scholarly journals A right-invariant lattice-order on groups of paraunitary matrices

2019 ◽  
Vol 524 ◽  
pp. 226-249 ◽  
Author(s):  
Carsten Dietzel
Keyword(s):  
Lattice Order

Extension of a partial order in a group to a lattice order

1995 ◽  
Vol 34 (3) ◽  
pp. 424-429
Author(s):  
S. A. Todorinov
Keyword(s):  
Partial Order ◽  
Lattice Order

Raman Spectra of Ion Implanted Graphite

1981 ◽  
Vol 7 ◽  
Author(s):  
B.S. Elman ◽  
H. Mazurek ◽  
M.S. Dresselhaus ◽  
G. Dresselhaus
Keyword(s):  
Raman Spectroscopy ◽  
Ion Implantation ◽  
Raman Spectra ◽  
Annealing Temperature ◽  
Annealing Process ◽  
Lattice Order ◽  
Annealing Temperatures ◽  
High Fluences ◽  
Lattice Damage ◽  
The Way

ABSTRACTRaman spectroscopy is used in a variety of ways to monitor different aspects of the lattice damage caused by ion implantation into graphite. Particular attention is given to the use of Raman spectroscopy to monitor the restoration of lattice order by the annealing process, which depends critically on the annealing temperature and on the extent of the original lattice damage. At low fluences the highly disordered region is localized in the implanted region and relatively low annealing temperatures are required, compared with the implantation at high fluences where the highly disordered region extends all the way to the surface. At high fluences, annealing temperatures comparable to those required for the graphitization of carbons are necessary to fully restore lattice order.

scholarly journals RATIONAL POLYHEDRA AND PROJECTIVE LATTICE-ORDERED ABELIAN GROUPS WITH ORDER UNIT

2012 ◽  
Vol 14 (03) ◽  
pp. 1250017 ◽  
Author(s):  
LEONARDO CABRER ◽  
DANIELE MUNDICI
Keyword(s):  
Abelian Group ◽  
Algebraic Topology ◽  
Lattice Structure ◽  
Order Unit ◽  
Finitely Generated ◽  
Lattice Order ◽  
Translation Invariant ◽  
Projective Lattice ◽  
Rational Polyhedra ◽  
Finitely Presented

An ℓ-groupG is an abelian group equipped with a translation invariant lattice-order. Baker and Beynon proved that G is finitely generated projective if and only if it is finitely presented. A unital ℓ-group is an ℓ-group G with a distinguished order unit, i.e. an element 0 ≤ u ∈ G whose positive integer multiples eventually dominate every element of G. Unital ℓ-homomorphisms between unital ℓ-groups are group homomorphisms that also preserve the order unit and the lattice structure. A unital ℓ-group (G, u) is projective if whenever ψ : (A, a) → (B, b) is a surjective unital ℓ-homomorphism and ϕ : (G, u) → (B, b) is a unital ℓ-homomorphism, there is a unital ℓ-homomorphism θ : (G, u) → (A, a) such that ϕ = ψ ◦ θ. While every finitely generated projective unital ℓ-group is finitely presented, the converse does not hold in general. Classical algebraic topology (à la Whitehead) is combined in this paper with the Włodarczyk–Morelli solution of the weak Oda conjecture for toric varieties, to describe finitely generated projective unital ℓ-groups.

Commutative L-algebras and measure theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wolfgang Rump
Keyword(s):  
Measure Theory ◽  
Measurable Space ◽  
Universal Covering ◽  
Continuous Functions ◽  
Stone Space ◽  
Integration Theory ◽  
General Measure ◽  
Lattice Order ◽  
Finitely Additive Measures ◽  
Additive Measures

Abstract Measure and integration theory for finitely additive measures, including vector-valued measures, is shown to be essentially covered by a class of commutative L-algebras, called measurable algebras. The domain and range of any measure is a commutative L-algebra. Each measurable algebra embeds into its structure group, an abelian group with a compatible lattice order, and each (general) measure extends uniquely to a monotone group homomorphism between the structure groups. On the other hand, any measurable algebra X is shown to be the range of an essentially unique measure on a measurable space, which plays the role of a universal covering. Accordingly, we exhibit a fundamental group of X, with stably closed subgroups corresponding to a special class of measures with X as target. All structure groups of measurable algebras arising in a classical context are archimedean. Therefore, they admit a natural embedding into a group of extended real-valued continuous functions on an extremally disconnected compact space, the Stone space of the measurable algebra. Extending Loomis’ integration theory for finitely additive measures, it is proved that, modulo null functions, each integrable function can be represented by a unique continuous function on the Stone space.

scholarly journals Membrane Fluctuations Destabilize Clathrin Protein Lattice Order

2014 ◽  
Author(s):  
Nicholas Cordella ◽  
Thomas J. Lampo ◽  
Shafigh Mehraeen ◽  
Andrew J. Spakowitz
Keyword(s):  
Lattice Order ◽  
Membrane Fluctuations

scholarly journals Self-assembly of highly ordered DNA origami lattices at solid-liquid interfaces by controlling cation binding and exchange

Nano Research ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 3142-3150 ◽  
Author(s):  
Yang Xin ◽  
Salvador Martinez Rivadeneira ◽  
Guido Grundmeier ◽  
Mario Castro ◽  
Adrian Keller
Keyword(s):  
Correlation Length ◽  
Self Assembly ◽  
High Speed ◽  
Time Course ◽  
Divalent Cations ◽  
Topological Analysis ◽  
Monovalent Cation ◽  
Cation Binding ◽  
Dna Origami ◽  
Lattice Order

Abstract The surface-assisted hierarchical self-assembly of DNA origami lattices represents a versatile and straightforward method for the organization of functional nanoscale objects such as proteins and nanoparticles. Here, we demonstrate that controlling the binding and exchange of different monovalent and divalent cation species at the DNA-mica interface enables the self-assembly of highly ordered DNA origami lattices on mica surfaces. The development of lattice quality and order is quantified by a detailed topological analysis of high-speed atomic force microscopy (HS-AFM) images. We find that lattice formation and quality strongly depend on the monovalent cation species. Na+ is more effective than Li+ and K+ in facilitating the assembly of high-quality DNA origami lattices, because it is replacing the divalent cations at their binding sites in the DNA backbone more efficiently. With regard to divalent cations, Ca2+ can be displaced more easily from the backbone phosphates than Mg2+ and is thus superior in guiding lattice assembly. By independently adjusting incubation time, DNA origami concentration, and cation species, we thus obtain a highly ordered DNA origami lattice with an unprecedented normalized correlation length of 8.2. Beyond the correlation length, we use computer vision algorithms to compute the time course of different topological observables that, overall, demonstrate that replacing MgCl2 by CaCl2 enables the synthesis of DNA origami lattices with drastically increased lattice order.

Evidence for Vacancy Clustering in Silicon Implanted Indium Phosphide

1992 ◽  
Vol 268 ◽  
Author(s):  
Peter J. Schultz ◽  
P.J. Simpson ◽  
U.G. Akano ◽  
I.V. Mitchell
Keyword(s):  
Room Temperature ◽  
Elevated Temperatures ◽  
Annihilation Radiation ◽  
Doppler Broadening ◽  
Lattice Order ◽  
Defect Reduction ◽  
Room Temperature Photoluminescence ◽  
Moderate Reduction ◽  
Vacancy Type Defect ◽  
Variable Energy

ABSTRACTDamage induced in InP wafers by ion implantation has been investigated using Doppler broadening of annihilation radiation from variable-energy positrons (VEP), Rutherford backscattering/channeling (RBS), and room temperature photoluminescence (PL). Si* ions were implanted at 600 keV incident energy to total fluences from 1011 to 1014 ions cm−2. Annealing at room temperature was monitored for ∼100 days, during which both VEP and RBS showed recovery of the crystal toward the pre–implanted condition. RBS measurements of samples annealed at elevated temperatures showed that full restoration of lattice order occurred at 375 K, but VEP data for isochronal annealing up to 720 K showed only a moderate reduction in the vacancy–type defect concentration with a significantly narrower lineshape, consistent with vacancy clustering. PL measurements for MOCVD grown InP layers annealed up to 1100 K after implantation also indicated only moderate defect reduction.

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