# I and i

TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

##### Citations

More filters

••

TL;DR: In this paper, a new type of metallic structure has been developed that is characterized by having high surface impedance, which is analogous to a corrugated metal surface in which the corrugations have been folded up into lumped-circuit elements and distributed in a two-dimensional lattice.

Abstract: A new type of metallic electromagnetic structure has been developed that is characterized by having high surface impedance. Although it is made of continuous metal, and conducts dc currents, it does not conduct ac currents within a forbidden frequency band. Unlike normal conductors, this new surface does not support propagating surface waves, and its image currents are not phase reversed. The geometry is analogous to a corrugated metal surface in which the corrugations have been folded up into lumped-circuit elements, and distributed in a two-dimensional lattice. The surface can be described using solid-state band theory concepts, even though the periodicity is much less than the free-space wavelength. This unique material is applicable to a variety of electromagnetic problems, including new kinds of low-profile antennas.

4,264 citations

### Cites background from "I and i"

...Periodic two- or three-dimensional dielectric [20]–[24], metallic [25]–[28], or metallodielectric [29]–[33] structures that prevent the propagation of electromagnetic waves are known as pho-...

[...]

••

TL;DR: VESTA as mentioned in this paper is a cross-platform program for visualizing both structural and volumetric data in multiple windows with tabs, including isosurfaces, bird's-eye views and two-dimensional maps.

Abstract: A cross-platform program, VESTA, has been developed to visualize both structural and volumetric data in multiple windows with tabs. VESTA represents crystal structures by ball-and-stick, space-filling, polyhedral, wireframe, stick, dot-surface and thermal-ellipsoid models. A variety of crystal-chemical information is extractable from fractional coordinates, occupancies and oxidation states of sites. Volumetric data such as electron and nuclear densities, Patterson functions, and wavefunctions are displayed as isosurfaces, bird's-eye views and two-dimensional maps. Isosurfaces can be colored according to other physical quantities. Translucent isosurfaces and/or slices can be overlapped with a structural model. Collaboration with external programs enables the user to locate bonds and bond angles in the `graphics area', simulate powder diffraction patterns, and calculate site potentials and Madelung energies. Electron densities determined experimentally are convertible into their Laplacians and electronic energy densities.

4,172 citations

••

TL;DR: A critical review of the synthesis methods for graphene and its derivatives as well as their properties and the advantages of graphene-based composites in applications such as the Li-ion batteries, supercapacitors, fuel cells, photovoltaic devices, photocatalysis, and Raman enhancement are described.

Abstract: Graphene has attracted tremendous research interest in recent years, owing to its exceptional properties. The scaled-up and reliable production of graphene derivatives, such as graphene oxide (GO) and reduced graphene oxide (rGO), offers a wide range of possibilities to synthesize graphene-based functional materials for various applications. This critical review presents and discusses the current development of graphene-based composites. After introduction of the synthesis methods for graphene and its derivatives as well as their properties, we focus on the description of various methods to synthesize graphene-based composites, especially those with functional polymers and inorganic nanostructures. Particular emphasis is placed on strategies for the optimization of composite properties. Lastly, the advantages of graphene-based composites in applications such as the Li-ion batteries, supercapacitors, fuel cells, photovoltaic devices, photocatalysis, as well as Raman enhancement are described (279 references).

3,340 citations

••

TL;DR: This work shows that absence of entanglement does not imply classicality, and considers the vanishing of discord as a criterion for the preferred effectively classical states of a system, i.e., the pointer states.

Abstract: Two classically identical expressions for the mutual information generally differ when the systems involved are quantum. This difference defines the quantum discord. It can be used as a measure of the quantumness of correlations. Separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord, thus showing that absence of entanglement does not imply classicality. We relate this to the quantum superposition principle, and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system, i.e., the pointer states.

3,244 citations

### Cites methods from "I and i"

...Above ai jaj di,j following the ideal einselection process, which transforms a pure r S ,A into a decohered r D S ,A satisfying the superselection identity [9,10]...

[...]

••

TL;DR: In this paper, the authors provide a classification of the main problems addressed in the literature with respect to the notion of explanation and the type of black box decision support systems, given a problem definition, a black box type, and a desired explanation, this survey should help the researcher to find the proposals more useful for his own work.

Abstract: In recent years, many accurate decision support systems have been constructed as black boxes, that is as systems that hide their internal logic to the user. This lack of explanation constitutes both a practical and an ethical issue. The literature reports many approaches aimed at overcoming this crucial weakness, sometimes at the cost of sacrificing accuracy for interpretability. The applications in which black box decision systems can be used are various, and each approach is typically developed to provide a solution for a specific problem and, as a consequence, it explicitly or implicitly delineates its own definition of interpretability and explanation. The aim of this article is to provide a classification of the main problems addressed in the literature with respect to the notion of explanation and the type of black box system. Given a problem definition, a black box type, and a desired explanation, this survey should help the researcher to find the proposals more useful for his own work. The proposed classification of approaches to open black box models should also be useful for putting the many research open questions in perspective.

2,805 citations

##### References

More filters

••

TL;DR: In this paper, a new type of metallic structure has been developed that is characterized by having high surface impedance, which is analogous to a corrugated metal surface in which the corrugations have been folded up into lumped-circuit elements and distributed in a two-dimensional lattice.

Abstract: A new type of metallic electromagnetic structure has been developed that is characterized by having high surface impedance. Although it is made of continuous metal, and conducts dc currents, it does not conduct ac currents within a forbidden frequency band. Unlike normal conductors, this new surface does not support propagating surface waves, and its image currents are not phase reversed. The geometry is analogous to a corrugated metal surface in which the corrugations have been folded up into lumped-circuit elements, and distributed in a two-dimensional lattice. The surface can be described using solid-state band theory concepts, even though the periodicity is much less than the free-space wavelength. This unique material is applicable to a variety of electromagnetic problems, including new kinds of low-profile antennas.

4,264 citations

••

TL;DR: VESTA as mentioned in this paper is a cross-platform program for visualizing both structural and volumetric data in multiple windows with tabs, including isosurfaces, bird's-eye views and two-dimensional maps.

Abstract: A cross-platform program, VESTA, has been developed to visualize both structural and volumetric data in multiple windows with tabs. VESTA represents crystal structures by ball-and-stick, space-filling, polyhedral, wireframe, stick, dot-surface and thermal-ellipsoid models. A variety of crystal-chemical information is extractable from fractional coordinates, occupancies and oxidation states of sites. Volumetric data such as electron and nuclear densities, Patterson functions, and wavefunctions are displayed as isosurfaces, bird's-eye views and two-dimensional maps. Isosurfaces can be colored according to other physical quantities. Translucent isosurfaces and/or slices can be overlapped with a structural model. Collaboration with external programs enables the user to locate bonds and bond angles in the `graphics area', simulate powder diffraction patterns, and calculate site potentials and Madelung energies. Electron densities determined experimentally are convertible into their Laplacians and electronic energy densities.

4,172 citations

••

TL;DR: A critical review of the synthesis methods for graphene and its derivatives as well as their properties and the advantages of graphene-based composites in applications such as the Li-ion batteries, supercapacitors, fuel cells, photovoltaic devices, photocatalysis, and Raman enhancement are described.

Abstract: Graphene has attracted tremendous research interest in recent years, owing to its exceptional properties. The scaled-up and reliable production of graphene derivatives, such as graphene oxide (GO) and reduced graphene oxide (rGO), offers a wide range of possibilities to synthesize graphene-based functional materials for various applications. This critical review presents and discusses the current development of graphene-based composites. After introduction of the synthesis methods for graphene and its derivatives as well as their properties, we focus on the description of various methods to synthesize graphene-based composites, especially those with functional polymers and inorganic nanostructures. Particular emphasis is placed on strategies for the optimization of composite properties. Lastly, the advantages of graphene-based composites in applications such as the Li-ion batteries, supercapacitors, fuel cells, photovoltaic devices, photocatalysis, as well as Raman enhancement are described (279 references).

3,340 citations

••

TL;DR: This work shows that absence of entanglement does not imply classicality, and considers the vanishing of discord as a criterion for the preferred effectively classical states of a system, i.e., the pointer states.

Abstract: Two classically identical expressions for the mutual information generally differ when the systems involved are quantum. This difference defines the quantum discord. It can be used as a measure of the quantumness of correlations. Separability of the density matrix describing a pair of systems does not guarantee vanishing of the discord, thus showing that absence of entanglement does not imply classicality. We relate this to the quantum superposition principle, and consider the vanishing of discord as a criterion for the preferred effectively classical states of a system, i.e., the pointer states.

3,244 citations

•

01 Jan 2000TL;DR: In this paper, a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics is presented, focusing on methods for linear elliptic boundary value problems.

Abstract: This monograph presents a summary account of the subject of a posteriori error estimation for finite element approximations of problems in mechanics. The study primarily focuses on methods for linear elliptic boundary value problems. However, error estimation for unsymmetrical systems, nonlinear problems, including the Navier-Stokes equations, and indefinite problems, such as represented by the Stokes problem are included. The main thrust is to obtain error estimators for the error measured in the energy norm, but techniques for other norms are also discussed.

2,607 citations