Theorem A. Let g : [0, T ]× IR 7→ IR be a bounded function. (i) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is continuous for each t, then the Cauchy problem (1.1) has at least one solution. (ii) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is Lipschitz continuous for each t, with a uniform Lipschitz constant, then the Cauchy problem (1...

The Banach-Stone theorem states that any surjective, linear mapping T between spaces of continuous functions that satisfies ‖T (f)− T (g)‖ = ‖f − g‖, where ‖ · ‖ denotes the uniform norm, is a weighted composition operator. We study a multiplicative analogue, and demonstrate that a surjective mapping T , not necessarily linear, between algebras of continuous functions with ‖T (f)T (g)‖ = ‖fg‖ m...

Let G denote a locally compact (not necessarily abelian) group and M(G) the collection of finite regular Borel measures on G. The set M(G) is a semisimple Banach algebra with identity under convolution *. It can be identified with the dml space of CO(G), the space of continuous complex-valued functions on G that vanish at infinity, with the sup-norm. The group G has a left-invariant regular Bor...

The paper establishes, within constructive mathematics, a full and faithful functor M from the category of locally compact complete metric spaces and continuous functions into the category of formal topologies (or equivalently locales). The functor preserves finite products, and moreover satisfies f ≤ g if, and only if, M ( f ) ≤ M (g) for continuous f ,g : X → R. This makes it possible to tran...

For a continuous nonvanishing complex-valued function g on the real line, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrixvalued symbol G to be semi-Fredholm in terms of mean winding numbers of detG. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made. AMS Sub...

For a continuous complex-valued function g on the real line without zeros, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of detG. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces

A b-coloring of a graph G by k colors is a proper k-coloring of G such that in each color class there exists a vertex having neighbors in all the other k− 1 color classes. The b-chromatic number of a graph G, denoted by φ(G), is the maximum k for which G has a b-coloring by k colors. It is obvious that χ(G) ≤ φ(G). A graph G is b-continuous if for every k between χ(G) and φ(G) there is a b-colo...

Beta-lactams are regularly administered in intermittent short-term infusions. The percentage of the dosing interval during which free drug concentrations exceed the MIC (fT(>MIC)) is the measure of drug exposure that best correlates with clinical outcome for beta-lactams. Therefore, administration by continuous infusion has gained increasing interest recently. We studied 20 critically ill patie...