Various embedding problems of lattices into complete lattices are solved. We prove that for any join-semilattice S with the minimal join-cover refinement property, the ideal lattice IdS of S is both algebraic and dually algebraic. Furthermore, if there are no infinite D-sequences in J(S), then IdS can be embedded into a direct product of finite lower bounded lattices. We also find a system of i...

We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them, provide a framework for solving fixed point equations involving non-monotone operations such as negation or complement, and have been used to give semantics to...

the purpose of this paper is the generalization of structure factor for rods by polygon section in two dimensional phononic crystals. if we use the plane wave expansion method (pwe) for the propagation of acoustic waves in 2d phononic crystals, structure factor will be an important quantity. in order to confirm the obtained relations, we have calculated the band structure for xy and z vibration...

In this article we continue the formalization of concept lattices following [4]. We give necessary and sufficient conditions for a complete lattice to be isomorphic to a given formal context. As a by-product we get that a lattice is complete if and only if it is isomorphic to a concept lattice. In addition we introduce dual formal concepts and dual concept lattices and prove that the dual of a ...

Lattice-valued entropy functions defined by a lattice-valued possibilistic distribution π on a space Ω are defined as the expected value (in the sense of Sugeno integral) of the complement of the value π(ω) with ω ranging over Ω. The analysis is done in parallel for two alternative interpretations of the notion of complement in the complete lattice in question. Supposing that this complete latt...

The problem of determining the size of a finite concept lattice is shown to be #P-complete. Since any finite lattice can be represented as a concept lattice, the problem of determining the size of a lattice given by the ordered sets of its irreducibles is also #P-complete. Some results about NP-completeness or polynomial tractability of decision problems related to concepts with bounded extent,...

in this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite hamiltonian group. the coverings with three proper subgroups and the principal series of such a group are also counted. finally, we give a complete description of the lattice of characteristic subgroups of a finite h...

It is known that folding a protein chain into a cubic lattice is an NP-complete problem. We consider a seemingly easier problem: given a three-dimensional (3D) fold of a protein chain (coordinates of its C(alpha) atoms), we want to find the closest lattice approximation of this fold. This problem has been studied under names such as "lattice approximation of a protein chain", "the protein chain...

We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such effect algebra E is separable and modular then there exists a faithful state on E. Further, if an atomic lattice effect algebra is densely embeddable into a c...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...