Flows of measures generated by vector fields

The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure ‘flows along’ the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.

Replication-Defective Adenovirus Vectors with Multiple Deletions Do Not Induce Measurable Vector-Specific T Cells in Human Trials

ABSTRACT The magnitude and character of adenovirus serotype 5 (Ad5)-specific T cells were determined in volunteers with and without preexisting neutralizing antibodies (NAs) to Ad5 who received replication-defective Ad5 (rAd5)-based human immunodeficiency virus vaccines. There was no correlation between T-cell responses and NAs to Ad5. There was no increase in magnitude or activation state of Ad5-specific CD4+ T cells at time points where antibodies to Ad5 and T-cell responses to the recombinant gene products could be measured. These data indicate that rAd5-based vaccines containing deletions in the E1, E3, and E4 regions do not induce appreciable expansion of vector-specific CD4+ T cells.

RELAXATION OF A WEAKLY DISCONTINUOUS FUNCTIONAL DEPENDING ON ONE CONTROL FUNCTION

The paper considers an optimal control problem of the typewhere the set M of admissible controls consists of all measurable vector‐functions h, which can take only two values h1 or h2. It is shown that the relaxation of this problem can be explicitly computed by rank‐one laminates.

Best L∞-approximation of measurable, vector-valued functions

Let (Ω, ,μ) be a probability space, and let be a sub-sigma-algebra of . Let X be a uniformly convex Banach space. Let A =L∞(Ω, , μ X) denote the Banach space of (equivalence classes of) essentially bounded μ-Bochner integrable functions g: Ω.→ X, normed by the function ∥.∥∞ defined for g ∈ A by(cf. [6] for a discussion of this space). Let B = L∞(Ω, , μ X), and let f ε A. A sufficient condition for g ε B to be a best L∞-approximation to f by elements of B is established herein.