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On the non-existence of quasi-3 designs

Wayne Broughton, Gary McGuire
2003 Discrete Mathematics  
In this survey article we discuss 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.  ... 
doi:10.1016/s0012-365x(02)00492-2 fatcat:dupefa3iuzgypeh3ky7ngwt6zm

Non-embeddable quasi-residual designs with k < built12v

Tran van Trung
1986 Journal of combinatorial theory. Series A  
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].  ...  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] .  ... 
doi:10.1016/0097-3165(86)90031-2 fatcat:7e4m2dfz5vbftf4vm3ms6bikdy

Some Non-embeddable Quasi-Derived Designs

Sanpei Kageyama, Ying Miao
1996 Journal of combinatorial theory. Series A  
described a sufficient condition for 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  ... 
doi:10.1006/jcta.1996.0106 fatcat:3u3mjq3ii5e33bbtaiphcdttju

Non-embeddable quasi-residual designs

J.H. van Lint
1978 Indagationes Mathematicae (Proceedings)  
Furthermore we give 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.  ... 
doi:10.1016/1385-7258(78)90044-6 fatcat:ne22qhp5t5g7lpmnacxtbv6vge

Separation Principle of Quasi-One-Sided Lipschitz Nonlinear Systems

Guang-Da Hu, Yangbin Zhao
2020 IET Control Theory & Applications  
For 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.  ... 
doi:10.1049/iet-cta.2019.0230 fatcat:x6dqt7fwrvfirl5zbkijt3vebm

Non-embeddable quasi-residual designs

J.H. Van Lint
1978 Indagationes Mathematicae (Proceedings)  
Furthermore we give 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.  ... 
doi:10.1016/s1385-7258(78)80017-1 fatcat:apxjwdpuijfdnesou6bjjpk26q

A class of non-embeddable designs

J.H van Lint, V.D Tonchev
1993 Journal of combinatorial theory. Series A  
DEDICATED TO 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.  ... 
doi:10.1016/0097-3165(93)90047-c fatcat:i5cyhtimc5bc3ooqqw23ekqtke

Pseudo quasi-3 designs and their applications to coding theory

Carl Bracken
2009 Journal of combinatorial designs (Print)  
We define a pseudo 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.  ... 
doi:10.1002/jcd.20208 fatcat:m5w744ongnezlkz72hjfw5nm2e

Pseudo Quasi-3 Designs and their Applications to Coding Theory [article]

Carl Bracken
2008 arXiv   pre-print
We define a pseudo 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.  ... 
arXiv:0804.1740v1 fatcat:xj6y36yqmfaifbn6y2jhatg6ca

An Infinite Family of Non-embeddable Quasi-Residual Designs withk<v/2

Kirsten Mackenzie-Fleming
1996 Journal of combinatorial theory. Series A  
A special case 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.  ... 
doi:10.1006/jcta.1996.0057 fatcat:76bmlziyefcylg5l4mywyr4kdy

Classes de fonctions non quasi-analytiques et existence de sous-espaces invariants

Karim Kellay, Mohamed Zarrabi
1998 Comptes rendus de l'Académie des sciences. Série 1, Mathématique  
We prove that some classes 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  ... 
doi:10.1016/s0764-4442(99)80106-2 fatcat:nq7a7wdl4ndwvjvzcxk7srqjpy

More on graphs with just three distinct eigenvalues

Peter Rowlinson
2017 Applicable Analysis and Discrete Mathematics  
We show that if µ is 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.  ... 
doi:10.2298/aadm161111033r fatcat:xmgwuhbp55gcllokynhx7iaihy

Applying Balanced Generalized Weighing Matrices to Construct Block Designs

Yury J. Ionin
2001 Electronic Journal of Combinatorics  
q$ and $r=(q^{d}-1)/(q-1)$ are prime powers, and a family 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] .  ... 
doi:10.37236/1556 fatcat:lbcixarys5bjffgcizmj72md7q

Non-Quasi-Static Large-Signal Model for RF LDMOS Power Transistors

Lei Zhang, Hernan Rueda, Kevin Kim, Peter Aaen
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.  ... 
doi:10.1109/mwsym.2018.8439238 fatcat:hptgu5frwfhnpoqq4phxdqntne

Non-symmetric nearly triply regular designs

Cheryl E. Praeger, Blessilda P. Raposa
1996 Discrete Mathematics  
All 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.  ... 
doi:10.1016/0012-365x(94)00097-3 fatcat:yhd26xmevnhyplbwvro5xhp7w4
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