In this paper, we study hypersurfaces of the homogeneous nearly Kähler manifold S 3 ×S 3 with typical properties. We first show that in the NK S 3 ×S 3 there exist neither totally umbilical ...hypersurfaces nor hypersurfaces of parallel second fundamental form. Then we investigate hypersurfaces of S 3 ×S 3 such that its shape operator A and induced almost contact structure satisfy the condition A = A, and as the main result, a complete classification of this remarkable family of hypersurfaces in S 3 ×S 3 is presented.
In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, Čech and witness complexes) built on top of totally bounded metric spaces. ...Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and Čech complexes built on top of compact spaces.
This volume contains the proceedings of the 13th $\mathrm{AGC^2T}$ conference, held March 14-18, 2011, in Marseille, France, together with the proceedings of the 2011 Geocrypt conference, held June ...19-24, 2011, in Bastia, France. The original research articles contained in this volume cover various topics ranging from algebraic number theory to Diophantine geometry, curves and abelian varieties over finite fields and applications to codes, boolean functions or cryptography. The international conference $\mathrm{AGC^2T}$, which is held every two years in Marseille, France, has been a major event in the area of applied arithmetic geometry for more than 25 years.
The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation ...between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.
This volume contains the proceedings of the 17th Workshop and International Conference on Representations of Algebras (ICRA 2016), held from August 10-19, 2016, at Syracuse University, Syracuse, NY. ...Included are three survey articles based on short courses in the areas of commutative algebraic groups, modular group representation theory, and thick tensor ideals of bounded derived categories. Other articles represent contributions to areas in and related to representation theory, such as noncommutative resolutions, twisted commutative algebras, and upper cluster algebras.
This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28-March 5, 2010 in Banff, Ontario, Canada. This volume ...contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale's 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed.
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