The problem we are dealing with is the following: find two sequences an and bn such that the average of the first bn triangular numbers (starting with the triangular number 1) is still a triangular number, precisely the an-th triangular number. We get also some side results: for instance one of the sequence instrumental to finding the asked for sequences turns out to be a bisection of the seque...

we survey some recent results on cocharacters of upper triangular matrices. in particular, we deal both with ordinary and graded cocharacter sequence; we list the principal combinatorial results; we show di erent tech-niques in order to solve similar problems.

Biliary stent migration occurs in approximately 6% of patients, with the stent migrating proximally in half of cases [1, 2]. Endoscopic retrieval of the proximally migrated stent can be problematic; however, good success rates are achievable [3]. In February 2013, a 62-year-old man with known recurrent pneumonia presented with shortness of breath and a productive cough that had been present for...

In this paper, some elementary operations on triangular fuzzynumbers (TFNs) are defined. We also define some operations on triangularfuzzy matrices (TFMs) such as trace and triangular fuzzy determinant(TFD). Using elementary operations, some important properties of TFMs arepresented. The concept of adjoints on TFM is discussed and some of theirproperties are. Some special types of TFMs (e.g. pu...

Gartner’s cyst accounts for 11% of all vaginal cysts. It results from total or partial occlusion duct, the mesonephric duct remainder. is often located in anterior lateral wall vagina cervix to introitus, however it has exceptionally been described posterior location also.It typically small and asymptomatic occurs along walls vagina, following course duct. Rarely can be congenital., ,

Hepatobiliary ultrasound is the most common initial diagnostic modality in early detection of biliary atresia. It not gold standard, but hepatobiliary examination can be used to determine appropriate further management. Objective: To determined value as a predictor atresia cholestasis infants. Methods: This was an observational study with test validity cholangiography standard. The research sub...