Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic

Let $I$ be a homogeneous Artinian ideal in a polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic 0. We study an equivalent condition for the generic initial ideal \gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fr\"{o}berg conjecture. And for the case \Codim I \le 3, we show that $R/I$ has the strong Lefschetz property if and only if \gin(I) is almost reverse lexicographic. Finally for a monomial complete intersection Artinian ideal $I=(x_1^{d_1},...,x_n^{d_n})$, we prove that \gin(I) is almost reverse lexicographic if $d_i > \sum_{j=1}^{i-1} d_j - i + 1$ for each $i \ge 4$. Using this, we give a positive partial answer to Moreno-Socias conjecture, and to Fr\"{o}berg conjecture.Comment: 10 page

Damped Euler system with attractive Riesz interaction forces

We consider the barotropic Euler equations with pairwise attractive Riesz interactions and linear velocity damping in the periodic domain. We establish the global-in-time well-posedness theory for the system near an equilibrium state. We also analyze the large-time behavior of solutions showing the exponential rate of convergence toward the equilibrium state as time goes to infinity.Comment: 24 page

Synchronous double primary malignant tumor of the gallbladder and liver: a case report

We report a case of synchronous double primary tumor of gallbladder and liver. A 63-year-old male was admitted to the hospital complaining of abdominal discomfort. Enhanced computed tomography of the abdomen showed acute cholecystitis with tiny gallbladder stones and a 2.2 cm size enhanced nodule in the left lobe of the liver. Under the impression of acute cholecystitis with gall bladder stones and hepatocellular carcinoma of the left Liver, the patient underwent a laparotomy. At laparotomy, a mass was palpated on the surface of the neck portion of the gall bladder. Intraoperative frozen diagnosis revealed adenocarcinoma of the gall bladder. The patient was diagnosed as having gall bladder cancer and hepatocellular carcinoma, so extended cholecystectomy with dissection of regional lymph nodes and left hemihepatectomy were performed. Histological examination revealed moderated differentiated adenocarcinoma of gallbladder and hepatocellular carcinoma of liver. To our knowledge, the simultaneous occurrence of primary malignant tumor of the gallbladder and liver has never been published before. The patient is doing well with no evidence of recurrence 17 months after surgery

Results of immediate loading for implant restoration in partially edentulous patients: a 6-month preliminary prospective study using SinusQuick™ EB implant system

STATEMENT OF PROBLEM. Many dental clinicians are concerned about immediate loading of inserted implants. However, there have been few clinical studies surveying the success rates of immediate loading, based on Korean implant systems. PURPOSE. The aim of this study was to evaluate the outcome of immediate functional loading of the implant (SinusQuickTM EB, Neobiotech Co., Seoul, Korea) in partially edentulous maxilla or mandible. MATERIAL AND METHODS. Total 15 implants were placed. Within 2 weeks after implant insertion, provisional implant-supported fixed partial dentures were delivered to the patients. Quantitatively, marginal bone loss was measured at the time of immediate loading, after 3-months of continued loading and at the last follow-up. The mean follow-up period was 4.8 months. RESULTS. Mean marginal bone loss from implant surgery to early loading, 3-months follow-up and last follow-up was 0.03 ± 0.07 mm, 0.16 ± 0.17 mm and 0.29 ± 0.19 mm. No implant failed up to 6 months after insertion, resulting in a 100% survival rate. CONCLUSION. Immediate loading exhibited high success rate in partial edentulism for up to 6 months. Well-controlled long term clinical studies with large sample size are necessary to confirm this finding