If (Ω,Σ, μ) is a finite measure space and X a Banach space, in this note we show that L w (μ,X∗), the Banach space of all classes of weak* equivalent X∗-valued weak* measurable functions f defined on Ω such that ‖f(ω)‖ ≤ g(ω) a.e. for some g ∈ L1(μ) equipped with its usual norm, contains a copy of c0 if and only if X∗ contains a copy of c0.

The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Walsh-Kaczmarz-Fourier series is of weak type (1,1) . Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Kaczmarz-Fourier series is of weak type (1,1) , provided that the supremum in the maximal operator is...

We prove an existence theorem for the equation x = f(t, xt), x(Θ) = φ(Θ), where xt(Θ) = x(t + Θ), for −r ≤ Θ < 0, t ∈ Ia, Ia = [0, a], a ∈ R+ in a Banach space, using the Henstock-KurzweilPettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose tha...

We study semicontinuity of multiple integrals ~ f~,u,Du)dx~ where the vector-valued function u is defined for xE ~C N with values in ~ . The function f(x,s,~) is assumed to be Carath@odory and quasiconvex in Morrey's sense. We give conditions on the growth of f that guarantee the sequential lower semicontinuity of the given integral in the weak topology 1 N of the Sobolev space H 'P(~;~ ). The ...

A (functorial) weak reflection in a category C is essentially a sharply pointed endofunctor (T, η) on C, i.e., one for which ηTA is a split mono for each A ∈C. Using a result in [AHRT], we obtain the following “weak” version of one of the main results of [CHK]: every weak reflection (T, η) (in a category with finite products) comes from a (functorial) weak factorization system (LT ,RT ) (throug...

In the mol-ecule of the title homoallylic amine, C(16)H(13)ClF(3)N, the dihedral angle between the two benzene rings is 84.63 (4)°. Weak intra-molecular N-H⋯F hydrogen bonds generate S(6) and S(5) ring motifs. In the crystal structure, weak inter-molecuar N-H⋯F hydrogen bonds link mol-ecules into centrosymmetric dimers which are arranged in mol-ecular sheets parallel to the ac plane.

We study local bifurcations of critical periods in the neighborhood of a nondegenerate center of a Liénard system of the form ẋ = −y + F(x), ẏ = g(x), where F(x) and g(x) are polynomials such that deg(g(x)) ≤ 3, g(0) = 0, and g′(0) = 1, F(0) = F ′(0) = 0 and the system always has a center at (0,0). The set of coefficients of F(x) and g(x) is split into two strata denoted by SI and SII and (0,0)...

We have discovered new features of the current-phase relation, I f , in superfluid 3He weak links. Firstly, we find that at any given temperature there are two distinct I f functions that characterize the weak link. Secondly, both functions continuously develop an unusual form that ultimately leads to the previously reported p state. The observed form of I f has recently been predicted for unco...

Let N be the set of natural numbers and let a: N -* N be an injection having no periodic points. Let M0 be the set of o-invariant means on lx. When / G lx let da(f) = sup X(/), where the supremum is taken over all X G M„. It is shown that when/ e lx, there is a sequence (\)TM=2 of extreme points of M„ which has no extreme weak* limit points and such that \s(f) = dQ(f) for s = 2, 3, .... As a co...

We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h)−f(x) has the Baire property for every h ∈ R can be written in the form f = g+H+φ where g has the Baire property, H is additive, and for every h ∈ R we have φ(x+h)−φ(x) 6= 0 only on a meager set. We also discuss the weak difference property of ...