Multiple Attribute Decision Making Based on Linguistic Generalized Weighted Heronian Mean

In actual multiple attribute decision making, people often use language to evaluate attributes of the object, and sometimes there are associations between the attributes. Therefore, the study of multiple attribute decision making with language as attributes and associations between attributes is of great theoretical significance and practical value. The Heronian mean is not only an operator which reflects the associations between attributes, but also has excellent properties, including idempotency, monotonicity, boundedness, parameter symmetry, and alternate symmetry. In this paper, firstly a new linguistic generalized weighted Heronian mean (LGWHM) was provided, and its properties including idempotency, monotonicity, boundedness, and limit were studied. Then, a new three-parameter linguistic generalized weighted Heronian mean (TPLGWHM) and its idempotency, monotonicity, and boundedness properties were proposed. Finally, multi-attribute decision making methods based on the new linguistic generalized weighted Heronian mean were given, and an example was analyzed and compared with other methods.

Evidence for even parity unconventional superconductivity in Sr2RuO4

Unambiguous identification of the superconducting order parameter symmetry in Sr2RuO4 has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid 3He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent 17O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates.

A Personal Perspective on the Unconventional Superconductivity of Sr2RuO4

I give a personal account of the unfolding story of the unconventional superconductivity of Sr2RuO4. This is a subject of topical importance in light of recent measurements that suggest that its order parameter may be even parity, contrary to the picture that had built up over the course of over two decades of research. With an eye on the past, I stress the generous encouragement that I received from Ted Geballe in the early years of my Sr2RuO4 research. Looking to the future, I give my opinion about why the Sr2RuO4 problem is of major significance to the development of the field of unconventional superconductivity, whatever order parameter symmetry is finally established to be the correct one.

London Penetration Depth as a Test of Order Parameter Symmetry in Sodium Cobaltate Superconductors

Temperature dependence of the magnetic field penetration depth λ was calculated for water intercalated sodium cobaltate superconductor Na x CoO 2 · y H 2 O. Assuming that the system is in the chiral d+id–wave superconducting state, it was shown that the shifting of the excitation spectrum nodal points off the normal phase Fermi surface due to variation of the sodium content x changes the functional form of the temperature dependence of λ − 2 from exponential to linear in the low temperatures region. It is argued that this change in the functional form of T–dependence of the λ − 2 can serve as a proof for the chiral symmetry of the superconducting order parameter in the sodium cobaltate.

Vanadium clusters formation in geometrically frustrated spinel oxide AlV2O4

The spinel oxide AlV2O4 is a unique material, in which the formation of clusters is accompanied by atomic, charge and orbital ordering and a rhombohedral lattice distortion. In this work a theory of the structural phase transition in AlV2O4 is proposed. This theory is based on the study of the order-parameter symmetry, thermodynamics, electron density distribution, crystal chemistry and mechanisms of formation of the atomic and orbital structures of the rhombohedral phase. It is established that the critical order parameter is transformed according to irreducible representation k 9(τ4) (in Kovalev notation) of the Fd \bar{3}m space group. Knowledge of the order-parameter symmetry allows us to show that the derived AlV2O4 rhombohedral structure is a result of displacements of all atom types and the ordering of Al atoms (1:1 order type in tetrahedral spinel sites), V atoms (1:1:6 order type in octahedral sites) and O atoms (1:1:3:3 order type), and the ordering of dxy , dxz and dyz orbitals. Application of the density functional theory showed that V atoms in the Kagomé sublattice formed separate trimers. Also, no sign of metallic bonding between separate vanadium trimers in the heptamer structure was found. The density functional theory study and the crystal chemical analysis of V—O bond lengths allowed us to assume the existence of dimers and trimers as main clusters in the structure of the AlV2O4 rhombohedral modification. The trimer model of the low-symmetry AlV2O4 structure is proposed. Within the Landau theory of phase transitions, typical diagrams of possible phase states are built. It is shown that phase states can be changed as a first-order phase transition close to the second order in the vicinity of tricritical points of the phase diagrams.

Andreev bound states at spin-active interfaces

Andreev bound states are ubiquitous in superconducting hybrid structures. They are formed near impurities, in Josephson junctions, in vortex cores and at interfaces. At spin-active superconductor–ferromagnet interfaces, Andreev bound states are formed due to spin-dependent scattering phases. Spin-dependent phase shifts are an important ingredient for the generation of triplet Cooper pairs in superconductor–ferromagnet hybrid structures. Spectroscopy of Andreev bound states is a powerful probe of superconducting order parameter symmetry, as well as spin-dependent interface scattering and the triplet proximity effect. This article is part of the theme issue ‘Andreev bound states’.

Influence of Magnetic Order Parameter Symmetry and Spin Fluctuations on Forming of Ferroelectric Order in Mn2O5 Oxides

The magnetic phase transitions from paramagnetic to magnetic phases have studied in RMn2O5 oxides. Using a symmetry analysis and renormalization group method it was shown that an appearance of the electric polarization or lack whereof in the magnetic phases are determined the symmetry of these phases and spin fluctuations in the vicinity of the phase transitions.