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On the non-existence of quasi-3 designs

2003
*
Discrete Mathematics
*

In this survey article we discuss

doi:10.1016/s0012-365x(02)00492-2
fatcat:dupefa3iuzgypeh3ky7ngwt6zm
*the**existence**of**quasi*-*3**designs*, and settle*the**existence*question for all v ¡ 144.*The*only such*designs*are*the**ones*already known. ... We also consider*the*question*of*whether*the*dual*design**of*a*quasi*-*3**design*is a*quasi*-*3**design*. ...*On**the*dual*of*a*quasi*-*3**design*In [5] and in [7, pp. 75-76] ,*the*authors point out that it is not known whether*the*dual*of*a*quasi*-*3*square*design*is necessarily*quasi*-*3*also. ...##
###
Non-embeddable quasi-residual designs with k < built12v

1986
*
Journal of combinatorial theory. Series A
*

This is

doi:10.1016/0097-3165(86)90031-2
fatcat:7e4m2dfz5vbftf4vm3ms6bikdy
*the*first*one*with k = fu. By contrast, if k> tu, a large number*of**non*-embeddable*quasi*-residual*designs*are known; see [S-7]. ... Let 9 be a symmetric (u, k, I)-*design*. A residual*design**of*9' is obtained by deleting*one**of**the*blocks*of*CS and all points occurring in that block. ... This is*the*first*one*with k = fu. By contrast, if k> tu, a large number*of**non*-embeddable*quasi*-residual*designs*are known; see [S-7] . ...##
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Some Non-embeddable Quasi-Derived Designs

1996
*
Journal of combinatorial theory. Series A
*

described a sufficient condition for

doi:10.1006/jcta.1996.0106
fatcat:3u3mjq3ii5e33bbtaiphcdttju
*the**non*-embeddability*of*a*quasi*-derived*design*into a symmetric balanced incomplete block*design*. ... Many infinite series*of**non*-embeddable*quasi*-derived*designs*are thus constructed. ... ACKNOWLEDGMENTS*The*research was supported in part by Grant-in-Aid for Co-operative Research (A)07304021 from*the*Ministry*of*Education and by research fellowships*of**the*Japan Society for Promotion*of*...##
###
Non-embeddable quasi-residual designs

1978
*
Indagationes Mathematicae (Proceedings)
*

Furthermore we give

doi:10.1016/1385-7258(78)90044-6
fatcat:ne22qhp5t5g7lpmnacxtbv6vge
*the*i%st example*of*a*non*-trivial*non*-embeddable*design**on*less than 16 points. 1. ... G. de Bruijn*on**the*occasion*of*his 60th birthday Communicated at*the*meeting*of*January 28, 1978 ARSTRACT We present a new*non*-embeddable*quasi*-residual de&n which has*the*same parameters as Bhattacharya's ... In this paper we consider small values*of*k.*The*smallest known*non*-trivial*non*-embeddable*quasi*-residual*design*is a BD(16, 6; 24,9,*3*) constructed by K. N. ...##
###
Separation Principle of Quasi-One-Sided Lipschitz Nonlinear Systems

2020
*
IET Control Theory & Applications
*

For

doi:10.1049/iet-cta.2019.0230
fatcat:x6dqt7fwrvfirl5zbkijt3vebm
*the**quasi*-*one*-sided Lipschitz*non*-linear system, a condition for*the**existence**of**the*observer is presented. ... In this study,*the*stabilisation*of**quasi*-*one*-sided Lipschitz*non*-linear systems is investigated. ... For*the*weak*quasi*-*one*-sided Lipschitz*non*-linear system, a state feedback controller is proposed and a condition is derived for*the**existence**of**the*state feedback controller.*3*. ...##
###
Non-embeddable quasi-residual designs

1978
*
Indagationes Mathematicae (Proceedings)
*

Furthermore we give

doi:10.1016/s1385-7258(78)80017-1
fatcat:apxjwdpuijfdnesou6bjjpk26q
*the*first example*of*a*non*-trivial*non*-embeddable*design**on*less than 16 points. ... We present a new*non*-embeddable*quasi*-residual*design*which has*the*same parameters as Bhattacharya's*design*but which is much easier to describe. ...*The*smallest v for which a*non*-trivial*non*-embeddable*design*might*exist*.*The*situation is unresolved. See section 4. In section*3**the*smallest known*non*-embeddable*design*is described. ...##
###
A class of non-embeddable designs

1993
*
Journal of combinatorial theory. Series A
*

DEDICATED TO

doi:10.1016/0097-3165(93)90047-c
fatcat:i5cyhtimc5bc3ooqqw23ekqtke
*THE*MEMORY*OF*PROFESSOR MARSHALL HALL A sufficient condition for*non*-embeddability*of**quasi*-derived*designs*into symmetric*designs*is proved. ... Using this condition, several series*of**non*-embeddable*designs*are constructed. ... I THEOREM*3*.*3*.*3*If n 2 -n -1 = q is a prime power, n > 2, then there*exists*a*non*-embeddable 2 -(n 2, n, n -1)*design*D*.*the*complement*of*an affine plane*of*order n. ...##
###
Pseudo quasi-3 designs and their applications to coding theory

2009
*
Journal of combinatorial designs (Print)
*

We define a pseudo

doi:10.1002/jcd.20208
fatcat:m5w744ongnezlkz72hjfw5nm2e
*quasi*-*3**design*as a symmetric*design*with*the*property that*the*derived and residual*designs*with respect to at least*one*block are*quasi*-symmetric. ... In this article we give a construction*of*an infinite family*of*pseudo*quasi*-*3**designs*whose residual*designs*allow us to construct a family*of*codes with a new parameter set that meet*the*Grey Rankin ... It can be seen from*the*construction in [2] that*the**non*-*existence**of*such a*design*implies*the**non*-*existence**of**the*projective plane*of*order 12. ...##
###
Pseudo Quasi-3 Designs and their Applications to Coding Theory
[article]

2008
*
arXiv
*
pre-print

We define a pseudo

arXiv:0804.1740v1
fatcat:xj6y36yqmfaifbn6y2jhatg6ca
*quasi*-*3**design*as a symmetric*design*with*the*property that*the*derived and residual*designs*with respect to at least*one*block are*quasi*-symmetric. ... In this article we give a construction*of*an infinite family*of*pseudo*quasi*-*3**designs*whose residual*designs*allow us to construct a family*of*codes with a new parameter set that meet*the*Grey Rankin ... It can be seen from*the*construction in [2] that*the**non*-*existence**of*such a*design*implies*the**non*-*existence**of**the*projective plane*of*order 12. ...##
###
An Infinite Family of Non-embeddable Quasi-Residual Designs withk<v/2

1996
*
Journal of combinatorial theory. Series A
*

A special case

doi:10.1006/jcta.1996.0057
fatcat:76bmlziyefcylg5l4mywyr4kdy
*of*this construction gives an infinite family*of**non*-embeddable*quasi*-residual*designs*, with parameters 2&(2(*3*d+1 )&2, 2(*3*d ),*3*d ), where d 1. 1996 Academic Press, Inc. ... A t&(v, k, *)*design*D is an (P, B, I ) incidence structure with*the*following properties: (i)*The*point set P*of*D has cardinality v; (ii) every block B # B is incident with exactly k points; (iii) every ...*The*aim*of*this paper is to demonstrate*the**existence**of*a previously unknown infinite family*of**non*-embeddable*quasi*-residual*designs*with parameters 2&(2(*3*d+1 )&2, 2(*3*d ),*3*d ), where d 1. ...##
###
Classes de fonctions non quasi-analytiques et existence de sous-espaces invariants

1998
*
Comptes rendus de l'Académie des sciences. Série 1, Mathématique
*

We prove that some classes

doi:10.1016/s0764-4442(99)80106-2
fatcat:nq7a7wdl4ndwvjvzcxk7srqjpy
*of*functions deJned*on*a compact set in*the*complex plune with plunar Lebesgue measure zero, are*non*-quasianal.vtic. ... ~~rmula, we establish*the**existence**of*invariant subspaces for operators ,for which a part*of**the*spectrum is*of*planar Lebesgue measure zero, provided that*the*resolvent has a moderate growth near this ...##
###
More on graphs with just three distinct eigenvalues

2017
*
Applicable Analysis and Discrete Mathematics
*

We show that if µ is

doi:10.2298/aadm161111033r
fatcat:xmgwuhbp55gcllokynhx7iaihy
*non*-main then δ(G) ≥ 1 + µ − λµ, with equality if and only if G is*of**one**of*three types, derived from a strongly regular graph, a symmetric*design*or a*quasi*-symmetric*design*(with ... In honour*of*Dragoš Cvetković*on**the*occasion*of*his 75th birthday. ... To formulate a partial converse implicit in [14, Section 4] we extend*the*construction in (*3*) to any*quasi*-symmetric*design*which has 0 as*one**of*its two intersection numbers. ...##
###
Applying Balanced Generalized Weighing Matrices to Construct Block Designs

2001
*
Electronic Journal of Combinatorics
*

q$ and $r=(q^{d}-1)/(q-1)$ are prime powers, and a family

doi:10.37236/1556
fatcat:lbcixarys5bjffgcizmj72md7q
*of**non*-embeddable*quasi*-residual $2-((r+1)(r^{m+1}-1)/(r-1),r^{m}(r+1)/2,r^{m}(r-1)/2)$*designs*, where $m$ is any positive integer and $r=2^{d} ... -1$, $*3*\cdot 2^{d}-1$ or $5\cdot 2^{d}-1$ is a prime power, $r\geq 11$. ... If a quasiresidual (*quasi*-derived)*design*is not a residual (derived)*design**of*a symmetric*design*, it is called*non*-embeddable. For further references*on*BIBDs see [1] . ...##
###
Non-Quasi-Static Large-Signal Model for RF LDMOS Power Transistors

2018
*
2018 IEEE/MTT-S International Microwave Symposium - IMS
*

*The*

*non*-

*quasi*-static large-signal model improves

*the*efficiency and gain predictions by 10% and 0.5 dB at 3.5 GHz. ... We show that industry-standard nonlinear large-signal models for LDMOS based

*on*

*quasi*-static assumptions are not sufficient for high-efficiency

*designs*at frequencies higher than 2 GHz. ... Fig.

*3*shows

*the*comparison

*of*high-frequency current between measurement data,

*the*proposed

*non*-

*quasi*-static model, and

*the*

*quasi*-static model. ...

##
###
Non-symmetric nearly triply regular designs

1996
*
Discrete Mathematics
*

All

doi:10.1016/0012-365x(94)00097-3
fatcat:yhd26xmevnhyplbwvro5xhp7w4
*non*-trivial*non*-symmetric*designs*with 2 = 1, and all*quasi*-symmetric*designs*with 2 = 2 are TR. ... It is interesting to note that this is*the*Hadamard*3*-*design**of*order*3*which is*the*extension*of**the*symmetric NTR Hadamard 2-(11, 5, 2)*design*. Example 4. ... Ito for pointing out*the*examples*of**the**non*-symmetric NTR 2-(12, 6, 5)*design*given in Example 4 and for finding a small error in*the*original version*of*Lemma 2. ...
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