In this paper, we consider the system ut = ∆u, vt = ∆v x ∈ R+ , t > 0, − ∂u ∂x1 = v, − ∂v ∂x1 = u x1 = 0, t > 0, u(x, 0) = u0(x), v(x, 0) = v0(x) x ∈ R+ , where R+ = {(x1, x′) | x′ ∈ RN−1, x1 > 0}, p, q > 0, and u0, v0 nonnegative. We prove that if pq ≤ 1 every nonnegative solution is global. When pq > 1 we let α = 1 2 p+1 pq−1 , β = 1 2 q+1 pq−1 . We show that if max(α, β) ≥ N 2 , all nontrivi...

We investigate the asymptotic properties as t → ∞ of the differential equation ẍ(t) + a(t)ẋ(t) +∇G(x(t)) = 0, t ≥ 0 where x(·) is R-valued, the map a : R+ → R+ is non increasing, and G : R → R is a potential with locally Lipschitz continuous derivative. We identify conditions on the function a(·) that guarantee or exclude the convergence of solutions of this problem to points in argminG, in the...

abstract- chrysanthemum (dendranthema grandiflorum) is one of the most important ornamental plants used as cut flower, flowering pot plant and groundcover worldwide. in this research, the effects of preservative solutions containing thymol (75 and 125 mg -l), menthol (75 and 125 mg l-1) and eugenol (75 and 125 mg l-1) on the quality and vase-life of chrysanthemum cut flowers at 3±1ºc and 75-80%...

Given an edge-capacitated undirected graph G = (V ,E,C) with edge capacity c :E → R+, n = |V |, an s − t edge cut C of G is a minimal subset of edges whose removal from G will separate s from t in the resulting graph, and the capacity sum of the edges in C is the cut value of C. A minimum s − t edge cut is an s − t edge cut with the minimum cut value among all s − t edge cuts. A theorem given b...

for values of x > 0. For values of x < 0, if r is an integer then one can employ the solution given by eq. (2) without modification. If r is not an integer, then one can obtain the solution from eq. (2) by analytic continuation in the complex plane. In particular, for non-integer r there is a branch point at x = 0 and it is convenient to choose the branch cut to lie along the negative real axis...

Rose (Rosa hybrida L.) is one of the mostly cultivated cut flowers in Iran and around the world. The study was carried out to increase the vase life and quality of cut rose ‘Grand Prix` and ‘Avallanche` by using various floral preservative solutions. Floral preservative solutions were AgNO3, 8-HQS, nano silver and distilled water. Treatments were compared with tap water as control. The experime...

An r-cut of the complete r-uniform hypergraph Kr n is obtained by partitioning its vertex set into r parts and taking all edges that meet every part in exactly one vertex. In other words it is the edge set of a spanning complete r-partite subhypergraph of Kr n. An r-cut cover is a collection of r-cuts so that each edge of K r n is in at least one of the cuts. While in the graph case r = 2 any 2...

It is known that if f : R → R is continuous then ẋ = f(x) with x(0) = x0 has at least one solution on some time interval [0, T (x0)). However, when f is not Lipschitz one cannot guarantee that the solutions are unique. In this paper we show that the set of points x0 ∈ R is a countable, nowhere dense set. (In particular, we show that if f(x0) 6= 0 then the solution must be locally unique.)