scholarly journals On Some Algebraic Properties of the Chinese Remainder Theorem with Applications to Real Life

2021 ◽  
Vol 5 (3) ◽  
pp. 219-224
Author(s):  
Elvis Adam Alhassan ◽  
Kaiyu Tian ◽  
Olivier Joseph Abban ◽  
Israel Enema Ohiami ◽  
Michael Michael Adjabui ◽  
...  
2014 ◽  
Vol 6 (4) ◽  
pp. 46-52
Author(s):  
E.A. Alhassan ◽  
K.N. Simon ◽  
J.M. Bunyan ◽  
A. Gregory

2014 ◽  
Vol 1 (2) ◽  
pp. 49-61 ◽  
Author(s):  
Mary A. Geetha ◽  
D. P. Acharjya ◽  
N. Ch. S. N. Iyengar

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.


Author(s):  
D. P. Acharjya ◽  
Mary A. Geetha

The fundamental concept of crisp set has been extended in many directions in the recent past. The notion of rough set by Pawlak is noteworthy among them. The rough set philosophy is based on the concept that there is some information associated with each object of the universe. There is a need to classify objects of the universe based on the indiscernibility relation among them. In the view of granular computing, rough set model is researched by single granulation. It has been extended to multigranular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. However, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multigranulation rough set on single universal set to multigranulation rough set on two universal sets. This chapter defines multigranulation rough set for two universal sets U and V. In addition, the algebraic properties, measures of uncertainty and topological characterization that are interesting in the theory of multigranular rough sets are studied. This helps in describing and solving real life problems more accurately.


2020 ◽  
Vol 48 (2) ◽  
pp. 399-409
Author(s):  
Baizhen Gao ◽  
Rushant Sabnis ◽  
Tommaso Costantini ◽  
Robert Jinkerson ◽  
Qing Sun

Microbial communities drive diverse processes that impact nearly everything on this planet, from global biogeochemical cycles to human health. Harnessing the power of these microorganisms could provide solutions to many of the challenges that face society. However, naturally occurring microbial communities are not optimized for anthropogenic use. An emerging area of research is focusing on engineering synthetic microbial communities to carry out predefined functions. Microbial community engineers are applying design principles like top-down and bottom-up approaches to create synthetic microbial communities having a myriad of real-life applications in health care, disease prevention, and environmental remediation. Multiple genetic engineering tools and delivery approaches can be used to ‘knock-in' new gene functions into microbial communities. A systematic study of the microbial interactions, community assembling principles, and engineering tools are necessary for us to understand the microbial community and to better utilize them. Continued analysis and effort are required to further the current and potential applications of synthetic microbial communities.


2010 ◽  
Vol 11 (2) ◽  
pp. 60-65
Author(s):  
Francine Wenhardt

Abstract The speech-language pathologist (SLP) working in the public schools has a wide variety of tasks. Educational preparation is not all that is needed to be an effective school-based SLP. As a SLP currently working in the capacity of a program coordinator, the author describes the skills required to fulfill the job requirements and responsibilities of the SLP in the school setting and advises the new graduate regarding the interview process and beginning a career in the public schools.


2006 ◽  
Vol 5 (1) ◽  
pp. 119-119
Author(s):  
M MACDONALD ◽  
N HAWKINS ◽  
M SHAW ◽  
J MCMURRAY ◽  
H DARGIE ◽  
...  

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