Infinite Schrödinger networks

Finite-difference models of partial differential equations such as Laplace or Poisson equations lead to a finite network. A discretized equation on an unbounded plane or space results in an infinite network. In an infinite network, Schrödinger operator (perturbed Laplace operator, $q$-Laplace) is defined to develop a discrete potential theory which has a model in the Schrödinger equation in the Euclidean spaces. The relation between Laplace operator $\Delta$-theory and the $\Delta_q$-theory is investigated. In the $\Delta_q$-theory the Poisson equation is solved if the network is a tree and a canonical representation for non-negative $q$-superharmonic functions is obtained in general case.

Non-uniform ISS small-gain theorem for infinite networks

We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork while it allows for non-uniform convergence of all components. For an infinite network consisting of input-to-state stable subsystems, which do not necessarily have a uniform $\mathscr{K}\mathscr{L}$-bound on the transient behaviour, we show the following: if the gain operator satisfies the uniform small-gain condition, then the whole network is non-uniformly input-to-state stable and all its finite subnetworks are input-to-state stable.

1,2-O-Isopropylidene-β-D-lyxo-furanose

In the title compound C8H14O5, the pentofuranose five-membered ring has a twisted conformation on two carbon atoms while the five-membered ring of the isopropylidene group has an envelope conformation on an oxygen atom. Hydroxy groups are involved an infinite network of O—H...O hydrogen bonds that leads to the formation of a layer parallel to the (001) plane. Only weak C—H...O contacts exist between neighboring layers.

Assembling La nueva novela: Juan Luis Martínez and a Material Poetics of Relation

Chapter 3 examines the material poetics of relation that contribute to the Juan Luis Martínez-assembled 1970s artist’s book La nueva novela. It is constructed from such diverse parts as: visual maths problems in which, for example, a painting of Rimbaud and a military jacket minus a shoe, a boot and a sock equals suspenders, a spat and a sock; metal fishhooks taped to a page; riddles and circular problems of logic; other people’s poems; musical scores; drawings, for example, of a pipe split in half (titled ‘Meditations on René Magritte’ and dedicated to Foucault); among many other things. This chapter turns to Édouard Glissant’s ‘poetics of relation’ and Manuel DeLanda’s elaboration of ‘assemblage theory’. By bringing together these texts, which both draw from Deleuze and Guattari’s concept of the rhizome, this chapter demonstrates poetry’s condition of being is as a ‘multiplicity’, one that, as Martínez says, ‘operate[s] permanently in every direction’. By comparing how the book’s contents work to both bind it together as a whole and unbind it into a near-infinite network of pieces that can and do belong to other assemblages, this chapter makes a case for understanding books and their contents as bound by relations of exteriority.

(Words and) Images of power in Pier Paolo Pasolini's Petrolio

This contribution focuses on an unfinished novel, Petrólio by Pier Paolo Pasolini to reflect on nature and images of power, as interpreted by one of the greatest Italian post-war intellectuals. The central thesis is that while the peasant and fascist society was based on the male command, on the normative force of tradition, the contemporary consumer society is based on female persuasion, on the push to conform and not to differentiate. However, while patriarchal authoritarianism allowed emancipatory rebellion, consumerist homologation was able to prevent forms of resistance by disseminating power in an infinite network of relationships, whose plot cannot be dissolved. The reading of Petrólio invites the jurist not to focus exclusively on the rational aspects of the rules and procedures that limit power, but also to devote herself to reflecting on the two dimensions of power, the discursive and the aesthetic.

Electrostatic potential in crystals of α-boron, γ-boron and boron carbide

An overview is given of the recently proposed method for computation of the electrostatic potential (ESP) of dynamic charge densities derived from multipole models [C. B. Hubschle, S. van Smaalen, J. Appl. Crystallogr. 2017, 50, 1627]. The dynamic ESP is presented for the multipole models of the boron polymorphs α-B12 and γ-B28, and stoichiometric boron carbide B13C2. Minimum values of the ESP are conspiciously equal at approximately −1 electron/Å. Regions with the ESP close to its minimum value form an extended network throughout the crystal structures at locations far away from atoms and bonds. Boron and boron carbide are extended solids containing an infinite network of strong chemical bonds. We have shown that for such solids, the ESP can usefully considered on Hirshfeld surfaces encompassing groups of atoms. Accordingly, we discuss bonding in boron and boron carbide with aid of the ESP on the Hirsfeld surface encompassing a B12 icosahedral cluster. The structure of the ESP corroborates the interpretation of the bonding characteristics previously proposed for α-B12, γ-B28 and B13C2.