PROOF. Let {Gn} and {Hn} denote monotonie decreasing sequences of open sets which close down upon .Pi and F2 respectively. We may suppose that d and Hi are so chosen that G i # i = 0. Now, by Mullikin's theorem, there is a connected subset of C— C(Gw+27n) which has a limit point in Gn and a limit point in Hn. The closure of such a connected set is a subcontinuum of C which "extends" from Gn to ...

A continuum means a compact connected metric space. For a positive integer n, a continuum X is said to be n-equivalent provided that X contains exactlyn topologically distinct subcontinua. A continuumX is said to be hereditarily n-equivalent provided that each nondegenerate subcontinuum of X is n-equivalent. If there exists a positive integer n such that X is n-equivalent, then X is said to be ...

In this paper, we answer a question by Krasinkiewicz, Reńska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane. We also consider a generalization of graphs by allowing vertices to be continua and replacing edges by not necessarily connected sets. We require only that two “vertices” be in the same quasi-component of...

TBC1D24 mutation-related epileptic syndrome includes a wide spectrum of epilepsies. We describe a case with a homozygous TBC1D24 mutation inherited from consanguineous parents. The patient manifested epilepsia partialis continua (EPC) and rare secondary generalized tonic-clonic seizure without intellectual disability or developmental delay. EPC, which involved focal limbs, came with waking and ...

Following a cursory review and synthesis of multipolar continua, the rudiments of graph theory, and granular mechanics, a graph-theoretic, energy-based homogenization is proposed for the systematic derivation of multipolar stress and kinematics in granular media. This provides a weakly non-local hierarchy of multipolar field equations for quasi-static mechanics based on polynomial representatio...

In this paper, a novel model for elasto-plastic continua is presented and developed from the ground up. It is based on the interdependence between plasticity, dislocation motion and strain incompatibility. A generalized form of the equilibrium equations is provided, with as additional variables the strain incompatibility and an internal thermodynamic variable called compatibility modulus, that ...

We implemented a new experimental scheme for the generation of single-shot extreme-UV continua that exploits a combination of transform-limited 15 fs, 800 nm pulses and chirped 35 fs, 800 nm pulses with orthogonal polarizations. Continua are interpreted as the formation of a single attosecond pulse and attributed to the interplay between polarization, ionization gating, and trajectory selection...

The problem of formation of generic structures in the Universe is addressed, whereby rst the kinematics of inertial continua for coherent initial data is considered. The generalization to self{gravitating continua is outlined focused on the classiication problem of singularities and metamorphoses arising in the density eld. Self{gravity gives rise to an internal hierarchy of structures, and, dr...