Canonical generator states and their symmetry adaptation

A gauge-invariant conformal particle model is studied. Its Lagrangian gauge transformations are obtained in a covariant way using a kind of canonical generator. On the other hand, the Hamiltonian transformations cannot be written in a covariant form despite the covariance of the Hamiltonian constraints.

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New Soft Set Based Class of Linear Algebraic Codes

Symmetry ◽

10.3390/sym10100510 ◽

2018 ◽

Vol 10 (10) ◽

pp. 510 ◽

Cited By ~ 7

Author(s):

Mumtaz Ali ◽

Huma Khan ◽

Le Son ◽

Florentin Smarandache ◽

W. Kandasamy

Keyword(s):

Error Detection ◽

Parity Check ◽

Generator Matrix ◽

Parity Check Matrix ◽

Soft Sets ◽

New Class ◽

Error Detection And Correction ◽

Check Matrix ◽

Algebraic Codes ◽

Canonical Generator

In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example.

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A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽

10.3390/info10020078 ◽

2019 ◽

Vol 10 (2) ◽

pp. 78 ◽

Cited By ~ 1

Author(s):

Jingpu Zhang ◽

Ronghui Liu ◽

Ligeng Zou ◽

Licheng Zeng

Keyword(s):

Formal Concept Analysis ◽

Concept Lattice ◽

Incremental Algorithm ◽

Formal Context ◽

Formal Concept ◽

Concept Lattices ◽

Covering Relation ◽

Canonical Generator ◽

Lattice Construction ◽

Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

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