On Factorization of a Special type of Vandermonde Rhotrix

Vandermonde matrices have important role in many branches of applied mathematics such as combinatorics, coding theory and cryptography. Some authors discuss Vandermonde rhotrices in the literature for its mathematical enrichment. Here, we introduce a special type of Vandermonde rhotrix and obtain its LR factorization, namely left and right triangular factorization which is further used to obtain the inverse of the rhotrix

On factorization of a special type of vandermonde rhotrix

Vandermonde matrices have important role in many branches of applied mathematics such as combinatorics, coding theory and cryptography. Some authors discuss the Vandermonde rhotrices in the literature for its mathematical enrichment. Here, we introduce a special type of Vandermonde rhotrix and obtain its LR factorization namely left and right triangular factorization, which is further used to obtain the inverse of the rhotrix

On Circulant-Like Rhotrices over Finite Fields

Circulant matrices over finite fields are widely used in cryptographic hash functions, Lattice based cryptographic functions and Advanced Encryption Standard (AES). Maximum distance separable codes over finite field GF2 have vital a role for error control in both digital communication and storage systems whereas maximum distance separable matrices over finite field GF2 are used in block ciphers due to their properties of diffusion. Rhotrices are represented in the form of coupled matrices. In the present paper, we discuss the circulant- like rhotrices and then construct the maximum distance separable rhotrices over finite fields

Comparative evaluation of coronally advanced flap using amniotic membrane and platelet-rich fibrin membrane in gingival recession: An 18-month clinical study

Background: An amnion membrane is a placenta-derived tissue that consists of numerous growth factors, proteins, and stem cell reserves which help in accelerated wound healing and regeneration. Platelet-rich fibrin (PRF) also releases growth factors after activation from the platelets and gets trapped within fibrin matrix which has been shown to stimulate the mitogenic response in the periosteum for bone repair and regeneration during normal wound healing. This preliminary, controlled, randomized clinical trial with an 18-month follow-up was aimed to evaluate the effectiveness of coronally advanced flap (CAF) with either PRF membrane or bioresorbable amniotic membrane (AM) in treatment of localized gingival recession defects. Materials and Methods: Sixteen healthy adult patients presenting with Miller Class I recession defects were treated surgically with CAF along with AM (Group I) or PRF (Group II) for coverage of the recession defects. For all patients, plaque index, gingival index, bleeding on probing, clinical attachment level, depth of recession, width of recession, width of attached gingiva, and gingival thickness were evaluated at 6 months and 18 months postoperatively. Statistical analysis was done using paired t-test, repeated measure analysis of variance test, Bonferroni test for intragroup comparison and unpaired t-test for intergroup comparison. Results: The results showed statistically nonsignificant (P < 0.01) difference in all clinical parameters at the 6- and 18-month follow-ups in both groups. Gingival recession in both PRF and amnion group when evaluated individually, significantly reduced from baseline to 6 months (P = 0.000) and from baseline to 18 months (P = 0.000). However, the mean value from 6 months to 18 months was statistically nonsignificant. Conclusion: The present study demonstrated that both CAF + PRF and CAF + AM are equally effective in providing clinically significant outcomes with respect to root coverage with AM showing the better percentage of root coverage as compared to PRF

Clinical comparison of placental membrane versus platelet-rich fibrin membrane for treatment of gingival recession: A 2-year follow-up case report

An amnion membrane is a placenta-derived tissue that has been introduced recently as a guided tissue regeneration membrane in dentistry. Numerous growth factors, proteins, and stem cell reserves in amnion could help in accelerated wound healing and regeneration. In addition, growth factors released after activation from the platelets in platelet-rich fibrin (PRF) gets trapped within fibrin matrix and also been shown to stimulate the mitogenic response in the periosteum for bone repair during normal wound healing. In this case report, a healthy 22-year-old male patient with bilateral Miller's Class I recession defects affecting canine were treated surgically with coronally advanced flap (CAF) along with amniotic membrane (AM) or PRF in a split-mouth design for coverage of the recession. Follow-up was done at baseline, 3 months, 6 months, and 18 months to evaluate the effectiveness of CAF with either PRF membrane or bioresorbable AM in the treatment of localized Miller's Class I gingival recession defects. This case report demonstrated that CAF + PRF and CAF + AM are equally effective in providing clinically significant outcomes in respect to root coverage with AM showing the better percentage of root coverage as compared to PRF. Thus, both the treatment modalities can be used for the coverage of gingival recession depending on the choice of clinician