A SURVEY OF THE DIFFERENT TYPES OF VECTOR SPACE PARTITIONS

A vector space partition is here a collection [Formula: see text] of subspaces of a finite vector space V(n, q), of dimension n over a finite field with q elements, with the property that every non-zero vector is contained in a unique member of [Formula: see text]. Vector space partitions relate to finite projective planes, design theory and error correcting codes. In the first part of the paper I will discuss some relations between vector space partitions and other branches of mathematics. The other part of the paper contains a survey of known results on the type of a vector space partition, more precisely: the theorem of Beutelspacher and Heden on T-partitions, rather recent results of El-Zanati et al. on the different types that appear in the spaces V(n, 2), for n ≤ 8, a result of Heden and Lehmann on vector space partitions and maximal partial spreads including their new necessary condition for the existence of a vector space partition, and furthermore, I will give a theorem of Heden on the length of the tail of a vector space partition. Finally, I will also give a few historical remarks.

Download Full-text

An Enhanced Two Stage MMSE Equalizer for Coded FBMC/OQAM Systems

International Journal of Embedded and Real-Time Communication Systems ◽

10.4018/ijertcs.2019010104 ◽

2019 ◽

Vol 10 (1) ◽

pp. 69-82 ◽

Cited By ~ 2

Author(s):

Mohammad Rizk Assaf ◽

Abdel-Nasser Assimi

Keyword(s):

Error Propagation ◽

Channel Model ◽

Error Correcting Codes ◽

Two Stage ◽

Probability Of Error ◽

Second Stage ◽

Different Types ◽

Mmse Equalizer ◽

And Performance ◽

Ici Cancellation

In this article, the authors investigate the enhanced two stage MMSE (TS-MMSE) equalizer in bit-interleaved coded FBMC/OQAM system which gives a tradeoff between complexity and performance, since error correcting codes limits error propagation, so this allows the equalizer to remove not only ICI but also ISI in the second stage. The proposed equalizer has shown less design complexity compared to the other MMSE equalizers. The obtained results show that the probability of error is improved where SNR gain reaches 2 dB measured at BER compared with ICI cancellation for different types of modulation schemes and ITU Vehicular B channel model. Some simulation results are provided to illustrate the effectiveness of the proposed equalizer.

Download Full-text

A class of factorable topological algebras

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s001309150002887x ◽

1990 ◽

Vol 33 (1) ◽

pp. 53-59 ◽

Cited By ~ 5

Author(s):

E. Ansari-Piri

Keyword(s):

Vector Space ◽

Topological Vector Space ◽

Approximate Identity ◽

Necessary Condition ◽

Topological Algebras ◽

Approximate Identities ◽

Cohen Factorization ◽

Locally Convex ◽

Space Property ◽

Uniformly Bounded

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

Download Full-text

A r-maximal vector space not contained in any maximal vector space

Journal of Symbolic Logic ◽

10.2307/2273519 ◽

1978 ◽

Vol 43 (3) ◽

pp. 430-441 ◽

Cited By ~ 9

Author(s):

J. Remmel

Keyword(s):

Vector Space ◽

Quotient Space ◽

Independent Set ◽

Scalar Multiplication ◽

Effective Procedure ◽

Natural Numbers ◽

Infinite Dimensional ◽

Vector Addition ◽

Zero Vector

In [4], Metakides and Nerode define a recursively presented vector space V∞. over a (finite or infinite) recursive field F to consist of a recursive subset U of the natural numbers N and operations of vector addition and scalar multiplication which are partial recursive and under which V∞ becomes a vector space. Throughout this paper, we will identify V∞ with N, say via some fixed Gödel numbering, and assume V∞ is infinite dimensional and has a dependence algorithm, i.e., there is a uniform effective procedure which determines whether any given n-tuple v0, …, vn−1 from V∞ is linearly dependent. Given a subspace W of V∞, we write dim(W) for the dimension of W. Given subspaces V and W of V∞, V + W will denote the weak sum of V and W and if V ∩ W = {0) (where 0 is the zero vector of V∞), we write V ⊕ W instead of V + W. If W ⊇ V, we write W mod V for the quotient space. An independent set A ⊆ V∞ is extendible if there is a r.e. independent set I ⊇ A such that I − A is infinite and A is nonextendible if it is not the case that A is extendible.

Download Full-text

Some necessary conditions for vector space partitions

Discrete Mathematics ◽

10.1016/j.disc.2011.09.023 ◽

2012 ◽

Vol 312 (2) ◽

pp. 351-361 ◽

Cited By ~ 8

Author(s):

Juliane Lehmann ◽

Olof Heden

Keyword(s):

Vector Space ◽

Necessary Conditions ◽

Vector Space Partitions

Download Full-text

Out of the Barracks: The Role of the Military in Democratic Revolutions

Armed Forces & Society ◽

10.1177/0095327x17708194 ◽

2017 ◽

Vol 45 (1) ◽

pp. 78-100 ◽

Cited By ~ 1

Author(s):

Marcos Degaut

Keyword(s):

South Korea ◽

Necessary Condition ◽

Tiananmen Square ◽

Velvet Revolution ◽

Different Types ◽

Key Factor ◽

Democratic Revolution ◽

Action Theories ◽

The Military

Why some democratic revolutions succeed while others fail? The scholarly community has sought to address this issue from various perspectives, from rational choice approaches to collective action theories. Too little attention, however, has been paid to analyzing the role of the military. By discussing the different types of interactions played by the military in five cases of successful democratic revolutions—the 1910 Portuguese Republican Revolution, the 1958 Venezuelan Revolution, the 1960 April Revolution in South Korea, the 1989 Velvet Revolution in Czechoslovakia, and the 2000 Bulldozer Revolution in Yugoslavia—and three cases of failed revolutions, the 1905 bourgeois-liberal revolution in Russia, the 1989 Tiananmen Square Protests in China, and the 2016 Turkey’s coup attempt, this study finds out that the key factor in determining their outcome is the army’s response and that the military backing is a necessary condition for a democratic revolution to succeed.

Download Full-text

Translation planes of odd order and odd dimension

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171279000181 ◽

1979 ◽

Vol 2 (2) ◽

pp. 187-208 ◽

Cited By ~ 2

Author(s):

T. G. Ostrom

Keyword(s):

Vector Space ◽

Finite Groups ◽

Translation Planes ◽

Solvable Subgroup ◽

Joint Paper ◽

Desarguesian Planes ◽

Odd Order ◽

Collineation Groups ◽

Zero Vector

The author considers one of the main problems in finite translation planes to be the identification of the abstract groups which can act as collineation groups and how those groups can act.The paper is concerned with the case where the plane is defined on a vector space of dimension2d overGF(q), whereqanddare odd. If the stabilizer of the zero vector is non-solvable, letG0be a minimal normal non-solvable subgroup. We suspect thatG0must be isomorphic to someSL(2,u)or homomorphic toA6orA7. Our main result is that this is the case whendis the product of distinct primes.The results depend heavily on the Gorenstein-Walter determination of finite groups having dihedral Sylow2-groups whendandqare both odd. The methods and results overlap those in a joint paper by Kallaher and the author which is to appear in Geometriae Dedicata. The only known example (besides Desarguesian planes) is Hering's plane of order27(i.e.,dandqare both equal to3) which admitsSL(2,13).

Download Full-text

A few remarks on bounded operators on topological vector spaces

Filomat ◽

10.2298/fil1603763z ◽

2016 ◽

Vol 30 (3) ◽

pp. 763-772

Author(s):

Omid Zabeti ◽

Ljubisa Kocinac

Keyword(s):

Tensor Product ◽

Vector Space ◽

Topological Vector Space ◽

Compact Operators ◽

Vector Spaces ◽

Locally Convex Spaces ◽

Bounded Operators ◽

Topological Vector Spaces ◽

Different Types ◽

Locally Convex

We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators. We also consider similar types of bounded bilinear mappings between topological vector spaces. Some properties of tensor product operators between locally convex spaces are established. In the last part of the paper we deal with operators on topological Riesz spaces.

Download Full-text

Research on Methodology of Correlation Analysis of Sci-Tech Literature Based on Deep Learning Technology in the Big Data

Journal of Database Management ◽

10.4018/jdm.2018070104 ◽

2018 ◽

Vol 29 (3) ◽

pp. 67-88 ◽

Cited By ~ 1

Author(s):

Wen Zeng ◽

Hongjiao Xu ◽

Hui Li ◽

Xiang Li

Keyword(s):

Big Data ◽

Deep Learning ◽

Correlation Analysis ◽

Vector Space ◽

Input Word ◽

Learning Technology ◽

Depth Analysis ◽

Different Types ◽

High Level ◽

Deep Learning Model

In the big data era, it is a great challenge to identify high-level abstract features out of a flood of sci-tech literature to achieve in-depth analysis of data. The deep learning technology has developed rapidly and achieved applications in many fields, but has rarely been utilized in the research of sci-tech literature data. This article introduced the presentation method of vector space of terminologies in sci-tech literature based on the deep learning model. It explored and adopted a deep AE model to reduce the dimensionality of input word vector feature. Also put forward is the methodology of correlation analysis of sci-tech literature based on deep learning technology. The experimental results showed that the processing of sci-tech literature data could be simplified into the computation of vectors in the multi-dimensional vector space, and the similarity in vector space could be used to represent similarity in text semantics. The correlation analysis of subject contents between sci-tech literatures of the same or different types can be made using this method.

Download Full-text

Understanding Development Discourse through Ontological Design

Conference Proceedings of the Academy for Design Innovation Management ◽

10.33114/adim.2019.03.241 ◽

2019 ◽

Vol 2 (1) ◽

Author(s):

Sharon PRENDEVILLE ◽

Boeun Bethany HONG

Keyword(s):

Design Theory ◽

Development Assistance ◽

Development Discourse ◽

The West ◽

Design Studies ◽

New Development ◽

Development Experience ◽

Different Types ◽

Ontological Design ◽

The Empirical Analysis

Discourse is a powerful way of understanding/forming the world. It consolidates/disassembles society by conforming/disarticulating. However, the work of discourses has not been explained sufficiently in terms of design theory. In this respect, this paper aims to explore how the work of discourses can be understood in relation to the concept of ontological design, especially from the perspective of coloniality. The case of South Korea’s development experience around different types of development assistance strategies was used to interrogate this question. A hermeneutic approach and discourse analysis were adopted for the empirical analysis. The research found the designed development assistance strategies of the “West” design back the development thinking and new development assistance strategies in South Korea. In doing so, the country replicates the “West-centred” discourse of developmentalism. From this, we conclude that discourses are shared through the ontological practices of designing. This informs design studies of how discourse relates to design.

Download Full-text

On r.e. and co-r.e. vector spaces with nonextendible bases

Journal of Symbolic Logic ◽

10.2307/2273351 ◽

1980 ◽

Vol 45 (1) ◽

pp. 20-34 ◽

Cited By ~ 18

Author(s):

J. Remmel

Keyword(s):

Vector Space ◽

Quotient Space ◽

Independent Set ◽

Effective Procedure ◽

Vector Spaces ◽

Natural Numbers ◽

Infinite Dimensional ◽

Recursively Enumerable ◽

Vector Addition ◽

Zero Vector

The concern of this paper is with recursively enumerable and co-recursively enumerable subspaces of a recursively presented vector spaceV∞ over a (finite or infinite) recursive field F which is defined in [6] to consist of a recursive subset U of the natural numbers N and operations of vector addition and scalar multiplication which are partial recursive and under which V∞ becomes a vector space. Throughout this paper, we will identify V∞ with N, say via some fixed Gödel numbering, and assume V∞ is infinite dimensional and has a dependence algorithm, i.e., there is a uniform effective procedure which determines whether or not any given n-tuple v0, …, vn−1 from V∞ is linearly dependent. Various properties of V∞ and its sub-spaces have been studied by Dekker [1], Guhl [3], Metakides and Nerode [6], Kalantari and Retzlaff [4], and the author [7].Given a subspace W of V∞, we say W is r.e. (co-r.e.) if W(V∞ − W) is an r.e. subset of N and write dim(V) for the dimension of V. Given subspaces V, W of V∞, V + W will denote the weak sum of V and W and if V ⋂ M = {0} (where 0 is the zero vector of V∞), we write V ⊕ Winstead of V + W. If W ⊇ V, we write Wmod V for the quotient space. An independent set A ⊆ V∞ is extendible if there is an r.e. independent set I ⊇ A such that I − A is infinite and A is nonextendible if it is not the case An is extendible. A r.e. subspace M ⊇ V∞ is maximal if dim(V∞ mod M) = ∞ and for any r.e. subspace W ⊇ Meither dim(W mod M) < ∞ or dim(V∞ mod W) < ∞.

Download Full-text