A monadic formula ψ(Y ) is a selector for a monadic formula φ(Y ) in a structure M if ψ defines inM a unique subset P of the domain and this P also satisfies φ inM. If C is a class of structures and φ is a selector for ψ in everyM ∈ C, we say that φ is a selector for φ over C. For a monadic formula φ(X, Y ) and ordinals α ≤ ω1 and δ < ω , we decide whether there exists a monadic formula ψ(X, Y ...

A scheme for construction of uncertainty relations (UR) for n observables and m states is presented. Several lowest order UR are displayed and briefly discussed. For two states |ψ〉 and |φ〉 and canonical observables the (entangled) extension of Heisenberg UR reads [∆p(ψ)][∆q(φ)]+[∆p(φ)][∆q(ψ)] ≥ 1/2. Some possible applications of the new inequalities are noted.

We define new classes of the family E(Φ,Ψ), in a unit disk U := {z ∈ C, |z| < 1}, as follows: for analytic functions F (z),Φ(z) and Ψ(z) so that <{ (z)∗Φ(z) F (z)∗Ψ(z)} > 0, z ∈ U, F (z) ∗Ψ(z) 6= 0 where the operator ∗ denotes the convolution or Hadamard product. Moreover, we establish some subordination results for these new classes.

The Rigged Hilbert Space (RHS) theory of resonance scattering and decay is reviewed and contrasted with the standard Hilbert space (HS) theory of quantum mechanics. The main difference is in the choice of boundary conditions. Whereas the conventional theory allows for the in-states φ and the out-states (observables) ψ of the S-matrix elements (ψ, φ) = (ψout, Sφin) any elements of the HS H, {ψ} ...

Starting from the 2-dimensional nonlinear σ-model living on a lattice Λ of lattice spacing a with action S[φ] = − 1 2 β z φ△φ, φ(z) ∈ S N we compute the Wilson effective action S eff [Φ] on a lattice of lattice spacingã in a 1-loop approximation for a choice of blockspin Φ(x) = Cφ(x) ≡ Cφ(x)/|Cφ(x)|, where C is averaging of φ(z) over a block x. We use a δ-function constraint to enforce Φ = Cφ. ...

Lemma 2.1. Let F be a field, let E = F (α) be a simple extension of F , where α is algebraic over F and f = irr(α, F, x), let ψ : F → K be a homomorphism from F to a field K, and let L be an extension of K. If β ∈ L is a root of ψ(f), then there is a unique extension of ψ to a homomorphism φ : E → L such that φ(α) = β. Hence there is a bijection from the set of homomorphisms φ : E → L such that...

We consider the second-order differential system with Hessian-driven damping ü+αu̇+β∇2Φ(u)u̇+∇Φ(u)+∇Ψ(u) = 0, where H is a real Hilbert space, Φ,Ψ : H → IR are scalar potentials, and α, β are positive parameters. An interesting property of this system is that, after introduction of an auxiliary variable y, it can be equivalently written as a first-order system involving only the time derivatives ...

In this paper, we study the computability of the solution operator of the initial problem for the nonlinear Kawahara equation, which is based on the Type-2 Turing machines. We will prove that in Sobolev space 2 ( ) s H R , for 0 s ≥ , the solution operator: 2 : ( ) s R K H R → ( ; C R 2 ( )) s H R is ( ,[ s H δ ρ → ]) s H δ -computable. The conclusion enriches the theory of computability. Key w...

Given a classical theory T, a Kripke structure K = (K,≤, (Aα)α∈K ) is called T-normal (or locally T) if for each α ∈ K, Aα is a classical model of T. It has been known for some time now, thanks to van Dalen, Mulder, Krabbe, and Visser, that Kripke models of HA over finite frames (K,≤) are locally PA. They also proved that models of HA over the frame (ω,≤) contain infinitely many Peano nodes. We...

Propositional program (dynamic, temporal and process) logics are basis for logical specification of program systems (including parallel, distributed and multiagent systems). Therefore development of efficient algorithms (decision procedures) for validation, provability and model checking of program logics is an important research topic for the theory of programming. The essence of a program sch...