Search results for " Geometry"

Non-wandering sets with non-empty interiors

2003

We study diffeomorphisms of a closed connected manifold whose non-wandering set has a non-empty interior and conjecture that C1-generic diffeomorphisms whose non-wandering set has a non-empty interior are transitive. We prove this conjecture in three cases: hyperbolic diffeomorphisms, partially hyperbolic diffeomorphisms with two hyperbolic bundles, and tame diffeomorphisms (in the first case, the conjecture is folklore; in the second one, it follows by adapting the proof in Brin (1975 Topological transitivity of a certain class of dynamical systems, and flows of frames on manifolds of negative curvature Funct. Anal. Appl. 9 9–19)).We study this conjecture without global assumptions and pro…

Partially hyperbolic diffeomorphisms on Heisenberg nilmanifolds and holonomy maps

2014

Abstract In this note we show that all partially hyperbolic automorphisms on a 3-dimensional non-Abelian nilmanifold can be C 1 -approximated by structurally stable C ∞ -diffeomorphisms, whose chain recurrent set consists of one attractor and one repeller. In particular, all these partially hyperbolic automorphisms are not robustly transitive. As a corollary, the holonomy maps of the stable and unstable foliations of the approximating diffeomorphisms are twisted quasiperiodically forced circle homeomorphisms, which are transitive but non-minimal and satisfy certain fiberwise regularity properties.

Towards efficient inductive synthesis: Rapid construction of local regularities

2006

Given several input/output examples of some function we can state the problem: what is the “simplest” function which complies with these examples. This problem is well studied and is known to be very hard in the general case. In this paper we address a special case of the problem, when the target function can be expressed as a simple composition of known functions. We propose a new inductive synthesis algorithm for this case and show that it is efficient enough to synthesize complex geometry formulas.

A new rotational integral formula for intrinsic volumes in space forms

2010

A new rotational version of Crofton's formula is derived for the intrinsic volumes of a domain Y in a space form. More precisely, a functional is defined on the intersection between Y and a totally geodesic submanifold (plane) through a fixed point, such that the rotational average of this functional is equal to the intrinsic volumes of Y. Particular cases of interest in stereology are considered for the Euclidean case. © 2009 Elsevier Inc. All rights reserved.

Visualization of Large Terrain Using Non-restricted Quadtree Triangulations

2004

This paper presents a set of new techniques oriented towards the real-time visualization of large terrains. These techniques are mainly focused on semi-regular triangulations of non-restricted quadtree terrain representations. Despite the fact that the paper shows that triangulations based on non-restricted quadtrees are as simple and efficient as those based on restricted quadtrees, the new triangulations avoid discontinuity problems among the boundaries of different patches without the need for tree balancing and extra triangles addition. Another important feature of the proposed triangulation is that it incorporates an efficient method for building triangle strips and triangle fans for t…

Coordinative Versatility of Guanazole [3,5‐Diamino‐1,2,4‐triazole]: Synthesis, Crystal Structure, EPR, and Magnetic Properties of a Dinuclear and a L…

2006

New complexes with guanazole (3,5-diamino-1,2,4-triazole = Hdatrz), [Cu 2 (Hdatrz) 2 (μ-OH 2 )(H 2 O) 4 (SO 4 )](SO 4 )·3.5H 2 O (1) and [Cu 3 (Hdatrz) 4 (μ-Cl) 2 (H 2 O) 4 (SO 4 ) 2 ]·11.4H 2 O (2), have been prepared and structurally characterized. Complex 1 is a noncentrosymmetric dinuclear compound in which the cop-per(II) ions are bridged by two triazole ligands and one μ-OH 2 molecule, with a Cu(1)···Cu(2) distance of 3.4945(8) A. The chromophores are Cu(1)N 2 O 2 O' (square pyramidal), and Cu(2)N 2 O 2 O'O" (octahedral). Complex 2 has a linear trinuclear copper(II) structure, with two crystallographically independent copper(II) atoms. Neighboring copper(II) ions are linked by two tri…

A Study of the Lack of Slow Magnetic Relaxation in Mononuclear Trigonal Bipyramidal Cobalt(II) Complexes

2021

ChemInform Abstract: Preparation and Structure of (EtO)2P(O)CH2Si(Me)2CH2SnMe2Cl. A Six- Membered Chelate Ring with Chair Conformation and a P=O××. t…

2010

Compressibility and phase stability of iron-rich ankerite

2021

ABSTRACT: The structure of the naturally occurring, iron-rich mineral Ca₁․₀₈(₆)Mg₀.₂₄(₂)Fe₀.₆₄(₄)Mn₀.₆₄(₄)(CO₃)₂ ankerite was studied in a joint experimental and computational study. Synchrotron X-ray powder diffraction measurements up to 20 GPa were complemented by density functional theory calculations. The rhombohedral ankerite structure is stable under compression up to 12 GPa. A third-order Birch-Murnaghan equation of state yields V₀ = 328.2(3) ų, bulk modulus B₀ = 89(4) GPa, and its first-pressure derivative B'₀ = 5.3(8)-values which are in good agreement with those obtained in our calculations for an ideal CaFe(CO₃)₂ ankerite composition. At 12 GPa, the iron-rich ankerite structure …

Ferromagnetic copper(II)–copper(II) interaction in a single chlorido and dicyanamido bridged mixed–valence copper(I/II) 2D polymer generated by in si…

2015

A mixed-valence 2-D Cu(I/II) complex, [{Cu(II)(dmen)(μ-Cl)(μ1,5-dca)}{Cu(I)(μ1,5-dca)}]n (1) (dmen = N,N-dimethylethylenediamine, dca = dicyanamide = [N(CN)2]−), has been synthesized by in situ partial reduction of Cu(II) to Cu(I) using benzoin (2-hydroxy-1,2-di(phenyl)ethanone) as reductant. Complex 1 was characterized by spectroscopic techniques, single crystal X-ray diffraction, and low temperature magnetic measurements. Structural investigation reveals that 1 represents a mixed-valence 2-D coordination polymer formed by parallel 1-D [Cu(II)(dmen)(Cl)Cu(I)(μ1,5-dca)2]n chains running along the b axis, where chloride bridges Cu(II) ions of adjacent polymers through long connections (2.840…