A collection L = P 1 ∪ P 2 ∪ · · · ∪ P t (1 ≤ t ≤ k) of t disjoint paths, s of them being singletons with |V (L)| = k is called a (k, t, s)-linear forest. A graph G is (k, t, s)ordered if for every (k, t, s)-linear forest L in G there exists a cycle C in G that contains the paths of L in the designated order as subpaths. If the cycle is also a hamiltonian cycle, then G is said to be (k, t, s)-o...

Linear constraint relations among loop-order five-point color-ordered amplitudes in SO(N) and Sp(2N) gauge theories are derived with the group-theoretic method. These constrains up to four-loop order. It is found that both theories, there n=6,22,34,44,50 linear at L=0,1,2,3,4 loop orders. Then numbers of independent under constraints respectively nind.=6,12,22,34,50. We find number begins diver...

The paper is devoted to a concept of a fuzzy ordered set and partially ordered set category fuzzyfication. The aim of this work is to define a fuzzy order relation on a usual set, on an L-valued set and on an L-set. Using the fuzzy order relation we construct fuzzy POS category and study the connection between this categories and SET(L).

We introduce the concept of complementary elements in ordered sets. If an ordered set S is a lattice, this concept coincides with that for lattices. The connections between distributivity and the uniqueness of complements are shown and it is also shown that modular complemented ordered sets represents \geometries" which are more general than projective planes. It was shown in 2], 4] and 6] that...

Based on the work of Hahn, Baer, Ostrowski, Krull, Kaplansky and the Artin-Schreier theory, and stimulated by the paper [L] of S. Lang in 1953, the theory of real places and convex valuations has witnessed a remarkable development and has become a basic tool in the theory of ordered fields and real algebraic geometry. Surveys on this development can be found in [LAM] and [PC]. In this paper, we...

(Day 1): References (for general background) →Varieties of lattice-ordered groups, N. R. Reilly, in Lattice-Ordered Groups, Advances and Techniques, A. M. W. Glass and W. C. Holland (eds.), Kluwer Academic Publishers, 1989. Lattice-Ordered Groups, an Introduction, M. Anderson and T. Feil, D. Reidel Pub. Co., 1988. Theory of Lattice-Ordered Groups, M. Darnel, Marcel Dekker, 1995. Partially Order...

We demonstrate ordered orientation of the hydration water at the surface of phospholipid bilayers by use of coherent anti-Stokes Raman scattering (CARS) microscopy, a highly sensitive vibrational imaging method recently developed. We investigated negatively charged POPS (1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-l-serine) and neutral POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) multi...

Although the convolution operators on Euclidean space and Heisenberg group satisfy same $L^p$ bounds with optimal constants, former has maximizers while latter does not. However, as work of Christ shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple trilinear form for must be close a particular type ordered Gaussians after adjusting by symmetry. ...