scholarly journals D-optimal designs of experiments for trigonometric regression on interval with heteroscedastic observations

2020 ◽  
pp. 80-85
Author(s):  
Valery P. Kirlitsa
Keyword(s):  
Optimal Designs ◽  
Different Types ◽  
Designs Of Experiments ◽  
Trigonometric Regression ◽  
Class Of Functions

In article the problem of construction continuous (number of observations is not fixed) D-optimal designs of experiments for trigonometric regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct continuous D-optimal designs of experiments. For trigonometric regression with three factors it is constructed continuous D-optimal designs of experiments with different types heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.

scholarly journals Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations

2019 ◽  
pp. 27-33
Author(s):  
Valery P. Kirlitsa
Keyword(s):  
Multiple Regression ◽  
Optimal Designs ◽  
Linear Multiple Regression ◽  
Different Types ◽  
Designs Of Experiments ◽  
Class Of Functions

In article the problem of construction exact D-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct D-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of D-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.

scholarly journals Some new Simpson-type inequalities for generalized p-convex function on fractal sets with applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
Zakia Hammouch ◽  
İmdat İşcan ◽  
Yu-Ming Chu
Keyword(s):  
Convex Functions ◽  
Fractional Derivatives ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Auxiliary Result ◽  
Fractal Sets ◽  
Different Types ◽  
Novel Applications ◽  
Class Of Functions ◽  
Harmonically Convex Functions

Abstract The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

D-optimal designs of experiments with non-interacting factors

1995 ◽  
Vol 44 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Rainer Schwabe ◽  
Werner Wierich
Keyword(s):  
Optimal Designs ◽  
Designs Of Experiments

Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
Radoslav Harman ◽  
Mária Trnovská
Keyword(s):  
Convex Hull ◽  
Positive Semidefinite ◽  
Optimal Designs ◽  
Quadratic Model ◽  
Positive Semidefinite Matrices ◽  
Multiplicative Algorithm ◽  
Finite Set ◽  
Designs Of Experiments ◽  
Information Matrices ◽  
Proof Of Convergence

AbstractIn the paper we solve the problem of D ℋ-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite set of positive semidefinite matrices. The problem of D ℋ-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D ℋ-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D ℋ-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane.

scholarly journals DEVELOPMENT OF A MATHEMATICAL MODEL FOR THE RESEARCH OF THE DYNAMICS OF VIBRATION MILL WITH TWO DRIVES FOR BULK MATERIALS FINE GRINDING

2021 ◽  
pp. 89-99
Author(s):  
Volodymyr Topilnytskyy ◽  
Dariya Rebot
Keyword(s):  
Mathematical Model ◽  
Optimal Designs ◽  
High Tech ◽  
Bulk Materials ◽  
Fine Grinding ◽  
Different Types ◽  
Parameterized Model ◽  
The Mathematical Model ◽  
Universal Equipment ◽  
Vibration Mill

Reducing by grinding the size of various materials as raw materials for its further use is an urgent applied task. The requirements for the final product obtained by fine grinding are its homogeneity in shape and size of individual parts. It is necessary to reduce the time of the grinding operation, reduce energy consumption to obtain a unit of product of the required quality. One way to solve the problem is to use high-tech universal equipment, namely mills for fine grinding of materials. One way to solve the given problem is to use high-tech universal equipment, namely mills for fine grinding of materials. Their optimal design, construction, manufacture and operation are ensured by studying their dynamics at the stage of their development. In particular, such a study of the dynamics can be carried out on the basis of previously created mathematical models of these mills. The use of computer technology and appropriate mathematical CAD systems will speed up and optimize the process of studying the dynamics of the corresponding mill of fine grinding of materials. The purpose of the research is to build a mathematical nonlinear parameterized model of vibrating mill with two drives for bulk materials fine grinding for further study on its basis the dynamics of the mill with the development of optimal designs for mills with similar structure and the principle of operation and selection of optimal modes of operation. The mathematical model is presented as a system of expressions describing the of the mill points motion, which will include in the form of symbolic symbols all its parameters (kinematic, geometric, dynamic, force). This model is constructed using the Lagrange equation of the second kind and asymptotic methods of nonlinear mechanics. The mathematical model for studying of the dynamics of vibration mill with two drives for bulk materials fine grinding is nonlinear and universal. The non linearity of the model makes it possible to adequately determine of the above parameters influence on the amplitude of oscillations of the mill working chamber as the main factor in the intensity in the technological process of the fine grinding bulk materials fine grinding. The possibility of a wide range of changes in the parameters of the mill in the obtained models makes it universal based on the possibility of application for the study of dynamic processes in vibrating mills of different types with two or one drive which are different by shape, size, location of the suspension and more. This model can also be used to develop optimal designs for vibrating mills for different industries, which will be used to grind different types of materials in different volumes and productivity.

scholarly journals Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis

2013 ◽  
Vol 124 ◽  
pp. 47-60 ◽  
Author(s):  
Eliška Janouchová ◽  
Anna Kučerová
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Designs ◽  
Designs Of Experiments

scholarly journals The escaping set of transcendental self-maps of the punctured plane

2016 ◽  
Vol 38 (2) ◽  
pp. 739-760 ◽  
Author(s):  
DAVID MARTÍ-PETE
Keyword(s):  
Different Types ◽  
Disjoint Sets ◽  
Escaping Orbits ◽  
Class Of Functions

We study the different rates of escape of points under iteration by holomorphic self-maps of $\mathbb{C}^{\ast }=\mathbb{C}\setminus \{0\}$ for which both zero and infinity are essential singularities. Using annular covering lemmas we construct different types of orbits, including fast escaping and arbitrarily slowly escaping orbits to either zero, infinity or both. We also prove several properties about the set of fast escaping points for this class of functions. In particular, we show that there is an uncountable collection of disjoint sets of fast escaping points, each of which has $J(f)$ as its boundary.

scholarly journals Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

2019 ◽  
Vol 29 (2) ◽  
pp. 421-436
Author(s):  
Seung Won Hyun ◽  
Weng Kee Wong ◽  
Yarong Yang
Keyword(s):  
Statistical Inference ◽  
Software Package ◽  
Logistic Models ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Model Parameters ◽  
Response Curves ◽  
Different Types ◽  
User Friendly

The 5-parameter logistic (5PL) model is frequently used to model and analyze responses from bioassays and immunoassays which can be skewed. Various types of optimal experimental designs for 2, 3 and 4-parameter logistic models have been reported but not for the more complicated 5PL model. We construct different types of optimal designs for studying various features of the 5PL model and show that commonly used designs in bioassays and immunoassays are generally inefficient for statistical inference. To facilitate use of such designs in practice, we create a user-friendly software package to generate various tailor-made optimal designs for the 5PL model and evaluate robustness properties of a design under a variation of criteria, model forms and misspecification in the nominal values of the model parameters.

Sign in / Sign up

Export Citation Format

Share Document