≥ 0 which implies J is increasing in q. Therefore, q∗ =min(q(k, t), p) = q(k, t, p). iii) Note that E(V |V > q) = q + E(V −q) + F̄(q) , then the optimal utility is given by J(k, t) = J(k, t, q∗) = E(V |V > q∗)min(tF̄ (q∗), k)+E(V −p) (tF̄(q )−k) F̄(q) = [q∗ + E(V −q ) F̄(q) ]min(tF̄ (q∗), k)+E(V −p) (tF̄(q )−k) F̄ (q) . If q∗ = q(k, t) then F̄ (q(k, t)) = k/t and J(k, t, q(k, t)) = [q(k, t)+ tE(V −q(k,t...

There are complex inter- and intra-relations between regressors (independent variables) andyield quantity (W) and quality (Q) in tobacco. For instance, nitrogen (N) increases W butdecreases Q; starch harms Q but soluble sugars promote it. The balance between (optimizationof) regressors is needed for simultaneous increase in W and Q components [higher potassium(K), medium nicotine and lower chlo...

Let T be a bounded linear operator on complex Hilbert space H. In this paper we introduce two new classes of operators: k−quasi class Q(N ) and Q*(N ). An ∈ L(H) is for fixed real number N ≥ 1 k natural number, if satisfies ∥T^k+1(x)∥^2 ≤ ∥T^k+2(x)∥^2 + ∥T^k(x)∥^2, all x satisfiesN ∥T*T^k(x)∥^2 We study structural spectral properties these operators. Also compare operators with other known

we study connected orientable spacelike hypersurfaces $x:m^{n}rightarrowm_q^{n+1}(c)$, isometrically immersed into the riemannian or lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~l_kx=ax+b$,~ where $l_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $h_{k+1}$ of the hypersurface for a fixed integer $0leq k

We study connected orientable spacelike hypersurfaces $x:M^{n}rightarrowM_q^{n+1}(c)$, isometrically immersed into the Riemannian or Lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~L_kx=Ax+b$,~ where $L_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $H_{k+1}$ of the hypersurface for a fixed integer $0leq k