A refined form of the ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution structure’ consisting of equivariant iterated fibrations of the boundary faces. T...

In the two-dimensional rotor-router walk (defined by Jim Propp and presented beautifully in [4]), the first time a particle leaves a site x it departs east; the next time this or another particle leaves x it departs south; the next departure is west, then north, then east again, etc. More generally, in any dimension d ≥ 1, for each site x ∈ Z fix a cyclic ordering of its 2d neighbors, and requi...

Binary-coded genetic algorithms (BGAs) traditionally use a uniform mapping to decode strings to corresponding real-parameter variable values. In this paper, we suggest a non-uniform mapping scheme for creating solutions towards better regions in the search space, dictated by BGA’s population statistics. Both variable-wise and vector-wise non-uniform mapping schemes are suggested. Results on fiv...

In recent decades, there have been strong calls for reforms in mathematics education, and in particular for changes in classroom practices. Teachers have been encouraged to organize instruction so that students participate in more collaborative, discussion-based activities with an eye to supporting a community of learners, rather than a set of individuals working on mathematics (NCTM, 1991). Or...

We consider the system of N (≥ 2) hard balls with masses m1, . . . , mN and radius r in the flat torus TL = R /L · Z of size L, ν ≥ 3. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection (m1, . . . , mN ; L) of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the c...

We present a study of the behavior of a ball under the influence of gravity on a platform. A propagating surface wave travels on the surface of the platform while the platform remains motionless. This is a modification of the classical bouncing ball problem and describes the transport of particles by surface waves. Phase and velocity maps cannot be expressed in the explicit form due to implicit...

OBJECTIVES Pathophysiology of chronic rhinosinusitis (CRS) is very complex and has not yet been clearly understood. To date, various factors have been researched to have relations with the pathogenesis of CRS, such as superantigens and biofilms. Recently, we found an unusual pathological finding in patients with CRS, and we called this new entity as bacteria ball (or bioball). In this study, we...

(-)-gephyrotoxin-223 was formally synthesized from chiral synthon 1 which has been chemoenzymatically synthesized  in the presence  of candida antartica lipase.