Action rules can be seen as logical terms describing knowledge about possible actions associated with objects which is hidden in a decision system. Classical strategy for discovering them from a database requires prior extraction of classification rules which next are evaluated pair by pair with a goal to build a strategy of action based on condition features in order to get a desired effect on...

Abstract The Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence a solution for partial fractional using α - ψ -contractive mappings. Also, we give an illustrative example. By -multifunctions, prove solutions inclusion version problem. Finally providing another example and some figures, try to i...

We prove: For all n and all n-cylic isometriesφ : ΛQ → ΛQ of the rational K3 lattice there exists an algebraic realization of φ, i.e. marked algebraic K3 surfaces (S,ηS) and (M,ηM), whereM is a moduli space of sheaves on S, and a Hodge isometry ψ : H2(S,Q)→ H2(M,Q) such that φ = ηM ◦ψ ◦ η−1 S . 1 Facts about cyclic isometries We need the existence of a triple ((S,ηS), (M,ηM),ψ) to have a point ...

Continuummodels with critical end points are considered whose HamiltonianH[φ,ψ] depends on two densities φ and ψ. Field-theoretic methods are used to show the equivalence of the critical behavior on the critical line and at the critical end point and to give a systematic derivation of critical-end-point singularities like the thermal singularity ∼ |t|2−α of the spectator-phase boundary and the ...

0 −−−−→ {O, (0, 0)} −−−−→ E(Q) φ −−−−→ E(Q) α −−−−→ Q×/Q× 2 0 −−−−→ {O, (0, 0)} −−−−→ E(Q) ψ −−−−→ E(Q) β −−−−→ Q×/Q× . Finally, we have ψ ◦ φ = [2]E (multiplication by 2 on E) and φ ◦ ψ = [2]E. Thus although the situation is more involved than for the 2-descent on curves with three rational points of order 2, we have managed to break up the multiplicationby-2 map into two homomorphisms φ and ψ...

In this paper, images of the tempered Ψ-Hilfer fractional integral and Ψ-Caputo derivative under generalized Laplace transform are derived. The results applied to find a solution an initial value problem for nonhomogeneous linear differential equation with order α n− 1 <α<n N. An illustrative example is given 0 <α<1 comparing solutions same but different tempering Ψ.

We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with anisotropic Gibbs–Thomson law with kinetic undercooling, and quasi-static variants thereof. The phase field model is given by θwt + λ %(φ)φt = ∇ . (b(φ)∇w) , cΨ a α %...

In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on L positive definite functions to matrix valued L positive definite functions. We show that a matrix-valued continuous L positive definite function can always be written as a convolution of a L positive definite function with itself. We also prove that, give...

Abstract. We present some recent trends in the theory of Klein-Gordon-Schrödinger type Systems. Then we give some resent results on the following special type of a dissipative Klein-Gordon-Schrödinger System iψt + κψxx + iαψ = φψ, x ∈ Ω, t > 0, φtt − φxx + φ+ λφt = −Reψx, x ∈ Ω, t > 0, satisfying the initial and boundary conditions ψ(x, 0) = ψ0(x), φ(x, 0) = φ0(x), φt(x, 0) = φ1(x), x ∈ Ω, ψ(x,...

and Applied Analysis 3 hard to obtain because they are highly nonlinear equations and most probably they are not integrable equations in general. Thus, large numbers of research results are still concentrated in the classical KdV equation and some other high-order equations with KdV type, such as KdV-Burgers equation [17, 18] and KdV-Burgers-Kuramoto equation [19], at present. Therefore, the in...