Sublattices of lattices of order-convex sets, I. The main representation theorem

For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some lattice of the form Co(P) iff L satisfies (S), (U), and (B). Furthermore, if L has an embedding into some Co(P), then it has such an embedding that preserves the existing bounds. If L is finite, then one can take P finite, of cardinality at most $2n^2-5n+4$, where n is the number of join-irreducible elements of L. On the other hand, the partially ordered set P can be chosen in such a way that there are no infinite bounded chains in P and the undirected graph of the predecessor relation of P is a tree

Sublattices of lattices of convex subsets of vector spaces

For a left vector space V over a totally ordered division ring F, let Co(V) denote the lattice of convex subsets of V. We prove that every lattice L can be embedded into Co(V) for some left F-vector space V. Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form $Co(V,Z)=\{X\cap Z | X\in Co(V)\}$, for some finite subset $Z$ of $V$. In particular, we obtain a new universal class for finite lower bounded lattices

Studies of proteinograms in dermatophytes by disc electrophoresis. 1. Protein bands in relation to growth phase

Homogenates were prepared from various growth phases of Microsporum gypseum grown on different amino acids as the nitrogen source. When analyzed on 7.5% polyacrylamide disc gels, the water-soluble proteins in these homogenates gave essentially identical banding patterns

Studies on proteinograms in dermatorphytes by disc electrophoresis. Part 2: Protein bands of keratinophilic fungi

Disc electrophoresis studies on keratinophili fungi demonstrated corresponding proteinograms in morphologically homogeneous strains of the same species, but different in different species of one and the same genus

A semiclassical analysis of the Efimov energy spectrum in the unitary limit

We demonstrate that the (s-wave) geometric spectrum of the Efimov energy levels in the unitary limit is generated by the radial motion of a primitive periodic orbit (and its harmonics) of the corresponding classical system. The action of the primitive orbit depends logarithmically on the energy. It is shown to be consistent with an inverse-squared radial potential with a lower cut-off radius. The lowest-order WKB quantization, including the Langer correction, is shown to reproduce the geometric scaling of the energy spectrum. The (WKB) mean-squared radii of the Efimov states scale geometrically like the inverse of their energies. The WKB wavefunctions, regularized near the classical turning point by Langer's generalized connection formula, are practically indistinguishable from the exact wave functions even for the lowest ($n=0$) state, apart from a tiny shift of its zeros that remains constant for large $n$.Comment: LaTeX (revtex 4), 18pp., 4 Figs., already published in Phys. Rev. A but here a note with a new referece is added on p. 1