Let X = (X; . . . ; X) be a continuous semimartingale and let b : IR 1 ! IR be a continuous function such that the process b = b(X; . . . ; X ) is a semimartingale. Setting C = f (x1; . . . ; xn) 2 IR j xn < b(x1; . . . ; xn 1) g and D = f (x1; . . . ; xn) 2 IR j xn > b(x1; . . . ; xn 1) g suppose that a continuous function F : IR ! IR is given such that F is C1n on C and F is C1 ;...;in on D w...

Let A + B be the pointwise (Minkowski) sum of two convex subsets A and B of a Banach space. Is it true that every continuous mapping h : X → A + B splits into a sum h = f + g of continuous mappings f : X → A and g : X → B? We study this question within a wider framework of splitting techniques of continuous selections. Existence of splittings is guaranteed by hereditary invertibility of linear ...

We prove that for a dense G± of shift-invariant measures on AZ d , all d shifts have purely singular continuous spectrum and give a new proof that in the weak topology of measure preserving Zd transformations, a dense G± is generated by transformations with purely singular continuous spectrum. We also give new examples of smooth unitary cocycles over an irrational rotation which have purely sin...

Consider a continuous function g ∈ L2(R) that is supported on [−1, 1] and generates a Gabor frame with translation parameter 1 and modulation parameter 0 < b < 2N 2N+1 for some N ∈ N. Under an extra condition on the zeroset of the window g we show that there exists a continuous dual window supported on [−N, N]. We also show that this result is optimal: indeed, if b > 2N 2N+1 then a dual window ...

Glucose was converted to ethanol by calcium-alginate-entrapped Saccharomyces cerevisiae NRRL Y-2034 cells that were 24, 48, 72, and 96 h old in continuous-flow and static repeated-batch fermentors. In general, older yeast cells were more efficient than younger ones. In most cases, the continuous fermentations were better than the static ones in producing maximum ethanol yields (5.11 g/10 g of g...

We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided functions \(g\) and \(\textbf{F}\) in suitable Lebesgue spaces.

Avila and Molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). This work is a further investigation of generalized weak structures due to Avila and Molina. Further we introduce the structures ro(g) and rc(g) and study the properties of the structures r...

E. Dyer [2] proved that there is no continuous decomposition of a compact irreducible continuum into decomposable continua which is an arc with respect to its elements. The author extends Dyer's result to the plane. Consider a continuous decomposition of the plane into nonseparating compact continua. R. L. Moore [6] has shown that the decomposition space is homeomorphic to the plane. Using Moor...

For an arbitrary localic étale groupoid G we provide simple descriptions, in terms of modules over the quantale O(G) of the groupoid, of the continuous actions of G, including actions on open maps and sheaves. The category of G-actions is isomorphic to a corresponding category of O(G)-modules, and as a corollary we obtain a new quantale based representation of étendues.