Let u = u(q) satisfy a hyperbolic equation with impulsive input: ∂ t u(x, t)−4u(x, t) + q(x)u(x, t) = δ(x1)δ(t) and let u|t<0 = 0. Then we consider an inverse problem of determining q(x), x ∈ Ω from data u(q)|ST and (∂u(q)/∂ν) |ST . Here Ω ⊂ {(x1, . . . , xn) ∈ R|x1 > 0}, n ≥ 2, is a bounded domain, ST = {(x, t); x ∈ ∂Ω, x1 < t < T + x1}, ν = ν(x) is the unit outward normal vector to ∂Ω at x ∈ ...

We give a complete picture regarding the asymptotic periodicity of positive solutions of the following difference equation: xn = f (xn−p1 , . . . ,xn−pk ,xn−q1 , . . . ,xn−qm), n∈N0, where pi, i ∈ {1, . . . ,k}, and qj , j ∈ {1, . . . ,m}, are natural numbers such that p1 < p2 < ··· < pk, q1 < q2 < ··· < qm and gcd(p1, . . . , pk,q1, . . . ,qm) = 1, the function f ∈ C[(0,∞), (α,∞)], α > 0, is i...

We study definability of second-order generalized quantifiers. We show that the question whether a second-order generalized quantifier Q1 is definable in terms of another quantifier Q2, the base logic being monadic second-order logic, reduces to the question if a quantifier Q1 is definable in FO(Q2, <,+,×) for certain first-order quantifiers Q1 and Q2. We use our characterization to show new de...

In this paper we consider the inventory problem with backorder such that both order and total demand quantities are triangular fuzzy numbers Q̃ = (q1, q0, q2), and R̃ = (r1, r0, r2) respectively, where q1 = q0−Δ1, q2 = q0+Δ2,r1 = r0−Δ3, r2 = r0+Δ4 such that 0 < Δ1 < q0, 0 < Δ2, 0 < Δ3 < r0, 0 < Δ4. Let s denote the maximum inventory quantity. Under conditions s ≤ q1 < q0 < q2 < r1 < r0 < r2, we f...

Definition 1. We say that the partial order P is a projection of the partial order Q and denote this by P Q, if there is an onto mapping π : Q→ P which is order preserving and such that ∀q ∈ Q∀p ∈ P s.t. π(q) ≤ p there is q′ ∈ Q (q ≤Q q′) ∧ (π(q) = p). Furthermore whenever π(q) ≤ p there is a condition q1 in Q which is usually denoted p + q such that q ≤ q1 and for every r ∈ Q such that p ≤ π(r...