This paper shows the coordinates influence on singularity of a three degree-of-freedom structure, namely, three-Universal-Prismatic-Spherical (3-UPS) parallel manipulator. Rotational coordinates, which are chosen to define the orientation of the platform, affect the singularity of the manipulator. Euler parameters, which don't have any inherent geometrical singularity are utilized, however they...

We consider suspension hypersurface singularities of type g = f (x, y) + z n , where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for two pathological cases, which can be completely described. Even in the pathological cases, the link and the Milnor number of g determine uniquely the ...

In this thesis we study several problems of analysis on domains with external cusps. Mainly: the density of smooth functions on Sobolev spaces, the extension problem and Korn’s inequality. It is known that many classical analysis results on standard Sobolev spaces, which are necessary for the study of partial differential equations and for approximating their solutions using numerical methods, ...

The eight-point scheme is the simplest and fastest scheme for estimating the fundamental matrix (FM) from a number of noisy correspondences. As it ignores the fact that the FM must be singular, the resulting FM estimate is often inaccurate. Existing schemes that take the singularity constraint into consideration are several times slower and significantly more difficult to implement and understa...

We study the relation among the genus 0 Gromov-Witten theories of the three spaces X ← Z ← Y , where X = [C/Z3], Z is obtained by a weighted blowup at the stacky point of X , and Y is the crepant resolution of the A2 singularity. We formulate and verify a statement similar to the Crepant Resolution Conjecture of Bryan and Graber.

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black ...

Recall that in an earlier paper by one of the authors DonaldsonThomas type invariants were expressed as certain weighted Euler characteristics of the moduli space. The Euler characteristic is weighted by a certain canonical Z-valued constructible function on the moduli space. This constructible function associates to any point of the moduli space a certain invariant of the singularity of the sp...

In continuing joint work with Walter Neumann, we consider the relationship between three different points of view in describing a (germ of a) complex normal surface singularity. The explicit equations of a singularity allow one to talk about hypersurfaces, complete intersections, weighted homogeneity, Hilbert function, etc. The geometry of the singularity could involve analytic aspects of a goo...

singularity based on fractal and multifractal is a technique for detection of depletion and enrichment for geochemical exploration, while the index of vertical geochemical zonality (vz) of pb.zn/cu.ag is a practical method for exploration of blind porphyry copper mineralization. in this study, these methods are combined for recognition, delineation, and enrichment of vz in jebal- barez in the s...