equation. On the basis of the above, the numerical solution of the function is obtained by the combination of incremental search and the false position method. Secondly, considering the initial drift when the impulse point is freely selected, the genetic algorithm-sequential quadratic programming (GA-SQP) combination optimization method is used to obtain the minimum time interception solution under the tangent impulse in a target motion cycle. Thirdly, under the high-precision orbit prediction (HPOP) model, the Nelder-Mead simplex method is used to optimize the impulse velocity and transfer time to obtain the accurate interception solution. Lastly, the effectiveness of the proposed method is verified by simulation examples.

Software-Defined Radio GNSS Instrumentation for Spoofing Mitigation: A Review and a Case Study

Recently, several global navigation satellite systems (GNSS) emerged following the transformative technology impact of the first GNSS: US Global Positioning System (GPS). The power level of GNSS signals as measured at the earths surface is below the noise floor and is consequently vulnerable against interference. Spoofers are smart GNSS-like interferers, which mislead the receivers into generating false position and time information. While many spoofing mitigation techniques exist, spoofers are continually evolving, producing a cycle of new spoofing attacks and counter-measures against them. Thus, upgradability of receivers becomes an important advantage for maintaining their immunity against spoofing. Software-defined radio (SDR) implementations of a GPS receiver address such flexibility but are challenged by demanding computational requirements of both GNSS signal processing and spoofing mitigation. Therefore, this paper reviews reported SDRs in the context of instrumentation capabilities for both conventional and spoofing mitigation modes. This separation is necessitated by significantly increased computational loads when in spoofing domain. This is demonstrated by a case study budget analysis.

A lightweight ANN based robust localization technique for rapid deployment of autonomous systems

The capability to localize or identify position in the field of deployment is a primary requirement of future autonomous system in domains such as warehouse transportation, ambient-assisted living/ health care systems, search and rescue, motion monitoring, etc. Although reliable indoor localization in the order of few centimeters can be achieved with the existing localization systems in Line-of-Sight (LOS) conditions, the localization under Non-line-of-Sight (NLOS) conditions is an open area of research. In range-based localization systems, distance estimation is a pre-requisite for location estimation. Time of Arrival (ToA) is considered to be the most accurate technique for distance estimation when compared to Time Difference of Arrival (TDoA) or Received Signal Strength Indication (RSSI). Most of the work available as literature on indoor localization under NLOS conditions is based on the profiling of the indoor deployment area under various NLOS conditions and mitigating NLOS affected timestamps from the ToA measurements. However, it is not practically possible to obtain a comprehensive data set containing all possible conditions of NLOS in indoor environments. In this paper, an Artificial Neural Network based Location Estimation Unit (ANN-LEU) based scheme is proposed to estimate the two-dimensional (2-D) location of an object under LOS and NLOS conditions. One of the unique features of the novel location estimation scheme is that the training of the system is required to be performed only under LOS conditions, thus facilitating the quick deployment in new environments. The proposed ANN-LEU is robust as it identifies the presence of NLOS if any, in the ToA measurements and thus removing false position estimations if any. The Mean Average Error (MAE) error in position estimated during the performance analysis of the proposed system was restricted to lesser than 20 cm, if the object is in range of three beacons in LOS, and also for the scenarios in which one of the three beacon nodes are in NLOS. The proposed scheme eliminates false position identification. The proposed scheme requires lesser number of beacons for localization when compared to the available indoor localization systems, thus also improving the cost and energy efficiency.

Detection of Induced GNSS Spoofing Using S-Curve-Bias.

In Global Navigation Satellite System (GNSS), a spoofing attack consists of forged signals which possibly cause the attacked receivers to deduce a false position, a false clock, or both. In contrast to simplistic spoofing, the induced spoofing captures the victim tracking loops by gradually adjusting it’s parameters, e.g., code phase and power. Then the victims smoothly deviates from the correct position or timing. Therefore, it is more difficult to detect the induced spoofing than the simplistic one. In this paper, by utilizing the dynamic nature of such gradual adjustment process, an induced spoofing detection method is proposed based on the S-curve-bias (SCB). Firstly, SCB in the inducing process is theoretically derived. Then, in order to detect the induced spoofing, a detection metric is defined. After that, a series of experiments using the Texas spoofing test battery (TEXBAT) are performed to demonstrate the effectiveness of the proposed algorithm.

Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation

This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.

NUMERICAL METHODS RESEARCH AND FRACTURE FAILURE ANALYSIS FOR CRITICAL CRACK SIZE

Safety analysis of fracture mechanics is an important part of structural integrity assessment and critical crack size is one ofmain concerns for fracture failure. From the perspective of mathematics, the calculation of critical crack size is the solving and analysis for nonlinear equation f(x)=0. About the solution of nonlinear equation, there are the bisection method, the false position method, the simple iteration method, the newton method and the secant method. For the complexity of load imposed on nuclear power equipment, there may be the multi-value phenomenon of critical crack size in analyzing fracture failure problems. Considering that the corresponding mechanical states of the shallow crack and the deep crack are different when the fracture failure occurs, the crack toughness factor needs to be considered in the fracture failure analysis of shallow cracks. Connecting the bottom head of nuclear power plant main equipment, the pipeline large break transient of accident condition and the welding research council bulletin 175, the algorithm and the convergence of multi-value phenomenon of critical size are studied. Using the crack toughness factor, the fracture failure critical crack size is deeply analyzed and discussed. The algorithm and fracture failure theory in the present study can provide the technical support for the prolonging operation life projects of nuclear power plant main equipment in future.

A New Root–Finding Algorithm Using Exponential Series

In this paper, we present a new root-finding algorithm to compute a non-zero real root of the transcendental equations using exponential series. Indeed, the new proposed algorithm is based on the exponential series and in which Secant method is special case. The proposed algorithm produces better approximate root than bisection method, regula-falsi method, Newton-Raphson method and secant method. The implementation of the proposed algorithm in Matlab and Maple also presented. Certain numerical examples are presented to validate the efficiency of the proposed algorithm. This algorithm will help to implement in the commercial package for finding a real root of a given transcendental equation.

Antropological horizons of gender equality: from religious cannons to business challenges

Relevance of research. Any religion in the world emphasizes the woman's femininity, namely an anthropological feature that does not require similarity with the functional features of her husband. However, in turn, it has the potential of a comprehensive development of the individual as a mother, and the realization of the role of women in society. The misconceptions that maternity lifts women's potential and suppresses their personal development causes a lot of controversial issues that lead to negative manifestations of gender inequality. Negative manifestations of the perception of false positions lead to terrible structural changes in society, ruin (or shake) the foundations of the laws of motherhood, have consequences of the aging of the nation, the loss of human spiritual humanism. Women lose the opportunity to feel like a mother and transfer their love of work to work as a child. Therefore, its main base anthropological identity is reduced to zero in this case and makes a woman uncertain gender, which will never find its place in society. The aim of the study.It based on the study of the anthropological horizons of gender inequality within the framework of religious canons and modern trends in the manifestation of business, the loss of anthropological value of women. The author's team has proved that each of the religions of the world pays much attention to women as mothers, their roles in society with exceptional abilities and special qualities. None of the religions does restrict women in revealing these abilities, but places anthropological peculiarity on the first place of a woman-mother, guardian of the family. Religion acts as a universal anthropological phenomenon, which reveals each individual essential element characteristic of every person and emphasizes its importance for society

Automated pipette failure monitoring using image processing for point-of-care testing devices

BackgroundThe accuracy and precision of liquid handling can be altered by several causes including wearing or failure of parts, and human error. The last cause is crucial since point-of-care testing (POCT) devices can be used by non-experienced users or patients themselves. Therefore it is important to improve the method of informing the users of POCT device malfunctions due to damage of parts or human error.MethodsIn this paper, image-based failure monitoring of the automated pipetting was introduced for POCT devices. An inexpensive, high-performance camera for smartphones was employed in our previous work to resolve various malfunctions such as incorrect insertion of the tip, false positioning of the tip and pump, and improper operation of the pump. The image acquired from the camera was analyzed to detect the malfunctions. In this paper, the reagent volume in the tip was estimated from the image processing to verify the pump operation. First, the color component corresponding to the reagent intrinsic color was extracted to identify the reagent area in the tip before applying the binary image processing. The extracted reagent area was projected horizontally and the support length of the projection image was calculated. As the support length was related to the reagent volume, it was referred to the volume length. The relationship between the measured volume length and the previously measured solution mass was investigated. If we can predict the mass of the solution by the volume length, we will be able to detect the pump malfunction.ResultsThe cube of the volume length obtained by the proposed image processing method showed a very linear relationship with the reagent mass in the tip injected by the pumping operation (R2 = 0.996), indicating that the volume length could be utilized to estimate the reagent volume to monitor the accuracy and precision of the pumping operation.ConclusionsAn inexpensive smartphone camera was enough to detect various malfunctions of a POCT device with pumping operation. The proposed image processing could monitor the level of inaccuracy of pumping volume in limited range. The simple image processing such as a fixed threshold and projections was employed for the cost optimization and system robustness. However it delivered the promising results because the imaging condition was highly controllable in the devices.

Students’ interest and performance analysis in power system numerical methods: General function calculation

Nonlinear equations are the most frequent numerical computation application occurring in scientific investigation or design activity specifically to different branches of power engineering. The objective of this study consisted of the analysis of the interest degree of students towards a specialised subject and the analysis of performance and concentration degree of students in case of solving a laboratory work during the laboratory sessions. Computer program used during laboratory sessions, ECUATIE, contains recent improvements. The first analysis presents the overall situation of student’s presences and absences during the laboratory and courses sessions. The second analysis presents the situation of marks obtained following the settlement of laboratory session. Participants are students of Politehnica University Timisoara, Romania. Participants are asked to solve an algebraic or transcendent equation, using different methods. The research found the high degree of student’s interest and also the high interest degree of students even if the calculation volume is relatively high. Keywords: Nonlinear equations, numerical coefficients, Newton–Raphson method, false position (chord) method.

Regula falsi based automatic regularization method for PDE constrained optimization

Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the mismatch between the observed data and the model predictions, including an extra regularization term, and use the PDE as a constraint. Often, a suitable regularization parameter is determined by solving the problem for a whole range of parameters -- e.g. using the L-curve -- which is computationally very expensive. In this paper we derive two methods that simultaneously solve the inverse problem and determine a suitable value for the regularization parameter. The first one is a direct generalization of the Generalized Arnoldi Tikhonov method for linear inverse problems. The second method is a novel method based on similar ideas, but with a number of advantages for nonlinear problems.

Struktur Konstruksi Wacana Sufisme

Normatively, the structure of Sufi discourse construction comes from within the religion of Islam itself. According to Ibn Khaldun, Sufism comes from authentic Islamic law. The seeds originally came from the first generation of Muslims as the path of truth and guidance. Sufi approaches based on their consistency in the service of God, reluctant to worldly pleasures, abstain from the false delights, wealth, and position hunted by most humans, and busy solitude in worship to God. Therefore in Islam, there can be no spirituality without the aid of the Qur'an, which teaches man everything he can know or can learn, and which can lead people to the ideals that are the object of his creation. This article will elaborate the structure of the construction of Sufism discourse originating from Islam

Detection of Faint Asteroids Based on Image Shifting and Stacking Method

In order to improve the ability to find the faint and small celestial bodies in the solar system, a method of shifting and stacking images which improves the detection efficiency of faint moving objects is applied to process the sequential optical images. This method determines the existence of moving objects by using the method of false position to pre-estimate the apparent velocities of moving objects, then determines iteratively the accurate positions of moving objects based on the SNR (Signal-to-Noise Ratio) and elongation of stellar image. Using the sequential images of the China Near Earth Object Survey Telescope (CNEOST), we carry out an experiment and succeed in detecting asteroids fainter than 21 magnitude which are invisible on a single image. Thus, the feasibility of this method is verified.

A <italic>k</italic>-NN-Based Localization Approach for Crowdsourced Air Traffic Communication Networks

In this paper, we argue that current state-of-the-art methods of aircraft localization such as multilateration are insufficient, in particular for modern crowdsourced air traffic networks with random, unplanned deployment geometry. We propose an alternative, a grid-based localization approach using the k -nearest neighbor ( k -NN) algorithm, to deal with the identified shortcomings. Our proposal does not require any changes to the existing air traffic protocols and transmitters, and is easily implemented using only low-cost, commercial-off-the-shelf hardware. Using an algebraic multilateration algorithm for comparison, we evaluate our approach using real-world flight data collected with our collaborative sensor network OpenSky. We quantify its effectiveness in terms of aircraft location accuracy, surveillance coverage, and the verification of false position data. Our results show that the grid-based k -NN approach can increase the effective air traffic surveillance coverage compared to multilateration by a factor of up to 2.5. As it does not suffer from dilution of precision to the same extent, it is more robust in noisy environments and performs better in pre-existing, unplanned receiver deployments. We further find that the mean aircraft location accuracy can be increased by up to 41% in comparison with multilateration while also being able to pinpoint the origin of potential spoofing attacks conducted from the ground.

Determination of Optimal Reserve Requirement for Fuel Cost Minimization of a Microgrid Under Load and Generation Uncertainties

In this paper, economic load dispatch (ELD) problem of a microgrid is formulated considering load and renewable generation uncertainties. Both load and generation uncertainties are modeled using triangular fuzzy numbers. The ELD problem minimizes the fuel cost of the dispatchable distributed generators (DGs) in the microgrid. The reserve requirement for generation and load uncertainties is formulated. Next, the reserve requirement for a stable transition of a grid-connected microgrid to islanded mode under load and generation uncertainties is also formulated. Moreover, the reserve requirement for a stable transition of an islanded microgrid to grid-connected mode under load and generation uncertainties is also formulated in this paper. The effects of these constraints on the daily fuel cost of dispatchable DGs are then investigated. A three-area microgrid test system is considered for the simulation. Each area in the microgrid comprises dispatchable DGs, loads, wind power DGs and solar power DGs. The economic dispatch problem is solved using four different techniques: (i) bisection method, (ii) regula falsi method, (iii) golden section method, and (iv) teaching–learning-based optimization (TLBO) technique. Simulation is carried out considering 24 h load, wind generation and solar generation profiles.

Determination of Approximated Root of Nonlinear Equation by Interpolation Technique

This beautiful universe is full of mathematical and engineering problems involving nonlinear equations 𝑓(𝑥)=0. The main theme of this paper is to develop an Algorithm to enhance the speed and convergence of bracketing methods for determining the root of nonlinear equations. For this cause, Newton forward interpolation difference formula and Bisection Method are recruit. Developed interpolation technique method guarantees that it converges towards thereal root faster than Bisection Method and RegulaFalsi Method. Few numerical examples are also conferred in this paper to inspect the efficiency of developed method and compared with other existing methods. It is examined from the results that the performance of developed method is better than the existing methods such as Bisection Method and RegulaFalsi Method.

Super Linear Iterated Method for Solving Non-Linear Equations

In this paper a super linear iterated method has been suggested for solving non-linear equations. The proposed super linear method is very much effective and convenient for solving non-linear equations, and it is a derivative free two-point method. The proposed iterated method is derived from Newton Raphson Method and Taylor Series. We have observed in numerical outcome is that the super line a rmethod is rapidly converge with the assessment of Bisection Method, Regula-Falsi Method and Secant Method. Its hypothetical out comes and efficacy is inveterate by Numerical problems. Throughout the study, it has been perceived that the developed super linear algorithm is a decent attainment for estimating a single root of nonlinear equations.