The generalized Chapman-Richards function and applications to tree and stand growth

The generalized Chapman-Richards model was derived from the Chapman-Richards function in which parameters h, k and m were unconstrained. Based on the structure of solutions and biological interpretations, the model could be classified into eight cases (three categories) at all and among them only 4 kinds of cases are suitable in forestry that represent four typical growth patterns of trees and stands. For each of 4 equations, the model properties and biological interpretations for parameters were discussed in detail. The generalized Chapman-Richards model was capable of describing a wide range of growth curves that was asymptotic or nonasymptotic, with or without inflection point. In order to illustrate the versatility of the model, it was fitted to a group of data sets concerning the DBH growth of cryptomeria plantations with 4 initial densities and the DBH and height growth of natural Korean pine tree. Comparing the generalized Chapman-Richards function and the Schnute model, it was found that the parameters and expressions of the two models were interchangeable in theory, and the fitting results were explicitly identical in empirical applications.

Evaluation of Generalized Error Function via Fast-Converging Power Series

A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.

Ostrowski’s Type Inequalities for Generalized(h,m)−Preinvex Functions with Its Applications

A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.

Analysis of Progressively Type-Ⅱ Inverted Generalized Gamma Censored Data and Its Engineering Application

A novel inverted generalized gamma(IGG)distribution,proposed for data modelling with an upside-down bathtub hazard rate,is considered.In many real-world practical situations,when a researcher wants to conduct a comparative study of the life testing of items based on cost and duration of testing,censoring strategies are frequently used.From this point of view,in the presence of censored data compiled from the most well-known progressively Type-Ⅱ censoring technique,this study examines different parameters of the IGG distribution.From a classical point of view,the likelihood and product of spacing estimation methods are considered.Observed Fisher information and the deltamethod are used to obtain the approximate confidence intervals for any unknown parametric function of the suggestedmodel.In the Bayesian paradigm,the same traditional inferential approaches are used to estimate all unknown subjects.Markov-Chain with Monte-Carlo steps are considered to approximate all Bayes’findings.Extensive numerical comparisons are presented to examine the performance of the proposed methodologies using various criteria of accuracy.Further,using several optimality criteria,the optimumprogressive censoring design is suggested.To highlight how the proposed estimators can be used in practice and to verify the flexibility of the proposed model,we analyze the failure times of twenty mechanical components of a diesel engine.

Winding Function Model-based Performance Evaluation of a PM Transverse Flux Generator for Applications in Direct-drive Systems

The magnetic flux in a permanent magnet transverse flux generator(PMTFG) is three-dimensional(3D), therefore, its efficacy is evaluated using 3D magnetic field analysis. Although the 3D finite-element method(FEM) is highly accurate and reliable for machine simulation, it requires a long computation time, which is crucial when it is to be used in an iterative optimization process. Therefore, an alternative to 3DFEM is required as a rapid and accurate analytical technique. This paper presents an analytical model for PMTFG analysis using winding function method. To obtain the air gap MMF distribution, the excitation magneto-motive force(MMF) and the turn function are determined based on certain assumptions. The magnetizing inductance, flux density, and back-electro-magnetomotive force of the winding are then determined. To assess the accuracy of the proposed method, the analytically calculated parameters of the generator are compared to those obtained by a 3D-FEM. The presented method requires significantly shorter computation time than the 3D-FEM with comparable accuracy.

The Chapman-Richards Distribution and its Relationship to the Generalized Beta

Background: The Chapman-Richards distribution is developed as a special case of the equilibrium solution to the McKendrick-Von Foerster equation. The Chapman-Richards distribution incorporates the vital rate assumptions of the Chapman-Richards growth function, constant mortality and recruitment into the mathematical form of the distribution. Therefore, unlike 'assumed' distribution models, it is intrinsically linked with the underlying vital rates for the forest area under consideration. Methods: It is shown that the Chapman-Richards distribution can be recast as a subset of the generalized beta distribution of the first kind, a rich family of assumed probability distribution models with known properties. These known properties for the generalized beta are then immediately available for the Chapman-Richards distribution, such as the form of the compatible basal area-size distribution. A simple two-stage procedure is proposed for the estimation of the model parameters and simulation experiments are conducted to validate the procedure for four different possible distribution shapes. Results: The simulations explore the efficacy of the two-stage estimation procedure;these cover the estimation of the growth equation and mortality-recruitment derives from the equilibrium assumption. The parameter estimates are shown to depend on both the sample size and the amount of noise imparted to the synthetic measurements. The results vary somewhat by distribution shape, with the smaller, noisier samples providing less reliable estimates of the vital rates and final distribution forms. Conclusions: The Chapman-Richards distribution in its original form, or recast as a generalized beta form, presents a potentially useful model integrating vital rates and stand diameters into a flexible family of resultant distributions shapes. The data requirements are modest, and parameter estimation is straightforward provided the minimal recommended sample sizes are obtained.

Generalized Numerical Radius of Real Quaternion Matrices with Symmetric Function

In the paper the generalized numerical radiuses of real quaternion matrices with symmetric function are defined and theirs inequalities are given.

The Fourier Transform of a Sort of Generalized Function

The Fourier transforms of functions X ln e are given. where λ is a complex constant (λ≠-1,-2. …), a is a complex number. m=0. 1. 2,…,and

Some new exact solutions of Jacobian elliptic function about the generalized Boussinesq equation and Boussinesq-Burgers equation

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include Jacobian elliptic function solutions, combined Jacobian elliptic function solutions, soliton solutions, triangular function solutions.

MONOTONICITY AND INEQUALITIES FOR THE GENERALIZED DISTORTION FUNCTION

The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.

THE HILBERT BOUNDARY VALUE PROBLEM FOR GENERALIZED ANALYTIC FUNCTIONS IN CLIFFORD ANALYSIS

Let R0,n be the real Clifford algebra generated by e1, e2,... , en satisfying eiej＋ejei=-2δij,i,j=1,2…,ne0 is the unit element.Let Ω be an open set. A function f is called left generalized analytic in ft if f satisfies the equation Lf=0,where ……qi 〉0, i =-, 1, - ……, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in Rn＋1 will be investigated.

The New Mixed Generalized Erlang Distribution

In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.

Improved theory of generalized meteo-ballistic weighting factor functions and their use

It follows from the analysis of artillery fire errors that approximately two-thirds of the inaccuracy of indirect artillery fire is caused by inaccuracies in the determination of the meteo parameters included in fire error budget model.Trajectories calculated under non-standard conditions are considered to be perturbed.The tools utilized for the analysis of perturbed trajectories are weighting factor functions(WFFs)which are a special kind of sensitivity functions.WFFs are used for calculation of meteo ballistic elements B(ballistic wind w B,densityρB,virtual temperatureτB,pressure p B)as well.We have found that the existing theory of WFF calculation has several significant shortcomings.The aim of the article is to present a new,improved theory of generalized WFFs that eliminates the deficiencies found.Using this theory will improve methods for designing firing tables,fire control systems algorithms,and meteo message generation algorithms.

Optimization of the Dressing Parameters in Cylindrical Grinding Based on a Generalized Utility Function

The existing studies, concerning the dressing process, focus on the major influence of the dressing conditions on the grinding response variables. However, the choice of the dressing conditions is often made, based on the experience of the qualified staff or using data from reference books. The optimal dressing parameters, which are only valid for the particular methods and dressing and grinding conditions, are also used. The paper presents a methodology for optimization of the dressing parameters in cylindrical grinding. The generalized utility function has been chosen as an optimization parameter. It is a complex indicator determining the economic, dynamic and manufacturing characteristics of the grinding process. The developed methodology is implemented for the dressing of aluminium oxide grinding wheels by using experimental diamond roller dressers with different grit sizes made of medium- and high-strength synthetic diamonds type AC32 and AC80. To solve the optimization problem, a model of the generalized utility function is created which reflects the complex impact of dressing parameters. The model is built based on the results from the conducted complex study and modeling of the grinding wheel lifetime, cutting ability, production rate and cutting forces during grinding. They are closely related to the dressing conditions （dressing speed ratio, radial in-feed of the diamond roller dresser and dress-out time）, the diamond roller dresser grit size/grinding wheel grit size ratio, the type of synthetic diamonds and the direction of dressing. Some dressing parameters are determined for which the generalized utility fimction has a maximum and which guarantee an optimum combination of the following： the lifetime and cutting ability of the abrasive wheels, the tangential cutting force magnitude and the production rate of the grinding process. The results obtained prove the possibility of control and optimization of grinding by selecting particular dressing parameters.

Trial function method and exact solutions to the generalized nonlinear Schrdinger equation with time-dependent coefficient

In this paper, the trial function method is extended to study the generalized nonlinear Schrodinger equation with time- dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrodinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrodinger equation with time-dependent coefficients under constraint conditions.

Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shock

This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.

Some inequalities for the generalized linear distortion function

In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.

APPROXIMATE CONVEXITY AND CONCAVITY OFGENERALIZED GROTZSCH RING FUNCTION

In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.

THIRD-ORDER DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS INVOLVING THE GENERALIZED BESSEL FUNCTIONS

In the present paper, we derive some third-order differential subordination results for analytic functions in the open unit disk, using the operator Bcκf by means of normalized form of the generalized Bessel functions of the first kind, which is defined as z（Bκ＋1^c f（z））′= κBκ^c f（z）-（κ- 1）Bκ＋1^c f（z）,where b, c, p ∈ C and κ = p ＋（b ＋ 1）/2 ∈ C ／ Z0^-（Z0^-= {0,-1,-2, … }）. The results are obtained by considering suitable classes of admissible functions. Various known or new special cases of our main results are also pointed out.

INVARIANT SUBSPACES AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM

Invariant subspace method is exploited to obtain exact solutions of the two- component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.