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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.

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In this paper, a new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric Mean of two Hermitian positive de nite matrices is constructed. Moreover, another e cient algorithm for this purpose is derived free from the computation of principal matrix square root. Finally, some tests are given to show their applicabilities.

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.

Let p ³ 1 and ( Wn) n w be a sequence with non-negative entries. If (tn,k) ³0, denote by ||T||p,x the infimum of those U satisfying the following inequality:(S¥n=1wn(S¥k=1 tn,k ak)p)1/p £U (S¥k=1 WKAPK)1/P ,whenever ( an) ∈lp (w ) n p a ∈l w . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,¥). We considered this problem for certain matrix operators such as Norlund, Weighted Mean, Ceasaro and Copson matrices. This problem is considered by some authors like Bennett, Jamson and the first author on sequence spaces lp and weighted sequence spaces for some kind of matrix operators. Also, this study is an extension of paper by Chang-Pao Chen, Dah-Chin Luor and Zong-Yin Ou.

In a systematic review and meta-analysis Published in the Urology entitled “ Low-Intensity Extracorporeal Shock Wave Therapy for Erectile Dysfunction: a Systematic Review and Meta-Analysis” by Libo and Guizhong (1) in 2017, the authors in methods section state that “ weighted Mean difference (MD) was used for continuous variables in their meta-analysis” . While, the authors used the endpoint scores as the Mean difference in each group regardless of the baseline scores and one study that baseline used as Mean difference Based on statistical literature in meta-analysis, the “ Mean difference” is change average from baseline to endpoint. So, to calculate the Mean difference, we should use endpoint minus baseline Mean score (2) (3). In our understanding, , it seems that the result of Libo’ s meta-analysis (1) should revise for the Mean difference as mentioned above...

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.