On a new method of the testing hypothesis of equality of two Bernoulli regression functions for group observations

In the paper, the limiting distribution is established for an integral square deviation of estimates of Bernoulli regression functions based on two group samples. Based on these results, the new test is constructed for the hypothesis testing on the equality of two Bernoulli regression functions. The question of consistency of the constructed test is studied, and the asymptotic of the test power is investigated for some close alternatives.

Optimization of Grouting Material Mixture Ratio Based on Multi-Objective Optimization and Multi-Attribute Decision-Making

As a solid waste produced by coal combustion, fly ash will cause serious environmental pollution. However, it can be considered as a sustainable and renewable resource to replace partial cement in grouting materials. Fly ash grouting materials re-cement the broken rock mass and improve the mechanical properties of the original structure. It can reinforce the broken surrounding rock of mine roadway. The utilization of fly ash also reduces environmental pollution. Therefore, this paper establishes a new material mixture ratio optimization model to meet the requirement of material property through combining the methods of experimental design and numerical analysis. Based on the Box–Behnken design with 3 factors and 3 levels, a mathematical model is constructed to fit the nonlinear multiple regression functions between material properties and raw materials ratios. The influence of raw materials is analyzed on material properties (the material’s 7-day uniaxial compressive strength, initial setting time, and slurry viscosity). Then, 80 Pareto solutions are obtained through NASG-II algorithm which takes the regression functions as the objective functions for multi-objective optimization of the grouting material ratio. Finally, the best ratio solution of water-cement ratio—0.71, silica fume content—1.73%, and sodium silicate content—2.61% is obtained through the NNRP-TOPSIS method.

THEORETICAL CONSIDERATIONS ON THE OPTIMIZATION OF THE WORKING PROCESS OF VARIABLE WIDTH PLOUGHS

The paper presents theoretical research conducted for the optimization of the working process of variable width ploughs. Thus, were determined multivariable regression functions for the traction force of the plough with variable working function of the control parameters: working depth, working width and working speed. The use of these theoretical considerations of the optimal points sought lead to the opportunity of making assessments on the possibilities to conduct their experimental validation. Conditions for an experimental plan were formulated to highlight such optimal points and the theoretical results were validated through experiments.

Approximation, characterization, and continuity of multivariate monotonic regression functions

We deal with monotonic regression of multivariate functions [Formula: see text] on a compact rectangular domain [Formula: see text] in [Formula: see text], where monotonicity is understood in a generalized sense: as isotonicity in some coordinate directions and antitonicity in some other coordinate directions. As usual, the monotonic regression of a given function [Formula: see text] is the monotonic function [Formula: see text] that has the smallest (weighted) mean-squared distance from [Formula: see text]. We establish a simple general approach to compute monotonic regression functions: namely, we show that the monotonic regression [Formula: see text] of a given function [Formula: see text] can be approximated arbitrarily well — with simple bounds on the approximation error in both the [Formula: see text]-norm and the [Formula: see text]-norm — by the monotonic regression [Formula: see text] of grid-constant functions [Formula: see text]. monotonic regression algorithms. We also establish the continuity of the monotonic regression [Formula: see text] of a continuous function [Formula: see text] along with an explicit averaging formula for [Formula: see text]. And finally, we deal with generalized monotonic regression where the mean-squared distance from standard monotonic regression is replaced by more complex distance measures which arise, for instance, in maximum smoothed likelihood estimation. We will see that the solution of such generalized monotonic regression problems is simply given by the standard monotonic regression [Formula: see text].

Contemporary Precalculus through Applications

The first edition of Contemporary Precalculus through Applications was published in 1993, well before the widespread use of computers in the classroom. Collaborating with students and teachers across the state, faculty from the North Carolina School of Science and Mathematics (NCSSM) have steadily developed, reviewed, and tested the textbook in the years since. It is the sole textbook used in NCSSM precalculus courses. This third edition contains extensively updated data, graphics, and material attuned to contemporary technology while keeping what made the book so revolutionary when it was first published—a focus on real-world problem solving and student discovery. This edition will prepare students to learn mathematics in the following major areas: · Data analysis and linear regression · Functions: linear, polynomial, rational, exponential, logarithmic, parametric, and trigonometric · Modifying functions through transformations and compositions · Recursive systems and sequences · Modeling real-world phenomenon and applications An open access edition of this book is available at cpta.ncssm.edu, along with supplementary materials and other information.

Growth Rate Prediction of Ornamental Trees using Regression Functions in Urban Landscapes

The present study aimed to predict the growth rate of the common urban trees using mathematical equations for the right plantation location in the landscape. Ginkgo biloba, Liquidambar styraciflua L., Parrotia persica, Zelkova carpinifolia, Acer negundo, and Fraxinus rotundifolia Mill. were selected from city of Rasht, Guilan province, in the northern part of Iran. The study used age as the independent variables and height, trunk height, and crown diameter as the dependent variables. The correlation among the variables were analyzed by different regressions (linear, logarithmic, exponential, power, and polynomial). The results showed that polynomial regression functions provided the best determination coefficient to predict the growth parameters with respect to age in the urban green spaces for aesthetic purposes and also, to reduce costs, tackle interference with transit, urban equipment, and finally developing ecosystems sustainably. Polynomial regression functions can be used to predict tree growth in new urban green spaces in terms of environmental factors and age. Keywords: Ecosystems sustainably, Green space, Growth rate, Urban landscape, Ornamental trees

A Global Meta-Analysis for Estimating Local Ecosystem Service Value Functions

The Meta-analysis has increasingly been used to synthesize the ecosystem services literature, with some testing of the use of such analyses to transfer benefits. These are typically based on local primary studies. However, meta-analyses associated with ecosystem services are a potentially powerful tool for transferring benefits, especially for environmental assets for which no primary studies are available. In this study we use the Ecosystem Service Valuation Database (ESVD), which brings together 1350 value estimates from more than 320 studies around the world, to estimate meta-regression functions for Provisioning, Regulating and maintenance, and Cultural ecosystem services across 12 biomes. We tested the reliability of these meta-regression functions and found that even using variables with high explanatory power, transfer errors could still be large. We show that meta-analytic transfer performs better than simple value transfer and, in addition, that local meta-analytical transfer (i.e., based on local explanatory variable values) provides more reliable estimates than global meta-analytical transfer (i.e., based on mean global explanatory variable values). Thus, we conclude that when taking into account the characteristics of the study area under analysis, including explanatory variables such as income, population density, and protection status, we can determine the value of ecosystem services with greater accuracy.

Modeling the Depth of Surface Cracks in Brake Disc

The article presents the state of knowledge and research in the field of surface cracks occurring in disc braking systems of rail and car vehicles. The craze formed during the operation of vehicles is particularly dangerous and leads to breaking the disc into several pieces. It may lead to a loss of braking force and damage to the entire disc brake caliper. The main aim of the research is to identify surface cracks in brake discs made of cast iron and use experimental methods to estimate their depth. Research were conducted on the disc braking system developed by the authors. In examining the location and depth of cracks, the penetration method, ultrasound, as well as a special probe were used. This device measures the crack depth based on the electrical resistance between two points on the surface of the metallic object. The tests showed that the first microcracks on the brake discs appeared after 309 braking tests on the test stand. In addition, it was observed that the surface cracks length of the disc increased linearly to depth until they reached about 11.5–12 mm with corresponded to crack lengths in the range of 65–70 mm. However, determination of the regression functions presented in the article allows to estimate the depth of surface cracks up to 70 mm long on cast iron brake discs by measuring their length.

Simple Closed Analytic Formulas to approximate the Legendre Complete Elliptic Integrals K(k) and E(k), by a Fast Converging Recurrent-Iterative Procedure

wo sets of closed analytic functions are proposed for the approximate calculus of the complete elliptic integrals K(k) and E(k) in the normal form due to Legendre, their expressions having a remarkable simplicity and accuracy. The special usefulness of the newly proposed formulas consists in they allow performing the analytic study of variation of the functions in which they appear, using derivatives (they being expressed in terms of elementary functions only, without any special function; this would mean replacing one difficulty by another of the same kind). Comparative tables of so found approximate values with the exact ones, reproduced from special functions tables, are given (vs. the elliptic integrals’ modulus k). Both sets of formulas are given neither by spline nor by regression functions. The new functions and their derivatives coincide with the exact ones at the left domain’s end only. As for their simplicity, the formulas in k / k' do not need mathematical tables (are purely algebraic). As for accuracy, the 2nd set, more intricate, gives more accurate values and extends itself more closely to the right domain’s end. An original fast converging recurrent-iterative scheme to get sets of formulas with the desired accuracy is given in appendix.

A Global Meta-Analysis for Estimating Local Ecosystem Service Value Functions

Meta-analysis has increasingly been used to synthesize the ecosystem services literature, with some testing of the use of such analyses to transfer benefits. These are typically based on local primary studies. However, meta-analyses associated with ecosystem services are a potentially powerful tool for transferring benefits, especially for environmental assets for which no primary studies are available. In this study we use the Ecosystem Service Valuation Database (ESVD), which brings together 1350 value estimates from more than 320 studies around the world, to estimate meta-regression functions for provisioning, regulating & maintenance and cultural ecosystem services across 12 biomes. We tested the reliability of these meta-regression functions and found that even using variables with high explanatory power, transfer errors could still be large. We show that meta-analytic transfer performs better than simple value transfer and, in addition, that local meta-analytical transfer (i.e. based on local explanatory variable values) provides more reliable estimates than global meta-analytical transfer (i.e. based on mean global explanatory variable values). Thus, we conclude that when taking into account the characteristics of the study area under analysis, including explanatory variables such as income, population density and protection status, we can determine the value of ecosystem services with greater accuracy.