Using a tight closure argument in characteristic p and then lifting the argument to characteristic zero with aid of ultraproducts, I present an elementary proof of the Briançon-Skoda Theorem: for an m-generated ideal a of C[[X1, . . . ,Xn]], the m-th power of its integral closure is contained in a. It is well-known that as a corollary, one gets a solution to the following classical problem. Let...

The paper reviews the potential of the ultrasonic small incidence method of testing, which enables us to characterize smaller tight cracks quantitatively under load-free conditions. Recently, an important characteristic of the method of being capable of evaluating the cracks from both the accessible and inaccessible sides of material structures with almost similar level of sensitivity, has been...

A case is presented of a male patient that presented with intestinal obstruction in the early postoperative period of a transabdominal preperitoneal inguinal repair (TAPP) that was diagnosed and repaired successfully using laparoscopy. Whenever a total extraperitoneal procedure (TEP) cannot be performed, the peritoneal closure of the TAPP should be done water-tight using interrupted stitches of...

The obstruction of the superior vena cava (SVC) of acute onset nature following surgery is a rare and serious condition. The tight closure of the pericardium over the heart during surgical procedures may cause external compression on the SVC. Echocardiography and Computed tomography (CT) scan aids in the diagnosis. Cutting open the pericardial stitches relieves the condition.

In [HH7], developing arguments in [HH5], Hochster and Huneke used classical tight closure techniques to prove a fine behavior of symbolic powers of ideals in regular rings. In this paper, we use generalized test ideals, which are a characteristic p analogue of multiplier ideals, to give a generalization of Hochster-Huneke's results.

We give a canonical construction of a balanced big Cohen-Macaulay algebra for a domain of finite type over C by taking ultraproducts of absolute integral closures in positive characteristic. This yields a new tight closure characterization of rational singularities in characteristic zero.

We construct normal hypersurfaces whose local cohomology modules have infinitely many associated primes. These include hypersurfaces of characteristic zero with rational singularities, as well as F-regular hypersurfaces of positive characteristic. As a consequence, we answer a question on the associated primes of certain families of ideals which arose from the localization problem in tight clos...

the emergent abdominal surgeries from either of traumatic or non traumatic causes can result in situations in which the abdominal wall cannot initially be closed. many techniques have been reported for temporary coverage of the exposed viscera, but the result of various techniques remains unclear. during 94 months, 19 critically ill patients whit an open abdomen underwent surgery using plastic ...

We prove that many of the results log minimal model program hold for threefolds over fields characteristic p > 5 $p>5$ which are not necessarily perfect. This includes existence flips, cone theorem, contraction theorem birational extremal rays and models. As well as pertaining to geometry fibrations relative dimension 3 algebraically closed fields, they have applications tight closure in 4.