In this paper, by conditioning on the Matrix variate Normal distribution (MVND) the construction of the Matrix t-type family is considered, thus providing a new perspective of this family. Some important statistical characteristics are given. The presented t-type family is an extension to the work of Dickey [8]. A Bayes estimator for the column covariance Matrix S of MVND is derived under Kullback Leibler divergence loss (KLDL). Further an application of the proposed result is given in the Bayesian context of the multivariate linear model. It is illustrated that the Bayes estimators of coefficient Matrix under both SEL and KLDL are identical.

Let A be any n-by-n Normal Matrix and let k>0 are an integer. By using the concept of the joint numerical range W (A, A2…, Ak), an analytic description of Vk (A) for Normal matrices will be presented. Additionally, new proof for Theorem 2.2 of Davis, Li and Salemi [Linear Algebra Appl., 428 (2008), pp. 137-153] is given.

Suppose that the random Matrix X has a Matrix variate Normal distribution with the mean Matrix Θ and covariance Matrix Σ⊗Ψ where Σ and Ψ are known positive definite covariance matrices. This paper studies the soft Bayesian shrinkage wavelet estimation of the mean Matrix Θ . Soft Bayesian shrinkage wavelet estimator is proposed based on quadratic balanced loss function and Matrix variate Normal $N_{p,m}(\mathbf{0}, \mathbf{\Lambda}\otimes \mathbf{\Psi})$ prior distribution. Λ is known positive definite covariance Matrix. By using the Bayes estimator as the target estimator in the quadratic balanced loss function and Stien's unbiased risk estimate technique, the soft Bayesian shrinkage wavelet threshold is obtained. Based on the new proposed threshold, we find the soft Bayesian shrinkage wavelet estimator of Θ mean Matrix. The simulation study and two real examples to measure the performance of the presented theoretical topics are used. The results show that the soft Bayesian shrinkage wavelet estimator dominates classical shrinkage wavelet estimators.

This article explores the adjacency Matrix of a two-sided group graph andits properties. We introduce the two-sided color group digraph to generalize the Cayley color graph and the two-sided group digraph. We alsoobtain the adjacency Matrix of the latter digraph and provide a criterion fordetermining the Normality of the adjacency Matrix of a two-sided group graph.Moreover, we prove that if all the two-sided group digraphs of valency two fora certain group G are Normal, then G is a Hamiltonian group. We also showthat if a strongly connected two-sided group digraph of valency two is Normal,the corresponding group is isomorphic to the product of two groups: a cyclicgroup with either Tk,n or Hp,q, or an abelian group.

The aim of the present study was the histological evaluation of Enamel Matrix Derivative (EMD) effectiveness for regeneration of periodontal defects. EMD activates cementum synthesis, PDL and bone during the maturation stage of follicole. In this research, EMD was used in surgical defects of premolar teeth in four adult sheep. Muccoperiosteal flap was reflected in buccal site of teeth. The buccal bone plate was removed from mesial to distal in 4 mm depth. After eliminating the cementum by bur and its etching, EMD was applied on exposed dentine and flap was sutured. In opposite sites of those teeth (control sites) the same process was performed without etching. After 100 days, sheep were sacrificed and histological study through light microscopic was performed on black sections of operation sites. The results showed that in test sites, regeneration of cementum and bone was 62/5% and 42/5-50% respectively. But in control sites regeneration of cementum and bone was 37.5% and 32/5-42/5% respectively. Also the migration of junctional epithelium in control sites was 8-10% more than test sites. The important point is that in test sites, cementum was completely attached to undermining dentine. But, in control sites, the gap between cementum and dentine was visible. As a result, this study suggests that EMD promotes periodontal regeneration, and EMD application is a successful achievement in regenerative periodontal therapy.

Different ossificant materials have been used used for induction of bone repair in many studies, and bone Matrix gelatin which contains bone morphogenic proteins one of the best ones.In present study we evaluated the role of this mat erial in acceleration of bone repair in rabbit tibia.A hole of 305mm diameter was made on right tibia of 10 and 12 rabbits as study and control group respectively, In the experiment group, in addittion to Bone Wax, we applied bone Matrix glatin in the hole. Radiographic images were taken in days 0, 20, 40 and 53 after operation In 6 rabbits of each group, photographic pictures were also taken after exposure of entire bone. In 6 controls less degree of restoration were seen on day 53. In 4 experimental animals restoration were completed by this time and in 2 speciments repair processing were better then controls. This results shows that bone Matrix gelatin can be used as an acclerator of bone repair.