Some Geometry of H(r)
نویسنده
چکیده
If X is a complete metric space, the collection of all non-empty compact subsets of X forms a complete metric space (H(X), h), where h is the Hausdorff metric. In this paper we explore some of the geometry of the space H(Rn). Specifically, we concentrate on understanding lines in H(R). In particular, we show that for any two points A, B ∈ H(Rn), there exist infinitely many points on the line joining A and B. We characterize some points on the lines formed using closed and bounded intervals of R and show that two distinct lines in H(R) can intersect in infinitely many points.
منابع مشابه
Theoretical study of hydrogen bond effects on Diphenylphosphorylazide
The interaction of DPPA which is an important component in cellular membrane with molecules of water asmedia, cause some changes in geometry of DPPA .In this study we focused our attention on comparing thismolecule with related hydrated complexes employing different basis sets at hartree-fock levels of theory. Thetheoretical NMR shielding tensor of some imported atoms were also reported.
متن کاملSynthesis and characterization of some transition metal complexes of Schiff base derived from 2,4 - dihydroxybenzaldehyde
Abstract New N2O2 type Schiff base has been designed and synthesized by condensing 2,4 dihydroxy benzaldehyde and α-naphthylamine in ethanol. Solid metal complexes of the schiff base with Cu(II), Ni(II) and Zn(II) metal ion were synthesized and characterized by elemental analysis, magnetic susceptibility, molar conductance, IR, UV-Vis and ‘H NMR spectral studies. The data shows that the c...
متن کاملEffective Parameters in Contact Mechanic for Micro/nano Particle Manipulation Based on Atomic Force Microscopy
The effect of geometry and material of the Micro/Nano particle on contact mechanic for manipulation was studied in this work based on atomic force microscopy. Hertz contact model simulation for EpH biological micro particle with spherical, cylindrical, and circular crowned roller shape was used to investigate the effect of geometry on contact simulation process in manipulation. Then, to val...
متن کاملA Comprehensive Model for Stiffness Coefficients in V-Shaped Cantilevers
During past decade the AFM based nanomanipulation has been focus of attention as the promising nano fabrication approach. The main challenge in this process is the real-time monitoring. Consequently, the dynamic models have been proposed as a solution to the existing challenge. In the modeling approach the magnitudes of the forces are proportional to the stiffness coefficients o...
متن کاملCOMPUTER AIDED OPTIMIZATION OF SPECIMEN GEOMETRY OF HOT TORSION TEST TO MINIMIZE MICROSTRUCTURE NONHOMOGENEITY AND TEMPERATURE GRADIENT BEFORE DEFORMATION
Abstract:Optimization of specimen geometry before subjecting it to hot torsion test (HTT) is essential for minimizingnon-uniform temperature distribution and obtaining uniform microstructure thought the specimen.In the present study, a nonlinear transient analysis was performed for a number of different geometries andtemperatures using the commercial finite element (FE) package ANSYSTM. FE ther...
متن کاملTriple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کامل