The octahedron theorem in Minkowski three-space a metric vector space proof of Miquel's theorem in the Laguerre plane

1987 ◽  
Vol 30 (2) ◽  
pp. 196-202 ◽  
Author(s):  
J. A. Lester
Keyword(s):  
Vector Space ◽  
Laguerre Plane ◽  
Miquel’S Theorem ◽  
Three Space

Translation Planes of Dimension Two with Odd Characteristic

1980 ◽  
Vol 32 (5) ◽  
pp. 1114-1125 ◽  
Author(s):  
T. G. Ostrom
Keyword(s):  
Vector Space ◽  
Vector Spaces ◽  
Translation Planes ◽  
Vector Form ◽  
Linear Transformations ◽  
Independent Vector ◽  
Translation Complement ◽  
Three Space ◽  
Zero Vector ◽  
Mutually Independent

A translation plane of dimension d over its kernel K = GF(q) can be represented by a vector space of dimension 2d over K. The lines through the zero vector form a “spread”; i.e., a class of mutually independent vector spaces of dimension d which cover the vector space.The case where d = 2 has aroused the most interest. The more exotic translation planes tend to be of dimension two; a spread in this case can be interpreted as a class of mutually skew lines in projective three-space.The stabilizer of the zero vector in the group of collineations is a group of semi-linear transformations and is called the translation complement. The subgroup consisting of linear transformations is the linear translation complement.

On Semi - Pre irresolute Topological Vector Space

2018 ◽  
Vol 14 (3) ◽  
pp. 184-192
Author(s):  
Radhi Ali ◽  
◽  
Jalal Hussein Bayati ◽  
Suhad Hameed
Keyword(s):  
Vector Space ◽  
Topological Vector Space

Aplikasi Deteksi Kemiripan Tugas Paper

2017 ◽  
Vol 15 (2) ◽  
pp. 5
Author(s):  
Anthony Anggrawan ◽  
Azhari
Keyword(s):  
Information Retrieval ◽  
Vector Space ◽  
Vector Space Model ◽  
Mean Average Precision ◽  
Average Precision ◽  
Information Searching ◽  
Space Model ◽  
Model Method

Information searching based on users’ query, which is hopefully able to find the documents based on users’ need, is known as Information Retrieval. This research uses Vector Space Model method in determining the similarity percentage of each student’s assignment. This research uses PHP programming and MySQL database. The finding is represented by ranking the similarity of document with query, with mean average precision value of 0,874. It shows how accurate the application with the examination done by the experts, which is gained from the evaluation with 5 queries that is compared to 25 samples of documents. If the number of counted assignments has higher similarity, thus the process of similarity counting needs more time, it depends on the assignment’s number which is submitted.

Unifying Bayesian Inference and Vector Space Models for Improved Decipherment

2015 ◽  
Author(s):  
Qing Dou ◽  
Ashish Vaswani ◽  
Kevin Knight ◽  
Chris Dyer
Keyword(s):  
Bayesian Inference ◽  
Vector Space ◽  
Vector Space Models

Aplikasi Rekomendasi Buku Pada Katalog Perpustakaan Universitas Multimedia Nusantara Menggunakan Vector Space Model

2018 ◽  
Vol 9 (2) ◽  
pp. 97-105
Author(s):  
Richard Firdaus Oeyliawan ◽  
Dennis Gunawan
Keyword(s):  
Vector Space ◽  
Vector Space Model ◽  
Vector Model ◽  
Library Management ◽  
Space Model ◽  
Library Management System ◽  
Index Terms ◽  
Library Catalogue ◽  
Language Sample ◽  
F Measure

Library is one of the facilities which provides information, knowledge resource, and acts as an academic helper for readers to get the information. The huge number of books which library has, usually make readers find the books with difficulty. Universitas Multimedia Nusantara uses the Senayan Library Management System (SLiMS) as the library catalogue. SLiMS has many features which help readers, but there is still no recommendation feature to help the readers finding the books which are relevant to the specific book that readers choose. The application has been developed using Vector Space Model to represent the document in vector model. The recommendation in this application is based on the similarity of the books description. Based on the testing phase using one-language sample of the relevant books, the F-Measure value gained is 55% using 0.1 as cosine similarity threshold. The books description and variety of languages affect the F-Measure value gained. Index Terms—Book Recommendation, Porter Stemmer, SLiMS Universitas Multimedia Nusantara, TF-IDF, Vector Space Model

Series expansions for monogenic functions in Clifford algebras and their application

2020 ◽  
Vol 17 (3) ◽  
pp. 365-371
Author(s):  
Anatoliy Pogorui ◽  
Tamila Kolomiiets
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Space ◽  
Clifford Algebra ◽  
Clifford Algebras ◽  
Monogenic Function ◽  
Second Order ◽  
Series Expansions ◽  
Monogenic Functions ◽  
Partial Differential

This paper deals with studying some properties of a monogenic function defined on a vector space with values in the Clifford algebra generated by the space. We provide some expansions of a monogenic function and consider its application to study solutions of second-order partial differential equations.

Vector geometry

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Vector Space ◽  
Velocity Vector ◽  
Cartesian Coordinates

This chapter defines the mathematical spaces to which the geometrical quantities discussed in the previous chapter—scalars, vectors, and the metric—belong. Its goal is to go from the concept of a vector as an object whose components transform as Tⁱ → 𝓡ⱼ ⁱTj under a change of frame to the ‘intrinsic’ concept of a vector, T. These concepts are also generalized to ‘tensors’. The chapter also briefly remarks on how to deal with non-Cartesian coordinates. The velocity vector v is defined as a ‘free’ vector belonging to the vector space ε‎3 which subtends ε‎3. As such, it is not bound to the point P at which it is evaluated. It is, however, possible to attach it to that point and to interpret it as the tangent to the trajectory at P.

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