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### Page 48 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews
Milner (3-CALG; Calgary, AB) 95a:06004 06A07 05A05 05D05 Shi, Feng (PRC-CRI-R; Changsha); Li, Wei Xuan (PRC-CRI-R; Changsha) The density of a maximum minimal cut in the subset lattice of a finite set is  ...  Let c(m) denote the maximum size of any minimal cutset in the Boolean lattice of all subsets of {1,---,}.  ...

### Equicontinuous Factors, Proximality and Ellis Semigroup for Delone Sets [chapter]

Jean-Baptiste Aujogue, Marcy Barge, Johannes Kellendonk, Daniel Lenz
2015 PROGRESS IN MATHEMATICS
Thus, a lattice is a Delone set of finite local complexity. Moreover, whenever L is a lattice then L * := {χ ∈ G : (χ, x) = 1 for all x ∈ L} is a lattice in G. It is called the dual lattice.  ...  Almost canonical cut-and-project sets Almost canonical cut-and-project sets are special types of complete Meyer sets.  ...

### Page 4326 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews
It is shown that the maximum density of a packing of the (k,n)-semicross by translations, where the translation vectors are from a sublattice of the integer lattice Z", is asymptotically equal to (nsec  ...  Let d, be the maximal density of lattice k-packings of unit circles. The author suggests a method for finding d, by means of a finite number of extremal geometric problems.  ...

### Equicontinuous factors, proximality and Ellis semigroup for Delone sets [article]

Jean-baptiste Aujogue, Marcy Barge, Johannes Kellendonk, Daniel Lenz
2014 arXiv   pre-print
We consider in particular, the maximal equicontinuous factor of a Delone dynamical system, the proximality relation and the enveloping semigroup of such systems.  ...  We discuss the application of various concepts from the theory of topological dynamical systems to Delone sets and tilings.  ...  Thus, a lattice is a Delone set of finite local complexity. Moreover, whenever L is a lattice then L * := {χ ∈ G : (χ, x) = 1 for all x ∈ L} is a lattice in G. It is called the dual lattice.  ...

### A guide to mathematical quasicrystals [article]

Michael Baake
1999 arXiv   pre-print
The emphasis is on proper generalizations of concepts and ideas from classical crystallography.  ...  This perfectly ordered world is augmented by a brief introduction to the stochastic world of random tilings.  ...  of density zero, because the autocorrelation of a set of positive density is not changed by adding or removing points of density 0).  ...

### Optimization Problems and Algorithms from Computer Science [chapter]

Heiko Rieger
2009 Encyclopedia of Complexity and Systems Science
is a special property of set functions, 1113 which are defined as follows: Let V be a finite set and 1114  V = X X V be the set of all the subsets of V.  ...  Thus the value of any flow x 611 is less or equal to the capacity of any cut in the network. 612 If one discovers a flow x whose value equals to the capac-613 ity of some cut [S, S], then x is a maximum  ...

### A new phasing method based on the principle of minimum charge

Pavel Kalugin
2001 Acta Crystallographica Section A Foundations of Crystallography
A new method of the phase determination in X-ray crystallography is proposed. The method is based on the so-called "minimum charge" principle, recently suggested by Elser.  ...  The norm ∫|ψ( x)|^2 d x is minimized under the constraint imposed by the measured data on the amplitudes of Fourier harmonics of ρ.  ...  Each component ψ α of ψ has a finite Fourier spectrum: ψ α (x) = K∈Λψ α,K e iK·x , (3) where Λ is a finite subset of reciprocal lattice vectors.  ...

### Superrigidity of actions on finite rank median spaces [article]

Elia Fioravanti
2017 arXiv   pre-print
If Γ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of Γ on a complete, finite rank median space has a global fixed point.  ...  This is in sharp contrast with the behaviour of actions on infinite rank median spaces.  ...  The author expresses special gratitude to Cornelia Druţu and Talia Fernós for contributing many of the ideas of this paper.  ...

### 2-D Compass Codes [article]

Muyuan Li, Daniel Miller, Michael Newman, Yukai Wu, Kenneth R. Brown
2018 arXiv   pre-print
The compass model on a square lattice provides a natural template for building subsystem stabilizer codes.  ...  In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault-tolerance of the Bacon-Shor code.  ...  the University of Michigan.  ...

### Exploring the structure of the quenched QCD vacuum with overlap fermions

E.-M. Ilgenfritz, K. Koller, Y. Koma, G. Schierholz, T. Streuer, V. Weinberg
2007 Physical Review D
Overlap fermions have an exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum.  ...  We conclude that the vacuum has a multifractal structure.  ...  Acknowledgement The numerical calculations have been performed on the IBM p690 at HLRN (Berlin) and  ...

### The Meyer property of cut-and-project sets

L'ubomíra Balková, Zuzana Masáková, Edita Pelantová
2004 Journal of Physics A: Mathematical and General
It is known that Σ(Ω) satisfies the Meyer property, i.e. is a Delone set and there exists a finite set F such that Σ(Ω) − Σ(Ω) ⊂ Σ(Ω) + F .  ...  The cardinality f (Ω) of the minimal covering is called the Meyer number of Ω.  ...  He calls a 'quasicrystal' a Delone set Λ which satisfies the property of 'almost-lattices' Λ − Λ ⊂ Λ + F (1) for some finite set F .  ...

### Cut-and-project quasicrystals, lattices, and dense forests [article]

Faustin Adiceam, Yaar Solomon, Barak Weiss
2021 arXiv   pre-print
On the other hand, we show that finite unions of lattices typically are dense forests, and give a bound on their visibility function, which is close to optimal.  ...  Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its visibility function.  ...  The authors gratefully acknowledge the support of grants BSF 2016256 and ISF 2095/15. The first named author wishes to thank Federico Ardila for a talk given at the University of Waterloo  ...

### Master index of volumes 121–130

1994 Discrete Mathematics
Li, The density of a maximum minimal cut in the subset lattice of a finite set is almost oneTakahashi, A., S. Ueno and Y.  ...  Hilton, The total chromatic number of regular graphs whose complement is bipartite Edelman, P.H. and R. Simion, Chains in the lattice of noncrossing partitions Ehrenfeucht, A., T. Harju and G.  ...

### Fast predictions of lattice energies by continuous isometry invariants of crystal structures [article]

Jakob Ropers, Marco M Mosca, Olga Anosova, Vitaliy Kurlin, Andrew I Cooper
2021 arXiv   pre-print
The lattice energy is a key physical property, which determines thermodynamic stability of a crystal but has no simple analytic expression.  ...  Our experiments on simulated crystals confirm that a small distance between the new invariants guarantees a small difference of energies.  ...  Then a crystal can be obtained as the infinite union of lattice translates M +Λ = {p + v : p ∈ M, v ∈ Λ} from a finite set (motif ) of points M ⊂ U in the cell U .  ...

### Arbeitsgemeinschaft: Limits of Structures

László Lovász, Balázs Szegedy
2013 Oberwolfach Reports
The goal of the Arbeitsgemeinschaft is to review current progress in the study of very large structures.  ...  The main emphasis is on the analytic approach that considers large structures as approximations of infinite analytic objects.  ...  Further, there is a p 0 such that for all p < p 0 there is a region (t, t ′ ) with p 3 /6 < t < t ′ < 1/6 where the constant function c t is not the minimizer of (3).  ...
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