Chapter 5 Sample Clauses

Chapter 5. The Fifth Chapter is devoted to the study of ▇▇▇▇▇▇▇ dice lattices. As it is known from experiments, the different stackings of the same single-atom- thick lattices give the systems with very different properties. The most prominent example is the twisted bilayer graphene [1], where the proper rotation angle between layers allowed to achieve superconductivity. The idea of the Fifth Chapter is to study more simple stackings of two identical dice lattices with different sublattices aligned on top of each other. Since the dice lattice itself has flat band in spectrum and thus contains the pseudospin-1 fermions as effective quasiparticles, it is interesting to see whether bilayer configuration would preserve such quasiparticles. The results of the Chapter show that while the triply degenerate points are always preserved, the effective dispersion of quasiparticles might change. The classification of all commensurate simple stackings is per- formed and it is shown that one can achieve pseudospin-1, semi-Dirac type of dispersion (with different dispersion law - linear and quadratic de- pending on direction) or nodal line crossings where two bands cross each other along high-symmetry line. Also the triple points are shifted from the charge-neutrality points, which means that the pseudospin-1 quasi- particles would be accessible upon doping. The results of this Chapter show how reach physics one could obtain out of bilayer stacking of a very simple flat band model. The studies of such multilayer systems might explain how the prop- erties of underlying simple flat band models result in nontrivial physics observed in more complicated crystals. As an example, one could think about Kagome metals where the perfect flat-band lattice is placed as a layer of 3D crystal [23] and several such layers separated from each other are present in chemically-stable order in a sample.

Chapter 5. The provisions of the OECD IHTMTC and its Commentary that can be improved the fiscal domicile of the donor, the Austrian foundation.28 The state of the beneficiaries’ residence will thus not seek to levy tax on the gift concerned also given that the immovable property is located in Austria.29This leads to double non-taxation. Moreover, I observe that, reversing the legal systems of the Contracting States, the donation from the Austrian foundation to its non-resident beneficiaries may be subject to double taxation. If Austria applies gift taxes to the inter vivos transfer of property, it may seek to apply the inheritance and gift tax treaty with the Contracting State of the non-resident beneficiaries. More specifically, it may seek to apply Article 7 of this treaty that grants exclusive rights to Austria with regard to immovable property located in Austria. On the other hand, the Contracting State of beneficiaries’ residence that levies income taxes on gifts, may seek to apply the income tax treaty with Austria and more specifically Article 21 (“other income”). This Article allocates exclusive taxing rights to this State since the bene- ficiaries are resident in its territory. As a result, the Contracting State of the beneficiaries’ residence may also seek to levy tax on the inter vivos transfer of property at hand under the income and capital tax treaty concluded with Austria. It follows that the same inter vivos transfer of property is taxed by both Austria and the state of the beneficiaries’ residence under two different tax treaties.30

Chapter 5. ‌ The topic of research presented in this Chapter is disjoint from the top- ics of others, and is related to hydrodynamic of electronic currents in graphene. Strong interaction among charge carriers can make them move like viscous fluid. In this Chapter we explore alternating current (AC) effects in viscous electronics. In the Ohmic case, incompressible current distribu- tion in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation and for the possibility of propagating slow shear waves. We focus on specific geometries that showcase interesting aspects of such waves: current par- allel to a one-dimensional defect and current applied across a long strip. We find that the phase velocity of the wave propagating along the strip respectively increases/decreases with the frequency for no-slip/no-stress boundary conditions. This is so because when the frequency or strip width goes to zero (alternatively, viscosity go to infinity), the wavelength of the current pattern tends to infinity in the no-stress case and to a finite value in a general case. We also show that for DC current across a strip 32 Chapter 1. Introduction with no-stress boundary, there only one pair of vortices, while there is an infinite vortex chain for all other types of boundary conditions. Chapter 2‌ 2.1 Introduction‌ In the seminal paper [172] ▇▇▇▇▇▇▇ and ▇▇▇▇▇▇ found ’exact solution’ to 4d = 2 super-symmetric gauge theory in the strong coupling regime. More strictly, the IR effective couplings were constructed geometrically, from the period integrals on a complex curve, whose moduli are determined by the condensates and bare couplings of the UV gauge theory. Shortly after, it has been also realized [72] that natural language for the Seiberg-Witten theory is given by classical integrable systems. In such context the pure supersymmetric gauge theories (with only = 2 vector supermultiplets) correspond to the Toda chains, while integrable systems for the gauge theories with fundamental matter multiplets are usually identified with classical spin chains of XXX-type. The next important step was proposed in [164], where this picture has been lifted to 5d. Then it has been shown that transition from 4d to 5d (actually – four plus one compact dimensions) results in ’relativization’ of the integrable systems [143] (in the sense of Ruijsenaars [159]). In the simplest case of SU (2) pure Yang-Mills theory, or affine Toda c...

Chapter 5. The provisions of the OECD IHTMTC and its Commentary that can be improved of Article 4(2) of the OECD ICTMTC confirms the above.19 Both tiebreaker rules, thus, give preference to the Contracting State of the person’s permanent home, his centre of vital interests, his habitual abode, his nationality and, as a last resort, to what the Contracting States will decide following a mutual agreement procedure. It follows that through the application of these connective criteria, the Contracting States aim at identifying the attachment of the individual with a state and at affording primary taxing rights to the Contracting State with which this person is the most attached. As a result, the attachment of a person with a Contracting State is examined alike in both models as also shown by the similarities of the commentaries on both OECD tiebreaker rules. Nevertheless, it could be argued that the assessment of the attachment of a person with a Contracting State under the same connective criteria for both inheritance/gift and income tax treaty purposes may be problematic in some cases. In my view, the OECD IHTMTC’s tiebreaker rule seems to counter the manner in which certain states establish the lifelong attachment of a person with their territory and the third element of the pro- posed inheritance and gift tax (connection with civil law). For example, the deceased’s or donor’s intention to fiscally domicile in a Contracting State – an essential element of some inheritance and gift tax legislations – seems to be deliberately ignored. Under paragraph 22 of the Commentary on Article 4, “[t]he determination of the individual’s intention can result in endless disputes and, what is more, to manipulation on the part of the heirs.” One would expect, however, that those who drafted the OECD IHTMTC would have explicitly mentioned in the Commentary on Article 4 of the OECD IHTMTC that states are free to insert an intention test into the tiebreaker rule of their inheritance and gift tax treaty. Likewise, the requirement of a minimum period of presence of a person in a Contracting State – usually forming part of the assessment of his lifelong attachment to the state – does also not seem to be reflected in the wording of the tiebreaker rule. For example, the determination of the fiscal domicile based on the availability of a permanent home without a minimum period of presence in a Contracting State seems again to contradict the manner in which certain states establish the lifelong ...

Chapter 5. (a) The header of Chapter 5 is replaced with the following: