Simple Breaker Index Formula Using Linear Model

Breaking waves generated by wave shoaling in coastal areas have a close relationship with various physical phenomena in coastal regions. Therefore, it is crucial to accurately predict breaker indexes such as breaking wave height and breaking depth when designing coastal structures. Many studies on wave breaking have been carried out, and many experimental data have been documented. Representative studies on wave breaking provide many empirical formulas for the prediction of breaking index, mainly through hydraulic model experiments. However, the existing empirical formulas for breaking index determine the coefficients of the assumed equation through statistical analysis of data under the assumption of a specific equation. This study presents an alternative method to estimate breaker index using representative linear-based supervised machine learning algorithms that show high predictive performance in various research fields related to regression or classification problems. Based on the used machine learning methods, a new simple linear equation for the prediction of breaker index is presented. The newly proposed breaker index formula showed similar predictive performance compared to the existing empirical formula, although it was a simple linear equation.

Equation for Tooth Size Prediction from Mixed Dentition Analysis for Taiwanese Population: A Pilot Study

Background: In mixed dentition analysis, estimation of the mesiodistal width of unerupted permanent canines and premolars is essential for successful diagnosis and treatment planning. The present study aimed to develop a simple linear equation to predict permanent tooth sizes from mixed dentition analysis for Taiwanese people. Methods: The sample comprised 200 dental casts, derived from Taiwanese patients (100 males and 100 females; age, 12–35 years). Mesial distal tooth widths were measured in dental casts with a digital caliper. A student’s t-test was conducted to detect tooth size correlations with gender-specific differences, as well as intra-arch counterparts. Standard linear regression was conducted to develop a simple equation representing predictions of canine-premolar relationships. Results: All teeth were not significantly different between the left and right sides, regardless of gender and upper or lower arches. In terms of types of teeth, males had larger tooth dimensions in both arches than females. New regression equations for estimating the dimensions of the unerupted canines and premolars in the Taiwanese population were developed. Conclusions: Using a sample of Taiwanese people, new models derived for females and males separately were developed, which should provide highly accurate predictions for unerupted canines and premolars in the Taiwanese population.

n-Point Correlation Functions: Descriptive Statistics

This chapter explores the statistical pattern of the galaxy distribution. It focuses on n-point correlation functions (analogs of the autocorrelation function and higher moments for a continuous function), the descriptive statistics that have proved useful. The approach has also proved useful in many other applications. Of considerable practical importance has been the fact that there is a simple linear equation relating the directly observable angular correlation function to the wanted spatial function. This means the translation from one to the other is fairly easy, and equally important it makes it easy to say how the statistical estimates ought to scale with the depth of the survey and hence to test for possible contamination of the estimates by systematic errors. A third useful result is that the dynamics of the galaxy distribution can be treated in terms of the mass correlation functions: the statistic that proves useful for the reduction of the data may also be useful for the analysis of the theory.

PENGARUH PENGAJARAN REMEDIAL TERHADAP HASIL BELAJAR PENDIDIKAN AGAMA KRISTEN (PAK) PADA SISWA KELAS XI SMK NEGERI 1 LAGUBOTI TAHUN PEMBELAJARAN 2019/2020

This study aims to determine the level of remedial teaching achievement, the level of learning outcomes before remedial and the level of PAK learning outcomes of students in SMK Negeri 1 Laguboti in the 2019/2020 academic year, as well as to determine the positive and significant influence between remedial teaching on the learning outcomes of PAK XI grade students of XI SMK Negeri 1 Laguboti 2019/2020 academic year. The hypothesis of this study is: there is a positive and significant influence of remedial teaching on the learning outcomes of PAK XI grade students of SMK Negeri 1 Laguboti 2019/2020 academic year. Researchers used quantitative inferential statistical research. The population in this study amounted to 105 people and a sample of 51 people. The research instrument used was a closed questionnaire and tests.The conclusions of this study were the level of remedial teaching achievement of 64.924% with a good scale range, the level of achievement of learning outcomes before remedial to students amounted to 59.51 with the completion criteria or 70, and the level of learning outcomes after learning remedial for students is 82.12 with naotas criteria or 70. And the positive relationship test results obtained value of 0.418 tute 0.297. The result of simple linear equation is Y-62.239 + 0.303, with tnne lutei value (3,260 1,684) and futur fme value (10,626 4,08) so that it can be collected that the hypothesis is accepted.Keywords: Remedial Teaching, Student PAK Learning outcomes

Strength Comparison of Accelerated Cured & Normal Cured Fly-Ash Based Concrete

The most important property of concrete is its compressive strength, which is carried out after 28-days of proper curing of concrete. This test is affected by other factors like the condition of curing, water to cement ratio, method of transportation, handling of the concrete, extent of vibrations and quality of the ingredients of mix proportion. This research study is an attempt to develop a simple mathematical model, by using linear regression analysis to estimate the 28-day fc’ (Compressive Strength) of concrete from the test results carried out at early age. This simple linear equation develops a relationship of 28.5 hours. These results show that most of the predicted values of compressive strength, calculated via equations, lie within permissible range difference for compressive strength achieved by experimental method, which is clear indication of credibility of the equations obtained for compressive strength at different age of concrete. The results show that compressive strength of concrete increases with the increase in content of FA (Fly Ash) upto 30% replacement, and the compressive strength of the concrete starts decreasing beyond 30% FA substitution. This argument is totally in line with all the literature carried out for this research.

Strength Comparison of Accelerated Cured & Normal Cured Fly-Ash Based Concrete

The most important property of concrete is its compressive strength, which is carried out after 28-days of proper curing of concrete. This test is affected by other factors like the condition of curing, water to cement ratio, method of transportation, handling of the concrete, extent of vibrations and quality of the ingredients of mix proportion. This research study is an attempt to develop a simple mathematical model, by using linear regression analysis to estimate the 28-day fc’ (Compressive Strength) of concrete from the test results carried out at early age. This simple linear equation develops a relationship of 28.5 hours. These results show that most of the predicted values of compressive strength, calculated via equations, lie within permissible range difference for compressive strength achieved by experimental method, which is clear indication of credibility of the equations obtained for compressive strength at different age of concrete. The results show that compressive strength of concrete increases with the increase in content of FA (Fly Ash) upto 30% replacement, and the compressive strength of the concrete starts decreasing beyond 30% FA substitution. This argument is totally in line with all the literature carried out for this research.

Strength Prediction Model for Accelerated Cured Fly-Ash Based Concrete

The most important property of concrete is its compressive strength, which is carried out after 28-days proper curing of concrete. This test is affected by other factors like the condition of curing, water to cement ratio, method of transportation, handling of the concrete, extent of vibrations and quality of the ingredients of mix proportion. This research study is an attempt to develop a simple Mathematical equation also known as mathematical model, by using linear regression analysis to estimate the 28-day fc’ (Compressive Strength) of concrete from the test results carried out atearly age. This simple linear equation develops a relationship of 28.5 hours accelerated cured compressive strength with normal cured compressive strength after 28-days. These results show that most of the predicted values of compressive strength, calculated via equations, lies within permissible range difference for compressive strength achieved by experimental method, which is clear indication of credibility of the equations obtained for compressive strength at different age of concrete. The results showed that compressive strength of concrete increases with the increase in content of FA (Fly Ash) upto 30% replacement, and the compressive strength of the concrete starts decreasing beyond 30% FA substitution. This argument is totally in line with all the literature carried out for this research.

Estimation of Leaf Area by Linear Dimensions in Coffea dewevrei

The objective of this research was to select the equation that best estimates the leaf area of the coffee tree Coffea dewevrei, from the linear dimensions of the leaves. For this purpose, 140 leaves of adult plants were collected from the Capixaba Institute for Research, Technical Assistance and Rural Extension, in the city of Linhares, North of the State of Espírito Santo, Brazil. The length (L), the width (W), the product of the multiplication between the length and width (LW) and the leaf area observed (OLA) were determined from all leaves. For the modeling, a 100 leaves sample was used, where OLA was used as a dependent variable in function of L, W and LW as independent variable, being obtained the following models: linear first degree, quadratic and power. For the validation, a sample of 40 leaves was used, where the values of L, W LW were substituted in the equations generated in the modeling, thus obtaining the estimated leaf area (ELA). A simple linear equation model was fitted for each modeling equation relating ELA in function of OLA. The hypotheses H0: β0 = 0 versus Ha: β0 ≠ 0 and H0: β1 = 1 versus Ha: β1 ≠ 1, were tested using Student's t test at 5% probability. The mean absolute error (MAE), root mean square error (RMSE) and Willmott's index d for all equations were also determined. The best model that estimates the area of Coffea dewevrei was chosen through the following criteria: β0 not different from zero, β1 not different from one, MAE and RMSE values closer to zero and index d closer to the unit. The area of the leaves can be determined by its greater width (W), through the quadratic model equation ELA=-10.255+1.020(W)+1.293(W)2.

Spherical solutions of the wave equation for a spin 3/2 particle

The wave equation for a spin 3/2 particle, described by 16-component vector-bispinor, is investigated in spherical coordinates. In the frame of the Pauli–Fierz approach, the complete equation is split into the main equation and two additional constraints, algebraic and differential. The solutions are constructed, on which 4 operators are diagonalized: energy, square and third projection of the total angular momentum, and spatial reflection, these correspond to quantum numbers {ε, j, m, P}. After separating the variables, we have derived the radial system of 8 first-order equations and 4 additional constraints. Solutions of the radial equations are constructed as linear combinations of the Bessel functions. With the use of the known properties of the Bessel functions, the system of differential equations is transformed to the form of purely algebraic equations with respect to three quantities a1, a2, a3. Its solutions may be chosen in various ways by solving the simple linear equation A1a1 + A2a2 + A3a3 = 0 where the coefficients Ai are expressed trough the quantum numbers ε, j. Two most simple and symmetric solutions have been chosen. Thus, at fixed quantum numbers {ε, j, m, P} there exists double-degeneration of the quantum states.

The Impact of Neglecting Ice Phase on Cloud Optical Depth Retrievals from AERONET Cloud Mode Observations

Cloud optical depth remains a difficult variable to represent in climate models, and hence there is a need for high-quality observations of cloud optical depth from locations around the world. Such observations could be readily obtained from Aerosol Robotic Network (AERONET) radiometers using a two-wavelength retrieval method. However, the method requires an assumption that all of the cloud in a profile is liquid, and this has the potential to introduce errors into long-term statistics of retrieved optical depth. Using a set of idealised cloud profiles, we find that the fractional error in retrieved optical depth is a linear function of the fraction of the optical depth that is due to the presence of ice cloud (“ice fraction”), with a magnitude of order 55 % to 70 % for clouds that are entirely ice. We derive a simple linear equation that could potentially be used as a correction at AERONET sites where ice fraction can be independently estimated. The greatest contribution to error statistics arises from optically thick cloud that is either mostly or entirely ice. Using this linear equation, we estimate the magnitude of the error for a set of cloud profiles measured at five sites of the Atmospheric Radiation Measurement programme. Instances of such clouds are not frequent, with less than 15 % of cloud profiles at each location showing an error of greater than 10. However, differences in the frequency of such clouds from one location to another affect the magnitude of the overall mean error, with sites dominated by deep tropical convection and thick frontal mixed-phase cloud showing greater errors than sites where deep clouds are less frequent. The mean optical depth error at the five locations spans the range 2.5 to 5.5, which we show to be small enough to allow calculation of top-of-atmosphere flux to within 10 %, and surface flux to about 15 %.