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### Gap Embedding for Well-Quasi-Orderings1 1This research was supported in part by The Israel Science Foundation (grant no. 254/01)

Nachum Dershowitz, Iddo Tzameret
2003 Electronical Notes in Theoretical Computer Science
We show that finite trees are well-quasiordered with respect to gap embedding when labels are taken from an arbitrary well-quasi-ordering such that each tree path can be partitioned into a bounded number  ...  Given a quasi-ordering of labels, a labelled ordered tree s is embedded with gaps in another tree t if there is an injection from the nodes of s into those of t that maps each edge in s to a unique disjoint  ...  There is also a gap embedding quasi-ordering → on trees with the following additional properties: s → t ¢ u ∧ t • u • ⇒ s → u (D) s → t ¢ u ∧ s • u • ⇒ s → u (E) A set of trees is well-quasi-ordered under  ...

### On Quasi Ordinal Diagram Systems

2019 Electronic Proceedings in Theoretical Computer Science
The purposes of this note are the following two; we first generalize Okada-Takeuti's well quasi ordinal diagram theory, utilizing the recent result of Dershowitz-Tzameret's version of tree embedding theorem  ...  with gap conditions.  ...  Well quasi ordering proof for (GQ(I, A), ≪ = ) via Dershowitz and Tzameret's tree embedding theorem We first recall Dershowitz-Tzameret's tree embedding with gap condition (cf. [6, Definition 3.3]).  ...

### From Kruskal's theorem to Friedman's gap condition [article]

Anton Freund
2020 arXiv   pre-print
Harvey Friedman's gap condition on embeddings of finite labelled trees plays an important role in combinatorics (proof of the graph minor theorem) and mathematical logic (strong independence results).  ...  In the present paper we show that the gap condition can be reconstructed from a small number of well-motivated building blocks: it arises via iterated applications of a uniform Kruskal theorem.  ...  Due to T 0 (X) ∼ = X it is clear that T 0 preserves well partial orders. If T n is a normal WPO-dilator, then so is M • T n .  ...

### Fan-Crossing Free Graphs and Their Relationship to other Beyond-Planar Graphs [article]

Franz J. Brandenburg
2020 arXiv   pre-print
Both are prominent examples for beyond-planar graphs. Further well-known beyond-planar classes are the k-planar, k-gap-planar, quasi-planar, and right angle crossing graphs.  ...  Finally, we show that some graphs have a unique fan-crossing free embedding, that there are thinned maximal fan-crossing free graphs, and that the recognition problem for fan-crossing free graphs is NP-complete  ...  is still missing for k-planar, k-gap-planar, fan-crossing free, and quasi-planar graphs if k ≥ 2 [40] .  ...

### Quantum criticality and excitations of a long-range anisotropic XY-chain in a transverse field [article]

P. Adelhardt, A. Schellenberger, K.P. Schmidt
2020 arXiv   pre-print
Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit.  ...  While for the limiting case of the isotropic long-range XY-model we can extract the elementary one quasi-particle dispersion analytically and calculate two quasi-particle excitation energies quantitatively  ...  To extract the correction we calculate the gap for α = 5/3 up to order 10 in the expansion parameter λ. As in Refs.  ...

### Prevalence of trivial zero-energy sub-gap states in non-uniform helical spin chains on the surface of superconductors [article]

Richard Hess, Henry F. Legg, Daniel Loss, Jelena Klinovaja
2022 arXiv   pre-print
Although our findings do not rule them out, the much reduced prevalence of zero-energy bound states in long non-uniform helical spin chains compared with equivalent semi-conductor nanowires, as well as  ...  Therefore, we perform an extensive search for zero-energy bound states in helical spin chain systems with varying rotation rates.  ...  The system hosts the socalled quasi MBSs (yellow) for (a) the aligned and (b) the embedded system.  ...

### p -embeddings

Papiya Bhattacharjee, Michelle L. Knox, Warren Wm. McGovern
2013 Topology and its Applications
We show that this concept lays between the concepts of C * -embeddings and z-embeddings.  ...  This is the sequel to [3] where the notion of a p-extension of commutative rings was investigated: a unital extension of commutative rings, say R → S, is a p-extension if for every s ∈ S there is an r  ...  We would like to thank the referee for their careful reading of our paper. Their comments and suggestions were useful in making this a more accurate and coherent paper.  ...

### Continuum Electronic Bound States in Rectangular Quantum Wells and Barriers

E. A. Carrillo-Delgado, Isaac Rodríguez-Vargas, Stoyan Jelev-Vlaev
2009 PIERS Online
We study the conditions necessary for the creation of these states. We find strong energetic and spatial localization of quasi-bound states at high energies in the conduction band.  ...  We present numerical calculations that support the existence of electronic states confined in the continuous part of the spectrum in single rectangular quantum wells and barriers.  ...  The results will facilitate the search for systems that contain embedded quantum wells between two superlattices where Capasso states appear with spatial localization in the well region and with strong  ...

### Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit

Sebastian Fey, Kai Phillip Schmidt
2016 Physical review B
For this model the elementary Quasiparticle gap is determined allowing to access the quantum-critical regime including critical exponents and multiplicative logarithmic corrections for the ferro- and antiferromagnetic  ...  Quasiparticle properties of quantum magnets with long-range interactions are investigated by high-order linked-cluster expansions in the thermodynamic limit.  ...  Acknowledgement: We thank Kris Coester and Michael Knap for fruitful discussions as well as Michael Knap and Luca Tagliacozzo for providing us with their numerical data.  ...

### Conjecture of Wilf: a survey [article]

2019 arXiv   pre-print
As it frequently happens with combinatorial problems, many researchers who got involved in the search for a solution thought at some point that a solution would be just around the corner, but in the present  ...  I would like to thank my colleges ate the FCUP's Mathematics department who made possible for me to benefit of a sabbatical year.  ...  I want also to thank Claude Marion whose interest shown on the topic highly contributed for my decision on writing this survey. His comments greatly contributed to improve the paper.  ...

### Invariant embedding approach to secondary electron emission from metals [article]

F. X. Bronold, H. Fehske
2021 arXiv   pre-print
Solving the embedding equation within a quasi-isotropic approximation and using the effective mass model for the solid, experimental data are fairly well reproduced provided (i) incoherent scattering on  ...  Based on an invariant embedding principle for the backscattering function we calculate the electron emission yield for metal surfaces at very low electron impact energies.  ...  ACKNOWLEDGMENTS We thank Kristopher Rasek from the University Greifswald for critical reading of the manuscript.  ...

### DUPLEXERS AND MULTIPLEXERS BASED ON MICROSTRIP LINE LOADED WITH COMPLEMENTARY SPLIT RING RESONATORS

Eduardo Jarauta, Francisco J. Falcone, Miguel Beruete, Jesús Illescas
2011 Progress In Electromagnetics Research Letters
By using microstrip lines with Complementary Split Ring Resonators (CSRRs) etched on the ground plane along with series capacitive gaps in the upper conductor, forward coupling will be inverted into backward  ...  The dimensions for the device in Fig. 3 are, r ext1 = 2.4 mm, r ext2 = 2.2 mm, r ext3 = 2 mm and r ext4 = 1.8 mm, which are chosen in order to obtain quasi-static resonance of the CSRR elements embedded  ...  The capacitive gap have a slot width g = 0.2 mm and is the same for all gaps in the article and the gap length depends on the external radius and it can be calculated from lo = r ext − c − d that for the  ...

### A Nonlinear Transmission Line Model for Simulating Distributed SIS Frequency Multipliers

John D. Garrett, Hawal Rashid, Ghassan Yassin, Vincent Desmaris, Alexey B. Pavolotsky, Victor Belitsky
2020 IEEE Transactions on Terahertz Science and Technology
This is beneficial for SIS frequency multipliers because their output power is proportional to the area of the junction.  ...  Superconductor / Insulator / Superconductor (SIS) junctions have extremely nonlinear electrical properties, which makes them ideal for a variety of applications, including heterodyne mixing and frequency  ...  I 0 dc (V b ) = (V b /V gap ) 2x+1 1 + (V b /V gap ) 2x · V gap R n (13) We simulated this DSJ using the quasi-nonlinear model (Eqns.  ...

### Design of a three-dimensional gap-coupled suspended substrate stripline bandpass filter

Y.-C. Chiang, C.-K.C. Tzuang, S. Su
1992 IEE Proceedings H (Microwaves Antennas and Propagation)
The filter is constructed in a bent channelised housing that suppresses any possibility of exciting higher-order modes, except the dominant quasi-TEM mode of propagation.  ...  The measured results for the experimental 21-22 GHz bandpass filter agree very well with the theoretic predictions considering the conductor losses (5.57 x lo-' dB/mm) of the SSS.  ...  Thus, only the quasi-TEM mode and higher-order evanescent modes are allowed to exist in the channelised filter.  ...

### Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe2 with spin-orbit coupling

Andrzej Ptok, Szczepan Głodzik, Tadeusz Domański
2017 Physical review B
We also study the bound states of double impurities for several relative positions in a triangular lattice.  ...  We study topography of the spin-polarized bound states of magnetic impurities embedded in triangular lattice of a superconducting host.  ...  Kapcia for valuable comments and discussions.  ...
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