the notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $cat(0)$ space, where the curvature is bounded from above by zero. in fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. in this paper, w...

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

This paper describes one approach for calculating the cohomology of a particular complex which arises in knot theory and which is used to prove the existence of ‘associators’, a key ingredient in the construction of a universal knot invariant. The approach taken is to show that the relevant complex can be interpreted, essentially, as the cohomology of the functor Hom(K, C), where C is the coalg...

The influence of the bead-bead interaction on the rotational dynamics of macromolecules which are immersed into a solution has been investigated by starting from the microscopic theory of the macromolecular motion, i.e., from a Fokker-Planck equation for the phase-space distribution function. From this equation, we then derived an explicit expression for the configuration-space distribution fun...

It is shown how the phase-space kinetic theory of polymeric liquid mixtures leads to a set of extended Maxwell-Stefan equations describing multicomponent diffusion. This expression reduces to standard results for dilute solutions and for undiluted polymers. The polymer molecules are modeled as flexible bead-spring structures. To obtain the Maxwell-Stefan equations, the usual expression for the ...

Investigating how tightly objects pack space is a long-standing problem, with relevance for many disciplines from discrete mathematics to the theory of glasses. Here we report on the fundamental yet so far overlooked geometric property that disordered mono-disperse spherical bead packs have significant local structural anisotropy manifest in the shape of the free space associated with each bead...

adsorption and water treatment of ca (ii) and mg (ii) hardness were investigated via adsorption of metal ions onto commercial polyacrylic acid hydrogel beads as a novel sorbent for metal ions (ca2+, mg2+) removal and water treatment. batch equilibrium technique was carried out under the influence of solution ph, contact time, sorbent dosage, initial metal concentration and competitive study. th...

Electron beam welding has proved phenomenal in welding of components used in space because it uses a vacuum environment which eliminates substances like oxygen, nitrogen, and hydrogen. The main advantage of EBW is its ability to weld dissimilar materials and incorporate desirable properties in the assembly. It has high depth to width ratio and focuses exactly on the portion to be welded, thereb...

microencapsulation has become a common technique in the production of controlled release dosage forms. many results have been reported, concerning the use of alginate beads as controlled release drug formulations. alginate has a unique gel-forming property in the presence of multivalent cations, in an aqueous medium. ibuprofen is an excellent analgesic and antipyretic, non-steroidal anti-inflam...