Suppose that A is a C∗-algebra acting on a Hilbert space H, and φ, ψ are mappings from A into B(H) which are not assumed to be necessarily linear or continuous. By a (φ, ψ)derivation we mean a linear mapping d : A → B(H) such that d(ab) = φ(a)d(b) + d(a)ψ(b) (a, b ∈ A). In this paper, we prove that if φ is a multiplicative(not necessary linear) ∗-mapping, then every ∗-(φ,φ)-derivation is automa...

In 2021, the Asian Art Museum of San Francisco inaugurated opening its new contemporary wing with teamLab: Continuity. The immersive exhibition spanned six galleries and was fully interactive via sensors digital projection mapping technology; flowers bloom grow, flying crows burst into colorful chrysanthemums, butterflies are born or killed at a moment’s touch. objects dynamically interact one ...

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

We extend to its spin 3/2 supersymmetric partner the very recent demonstration that the massless limit of massive spin 2 exchange amplitudes can be made continuous in background AdS spaces, in contrast to the known flat space discontinuities for both systems. In an AdS background, unlike spin 2 where the limit m → 0 is the massless one, spin 3/2 “masslessness” requires m → √ −Λ/3 , the supergra...

Filmmakers use continuity editing to engender a sense of situational continuity or discontinuity at editing boundaries. The goal of this study was to assess the impact of continuity editing on how people perceive the structure of events in a narrative film and to identify brain networks that are associated with the processing of different types of continuity editing boundaries. Participants vie...

The paper is an investigation into different notions of spatial, temporal, and spatio-temporal continuity. A formal framework is proposed in which a number of different notions of continuity is situated.

Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f i...