scholarly journals Construction of random pooling designs based on singular linear space over finite fields

2021 ◽  
Vol 7 (3) ◽  
pp. 4376-4385
Author(s):  
Xuemei Liu ◽  
◽  
Yazhuo Yu
Keyword(s):  
Linear Space ◽  
Finite Fields ◽  
Pooling Designs ◽  
Linear Spaces ◽  
Disjunct Matrix ◽  
Short Time ◽  
Singular Linear Spaces

<abstract><p>Faced with a large number of samples to be tested, if there are requiring to be tested one by one and complete in a short time, it is difficult to save time and save costs at the same time. The random pooling designs can deal with it to some degree. In this paper, a family of random pooling designs based on the singular linear spaces and related counting theorems are constructed. Furtherly, based on it we construct an $ \alpha $-$ almost\ d^e $-disjunct matrix and an $ \alpha $-$ almost\ (d, r, z] $-disjunct matrix, and all the parameters and properties of these random pooling designs are given. At last, by comparing to Li's construction, we find that our design is better under certain condition.</p></abstract>

Quasi-regular semilattices in singular linear spaces

2016 ◽  
Vol 08 (01) ◽  
pp. 1650005
Author(s):  
Baohuan Zhang ◽  
Yujun Liu ◽  
Zengti Li
Keyword(s):  
Finite Field ◽  
Linear Space ◽  
Fixed Integer ◽  
Linear Spaces ◽  
Partially Ordered ◽  
Type Formula ◽  
Singular Linear Spaces

Let [Formula: see text] denote the [Formula: see text]-dimensional singular linear space over a finite field [Formula: see text]. For a fixed integer [Formula: see text], denote by [Formula: see text] the set of all subspaces of type [Formula: see text], where [Formula: see text]. Partially ordered by ordinary inclusion, one family of quasi-regular semilattices is obtained. Moreover, we compute its all parameters.

Linear geometries on the Moebius strip: A theorem of Skornyakov type

2005 ◽  
Vol 72 (1) ◽  
pp. 17-30
Author(s):  
Rainer Löwen ◽  
Burkard Polster
Keyword(s):  
Linear Space ◽  
Real Line ◽  
Open Disk ◽  
Stable Plane ◽  
Linear Spaces ◽  
Unique Line ◽  
The Real ◽  
Continuity Properties ◽  
Point Set ◽  
Moebius Strip

We show that the continuity properties of a stable plane are automatically satisfied if we have a linear space with point set a Moebius strip, provided that the lines are closed subsets homeomorphic to the real line or to the circle. In other words, existence of a unique line joining two distinct points implies continuity of join and intersection. For linear spaces with an open disk as point set, the same result was proved by Skornyakov.

scholarly journals Nearly directed subspaces of partially ordered linear spaces

1968 ◽  
Vol 16 (2) ◽  
pp. 135-144
Author(s):  
G. J. O. Jameson
Keyword(s):  
Linear Space ◽  
Transitive Relation ◽  
Linear Spaces ◽  
Real Linear Space ◽  
Partially Ordered ◽  
Real Linear ◽  
Image Position ◽  
Ordered Linear Spaces

Let X be a partially ordered linear space, i.e. a real linear space with a reflexive, transitive relation ≦ such that

New Fixed Point Theorems via Contraction Mappings in Complete Intuitionistic Fuzzy Normed Linear Space

2018 ◽  
Vol 15 (01) ◽  
pp. 65-83
Author(s):  
Nabanita Konwar ◽  
Ayhan Esi ◽  
Pradip Debnath
Keyword(s):  
Fixed Point ◽  
Mathematical Models ◽  
Linear Space ◽  
Fixed Point Theorems ◽  
Normed Linear Space ◽  
Existence Of A Solution ◽  
Linear Spaces ◽  
Contraction Mappings ◽  
Normed Linear Spaces ◽  
Intuitionistic Fuzzy

Contraction mappings provide us with one of the major sources of fixed point theorems. In many mathematical models, the existence of a solution may often be described by the existence of a fixed point for a suitable map. Therefore, study of such mappings and fixed point results becomes well motivated in the setting of intuitionistic fuzzy normed linear spaces (IFNLSs) as well. In this paper, we define some new contraction mappings and establish fixed point theorems in a complete IFNLS. Our results unify and generalize several classical results existing in the literature.

Gaps between Spheres in Normed Linear Spaces

1980 ◽  
Vol 23 (3) ◽  
pp. 347-354 ◽  
Author(s):  
Robert H. Lohman
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Linear Spaces ◽  
Infinite Dimensional ◽  
Normed Linear Spaces ◽  
Concentric Spheres ◽  
General Conditions

AbstractThe geometric notions of a gap and gap points between “concentric” spheres in a normed linear space are introduced and studied. The existence of gap points characterizes finitedimensional spaces. General conditions are given under which an infinite-dimensional normed linear space admits concentric spheres such that both these spheres and their dual spheres fail to have gap points.

On the calculation of the Dunkl-Williams constant of normed linear spaces

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Hiroyasu Mizuguchi ◽  
Kichi-Suke Saito ◽  
Ryotaro Tanaka
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Normal Structure ◽  
Linear Spaces ◽  
Normed Linear Spaces

AbstractRecently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the Dunkl-Williams constant DW(X) of a normed linear space X. In this paper we present some characterizations of this constant. As an application, we calculate DW(ℓ2-ℓ∞) in the Day-James space ℓ2-ℓ∞.

scholarly journals Bounds on Subspace Codes Based on Subspaces of Type(m,1)in Singular Linear Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
You Gao ◽  
Gang Wang
Keyword(s):  
Linear Space ◽  
Finite Fields ◽  
Sphere Packing ◽  
Subspace Codes ◽  
Singleton Bound ◽  
Johnson Bound

The Sphere-packing bound, Singleton bound, Wang-Xing-Safavi-Naini bound, Johnson bound, and Gilbert-Varshamov bound on the subspace codesn+l,M,d,(m,1)qbased on subspaces of type(m,1)in singular linear spaceFq(n+l)over finite fieldsFqare presented. Then, we prove that codes based on subspaces of type(m,1)in singular linear space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures inFq(n+l).

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