We investigate the relations between decreasing sequences of sets and the insertion of semi-continuous functions, and give
some characterizations of countably metacompact spaces, countably paracompact spaces, monotonically countably paracompact
spaces (MCP), monotonically countably metacompact spaces (MCM), perfectly normal spaces and stratifiable spaces.
monotonically toward higher temperatures. Using the T g and T p obtained at various heating rates, following Eqs. 1 and 2 , the ln q vs. 1/ T g and ln ( q/T p 2 ) vs. 1/ T p plots are found to be linear with slope giving the E s and E c
Relations between I-approximate Dini derivatives and monotonicity are presented. Next, some generalizations of the Denjoy–Young–Saks Theorem
for I-approximate Dini derivatives of an arbitrary real function are proved.
The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Woeginger (Math Soc Sci 56: 224–232, 2008a; J Informetr 2: 298–303, 2008b) suggests two axiomatic characterizations
of the Hirsch index using monotonicity as one of the axioms. This note suggests three characterizations without adopting the
Stochastic evolution equations with monotone operators in Banach spaces are considered. The solutions are characterized as minimizers of certain convex functionals. The method of monotonicity is interpreted as a method of constructing minimizers to these functionals, and in this way solutions are constructed via Euler-Galerkin approximations.
Summary Utilizing the good properties of the sequences of rest bounded variation, the usual monotonicity hypothesis on the coefficients of Fourier cosine series given in previous theorems will be weakened in the sense that the sequence of coefficients is of rest bounded variation. The theorems in question reformulate the conditions in some theorems on embedding relations of Besov classes.
Properties of Fourier–Haar coefficients of continuous functions are studied. It is established that Fourier–Haar coefficients of continuous functions are monotonic in a certain sense for convex functions. Questions of quasivariation of Fourier–Haar coefficients of continuous functions are also considered.
A definition of a generalized quotient topology is given and some characterizations of this concept, up to generalized homeomorphisms, are furnished. For the first approach, we exhibit a monotonic map spanning that generalized quotient topology. We also prove that the notions of generalized normality and generalized compactness are preserved by those quotient structures.