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.

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

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>

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 Graphs on Affine and Linear Spaces and Deuber Sets

10.37236/2732 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
David S. Gunderson ◽  
Hanno Lefmann
Keyword(s):  
Abelian Group ◽  
Finite Field ◽  
Recent Work ◽  
Independent Set ◽  
Large Set ◽  
Free Graph ◽  
Linear Spaces ◽  
Ramsey’S Theorem ◽  
Positive Integers ◽  
Arbitrary Abelian Group

If $G$ is a large $K_k$-free graph, by Ramsey's theorem, a large set of vertices is independent. For graphs whose vertices are positive integers, much recent work has been done to identify what arithmetic structure is possible in an independent set. This paper addresses  similar problems: for graphs whose vertices are affine or linear spaces over a finite field,  and when the vertices of the graph are elements of an arbitrary Abelian group.

On General Polynomials

1967 ◽  
Vol 10 (4) ◽  
pp. 579-583 ◽  
Author(s):  
Kenneth S. Williams
Keyword(s):  
Finite Field ◽  
Number Of Solutions ◽  
Fixed Integer ◽  
Image Position

Let d denote a fixed integer > 1 and let GF(q) denote the finite field of q = pn elements. We consider q fixed ≥ A(d), where A(d) is a (large) constant depending only on d. Let1where each aiεGF(q). Let nr(r = 2, 3, …, d) denote the number of solutions in GF(q) offor which x1, x2, …, xr are all different.

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.

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