In the spotlight of this study is a particular type of first order dynamic initial value problem of the form u = f(t, u) + g(t, u), u(t0) = u0, where f, g ∈ Crd [T × R,R] are nondecreasing and nonincreasing in u, respectively. A quasilinearization technique utilizing the nature of natural lower and upper solutions as well as coupled lower and upper solutions is developed for this problem. Begin...

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function Sobolev`s space by polynomials. The prob-lem positive estimate pointwise degree approxi-mation r times continuously differentiable and func-tions [0, 1]. Estimates form (1) for are known ([1, 2]). problem monotone that estimating de-gree nondecreasing bymonotone were proved [3, 4, 7]. In ...

In the standard setting of one-way ANOVA with normal errors, a new algorithm, called the Step Down Maximum Mean Selection Algorithm (SDMMSA), is proposed to estimate the treatment means under an assumption that the treatment mean is nondecreasing in the factor level. We prove that i) the SDMMSA and the Pooled Adjacent Violator Algorithm (PAVA), a widely used algorithm in many problems, generate...

In [22], we proved a main theorem dealing an application of almost increasing and quasi monotone sequences. In this paper, we prove that theorem under weaker conditions. We also obtained some new and known results.

Abstract: Unlike a uniformity, a quasi-uniformity is not determined by its quasiuniform covers. However, a classical construction, due to Fletcher, which assigns a transitive quasi-uniformity to each family of interior-preserving open covers, allows to describe all transitive quasi-uniformities on the topological spaces in terms of those families of covers. In this paper we develop a pointfree ...

We define a new graph invariant called the scramble number. show that number of is lower bound for gonality and an upper treewidth. Unlike treewidth, not minor monotone, but it subgraph monotone under subdivision. compute several families graphs which these invariants are strictly greater than

Le savant n'étudie pas la nature parce que cela est utile ; il l'étudie parce qu'il y prend plaisir et il y prend plaisir parce qu'elle est belle. A The Meyer-Zheng Topology 95 References 100 Introduction In the last years the theory of irreversible investment under uncertainty has received much attention in Economics as well as in Mathematics (see, for example, the extensive review in Dixit an...

We study the complexity of approximating monotone Boolean functions with disjunctive normal form (DNF) formulas, exploring two main directions. First, we construct DNF approximators for arbitrary monotone functions achieving one-sided error: we show that every monotone f can be ε-approximated by a DNF g of size 2n−Ωε( √ n) satisfying g(x) ≤ f(x) for all x ∈ {0, 1}. This is the first non-trivial...

Abstract: In problems of optimal insurance design, Arrow’s classical result on the optimality of the deductible indemnity schedule holds in a situation where the insurer is a risk-neutral Expected-Utility (EU) maximizer, the insured is a risk-averse EU-maximizer, and the two parties share the same probabilistic beliefs about the realizations of the underlying insurable loss. Recently, Ghossoub ...