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In the branch of mathematics called order theory, a modular lattice is a lattice that satisfies the following self- dual condition, Modular law. a ≤ b implies a ∨ (x ∧ b) = (a ∨ x) ∧ b. where x, a, b are arbitrary elements in the lattice, ≤ is the partial order, and ∨ and ∧ (called join and meet respectively) are the operations ...
In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum ( join) and an infimum ( meet ). A conditionally complete lattice satisfies at least one of these properties for bounded subsets. For comparison, in a general lattice, only pairs of elements need to have a supremum and an infimum.
Geometric lattice. In the mathematics of matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular lattice without the assumption of finiteness. Geometric lattices and matroid lattices, respectively, form the lattices of flats of finite, or finite and infinite ...
Spinel group. The spinels are any of a class of minerals of general formulation AB. 2X. 4 which crystallise in the cubic (isometric) crystal system, with the X anions (typically chalcogens, like oxygen and sulfur) arranged in a cubic close-packed lattice and the cations A and B occupying some or all of the octahedral and tetrahedral sites in ...
A Virginia man became the third HIV-positive person in the U.S. to donate his heart, and the first for the hospital where the surgery was performed. Zack Pate of Hampton Roads recently died by ...
Skateboarder Andy Macdonald competed in another Summer Olympics in Paris this year — and at 51 years old, he is also wrapping up his last. On Wednesday, Aug. 7, the British-American who was ...
That's what we imagine was going through one woman's head when she realized that her orange cat was trapped inside her cup holder. The woman was stunned as to how her cat got itself in there ...
The trihexagonal tiling has Schläfli symbol of r{6,3}, or Coxeter diagram, , symbolizing the fact that it is a rectified hexagonal tiling, {6,3}. Its symmetries can be described by the wallpaper group p6mm, (*632), [ 15 ] and the tiling can be derived as a Wythoff construction within the reflectional fundamental domains of this group .