We have two goals in this paper. First, we investigate and construct cofree coalgebras over n-representations of quivers, limits and colimits of n-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of n-representations of quivers. Second, for any given quivers Q1, Q2, . . ., Qn, we construct a new quiver Q(Q1, Q2, . . ., Qn), called an nquiver, and identify each category Repk(Qj) of representations of a quiver Qj as a full subcategory of the category Repk(Q(Q1, Q2, . . ., Qn) ) of representations of Q(Q1, Q2, . . ., Qn) for every j 2 {1, 2, . . ., n}.

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In special purpose circuits, the amount of energy consumed and the speed of operation are the main challenges. There are wide researches and methods to improve the performance of these types of circuits. One of these methods is to use a Residue Number System (RNS). In the RNS, there are a number of modules (channels) as a set to represent the number and perform parallel arithmetic operations. The most famous set is the 3-modlui set {2n-1, 2n, 2n +1}. The form of modules to the power of 2 makes it easier to perform binary computational operations. To use this system, you need to perform conversion operations from binary to residue (forward conversion) and residue to binary (reverse conversion). The greater the number of modules (channels) in the set, the higher the degree of parallelism of computational operations. In contrast, more complex forward and reverse conversion circuits are required. The overhead of conversion computing can reduce the efficiency of using this system, unless the number of consecutive operations is large enough to cover the conversion overhead time. In this paper, based on 3-moduli set {2n-1, 2n, 2n +1} evaluation, it was determined that for how many consecutive addition or multiplication operations, the use of RNS operations leads to greater speed. In this paper, we evaluate the carry propagation adder as the most popular adder and parallel prefix adder as the high speed adder. Also, the parallel block multiplier circuit was used to evaluate the multiplication operations. First, modular adder/multiplier, binary, and forward and reverse conversion circuits were implemented and synthesized. We used Synopsys Design Compiler, K-2015. 06 version and 45nm technology. The results show that if the carry propagation adder is used, in modules with a width of more than 8 bits (n≥8), if the number of consecutive operations is at least 4, it will speed up the calculations. Likewise, in the multiplication operation and parallel prefix addition, the number of sequences is reduced to two.

In this paper, we introduce the gn- complete hyper group and gn*-complete hyper group. The hyper group H is called gn - complete hyper group if for every sÎ Sn (z1,z2,….zn ) Î Hn we have Pni=1 Zs(i)= g (Pni=1 zi ) we prove that if H is a gn -complete hyper group then g*=gn. If H is a g2 complete hyper group then H is a complete hyper group and we have gn=g , gn*¹ gn*-1 finally we prove that H is a gn*- complete hyper group if and only if it is an Abelian group.

Effects of deferent concentrations of N, P and K on micropropagation of jojoba were investigated. The apical and lateral buds of jojoba were aseptically grown on Ms medium for 30 days under controlled environment., conditious in 18 hours day length and 25°C temperature. Then, they were transferred to the treatment media and left in the mentioned controlled environment 30 and 45 days after transplanting. Shoot numbers, bud numbers, chlorophyll content of leaves. Fresh and dry weights of plants were determined. 30 days after transplanting, the highest relative growth rate was observed in plants that were grown on media containing concentrations of 0.8A N and P, LOA and 1.2A, K compared to MS medium (as 1.0). 45 days after transplanting, the highest relative growth rate was observed in plants grown on media containing concentrations of 0.6 A, N and 1.2 for K and P compared to MS medium. Data were analyzed with MSTAT-C computer program and the means of growth parameters were compared with the least significant difference (LSD) test at the 5% level.