Coordination shells and coordination numbers of the vertex graph of the Ammann–Beenker tiling

2019 ◽  
Vol 75 (5) ◽  
pp. 746-757
Author(s):  
Anton Shutov ◽  
Andrey Maleev
Keyword(s):  
Asymptotic Formula ◽  
Growth Form ◽  
Rotational Symmetry ◽  
Coordination Sequence ◽  
Coordination Numbers ◽  
Vertex Graph ◽  
Regular Octagon

The vertex graph of the Ammann–Beenker tiling is a well-known quasiperiodic graph with an eightfold rotational symmetry. The coordination sequence and coordination shells of this graph are studied. It is proved that there exists a limit growth form for the vertex graph of the Ammann–Beenker tiling. This growth form is an explicitly calculated regular octagon. Moreover, an asymptotic formula for the coordination numbers of the vertex graph of the Ammann–Beenker tiling is also proved.

Coordination numbers of the vertex graph of a Penrose tiling

2018 ◽  
Vol 74 (2) ◽  
pp. 112-122 ◽  
Author(s):  
Anton Shutov ◽  
Andrey Maleev
Keyword(s):  
Asymptotic Formula ◽  
Penrose Tiling ◽  
New Approach ◽  
Coordination Numbers ◽  
Vertex Graph

A new approach to study coordination shells and coordination sequences of quasiperiodic graphs is suggested. The structure of the coordination shells in the vertex graph of a Penrose tiling is described. An asymptotic formula for its coordination numbers is obtained. An essentially different behaviour of the coordination numbers for even and odd shells is revealed.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

Herbicide Tolerance Of Transgenic `Stevens' Cranberry Plants Depends on the Test Environment

HortScience ◽  
1998 ◽  
Vol 33 (3) ◽  
pp. 517a-517
Author(s):  
Eric L. Zeldin ◽  
Rodney A. Serres ◽  
Brent H. McCown
Keyword(s):  
Growth Form ◽  
Herbicide Tolerance ◽  
Genetically Engineered ◽  
Shoot Tip ◽  
Test Environment ◽  
Growth Environment ◽  
Commercial Formulation ◽  
Tolerance Level ◽  
Delayed Growth ◽  
Significant Injury

`Stevens' cranberry was genetically engineered to confer tolerance to the broad spectrum herbicide glufosinate. Initially, herbicide tolerance was verified by spraying greenhouse plants with the commercial formulation Liberty. Although one transformant showed significant tolerance, the tolerance level was below that required to kill goldenrod, a common weed of cranberry beds. This transformant was propagated and the plants established outdoors in a coldframe, yielding a growth form more typical of field-grown plants than that of greenhouse-grown plants. These plants, as well as untransformed cranberry and goldenrod plants, were sprayed with various levels of the herbicide. The transformed plants were not killed at glufosinate concentrations up to 1000 ppm, although delayed growth did occur. Some runner tip injury was observed at 500 ppm as well as widespread shoot tip death at higher levels. The above-ground parts of goldenrod plants were killed at 400 ppm with significant injury at 200 ppm. Untransformed cranberry plants were killed at 300 ppm and had extensive tip death even at 100 ppm. Transformed cranberry plants with confirmed “field” tolerance were re-established in the greenhouse and new vegetative growth was forced. When these plants were sprayed with glufosinate, significant shoot tip injury was observed at levels as low as 100 ppm. The degree of herbicide tolerance of transformed cranberry appears to be modulated by the growth environment, which may affect the expression of the inserted genes or the physiological sensitivity of the impacted tissues.

Approximation properties of Szász type operators involving Charlier polynomials

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 479-487
Author(s):  
Didem Arı
Keyword(s):  
Asymptotic Formula ◽  
Weighted Space ◽  
Approximation Properties ◽  
Charlier Polynomials

In this paper, we give some approximation properties of Sz?sz type operators involving Charlier polynomials in the polynomial weighted space and we give the quantitative Voronovskaya-type asymptotic formula.

Form and Function of Mediterranean Shrublands

2018 ◽  
Author(s):  
Karen J. Esler ◽  
Anna L. Jacobsen ◽  
R. Brandon Pratt
Keyword(s):  
Convergent Evolution ◽  
Growth Form ◽  
Structure And Function ◽  
Adaptive Traits ◽  
Shrub Species ◽  
Leaf Type ◽  
Evergreen Shrub ◽  
Form And Function ◽  
Considerable Research ◽  
And Function

The archetypal shrub type that dominates most of the regions that experience mediterranean-type climate (MTC) is an evergreen shrub with thick and leathery leaves (sclerophyllous). The occurrence of large stands of such shrubs in all MTC regions led early biogeographers to hypothesize that the MTC selects for this growth form and leaf type and that this had led to convergent evolution (see Chapters 1 and 2). This hypothesis has received considerable research interest and continues to be examined. In this chapter we consider the structure and physiology of these archetypal MTC region shrub species and examine evidence for convergent evolution in their structure and function. We also assess the key adaptive traits that enable the shrub species that compose mediterranean-type vegetation (MTV) communities to thrive in MTC regions.

scholarly journals Integrating dark diversity and functional traits to enhance nature conservation of epiphytic lichens: a case study from Northern Italy

2021 ◽  
Author(s):  
Diego Pires Ferraz Trindade ◽  
Meelis Pärtel ◽  
Carlos Pérez Carmona ◽  
Tiina Randlane ◽  
Juri Nascimbene
Keyword(s):  
Climate Change ◽  
Nature Conservation ◽  
Functional Traits ◽  
Growth Form ◽  
Northern Italy ◽  
Epiphytic Lichens ◽  
Mountain Areas ◽  
High Elevations ◽  
Harsh Conditions

AbstractMountains provide a timely opportunity to examine the potential effects of climate change on biodiversity. However, nature conservation in mountain areas have mostly focused on the observed part of biodiversity, not revealing the suitable but absent species—dark diversity. Dark diversity allows calculating the community completeness, indicating whether sites should be restored (low completeness) or conserved (high completeness). Functional traits can be added, showing what groups should be focused on. Here we assessed changes in taxonomic and functional observed and dark diversity of epiphytic lichens along elevational transects in Northern Italy spruce forests. Eight transects (900–1900 m) were selected, resulting in 48 plots and 240 trees, in which lichens were sampled using four quadrats per tree (10 × 50 cm). Dark diversity was estimated based on species co-occurrence (Beals index). We considered functional traits related to growth form, photobiont type and reproductive strategy. Linear and Dirichlet regressions were used to examine changes in taxonomic metrics and functional traits along gradient. Our results showed that all taxonomic metrics increased with elevation and functional traits of lichens differed between observed and dark diversity. At low elevations, due to low completeness and harsh conditions, both restoration and conservation activities are needed, focusing on crustose species. Towards high elevations, conservation is more important to prevent species pool losses, focusing on macrolichens, lichens with Trentepohlia and sexual reproduction. Finally, dark diversity and functional traits provide a novel tool to enhance nature conservation, indicating particular threatened groups, creating windows of opportunities to protect species from both local and regional extinctions.

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