1,097,081 research outputs found
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 , and and types and ,
respectively. In this paper, we first show that there does not exist any
product design of order , , and type where the notation is used to show that repeats
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 and type is constructed.Comment: 12 pages, To appear in the Australasian Journal of Combinatoric
Construction of optimal multi-level supersaturated designs
A supersaturated design is a design whose run size is not large enough for
estimating all the main effects. The goodness of multi-level supersaturated
designs can be judged by the generalized minimum aberration criterion proposed
by Xu and Wu [Ann. Statist. 29 (2001) 1066--1077]. A new lower bound is derived
and general construction methods are proposed for multi-level supersaturated
designs. Inspired by the Addelman--Kempthorne construction of orthogonal
arrays, several classes of optimal multi-level supersaturated designs are given
in explicit form: Columns are labeled with linear or quadratic polynomials and
rows are points over a finite field. Additive characters are used to study the
properties of resulting designs. Some small optimal supersaturated designs of
3, 4 and 5 levels are listed with their properties.Comment: Published at http://dx.doi.org/10.1214/009053605000000688 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Some results on λ-designs
AbstractA λ-design as introduced by Ryser [3] is a (0, 1)-square matrix with constant column inner products but not all column sums equal. Ryser has shown such a matrix to have two row sums and he constructs an infinite family of λ-designs called H-designs. This paper does three things: (1) generalizes Ryser's H-design construction to an arbitrary (ν, k, λ)-configuration, (2) establishes some additional general properties of λ-designs, and (3) determines all 4-designs
A study of structural concepts for ultralightweight spacecraft
Structural concepts for ultralightweight spacecraft were studied. Concepts for ultralightweight space structures were identified and the validity of heir potential application in advanced spacecraft was assessed. The following topics were investigated: (1) membrane wrinkling under pretensioning; (2) load-carrying capability of pressurized tubes; (3) equilibrium of a precompressed rim; (4) design of an inflated reflector spacecraft; (5) general instability of a rim; and (6) structural analysis of a pressurized isotensoid column. The design approaches for a paraboloidal reflector spacecraft included a spin-stiffened design, both inflated and truss central columns, and to include both deep truss and rim-stiffened geodesic designs. The spinning spacecraft analysis is included, and the two truss designs are covered. The performances of four different approaches to the structural design of a paraboloidal reflector spacecraft are compared. The spinning and inflated configurations result in very low total masses and some concerns about their performance due to unresolved questions about dynamic stability and lifetimes, respectively
An enhanced integrated aerodynamic load/dynamic optimization procedure for helicopter rotor blades
An enhanced integrated aerodynamic load/dynamic optimization procedure is developed to minimize vibratory root shears and moments. The optimization is formulated with 4/rev vertical and 3/rev inplane shears at the blade root as objective functions and constraints, and 4/rev lagging moment. Constraints are also imposed on blade natural frequencies, weight, autorotational inertia, centrifugal stress, and rotor thrust. The 'Global Criteria Approach' is used for formulating the multi-objective optimization. Design variables include spanwise distributions of bending stiffnesses, torsional stiffness, nonstructural mass, chord, radius of gyration, and blade taper ratio. The program CAMRAD is coupled with an optimizer, which consists of the program CONMIN and an approximate analysis, to obtain optimum designs. The optimization procedure is applied to an advanced rotor as a reference design. Optimum blade designs, obtained with and without a constraint on the rotor thrust, are presented and are compared to the reference blade. Substantial reductions are obtained in the vibratory root forces and moments. As a byproduct, improvements are also found in some performance parameters, such as total power required, which were not considered during optimization
Single-Change Circular Covering Designs
A single-change circular covering design (scccd) based on the set [v] = {1, . . . ,v} with block size k is an ordered collection of b blocks, B = {B1, . . . ,Bb}, each Bi ⊂ [v], which obey: (1) each block differs from the previous block by a single element, as does the last from the first, and, (2) every pair of [v] is covered by some Bi. The object is to minimize b for a fixed v and k. We present some minimal constructions of scccds for arbitrary v when k = 2 and 3, and for arbitrary k when k+1 ≤ v ≤ 2k. Tight designs are those in which each pair is covered exactly once. Start-Finish arrays are used to construct tight designs when v \u3e 2k; there are 2 non-isomorphic tight designs with (v, k) = (9, 4), and 12 with (v, k) = (10, 4). Some non-existence results for tight designs, and standardized, element-regular, perfect, and column-regular designs are also considered
Codes and Pseudo-Geometric Designs from the Ternary -Sequences with Welch-type decimation
Pseudo-geometric designs are combinatorial designs which share the same
parameters as a finite geometry design, but which are not isomorphic to that
design. As far as we know, many pseudo-geometric designs have been constructed
by the methods of finite geometries and combinatorics. However, none of
pseudo-geometric designs with the parameters is constructed by the approach of coding theory. In
this paper, we use cyclic codes to construct pseudo-geometric designs. We
firstly present a family of ternary cyclic codes from the -sequences with
Welch-type decimation , and obtain some infinite family
of 2-designs and a family of Steiner systems
using these cyclic codes and their duals. Moreover, the parameters of these
cyclic codes and their shortened codes are also determined. Some of those
ternary codes are optimal or almost optimal. Finally, we show that one of these
obtained Steiner systems is inequivalent to the point-line design of the
projective space and thus is a pseudo-geometric design.Comment: 15 pages. arXiv admin note: text overlap with arXiv:2206.15153,
arXiv:2110.0388
Shape optimization of pressurized air bearings
Use of externally pressurized air bearings allows for the design of mechanical systems requiring extreme precision in positioning. One application is the fine control for the positioning of mirrors in large-scale optical telescopes. Other examples come from applications in robotics and computer hard-drive manufacturing. Pressurized bearings maintain a finite separation between mechanical components by virtue of the presence of a pressurized flow of air through the gap between the components. An everyday example is an air hockey table, where a puck is levitated above the table by an array of vertical jets of air. Using pressurized bearings there is no contact between “moving parts” and hence there is no friction and no wear of sensitive components.
This workshop project is focused on the problem of designing optimal static air bearings subject to given engineering constraints. Recent numerical computations of this problem, done at IBM by Robert and Hendriks, suggest that near-optimal designs can have unexpected complicated and intricate structures. We will use analytical approaches to shed some light on this situation and to offer some guides for the design process.
In Section 2 the design problem is stated and formulated as an optimization problem for an elliptic boundary value problem.
In Section 3 the general problem is specialized to bearings with rectangular bases.
Section 4 addresses the solutions of this problem that can be obtained using variational formulations of the problem.
Analysis showing the sensitive dependence to perturbations (in numerical computations or manufacturing constraints) of near-optimal designs is given in Section 5.
In Section 6, a restricted class of “groove network” designs motivated by the original results of Robert and Hendriks is examined.
Finally, in Section 7, we consider the design problem for circular axisymmetric air bearings
Infinite families of cyclic and negacyclic codes supporting 3-designs
Interplay between coding theory and combinatorial -designs has been a hot
topic for many years for combinatorialists and coding theorists. Some infinite
families of cyclic codes supporting infinite families of -designs have been
constructed in the past 50 years. However, no infinite family of negacyclic
codes supporting an infinite family of -designs has been reported in the
literature. This is the main motivation of this paper. Let , where
is an odd prime and is an integer. The objective of this paper is to
present an infinite family of cyclic codes over \gf(q) supporting an infinite
family of -designs and two infinite families of negacyclic codes over
\gf(q^2) supporting two infinite families of -designs. The parameters and
the weight distributions of these codes are determined. The subfield subcodes
of these negacyclic codes over \gf(q) are studied. Three infinite families of
almost MDS codes are also presented. A constacyclic code over GF()
supporting a -design and six open problems are also presented in this paper
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