The main goal of this article is to extend the concept of special matrix functions through the study of modified degenerate Gamma matrix function. For this, the modified degenerate Gamma matrix function has been introduced and some of its properties have been established. The article also presents limit representations, asymptotic equality, and infinite product representations. The new function of matrix argument is an analogue of the Gamma matrix function, and the properties are analogues of those satisfied by the Gamma matrix function. Upon taking the limit as $\lambda \to 0^{+}$, the established results reduce to the results of the Gamma matrix function.

This research presents a numerical tool to estimate the Green's function operator matrix of intraplate faults. Having this matrix and its inverse, spatial distribution of fault slippage could be investigated through the inverse analysis of geodetic data. This information could be employed to predict the location of future powerful earthquakes. To implement fault sliding in FE calculations, Soft Material Technique as a simple method is applied. In this technique, the fault is modeled by a flexible (very low elasticity modulus) thin element. This material not only prevents fault planes overlapping, but exhibits a good consistency with the physical behavior of fault. In other words, this material ignores the strength of neighboring rocks ready to trigger sliding. In this research, without involving the nonlinear contact problem, two sides of the fault are dislocated as one unit, and the ground surface deformation is measured.Available geodetic data provides a proper opportunity to detect underground interactions. We can express observation equations with m observation data as:Bi=åj Aij Xj + Ei (i=1, …, m)                                                                                                             (1)where Bi are the observed surface deformations, Xj the slippage components along the fault, Ei the random errors, and Aij Green’s function operators (i.e., the elastic response at a point i to a unit source at a point j on the model source region). This equation can be rewritten in a matrix form as:B = AX + E                                                                                                                                      (2)where A is an m×n coefficient matrix.To minimize the errors, the length of the vector E has to be minimized. It may be shown that, standard inversion equations based on the least-square method are obtained as:   X=(ATA)-1ATB                                                                                                                                (3)where superscripts T and -1 indicate the transpose and inverse of a matrix, respectively.This relation offers a straightforward way for finding the source vector X. One of the new aspects of the present study is the calculation of the Green’s function operator matrix A by means of FEM. This issue enables us to overcome all limitations of traditional inverse methods.How can the Green’s function operators be found by FEM? By applying unit source vectors in each degree of freedom, the relevant response of ground surface nodes is the corresponding component of the coefficient matrix A.The proposed numerical model is first compared by available analytical approaches, and gains its proper validity, one of the Tehran faults is modeled by this method to calculate the corresponding Green's function operator matrix.

Background & aim: Considering that overweight and obesity in transplant patients are considered as a risk factor for the occurrence of metabolic disorders, heart diseases and reduced kidney function, therefore, the purpose of the present study was to determine and investigate the relationship between anthropometric indicators and kidney function. In addition, the serum levels of fibroblast growth factor-23 and matrix Gamma carboxyglutamate protein were markers of cardiovascular disease risk in kidney transplant patients. Methods: The present study was conducted as a cross-sectional study in 2016-2019. Ninety kidney transplant patients referred to Tabriz Imam Reza (AS) hospital clinic, between 18 and 70 years of age and had normal kidney function and were within 6-12 months after transplant, were selected. Weight, height, waist circumference, body mass index and ratio of waist circumference to height were measured. Serum levels of fibroblast growth factor-23 and dephosphorylated and noncarboxylated protein matrix Gamma carboxyglutamate were measured and glomerular filtration rate was calculated as an index of kidney function. Collected data were analyzed using KolmogorovSmirnov, Pearson and Spearman statistical tests. Results: The mean and standard deviation of the age of the subjects was 44. 10±, 13. 05 years and 59% of the patients were male. Mean ±,standard deviation of weight, body mass index, waist circumference and ratio of waist circumference to height of the patients were 69. 61±, 11. 59 kg, 25. 77±, 4. 42 kg/m2, 94. 07±, 15. 48 cm and respectively. It was 0. 58±, 0. 11. The prevalence of overweight and obesity based on body mass index was 38% and 17%, respectively. The mean ±,standard deviation of the glomerular filtration rate is 57. 45±, 12. 61 ml/min per 1. 73 square meter and the serum level of fibroblast growth factor-23 is 73. 63±, 20. 9 units/ml and the median (25th percentile) and the 75th percentile) the dephosphorylated and non-carboxylated protein Gamma carboxy glutamate matrix of serum was also (1. 3, 60. 20) 2. 40 micrograms/liter. Significant correlation between anthropometric indices with glomerular filtration rate and serum levels of fibroblast growth factor-23 and matrix Gamma carboxy glutamate dephosphorylated and non-carboxylated protein, as well as between glomerular filtration rate and serum levels of fibroblast growth factor-23 and matrix Gamma carboxy glutamate dephosphorylated protein and Non-carboxylated was not observed (p>0. 05). A significant inverse correlation was observed between serum levels of fibroblast growth factor-23 and dephosphorylated and non-carboxylated protein Gamma-carboxyglutamate matrix (p=0. 036). Conclusion: Considering that in the present study, the average weight, body mass index and also the performance of all patients were almost within the normal range, therefore, there is a significant relationship between anthropometric indices with glomerular filtration rate and serum levels of fibroblast growth factor-23 and Gamma carboxy matrix. Dephosphorylated and non-carboxylated protein glutamate was not observed.

Background: Gamma irradiation has been widely used for secondary sterilization of bone allograft before clinical use to reduce the risk of infection and associated complications. The current study evaluated the effect of Gamma irradiation sterilization on the osteoinductive capability of human demineralized bone matrix using a rat model.Methods: Eighteen euthymic rats received two separate implants consisting of 30 mg sterile-harvest demineralized bone matrix and 30 mg Gamma irradiation-sterilized demineralized bone matrix. The demineralized bone matrix from each group was placed into two separate muscle pouches created in the paravertebral muscles of each rat. All 18 rats were euthanized after 4 weeks and each implantation site was removed with 0.5 cm normal tissue around the implant. Histological examination was performed to determine the presence or absence of new bone, cartilage and bone marrow elements.Findings: All except one of 18 (94.4%) sterile-harvest demineralized bone matrix sites histologically contained new bone elements and five of 18 (27.7%) ethylene oxide sterilized demineralized bone matrix sites showed evidence of new bone elements, which was statistically significant (p<0.05).Conclusion: The results of this study indicate that demineralized bone matrix sterilized with Gamma irradiation loses its osteoinductive capacity in a manner similar to that of steamsterilized demineralized bone matrix, making it unsuitable as a method of secondary sterilization of demineralized bone matrix.

Let Xi1, …, Xini be a random sample from a Gamma distribution with known shape parameter ni>0 and unknown scale parameter bi>0, i= 1, 2, satisfying 0< b1 £ b2. We consider the class of mixed estimators for estimation of b1 and b2 under reflected Gamma loss function. It has been shown that the minimum risk equivariant estimator of bi, i= 1, 2, which is admissible when no information on the ordering of parameters are given, is inadmissible and dominated by a class of mixed estimators when it is known that the parameters are ordered. Also, the inadmissible estimators in the class of mixed estimators are derived. Finally the results are extended to some subclass of exponential family.