The physical mechanism of seed germination and its inhibition by abscisic acid (ABA) in Brassica napus L. was investigated, using volumetric growth (= water uptake) rate (dV/dt), water conductance (L), cell wall extensibility coefficient (m), osmotic pressure ( product operator(i)), water potential (Psi(i)), turgor pressure (P), and minimum turgor for cell expansion (Y) of the intact embryo as ...

Let x : M → Sn+1(1) be an n-dimensional compact hypersurface with constant scalar curvature n(n − 1)r, r ≥ 1, in a unit sphere Sn+1(1), n ≥ 5, and let Js be the Jacobi operator of M . In 2004, L. J. Aĺıas, A. Brasil and L. A. M. Sousa studied the first eigenvalue of Js of the hypersurface with constant scalar curvature n(n− 1) in Sn+1(1), n ≥ 3. In 2008, Q.-M. Cheng studied the first eigenvalue...

We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m− 1)-dimensional simplex, where l ∈ {0, 1, ...,m}. The l-Volterra operator is a Volterra operator if and only if l = m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m = 2 and m = 3 we describe behavior of ...

X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p ...

‎In this short note‎, ‎we present some inequalities for relative operator entropy which are generalizations of some results obtained by Zou [Operator inequalities associated with Tsallis relative operator entropy‎, ‎{em Math‎. ‎Inequal‎. ‎Appl.}‎ ‎{18} (2015)‎, ‎no‎. ‎2‎, ‎401--406]‎. ‎Meanwhile‎, ‎we also show some new lower and upper bounds for relative operator entropy and Tsallis relative o...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...

Let H be the Hill operator and let G n = (A ? n ; A + n) and M n ; n 1; be the corresponding gaps and the eeective masses for the Hill operator. Denote by F(E) the Lyapunov function for the Hill operator. Let n 2 A ? n ; A + n ] be such that F 0 (n) = 0 and h n 0 be the solution of the equation cosh h n = (?1) n F(n): We prove some identities for the eeective masses M n : Then we nd "second ord...

Let M be a complete Riemannian manifold and D : C∞ 0 (E) → C∞ 0 (F ) a first order differential operator acting between sections of the hermitian vector bundles E, F . Moreover, let V : C∞(E) → L∞ loc (E) be a self–adjoint zero order differential operator. We give a sufficient condition for the Schrödinger operator H = DD + V to be essentially self–adjoint. This generalizes recent work of I. Ol...

We construct some separable infinite dimensional homogeneous Hilbertian operator spaces H ∞ and H m,L ∞ , which generalize the row and column spaces R and C (the case m = 0). We show that separable infinitedimensional Hilbertian JC∗-triples are completely isometric to an element of the set of (infinite) intersections of these spaces . This set includes the operator spaces R, C, R ∩ C, and the s...

For a system of M coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra corresponding to the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The double set of norming vectors and associated spectrum of one of...