scholarly journals On the eigenvalues of quantum graph Laplacians with large complex $\delta$ couplings

2020 ◽  
Vol 77 (2) ◽  
pp. 133-161
Author(s):  
James Kennedy ◽  
Robin Lang
Keyword(s):  
Quantum Graph ◽  
Large Complex ◽  
Graph Laplacians

scholarly journals Asymptotics and Estimates for Spectral Minimal Partitions of Metric Graphs

2021 ◽  
Vol 93 (3) ◽  
Author(s):  
Matthias Hofmann ◽  
James B. Kennedy ◽  
Delio Mugnolo ◽  
Marvin Plümer
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Behaviour ◽  
Lower Bounds ◽  
Upper Bounds ◽  
Isoperimetric Inequalities ◽  
Quantum Graph ◽  
Combinatorial Structure ◽  
Metric Graphs ◽  
Metric Graph ◽  
Graph Laplacians

AbstractWe study properties of spectral minimal partitions of metric graphs within the framework recently introduced in Kennedy et al. (Calc Var 60:6, 2021). We provide sharp lower and upper estimates for minimal partition energies in different classes of partitions; while the lower bounds are reminiscent of the classic isoperimetric inequalities for metric graphs, the upper bounds are more involved and mirror the combinatorial structure of the metric graph as well. Combining them, we deduce that these spectral minimal energies also satisfy a Weyl-type asymptotic law similar to the well-known one for eigenvalues of quantum graph Laplacians with various vertex conditions. Drawing on two examples we show that in general no second term in the asymptotic expansion for minimal partition energies can exist, but show that various kinds of behaviour are possible. We also study certain aspects of the asymptotic behaviour of the minimal partitions themselves.

scholarly journals Zero Modes of Quantum Graph Laplacians and an Index Theorem

2014 ◽  
Vol 16 (5) ◽  
pp. 1155-1189
Author(s):  
Jens Bolte ◽  
Sebastian Egger ◽  
Frank Steiner
Keyword(s):  
Index Theorem ◽  
Quantum Graph ◽  
Zero Modes ◽  
Graph Laplacians

Using the principles and approaches of flexible methodology (agile) in the planning and implementation of the educational process

2020 ◽  
pp. 48-55
Author(s):  
TING ZHU
Keyword(s):  
Labor Market ◽  
Program Development ◽  
Development Process ◽  
Project Manager ◽  
Educational Process ◽  
Large Complex ◽  
Complex Projects ◽  
Quality Risk ◽  
The Government

The educatonal program development process is challenging with many stakeholders: students, teachers, parents, administrators, employers, and the government. Each stakeholder has compettve priorites; Quality, risk, resources and costs limitaton. Large complex projects require the management of a skilled and experienced project manager. It is the preparaton of curricula for joint internatonal educatonal programs with the use of Agile tools and technologies. The main "customer" in this program is a student, and the ultmate goal of each project within the program-the competence of the student in the labor market afer receiving the diploma. Therefore, this program can be considered difcult, and it is constantly evolves, because the demands of the labor market of China is constantly changing and developing.

scholarly journals Winding uplifts and the challenges of weak and strong SUSY breaking in AdS

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Arthur Hebecker ◽  
Sascha Leonhardt
Keyword(s):  
Complex Structure ◽  
Susy Breaking ◽  
Technical Level ◽  
De Sitter ◽  
Large Complex ◽  
Breaking Scale ◽  
Large Complex Structure

Abstract We discuss the problem of metastable SUSY breaking in the landscape. While this is clearly crucial for the various de Sitter proposals, it is also interesting to consider the SUSY breaking challenge in the AdS context. For example, it could be that a stronger form of the non-SUSY AdS conjecture holds: it would forbid even metastable non-SUSY AdS in cases where the SUSY-breaking scale is parametrically above/below the AdS scale. At the technical level, the present paper proposes to break SUSY using the multi-cosine-shaped axion potentials which arise if a long winding trajectory of a ‘complex-structure axion’ appears in the large-complex-structure limit of a Calabi-Yau orientifold. This has been studied in the context of ‘Winding Inflation’, but the potential for SUSY breaking has not been fully explored. We discuss the application to uplifting LVS vacua, point out the challenges which one faces in the KKLT context, and consider the possibility of violating the non-SUSY AdS conjecture in the type-IIA setting of DGKT.

scholarly journals Nonlinearity-generated resilience in large complex systems

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
S. Belga Fedeli ◽  
Y. V. Fyodorov ◽  
J. R. Ipsen
Keyword(s):  
Complex Systems ◽  
Large Complex

scholarly journals Off-line programming of robot on laser cleaning for large complex components

2021 ◽  
Vol 1748 ◽  
pp. 022027
Author(s):  
Jin Shuo ◽  
Ren Yuan ◽  
Ma Qingzeng ◽  
Ge Hailong ◽  
Li Wenlong ◽  
...  
Keyword(s):  
Laser Cleaning ◽  
Large Complex ◽  
Complex Components
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