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 this study, structural and electronic properties of GanNn clusters (n=1-10) are investigated using formalism of density functional theory (DFT) and projector augmented plane waves (PAW) within VASP software package. Results of calculations show that more tendency of N atoms in more stable structures of small clusters is the formation of building blocks N2 and AWT IMAGE azid, whereas the 3D structures are revealed as cage-like shape with Ga-N bonds. A sharp increase in binding energy per atom from n=1 to n=2 is due to structure transition from 1D to 2D and increase of overlapping between N and Ga orbitals in order to obtain more stability. These changes for clusters with n>3 follow approximately a linear trend. Charge density contour shows an ionic bond with partial covalent character for Ga-N. Also, the lowest energy levels devote to N-s orbitals, middle levels to a hybridized case of Ga-s and N-p orbitals and levels close to Fermi level to a hybridized case of Ga-p and N-p orbitals.

In this research, structural and electronic properties of ZnCdn-1Ten clusters (n=1-10) have been studied by formalism of density functional theory and using the projector augmented wave within local density approximation. The structural properties (such as bond length/angle and coordination number), electronic and optical properties (such as binding energy, Kohn-Sham spectrum and partial charge density, absorption spectrum) of ZnCdTe clusters were investigated and compared to these of CdTe clusters. A transition from Two-dimensional (2D) to Three-dimensional (3D) structures is observed from n=5®n=6. Results obtained for the most stable geometrics of the ZnCdTe clusters show that a Zn atom increases binding energy and consequently stability of CdTe clusters. It also decreases (increases) bond lengths (angles) for it’s nearest neighbor atoms. An analysis of partial charge density and eigenvalue spectrum for ZnCdn-1Ten clusters reveals that there are Te- s and Cd- d hybridizations for low energy levels.

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.

In this research, first in a sample aza-Michael addition reaction, the catalytic activity of some protic ionic liquids was investigated. The results show that 4-(N, N-dimethylamino)pyridinium acetate had a superior catalytic activity. Then, Michael's addition reaction of different amines with Michael acceptors including n-butyl acrylate, acrylonitrile, and methyl vinyl ketone in the presence of 4-(N, N-dimethylamino)pyridinium acetate under solvent-free conditions at 100 º C was studied. The reaction of aromatic and aliphatic primary amines with n-butyl acrylate and acrylonitrile was successful and only mono N-alkylated product was obtained. The reaction of morpholine as a secondary aliphatic amine with three Michael acceptors including n-butyl acrylate, acrylonitrile, and methyl vinyl ketone was accomplished very fast.

A simple, rapid, and efficient procedure for formylation of primary and secondary amines and alcohols using ethyl formate catalyzed with poly(N,N'-dichloro-N-ethyl-benzene-1,3-disulfonamide (PCBS), N,N,N',N'-tetrachlorobenzene-1,3-disulfonamide (TCBDA), poly(N,N'-dibromo-N-ethyl-benzene-1,3-disulfonamide (PBBS) and also N,N,N',N'-tetrabromobenzene-1,3- disulfonamide (TBBDA) was adopted. The reactions were performed under microwave irradiation with high yields.