8221. Application Groupoids in the algebra
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Ebrahim Nazari, Omid Rashtizadeh, Hasan Rahimi, Hamid Reza Rostami, Solaiman Nosratipour, Afshar Havasi and Gholamreza Sharifi |
Abstract |
Pdf
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Category : Mathematical Sciences | Sub Category : Applied Mathematics |
Application Groupoids in the algebra
A groupoid is medial if it satis_es the identity wx • yz = wy • xz. A groupoid is trimedial if every subgroupoid generated by 3 elements is medial. Medial groupoids and quasigroups have also been called abelian, entropic, and other names, while trimedial quasigroups have also been called triabelian, terentropic, etc. (See [5], especially p. 120, for further background). The notion of variety of algebras having the property (k, n) was given in [6] and equationally defined classes of cancellative groupoids having the property (2, 4) and (2, 5) were considered there. This notion was qeneralized in [7], where it was shown that the condition of the cancellativity is superfluous, that is, any variety of groupoids with the property (2, n) is a variety of quasigroups. Let k and n be two positive integers and k n. An algebra A is said to have the property (k, n) if every subalgebra of A generated by k distinct elements has exactly n elements. We also say that A is a (k, n)-algebra. A class K of algebras is said to be a (k, n)-class if every algebra in K is a (k, n)-algebra. A variety is called a (k, n)-variety if it is a (k, n)-class of algebras. Trivially, the variety of Steiner quasigroups (xx = x, xy = yx, x•xy = y) is a (2, 3)-variety. It is the unique variety of groupoids with the stated property, and the same holds for the (2, 4)-variety (x•xy = yx, xy•yx = x) given by Padmanabhan in [6]. He has also constructed two (2, 5)-varieties. One of them is commutative (xy = yx, x(y•xy) = y, x(x•xy) = y•xy), while the other one (x•xy = y, xy•y = yx) consists of anticommutative quasigroups. It is an verify the existence of (2, n)-varieties for n?10
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Application specific NOC: power optimization by custom topology generation using network partitioning approach
In Networks-On-Chips, (NOC) global interconnection links and routers are the main sources of the power Consumption. In Application Specific NOC (ASNOC) power can be minimized by mapping the Processing Element (PE) on the custom topology rather than mapping on the standard topologies. In ASNOC, the design of the topology plays an important role in minimizing the power consumption. In this paper, we propose a custom topology generation algorithm using network partitioning, to reduce the power of the global interconnection links that connects the router to router. The proposed method is validated through a case study for benchmark video applications MPEG 4 decoder and PIP. The experimental case study shows 26.8% and 37.5% of power saving for the applications MPEG 4 decoder and PIP respectively compared to the existing algorithm. We also achieve 11.76% and 9 % of reduction in average number of hops for MPEG 4 decoder and PIP respectively.
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Oral habits are very common and one of the most deleterious habits which pose a problem to pediatric dentists. Oral appliances, if inserted for several months, usually eliminate the habit, however, emotional problems, difficulty with speech and hearing, and self inflicted wounds can occur with such appliances. We present a case of 8 year old girl with thumb sucking habit, successfully managed by a non punitive bluegrass appliance.
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Comparison between Artificial Neural Networks and Khazaei Mathematical model for Moisture Content Prediction in Three Varieties of Bean
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