We propose a solution to the symmetric nonlinear Ψ-Caputo fractional integro differential equations involving non-instantaneous impulsive boundary conditions. investigate existence and uniqueness of for proposed problem. Banach contraction theorem is employed prove results, while Krasnoselkii’s fixed point technique used results. Additionally, an example explain In this manner, our results repr...

U+ = {[λ1̇ : λ2̇]|λ1̇ 6= 0}, φ+ : [λ1̇ : λ2̇] 7→ λ2̇ λ1̇ = λ+, U− = {[λ1̇ : λ2̇]|λ2̇ 6= 0}, φ− : [λ1̇ : λ2̇] 7→ λ1̇ λ2̇ = λ−. We can immediately see that on the overlap U+ ∩U− we have that λ+ = λ−1 − . We can immediately compute that the map ψ+− = φ+ ◦ φ−1 − : φ−(U+ ∩ U−)→ φ+(U+ ∩ U−) satisfies ψ+−(λ−) = φ+ ◦ φ−1 − ◦ φ−([λ1̇ : λ2̇]) = φ0([λ1̇ : λ2̇]) = λ+. (1.2) To understand the bundle O(−1) we consider the two...

Let φ be a compactly supported symmetric real-valued refinable function in L2(R) with a finitely supported symmetric real-valued mask on Z. Under the assumption that the shifts of φ are stable, in this paper we prove that one can always construct three wavelet functions ψ, ψ and ψ such that (i) All the wavelet functions ψ, ψ and ψ are compactly supported, real-valued and finite linear combinati...

The proposal. Let W ck be the set of possible worlds where common knowledge holds. Assume that an individual-level (i-) predicate such as ‘tall’ has a davidsonian argument as well as a stage-level (s-) predicate as ‘available’, but that it is subject to the constraint in (1). (1) For every world w∈W ck , for every individual d∈De and for every situation/time s̃: if [[tall]](d, s̃)=1, then [[tall]...

We define the paraconsistent supra-logic Pσ by a type-shift from the booleans o of propositional logic Po to the supra-booleans σ of the propositional type logic P obtained as the propositional fragment of the transfinite type theory Q defined by Peter Andrews (North-Holland Studies in Logic 1965) as a classical foundation of mathematics. The supra-logic is in a sense a propositional logic only...

ABSTRACT. The key result in the paper concerns two transformations, Φ : (ρ, ψ) 7→ φ and Bt : ψ 7→ φ, where ρ, ψ, φ are states on the algebra of non-commutative polynomials, or equivalently joint distributions of d-tuples of non-commuting operators. These transformations are related to free probability: if ⊞ is the free convolution operation, and {ρt} is a free convolution semigroup, we show tha...

Everett’s concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent generalization of the relative state geometric phase to mixed quantum states is outlined. Introduction. – Pancharatnam’s geometric phase [1] is a property of ...

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...

We refine the interpolation property of the {∧,∨,¬}-fragment of classical propositional logic, showing that if 2 ¬φ, 2 ψ and φ ψ then there is an interpolant χ, constructed using at most atomic formulas occurring in both φ and ψ and negation, conjunction and disjunction, such that (i) φ entails χ in Kleene’s strong three-valued logic and (ii) χ entails ψ in Priest’s Logic of Paradox.

Let X1,X2, . . . be a discrete-time stochastic process with a distribution Pθ, θ ∈ Θ, where Θ is an open subset of the real line. We consider the problem of testing a simple hypothesis H0 : θ = θ0 versus a composite alternative H1 : θ > θ0, where θ0 ∈ Θ is some fixed point. The main goal of this article is to characterize the structure of locally most powerful sequential tests in this problem. ...