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Lattices of Optimal Finite Lattice Packings
Monatshefte f�r Mathematik, 2004The densest finite lattice packings of \(n\) balls of parametric density \(\rho>\rho_C(B^d)\), where \(\rho_C(B^d)\) is a positive constant, are shown to be subsets of critical lattices for all large enough cardinalities \(n\). The result follows for all \(n\) in two dimensions and is conjectured to be true for all \(n\) in all dimensions. On the other
Betke, Ulrich, Schürmann, Achill
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Geometriae Dedicata, 2001
Let \(K\) be a centrally symmetric convex body in \(\mathbb{R}^d\). A finite lattice packing of \(K\) is a family \(C+K\), where \(C\) is a finite subset of a packing lattice of \(K\). Due to J. M. Wills, the parametric density, for a parameter \(\rho>0\), of the packing is defined by \[ \delta (C;K,\rho) ={n\cdot V(K)\over V(\text{conv} C+\rho K ...
Arhelger, Volker +2 more
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Let \(K\) be a centrally symmetric convex body in \(\mathbb{R}^d\). A finite lattice packing of \(K\) is a family \(C+K\), where \(C\) is a finite subset of a packing lattice of \(K\). Due to J. M. Wills, the parametric density, for a parameter \(\rho>0\), of the packing is defined by \[ \delta (C;K,\rho) ={n\cdot V(K)\over V(\text{conv} C+\rho K ...
Arhelger, Volker +2 more
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Il Nuovo Cimento B Series 11, 1995
The hypothesis of simultaneous conformal compactification of both space-time and momentum space, possibly identified as two homogeneous spaces of the conformal group, leads to the need to define on them two dual finite lattices correlated by conformal inversions. It is shown that, with the help of orthonormal sets of (Hahn) polynomials onSn identifying
BUDINICH P +2 more
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The hypothesis of simultaneous conformal compactification of both space-time and momentum space, possibly identified as two homogeneous spaces of the conformal group, leads to the need to define on them two dual finite lattices correlated by conformal inversions. It is shown that, with the help of orthonormal sets of (Hahn) polynomials onSn identifying
BUDINICH P +2 more
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Finite Projective Distributive Lattices
Canadian Mathematical Bulletin, 1970The theorem stated below is due to R. Balbes. The present proof is direct; it uses only the following two well-known facts: (i) Let K be a category of algebras, and let free algebras exist in K; then an algebra is projective if and only if it is a retract of a free algebra, (ii) Let F be a free distributive lattice with basis {xi | i ∊ I}; then ∧(xi ...
Grätzer, G., Wolk, B.
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Algebras and Representation Theory, 2005
An algebra is representation finite if there are only finitely many isomorphism classes of indecomposable \(A\)-modules. If \(R\) is a left Noetherian ring then the author calls an \(R\)-module a lattice if its socle is \(0\). In the classical case this coincides with the usual concept of lattices over classical orders.
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An algebra is representation finite if there are only finitely many isomorphism classes of indecomposable \(A\)-modules. If \(R\) is a left Noetherian ring then the author calls an \(R\)-module a lattice if its socle is \(0\). In the classical case this coincides with the usual concept of lattices over classical orders.
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On Finitely Generated Lattices of Finite Width
Canadian Journal of Mathematics, 1981The width of a lattice L is the maximum number of pairwise noncomparable elements in L.It has been known for some time ([5] ; see also [4]) that there is just one subdirectly irreducible lattice of width twro, namely the five-element nonmodular lattice N5.
Poguntke, W., Sands, B.
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Finite-volume lattice Boltzmann method
Physical Review E, 1999We present a finite-volume formulation for the lattice Boltzmann method (FVLBM) based on standard bilinear quadrilateral elements in two dimensions. The accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the Navier-Stokes equations for time dependent rotating Couette flow and Taylor vortex flow.
H, Xi, G, Peng, S H, Chou
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Order, 2004
The author studies lattice-ordered D-posets (= D-lattices). She finds conditions when a commutator-finite D-lattice \(L\) can be uniquely decomposed in the form \(L \cong M\times L_1 \times \cdots\times L_n\), where \(M\) is an MV-algebra and \(L_1,\ldots,L_n\) are irreducible D-lattices which are not MV-algebras.
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The author studies lattice-ordered D-posets (= D-lattices). She finds conditions when a commutator-finite D-lattice \(L\) can be uniquely decomposed in the form \(L \cong M\times L_1 \times \cdots\times L_n\), where \(M\) is an MV-algebra and \(L_1,\ldots,L_n\) are irreducible D-lattices which are not MV-algebras.
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Block-Finite Orthomodular Lattices
Canadian Journal of Mathematics, 1979Introduction. Every orthomodular lattice (abbreviated : OML) is the union of its maximal Boolean subalgebras (blocks). The question thus arises how conversely Boolean algebras can be amalgamated in order to obtain an OML of which the given Boolean algebras are the blocks.
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Whaley's Theorem for Finite Lattices
Order, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Freese, Ralph +2 more
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