New exact travelling wave solutions for some famous nonlinear partial differential equations using the improved tanh-function method

The improved tanh-function method is a powerful The improved tanh-function method is a powerful tool for obtaining exact travelling wave solutions. The method is used for constructing exact travelling wave solutions and new kinds of solutions for the modified dispersive water wave equation, the Abrahams–Tsuneto reaction diffusion system, and for a class of reaction diffusion models. The solutions obtained are different from those reported in the literature

EXACT AND APPROXIMATE SOLUTIONS OF THE TELEGRAPH MODEL OF DISPERSIVE VARIABILITY

Using the improved tanh function method, several types of exact solutions to the Telegraph model of dispersive variability are obtained. The Adomian decomposition method is used to solve the same model. The approximate solution is compared with one of the exact solutions. Moreover we analyze the absolute error with some values of the probability that an individual is a disperser and the time delay. It is easy to find exact and approximate solutions for the Julian Cook model and Fisher-Kolmogoroff model using special values of the time delay and the probability that an individual is a disperser

Adomian decomposition method for nonlinear reaction diffusion system of Lotka-Volterra type

In this paper the Adomian decomposition method is used to find an analytic approximate In this paper the Adomian decomposition method is used to find an analytic approximate solution for nonlinear reaction diffusion system of Lotka-Volterra type. The results obtained indicate that the method is efficient and accurate.

Inverted T-shape free gingival graft for treatment of RT3 gingival recession defects: Reporting of two cases

IntroductionOne of the most challenging aspects of treating gingival recession type 3 (RT3) is reconstructing lost interdental papillae, which is directly related to the loss of interproximal bone. Free gingival graft (FGG) has been successfully used to increase the keratinized tissue width (KTW) with minimal trauma to the interdental papilla. This presented case suggests that FGG can be used for reconstruction of lost initerdental papilla creeping attachment also plays an additional role in improving the results.Case PresentationThe included two case reports suggest a novel technique using an FGG that is shaped in an inverted T-shape to achieve partial root coverage, improve the compromised interdental papilla, and increase the KTW in RT3 defects.ConclusionsThis report presents a novel yet intuitive surgical technique for partial coverage of RT3 defects and reconstruction of the interdental papilla.SummaryThe inverted T-shape soft tissue graft may be a valuable technique for papillary reconstruction in the challenge of RT3 recessions.Key pointsWhy is this case new information?Reporting innovative technique with the interproximal extension of the FGG that sutured lingually with the lingual marginal gingiva.Improve interdental clinical attachment phenotype and height.More predictable root coverage because of increased vascularized interproximal bed for the graft to be survived.What are the keys to the successful management of this case?Having at least 2mm interproximal space for graft survival.Good Extension with proper fixation of the lingual part of the graft, and stabilization of the graft.What are the primary limitations to success in this case?limited capacity for perfusion and survival of the lingual extension due to limited vascularity.More investigations are necessary to confirm the validity of this technique.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/176055/1/cap10231.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/176055/2/cap10231_am.pd

Auto‐dentin platelet‐rich fibrin matrix is an alternative biomaterial for different augmentation procedures: A retrospective case series report

Abstract Objectives Autologous dentin grafts derived from extracted teeth have shown promise as bone graft materials for promoting bone regeneration. This retrospective case series aimed to evaluate clinical, radiographic, and histologic outcomes of using autologous dentin matrices in various bone regeneration procedures. Materials and Methods This case series included 26 eligible patients and encompassed 4 socket preservation cases, 5 cases of guided tissue regeneration, 5 cases of guided bone regeneration (GBR), 10 cases of sinus augmentation procedures, 2 immediate placement implants, and 2 socket shields. Dentin grafts were prepared from extracted teeth, cleaned, and processed. These grafts were combined with platelet‐rich fibrin (PRF) to create adhesive dentin matrices, then covered with collagen membranes for simultaneous guided bone augmentation cases. Cone beam computed tomography (CBCT) scans were conducted before surgery and 4 months postoperatively to assess ridge dimensions. Histologic evaluation was performed through bone core biopsies for socket preservation cases at the 4‐month mark. Results A total of 42 implants were placed in 26 patients, with an average follow‐up of 32 months. Notably, two implant failures occurred following lateral maxillary sinus augmentation. CBCT scans at the 4‐month interval revealed bone coverage over implant platforms in the majority of cases. Histologic analysis from two cases of socket preservation demonstrated dentin granules enveloped by newly formed bone undergoing continuous remodeling. The quantitative histomorphometric assessment revealed a bone area of 42.8 ± 3.56%, a remaining graft area of 19.05 ± 4.58%, and a viable bone of 38.15 ± 7.84%. Conclusions The utilization of autologous dentin particles mixed with PRF proved effective as an alternative to conventional bone graft materials in GBR and maxillary sinus augmentation procedures. Larger controlled clinical trials are recommended to further substantiate these findings

Bilateral Double Ureters with Bladder Neck Diverticulum in a Nigerian Woman Masquerading as an Obstetric Fistula

A 43-year-old woman presented with 20-year history of leakage of urine per vaginam. She had one failed repair attempt. Pelvic examination with dye test showed leakage of clear urine suggestive of ureterovaginal fistula. The preoperative intravenous urogram revealed duplex ureter and cystoscopy showed normally cited ureteric orifices with two other ectopic ureteric openings and bladder diverticula. The definitive surgery performed was ureteric reimplantation (ureteroneocystostomy) of the two distal ureteric to 2 cm superiolateral to the two normal orifices and diverticuloplasty. There was resolution of urinary incontinence after surgery. Three months after surgery, she had urodynamic testing done (cystometry), which showed 220 mLs with no signs of instability or leakage during filling phase but leaked on coughing at maximal bladder capacity. This is to showcase some diagnostic dilemma that could arise with obstetric fistula, which is generally diagnosed by clinical assessment