Class 2 design update for the family of commuter airplanes

This is the final report of seven on the design of a family of commuter airplanes. This design effort was performed in fulfillment of NASA/USRA grant NGT-8001. Its contents are as follows: (1) the class 1 baseline designs for the commuter airplane family; (2) a study of takeoff weight penalties imposed on the commuter family due to implementing commonality objectives; (3) component structural designs common to the commuter family; (4) details of the acquisition and operating economics of the commuter family, i.e., savings due to production commonality and handling qualities commonality are determined; (5) discussion of the selection of an advanced turboprop propulsion system for the family of commuter airplanes, and (6) a proposed design for an SSSA controller design to achieve similar handling for all airplanes. Final class 2 commuter airplane designs are also presented

New 22-designs from strong difference families

Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to $2$-designs, and have applications in constructions for many significant codes, such as optical orthogonal codes and optical orthogonal signature pattern codes. In this paper, with a careful use of cyclotomic conditions attached to strong difference families, we improve the lower bound on the asymptotic existence results of $(\mathbb{F}_{p}\times \mathbb{F}_{q},\mathbb{F}_{p}\times \{0\},k,\lambda)$-DFs for $k\in\{p,p+1\}$. We improve Buratti's existence results for $2$-$(13q,13,\lambda)$ designs and $2$-$(17q,17,\lambda)$ designs, and establish the existence of seven new $2$-$(v,k,\lambda)$ designs for $(v,k,\lambda)\in\{(694,7,2),(1576,8,1),(2025,9,1),(765,9,2),(1845,9,2),(459,9,4)$, $(783,9,4)\}$.Comment: Version 1 is named "Improved cyclotomic conditions leading to new 2-designs: the use of strong difference families". Major revision according to the referees' comment

Some Constructions for Amicable Orthogonal Designs

Hadamard matrices, orthogonal designs and amicable orthogonal designs have a number of applications in coding theory, cryptography, wireless network communication and so on. Product designs were introduced by Robinson in order to construct orthogonal designs especially full orthogonal designs (no zero entries) with maximum number of variables for some orders. He constructed product designs of orders $4$, $8$ and $12$ and types $\big(1_{(3)}; 1_{(3)}; 1\big),$ $\big(1_{(3)}; 1_{(3)}; 5\big)$ and $\big(1_{(3)}; 1_{(3)}; 9\big)$, respectively. In this paper, we first show that there does not exist any product design of order $n\neq 4$, $8$, $12$ and type $\big(1_{(3)}; 1_{(3)}; n-3\big),$ where the notation $u_{(k)}$ is used to show that $u$ repeats $k$ times. Then, following the Holzmann and Kharaghani's methods, we construct some classes of disjoint and some classes of full amicable orthogonal designs, and we obtain an infinite class of full amicable orthogonal designs. Moreover, a full amicable orthogonal design of order $2^9$ and type $\big(2^6_{(8)}; 2^6_{(8)}\big)$ is constructed.Comment: 12 pages, To appear in the Australasian Journal of Combinatoric

Optimal designs which are efficient for lack of fit tests

Linear regression models are among the models most used in practice, although the practitioners are often not sure whether their assumed linear regression model is at least approximately true. In such situations, only designs for which the linear model can be checked are accepted in practice. For important linear regression models such as polynomial regression, optimal designs do not have this property. To get practically attractive designs, we suggest the following strategy. One part of the design points is used to allow one to carry out a lack of fit test with good power for practically interesting alternatives. The rest of the design points are determined in such a way that the whole design is optimal for inference on the unknown parameter in case the lack of fit test does not reject the linear regression model. To solve this problem, we introduce efficient lack of fit designs. Then we explicitly determine the $\mathbf{e}_k$-optimal design in the class of efficient lack of fit designs for polynomial regression of degree $k-1$.Comment: Published at http://dx.doi.org/10.1214/009053606000000597 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org