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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 ...
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 ...
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 ...
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 ...
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 reciprocal lattice is a term associated with solids with translational symmetry, and plays a major role in many areas such as X-ray and electron diffraction as well as the energies of electrons in a solid. It emerges from the Fourier transform of the lattice associated with the arrangement of the atoms. The direct lattice or real lattice is ...
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