We report a self-recognition phenomenon based on an assembly process in a homogeneous dilute aqueous solution of two nano-scaled, spherical polyprotic metal oxide-based macroions (neutral species in crystals), also called Keplerates of the type [(linker)₃₀(pentagon)₁₂]≡[{M(H₂O)}₃₀{(Mo)Mo₅}₁₂] where M is Fe(III) or Cr(III). Upon deprotonation of the neutral species, the resulting macroions assem...

Porous hydroxyapatite spheres were prepared by a modified gelcasting method producing a ceramic prosthesis with controled porosity. The spheres are approximately 2.2 cm in diameter with a relatively homogeneous pore size distribution from 10 to 40 microm in diameter. The samples were characterized by X-ray powder diffractometry (XRD) and Fourier transform infra-red spectroscopy (FTIR) to identi...

Forty years after conversion from chaparral to perennial veldt grass in the San Dimas Experimental Forest, we compared land surface and soil properties between areas of the two vegetation types. Our objective was to evaluate the impact of this vegetation conversion on the soil physical properties likely to impact zero-order watershed hydrology. In three watersheds of each vegetation type, surfa...

Let K be a convex body in Rn with centroid at 0 and B be the Euclidean unit ball in Rn centered at 0. We show that limt→0 |K| − |Kt| |B| − |Bt| = Op(K) Op(B) , where |K| respectively |B| denotes the volume of K respectively B, Op(K) respectively Op(B) is the p-affine surface area of K respectively B and {Kt}t≥0, {Bt}t≥0 are general families of convex bodies constructed from K, B satisfying cert...

1. INTRODUCTION. A cycloid is the path traced by a point on the boundary of a circular disk that rolls without slipping along a straight line. It forms a sequence of arches resting on the line, as shown in Figure 1. It is known that the area of the shaded region below one arch is three times the area of the rolling disk. Our analysis shows that the factor 3 reflects a much deeper property of cy...

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of the metric, the second fundamental form, and data arising from an ambient Killing field. This class of 3-manifolds includes in particular the Berger spheres,...

1. Introduction One of the most important recent applications of sonochemistry has been to the synthesis and modification of inorganic materials [1-5]. In liquids irradiated with high intensity ultrasound, acoustic cavitation drives bubble collapse producing intense local heating, high pressures, and very short lifetimes; these transient, localized hot spots drive high energy chemical reactions...