Abstract In this paper, we first introduce several new contractions by some auxiliary functions. Then establish φ -fixed point results for $(\gamma ,\psi ,\varphi ,\phi )$ ( γ , ψ φ ϕ ) contractions, rational...

Using a previous result by Gali and El-Saify (1983) and the theory of Kotarski (1989), and Lions (1971), we formulate the boundary control problem for a system governed by Neumann problem involving selfadjoint elliptic operator of 2 th order with an infinite number of variables. The inequalities which characterize the optimal control in terms of the adjoint system are obtained, it is studied in...

In fundamental-measure theories the bulk excess free-energy density of a hard-sphere fluid mixture is assumed to depend on the partial number densities {ρ(i)} only through the four scaled-particle-theory variables {ξ(α)}, i.e., Φ({ρ(i)})→Φ({ξ(α)}). By imposing consistency conditions, it is proven here that such a dependence must necessarily have the form Φ({ξ(α)})=-ξ(0)ln(1-ξ(3))+Ψ(y)ξ(1)ξ(2)/(...

– four new types: type variable X, universal type ∀X : K.τ , type operator abstraction λi :: S.τ and type operator application τ I. – A new kinding judgment Ψ; ∆ ` T :: K that assigns kinds to types – Typing judgment ∆; Φ; Γ ` e :κ τ changes to Ψ; ∆; Φ; Γ ` e :κ τ in which the context Ψ binds the type variables. – The subtyping judgment is changed as follows: Ψ; ∆; Φ |= τ1 v τ2 : K. – Semantics...

In this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form φ(s)=ψ(s)+ ∫ R κ(s − t)z(t)φ(t) dt, s ∈R, where κ ∈ L1(R), z ∈ L∞(R), and ψ ∈ BC(R), the space of bounded continuous complex-valued functions on R, are assumed known and the function φ ∈ BC(R) is to be determined. We introduce...

Recently‎, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $alpha-psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractiv...

By this we mean that φ > 0 and φ ∈ C2(R3). It is a classical fact (see Coffman [Cof]) that such solutions exist and are unique for the cubic nonlinearity. Moreover, they are radial and smooth. Similar facts are known for more general nonlinearities, see e.g., Berestycki and Lions [BerLio] for existence and Kwon [Kwo] for uniqueness in greater generality. Clearly, ψ = eitα 2 φ solves (1). We see...

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 ...

study of the limit-point concept [16]. Which factors could dictate the introduction of a topology for a given system of informational formulas? In informational cases, different kinds of reasonable topologies, corresponding intuitive ideas what an understanding, interpretation, conception, perception and meaning should be, are coming to the consciousness, that is, into the modeling foreground. ...