70 100 100 100 100 h Discrete: p (n) 1 = 6 12 = 0.5 p (n) 1|1 = 3 3 = 1, p (n) 1|2 = 3 3 = 1, p (n) 1|3 = 0 3 = 0, p (n) 1|4 = 0 3 = 0 Continuous: p (n) 1 = 1 12 (σ(100) + σ(70) + . . .+ σ(−70) + σ(−100)) ≈ 0.5 p (n) 1|1 = 1 3 (σ(100) + σ(70) + σ(100)) ≈ 1 p (n) 1|2 = 1 3 (σ(100) + σ(70) + σ(100)) ≈ 1 p (n) 1|3 = 1 3 (σ(−100) + σ(−70) + σ(−100)) ≈ 0 p (n) 1|4 = 1 3 (σ(−100) + σ(−70) + σ(−100)) ...

The celebrated Kadison–Sakai theorem states that every derivation on a von Neumann algebra is inner. In this paper, we prove this theorem for ultraweakly continuous ∗-σ-derivations, where σ is an ultraweakly continuous surjective ∗-linear mapping. We decompose a σ-derivation into a sum of an inner σ-derivation and a multiple of a homomorphism. The so-called ∗-(σ, τ)-derivations are also discussed.

A mixed-signal continuous time behavioral model of a continuous time delta-sigma modulator (CT ∆Σ) is presented. CT ∆Σ modulators, by their nature, are mixed-signal systems. That fact creates a discontinuity in the traditional IC design flow which assumes that “discrete” and “continuous” time domain designs require separate design tools. In this work, we present a top level behavioral CT ∆Σ mod...

ion and restriction Let SP ′ = (Σ′, AX ′) be a swinging type with base type SP = (Σ, AX) and primitive subtype SP0 = (Σ0, AX0), σ be the relation transformer of SP ′ and A be an SP0model. Suppose that SP ′ satisfies (7). Let Ini be initial in ModEU(A, SP ). If σ is continuous, then lfp(σ)/≡ is initial in ModEU(A, SP ′). Suppose that SP ′ satisfies (8). Let Ini be initial in ModEU(A, SP ). If σ ...

Quantum walks have recently been introduced and investigated, with the hope that they may be useful in constructing new efficient quantum algorithms. For reviews of quantum walks, see Refs. [4, 16, 24]. There are two distinct types of the quantum walk: one is a discrete-time case [2, 5, 12, 14, 17, 18, 19, 22, 23], the other is a continuous-time case [1, 3, 7, 8, 10, 15, 20]. The quantum walk c...

We associate with every commutative continuous semiring S and alphabet Σ a category whose objects are all sets and a morphism X → Y is determined by a function from X into the semiring of formal series S⟪(Y ⊎Σ) ⟫ of finite words over Y ⊎Σ, an X × Y -matrix over S⟪(Y ⊎Σ) ⟫, and a function from X into the continuous S⟪(Y ⊎Σ) ⟫-semimodule S⟪(Y ⊎Σ) ⟫ of series of ωwords over Y ⊎Σ. When S is also an...

A general construction for σ−finite absolutely continuous invariant measure will be presented. It will be shown that the local bounded distortion of the Radon-Nykodym derivatives of fn ∗ (λ) will imply the existence of a σ−finite invariant measure for the map f which is absolutely continuous with respect to λ, a measure on the phase space describing the sets of measure zero. Furthermore we will...

For given quasi-continuous functions g, h with g ≤ h and diffusion process M determined by stochastic differential equations or symmetric Dirichlet forms, characterizations of the value functions eg(s, x) = sup σ J (s,x) (σ) and ¯ w(s, x) = infτ sup σ J (s,x) (σ, τ) are well studied so far. In this paper, by using the time dependent Dirichlet forms, we generalize these results to time inhomogen...

We prove an integration by parts formula for the probability measure induced by the semi-classical Riemmanian Brownian bridge over a manifold with a pole. 1 Introdcution Let M be a finite dimensional smooth connected complete and stochastically complete Riemannian manifold M whose Riemannian distance is denoted by r. By stochastic completeness we mean that its minimal heat kernel satisfies that...