We introduce a natural topology on the space of left orderings of an arbitrary semi-group G. We prove that this space is always compact and that for free abelian groups it is homeomorphic to the Cantor set. We use our topological approach to provide a simple proof of the existence of universal Gröbner bases. 1. Orderings for semi-groups Given a semi-group G (ie. a set with an associative binary...

Ultrasound imaging of the heart is a non-invasive method widely used for different applications. One of them is to measure the blood volume in the left ventricle at different stages of the heart cycle. This demands a proper segmentation of the left ventricle and a (semi-) automated method would decrease intra-variability as well as workload. This paper presents a semi-automated segmentation met...

The establishment of a single validated endoscopic laryngeal grading system for assessing recurrent laryngeal neuropathy (RLN) is desirable to facilitate direct comparisons between the findings of different clinical and research groups worldwide. The objective of this study was to assess the relationship between the Havemeyer endoscopic laryngeal grading system and histopathological changes con...

In this work, the interaction between the semi-circular space and the neighboring joint with and without the presence of rock bolts was investigated using the particle flow code (PFC) approach. For this purpose, firstly, the calibration of PFC was performed using both the Brazilian experimental test and the uniaxial compression test. Secondly, a numerical model with the dimension of 100 m...

For a complete, i.e., connuent and terminating term rewriting system (TRS) it is well-known that simpliication (also called interreduction) into an equivalent canonical, i.e., complete and interreduced TRS is easily possible. This can be achieved by rst normalizing all right-hand sides of the TRS and then deleting all rules with a reducible left-hand side. Here we investigate the logical and op...

We introduce the notions of one-sided dirings, 3-irreducible left modules, 3-primitive left dirings, 3-semi-primitive left dirings, 3-primitive ideals and 3-radicals. The main results consists of two parts. The first part establishes two external characterizations of a 3-semi-primitive left diring. The second part characterizes the 3-radical of a left diring by using 3-primitive ideals. By forg...

We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under C perturbation. In particular, we extend well known finite-dimensional results to the setting of an infinite-dimensional Hilbert manifold with a semi-group that leaves a submanifold invariant. We...

A generalized Itô formula for time dependent functions of two-dimensional continuous semi-martingales is proved. The formula uses the local time of each coordinate process of the semi-martingale, left space and time first derivatives and second derivative ∇1 ∇ − 2 f only which are assumed to be of locally bounded variation in certain variables, and stochastic Lebesgue-Stieltjes integrals of two...