We prove that every ω-categorical, generically stable group is nilpotent-byfinite and that every ω-categorical, generically stable ring is nilpotent-by-finite.

The occurrence of liquid-vapor phase transition and the possible existence of a critical point in complex plasmas--systems that consist of charged micrograins in a neutralizing plasma background--is investigated theoretically. An analysis based on the consideration of the intergrain interaction potential suggests that under certain conditions systems near and at the critical point should be obs...

The critical behavior of electrolyte mixtures was studied using grand canonical Monte Carlo simulations. Mixtures consist of large multivalent macroions and small monovalent co- and counterions. The system can be viewed as a binary mixture of macroions (with their counterions) and salt (co- and counterion pair). The primitive model description was used, in which the ions are point charges with ...

Let A be a C*-algebra with unit 1 and a ∈ A be a nilpotent. By Donoghue’s Theorem, all corner points of its numerical range V (a) belong to the spectrum σ(a). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂V (a) of V (a) to σ(a) should be in some sense bounded by the radius of curvature of ∂V (a) at p.

We construct embeddings Yn,τ → Hilb (Στ ) for each of the classical Lie algebras sp2m(C), so2m(C), and so2m+1(C). The space Yn,τ is the fiber over a point τ ∈ h/W of the restriction of the adjoint quotient map χ : g → h/W to a suitably chosen transverse slice of a nilpotent orbit. These embeddings were discovered for sl2m(C) by Ciprian Manolescu. They are related to the symplectic link homology...

generally, the evaluation and assessment critical condition of rill formation are useful for a better understanding of soil erosion processes. the inherence characteristics of soils, which have much dynamic variations on the hill-slopes and are affected by rill formation, are the soil critical shear stress and soil erodibility factors. this study aims to assess experimental rill incision thresh...

Critical slowing down of the relaxation of the order parameter has phenomenological consequences in early universe cosmology and in ultrarelativistic heavy ion collisions. We study the relaxation rate of long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transit...

A purpose of critical point theory is the counting of critical points of functions. Principal theorems in the subject state in precise terms that topological complexity of the underlying space is reflected in the existence and nature of critical points of any smooth real-valued function defined on the space. The initial development of critical point theory is peculiarly the work of one man, Mar...

for Ak−1 models with open boundaries, by constructing polynomial solutions of level one boundary quantum Knizhnik–Zamolodchikov equations for Uq(sl(k)). The result takes the form of a character of the symplectic group, that leads to a generalization of the number of vertically symmetric alternating sign matrices. We also investigate the other combinatorial point q = −1, presumably related to th...