scholarly journals Addition to “News from the Periodic Table: An Introduction to ‘Periodicity Symbols, Tables, and Models for Higher-Order Valency and Donor–Acceptor Kinships’”

2019 ◽  
Vol 96 (5) ◽  
pp. 1051-1051
Author(s):  
Frank Weinhold
Keyword(s):  
Periodic Table ◽  
Higher Order ◽  
Donor Acceptor

scholarly journals Higher-Order Hamiltonian for Circuits with (α,β) Elements

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 412
Author(s):  
Zdeněk Biolek ◽  
Dalibor Biolek ◽  
Viera Biolková ◽  
Zdeněk Kolka
Keyword(s):  
Predictive Modeling ◽  
Periodic Table ◽  
Constitutive Relations ◽  
Lagrange Function ◽  
Higher Order ◽  
Simulation Scheme

The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen’s theorem. According to the ideas of predictive modeling, the resulting Hamiltonian is made up exclusively of the constitutive relations of the elements in the circuit. Within the frame of Ostrogradsky’s formalism, the simulation scheme of Σ-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator.

scholarly journals Classification of topological invariants related to corner states

2021 ◽  
Vol 111 (5) ◽  
Author(s):  
Shin Hayashi
Keyword(s):  
Periodic Table ◽  
Topological Insulators ◽  
Higher Order ◽  
Topological Invariants ◽  
Bulk Surface ◽  
Definition Of

AbstractWe discuss some bulk-surface gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four things: (1) the definition of topological invariants, (2) a proof of their relation with corner states, (3) computations of K-groups and (4) a construction of explicit examples.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Multislice calculations for quasi-periodic and non-periodic objects

1990 ◽  
Vol 48 (4) ◽  
pp. 138-139
Author(s):  
R. Herrera ◽  
A. Gómez
Keyword(s):  
Electron Diffraction ◽  
Computer Simulations ◽  
Periodic Table ◽  
Amorphous Materials ◽  
Space Group ◽  
Essential Step ◽  
Shape Effects ◽  
Atomic Scattering ◽  
Diffraction Patterns ◽  
Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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