Some sufficient conditions for the type 1 optimality of block designs

1985 ◽  
Vol 11 (3) ◽  
pp. 385-398 ◽  
Author(s):  
Mike Jacroux
Keyword(s):  
Sufficient Conditions ◽  
Block Designs

Designs Robust Against Aberrations

1993 ◽  
Vol 43 (1-2) ◽  
pp. 95-108 ◽  
Author(s):  
N. K. Mandal ◽  
K. R. Shah
Keyword(s):  
Sufficient Conditions ◽  
Subject Classification ◽  
Alternative Formulation ◽  
Block Designs ◽  
Ams Subject Classification ◽  
Secondary 62K05

In this paper, we obtain sufficient conditions for a design to be robust against aberrations in the sense of Box and Draper. Block designs, row-column designs and fractional designs are considered here. An alternative formulation of robustness is also presented. AMS Subject Classification: Primary 62K99; Secondary 62K05.

Optimal control of a flexible server

2004 ◽  
Vol 36 (01) ◽  
pp. 139-170 ◽  
Author(s):  
Hyun-Soo Ahn ◽  
Izak Duenyas ◽  
Rachel Q. Zhang
Keyword(s):  
Optimal Policy ◽  
Dynamic Scheduling ◽  
Sufficient Conditions ◽  
Holding Costs ◽  
Switching Curve ◽  
Necessary And Sufficient ◽  
Dynamic Arrivals ◽  
Flexible Server

We consider the dynamic scheduling of a multiclass queueing system with two servers, one dedicated (server 1) and one flexible (server 2), with no arrivals. Server 1 is dedicated to processing type-1 jobs while server 2 is primarily responsible for processing type-2 jobs but can also aid server 1 with its work. We address when it is optimal for server 2 to aid server 1 with type-1 jobs rather than process type-2 jobs. The objective is to minimize the total holding costs incurred until all jobs in the system are processed and leave the system. We show that the optimal policy can exhibit one of three possible structures: (i) an exhaustive policy for type-2 jobs, (ii) a nonincreasing switching curve in the number of type-1 jobs and (iii) a nondecreasing switching curve in the number of type-1 jobs. We characterize the necessary and sufficient conditions under which each policy will be optimal. We also explore the use of the optimal policy for the problem with no arrivals as a heuristic for the problem with dynamic arrivals.

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 Optical solitons of fractional complex Ginzburg–Landau equation with conformable, beta, and M-truncated derivatives: a comparative study

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amjad Hussain ◽  
Adil Jhangeer ◽  
Naseem Abbas ◽  
Ilyas Khan ◽  
El-Syed M. Sherif
Keyword(s):  
Landau Equation ◽  
Sufficient Conditions ◽  
Detailed Comparison ◽  
Optical Solitons ◽  
Comparative Approach ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Kerr Law Nonlinearity ◽  
Algebraic Scheme

Abstract In this paper, we investigate the optical solitons of the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law nonlinearity which shows various phenomena in physics like nonlinear waves, second-order phase transition, superconductivity, superfluidity, liquid crystals, and strings in field theory. A comparative approach is practised between the three suggested definitions of derivative viz. conformable, beta, and M-truncated. We have constructed the optical solitons of the considered model with a new extended direct algebraic scheme. By utilization of this technique, obtained solutions carry a variety of new families including dark-bright, dark, dark-singular, and singular solutions of Type 1 and 2, and sufficient conditions for the existence of these structures are given. Further, graphical representations of the obtained solutions are depicted. A detailed comparison of solutions to the considered problem, obtained by using different definitions of derivatives, is reported as well.

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.

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