In 1922, J. F. Ritt [13] proved two remarkable theorems on decompositions of polynomial maps of C[x] into irreducible polynomials (with respect to the composition ◦ of maps). Briefly, the first theorem states that in any two decompositions of a given polynomial function into irreducible polynomials the number of the irreducible polynomials and their degrees are the same (up to order). The secon...

aim: the aim of this study was to compare cusp deflection, infraction and fracture in teeth filled with three temporary filling materials. materials & method: forty five extracted human premolar teeth were chosen. after root canal therapy and mesio-occluso-distal cavity preparation, samples were randomly divided into three groups , each contained 15 teeth and filled with three temporary filling...

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has observed the northern magnetospheric cusp of Mercury regularly since the probe was inserted into orbit about the innermost planet in March 2011. Observations from the Fast Imaging Plasma Spectrometer (FIPS) made at altitudes< 400 km in the planet’s cusp have shown average proton densities (>10 cm ) that...

In this paper we investigate the statistical properties of magnetic field fluctuations measured by the four Cluster spacecraft in the cusp and close to the interface with the magnetospheric lobes, magnetopause and magnetosheath. At lower altitudes along the outbound orbit of 26 February 2001, the magnetic field fluctuations recorded by all four spacecraft are random and their Probability Distri...

OBJECTIVES Our purpose was to investigate a new approach to bicommissural repair of regurgitant aortic valves. BACKGROUND Repair of regurgitant aortic valves is not widely accepted, but interest is increasing, particularly for bicuspid valves. We hypothesize that a systematic, segmental approach to morphology and corresponding morphology-directed repair will improve decision making and succes...

1 Characteristic 0 We start with a basic question: given a polynomial f ∈ C[z1, · · · , zn] with a singularity at 0, how can we measure the “singularness” of this polynomial in a precise way? In other words: we can look at various singularities and see intuitively that some singularities are worse than others. For instance, it feels like a transverse self-intersection is probably not as bad as ...

Talon’s cusp is a properly delineated additional cusp which is said to arise due to evagination on the tooth surface even before the calcification has taken place. Hence it is also known as dens evaginatus. Fusion is a condition wherein the crowns of two separate teeth are seen to have joined togetherduring the time of crown development. The present article describes a case where in both the pr...