For an arbitrary in nite-dimensional Banach space X, we construct examples of strongly-measurable X-valued Pettis integrable functions whose indefinite Pettis integrals are nowhere weakly di erentiable; thus, for these functions the Lebesgue Di erentiation Theorem fails rather spectacularly. We also relate the degree of nondi erentiability of the inde nite Pettis integral to the cotype of X, fr...

then we say that p is the Catathéodory function. LetA denote the class of all functions f analytic in the open unit disk U {z : |z| < 1} with the usual normalization f 0 f ′ 0 − 1 0. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z , if g is univalent, f 0 g 0 and f U ⊂ g U . For 0 < α ≤ 1, let STC α and STS α denote the classes of functions f ∈ A whic...

As we have announced in the title of this work, we show that a broad class of linear evolution equations are exactly controllable. This class is represented by the following infinite dimensional linear control system: ż = Az + Bu(t), t > 0, z ∈ Z, u(t) ∈ U where Z, U are Hilbert spaces, the control function u belong to L2(0, t1; U), t1 > 0, B ∈ L(U,Z), A generates a strongly continuous semigrou...

Priming refers to a mechanism whereby plants are sensitized to respond faster and/or more strongly to future pathogen attack. Here, we demonstrate that preexposure to the green leaf volatile Z-3-hexenyl acetate (Z-3-HAC) primed wheat (Triticum aestivum) for enhanced defense against subsequent infection with the hemibiotrophic fungus Fusarium graminearum. Bioassays showed that, after priming wit...

BACKGROUND The development of novel highly efficacious fungicides that lack cross-resistance is extremely desirable. Fenpicoxamid (Inatreq™ active) possesses these characteristics and is a member of a novel picolinamide class of fungicides derived from the antifungal natural product UK-2A. RESULTS Fenpicoxamid strongly inhibited in vitro growth of several ascomycete fungi, including Zymosepto...

The interaction of sanguinarine with right-handed (B-form), left-handed (Z-form) and left-handed (HL-form) structures of poly(dG-dC).poly(dG-dC) has been investigated by measuring the circular dichroism (CD) and UV-absorption spectral analysis. Sanguinarine binds strongly to the B-form DNA and does not bind to Z-form or HL-form, but it converts the Z-form and the HL-form back to the bound right...

In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

where Z, U are Hilbert spaces, A : D(A) ⊂ Z −→ Z is the infinitesimal generator of strongly continuous semigroup {T (t)}t≥0 inZ, B ∈ L(U,Z), the control function u belongs to L(0, τ ;U) and F : [0, τ ]× Z × U −→ Z is a suitable function. First, we give a necessary and sufficient condition for the exact controllability of the linear system z′ = Az + Bu(t); Second, under some conditions on F , we...

‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.

In this paper, we study the Cauchy–Dirichlet problem for parabolic complex Monge–Ampère equations on strongly pseudoconvex domains using viscosity method. We prove a comparison principle and use it to existence uniqueness of solution in certain cases where sets $$\{z\in \Omega : f(t, z)=0 \}$$ may be pairwise disjoint.