scholarly journals A Regular D‑optimal Weighing Design with Negative Correlations of Errors

2019 ◽  
Vol 5 (344) ◽  
pp. 7-16
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Sufficient Conditions ◽  
Optimal Estimation ◽  
Block Designs ◽  
Correlated Errors ◽  
Unknown Parameters ◽  
Chemical Balance ◽  
Construction Methods ◽  
New Construction ◽  
Balanced Incomplete Block ◽  
Necessary And Sufficient

The issues concerning optimal estimation of unknown parameters in the model of chemical balance weighing designs with negative correlated errors are considered. The necessary and sufficient conditions determining the regular D‑optimal design and some new construction methods are presented. They are based on the incidence matrices of balanced incomplete block designs and balanced bipartite weighing designs.  

scholarly journals Highly D‑efficient Weighing Design and Its Construction

2018 ◽  
Vol 5 (331) ◽  
pp. 143-151
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Sufficient Conditions ◽  
Block Designs ◽  
Incidence Matrices ◽  
Balanced Incomplete Block Designs ◽  
Construction Methods ◽  
Design Optimality ◽  
Spring Balance ◽  
New Construction ◽  
Balanced Incomplete Block ◽  
Necessary And Sufficient

In this paper, some aspects of design optimality on the basis of spring balance weighing designs are considered. The properties of D‑optimal and D‑efficiency designs are studied. The necessary and sufficient conditions determining the mentioned designs and some new construction methods are introduced. The methods of determining designs that have the required properties are based on a set of incidence matrices of balanced incomplete block designs and group divisible designs.

scholarly journals A-optimal chemical balance weighing design under certain condition

2007 ◽  
Vol 4 (1) ◽  
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Lower Bound ◽  
Sufficient Conditions ◽  
Design Matrix ◽  
Block Designs ◽  
Chemical Balance ◽  
Incidence Matrices ◽  
Construction Methods ◽  
New Construction ◽  
The Right ◽  
Necessary And Sufficient

The paper is studying the estimation problem of individual weights of \(p\) objects using the design matrix \(\mathbf{X}\) of the A-optimal chemical balance weighing design under the restriction \(p_1 + p_2 = q  \leq p\), where \(p_1\) and \(p_2\) represent the number of objects placed on the left pan and on the right pan, respectively, in each of the measurement operations. The lower bound of \(\mathrm{Tr}(\mathbf{X}^{\prime}\mathbf{X})^{-1}\) is attained and the necessary and sufficient conditions for this lower bound to be obtained are given. There are given new construction methods of the A-optimal chemical balance weighing designs based on incidence matrices of the balanced bipartite weighing designs and the ternary balanced block designs.

scholarly journals Some new construction methods of variance balanced block designs with repeated blocks

2008 ◽  
Vol 5 (1) ◽  
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Block Designs ◽  
Incomplete Block ◽  
Incidence Matrices ◽  
Balanced Incomplete Block Designs ◽  
Construction Methods ◽  
New Construction ◽  
Balanced Incomplete Block

Some new construction methods of the variance balanced block designs with repeated blocks are given. They are based on the specialized product of incidence matrices of the balanced incomplete block designs.

scholarly journals ON D-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS

2015 ◽  
Vol 1 (311) ◽  
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Optimal Design ◽  
Measurement Errors ◽  
Block Designs ◽  
Incomplete Block ◽  
Chemical Balance ◽  
Incidence Matrices ◽  
Balanced Incomplete Block Designs ◽  
Construction Methods ◽  
Existence Conditions ◽  
Balanced Incomplete Block

The paper deals with the problem of determining the chemical balance weighing designs satisfying the criterion of D-optimality under assumption that the measurement errors are equal correlated and they have the same variances. The existence conditions and the form of the optimal design are given. Moreover, some construction methods of the design matrices based on the incidence matrices of the balanced incomplete block designs and ternary balanced block designs are presented. Any example of construction is given.

scholarly journals A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS

2009 ◽  
Vol 86 (2) ◽  
pp. 177-187 ◽  
Author(s):  
XIANGJUN KONG ◽  
XIANZHONG ZHAO
Keyword(s):  
Regular Semigroup ◽  
Structure Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Green’S Relations ◽  
Regular Semigroups ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Equivalent Conditions ◽  
Orthodox Semigroups

AbstractIn any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.

scholarly journals Geometric Construction-Based Realization of Planar Elastic Behaviors With Parallel and Serial Manipulators

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Elastic Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Construction ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Serial Manipulators ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

scholarly journals CONSTRUCTION METHOD OF A-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGNS

2015 ◽  
Vol 3 (314) ◽  
Author(s):  
Bronisław Ceranka ◽  
Małgorzata Graczyk
Keyword(s):  
Optimal Design ◽  
Measurement Errors ◽  
Construction Method ◽  
Block Designs ◽  
Chemical Balance ◽  
Incidence Matrices ◽  
New Construction

Here, we study the design in that we determine unknown measurements of p objects by used of n measurement operations. For that reason we consider the chemical balance weighing design under assumption that the measurement errors are uncorrelated and they have the same variances. We give new construction method of the A-optimal chemical balance weighing design based on the incidence matrices of the balanced bipartite weighing designs and the ternary balanced block designs. The consequence of the proposed method is widening of possible classes in that A-optimal design exists.

Trend‐Free Nested Balanced Incomplete Block Designs and Designs for Diallel Cross Experiments

2007 ◽  
Vol 59 (3-4) ◽  
pp. 203-221
Author(s):  
Kishan Lal ◽  
Rajender Prasad ◽  
V. K. Gupta
Keyword(s):  
Block Design ◽  
Block Size ◽  
Diallel Cross ◽  
Block Designs ◽  
Incomplete Block ◽  
Diallel Crosses ◽  
Balanced Incomplete Block Designs ◽  
Block Level ◽  
Balanced Incomplete Block ◽  
Necessary And Sufficient

Abstract: Nested balanced incomplete block (NBIB) designs are useful when the experiments are conducted to deal with experimental situations when one nuisance factor is nested within the blocking factor. Similar to block designs, trend may exist in experimental units within sub‐blocks or within blocks in NBIB designs over time or space. A necessary and sufficient condition, for a nested block design to be trend‐free at sub‐block level, is derived. Families and catalogues of NBIB designs that can be converted into trend‐free NBIB designs at sub‐block and block levels have been obtained. A NBIB design with sub‐block size 2 has a one to one correspondence with designs for diallel crosses experiments. Therefore, optimal block designs for dialled cross experiments have been identified to check if these can be converted in to trend‐free optimal block designs for diallel cross experiments. A catalogue of such designs is also obtained. Trend‐free design is illustrated with example for a NBIB design and a design for diallel crosses experiments. AMS (2000) Subject Classification: 62K05, 62K10.

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