| This requires that their underlying lattices be based on triangles, parallelograms, or hexagons. |
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| There are only fourteen distinct types of Bravais lattices, and these are associated with seven crystal systems. |
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| Pergolas, open steel stairs, lattices and wooden blinds all act as shadow-casters and gnomons. |
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| Using nails or screws, connect the sides of the archways with wood or wire lattices from which the vines will grow. |
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| These lattices join together into one of seven different crystal systems, each contributing to a crystal's unique qualities. |
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| Crystal lattices consist of repeating units of a molecule, ion, or atom arranged in a symmetrical array. |
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| He also perceived that the 14 space lattices consisted of 7 different lattice symmetries, which correspond to 7 crystal systems. |
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| Bravais space lattices represent the 14 basic lattice types from which according to Bravais, practically all natural crystals originate. |
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| For 3-dimensional space lattices we need 3 or in some cases 4 crystallographic axes that define directions within the crystal lattices. |
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| In Undecidable theories Tarski showed that group theory, lattices, abstract projective geometry, closure algebras and others mathematical systems are undecidable. |
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| Because water molecules can bond only at certain angles, these lattices are full of empty space, and the solid takes up more room than the liquid. |
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| Ultimately, confining logical molecules in layers or three-dimensional lattices of nanoscopic bubbles might allow a true molecular computer to be built. |
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| The intricate, multiangled vectors of ductwork, scaffolding, lattices, building cranes and raw beams conjure a kind of teeming energy field with light at its core. |
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| Equivalent mechanical properties of auxetic lattices from discrete homogenization. |
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| The motifs also included geometric patterns, lattices and spools, possibly influenced by styles from highland Oaxaca, outside the Maya area. |
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| Kutyniok, The Balian-Low Theorem for symplectic lattices in higher dimensions, Appl. |
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| To make this happen, the engineers layered a ferroelectric material on an insulator whose crystal lattices were closely matched. |
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| He investigated lattices in higher dimensions, and was the first to determine the symmetry group of the Leech lattice. |
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| However, we will consider lower dimensional section lattices of cubic or orthorhombic lattices, too, which are not necessarily orthogonal. |
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| We have chosen the surfaces of a pentatope as well as a hexadecachoron, which are simple standard triangulations of a 3-sphere, shown in figure, as our underlying lattices. |
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| Antiferromagnetic materials are composed of two interpenetrating lattices. |
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| With an eye on the classical Cauchy-Born rule for crystal lattices, they establish an analog for the electronic structure of the deformed crystal under specific conditions. |
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| Ordinary metals dent, bend, stretch, and otherwise deform because the rows of atoms that make up the crystal lattices of metals can shift and rearrange. |
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| When the power constraint is taken into consideration, we show that polar lattices with lattice Gaussian shaping achieve the egodic capacity of fading channels. |
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