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Cauchy problem in the class of monotone increasing functions

Journal of Contemporary Mathematical Analysis, 2007
The paper establishes some solvability conditions of the Cauchy problem for linear differential equation in the class of monotone increasing functions. The results are applied for clarifying the possibility of flight along a given trajectory under existence of braking forces.
N. E. Tovmasyan, H. A. Babayan
openaire   +1 more source

Bounds for the closure ordinals of essentially monotonic increasing functions

Journal of Symbolic Logic, 1993
AbstractLet Ω ≔ ℵ1. For any α< εΩ + 1 ≔ min {ξ > Ω: ξ = ωξ} let EΩ(α) be the finite set of ε-numbers below Ω which are needed for the unique representation of α in Cantor-normal form using 0, Ω, +, and ω. Let α* ≔ max(EΩ(α) ∪ {0}). A function f: εΩ + 1 → Ω is called essentially increasing, if for any α < εΩ + 1; f(α) ≥ α*: f is called ...
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Bounds for the closure ordinals of replete monotonic increasing functions

Journal of Symbolic Logic, 1975
Whenever particular ordinals are used as tools in a proof or a definition, it is necessary to find a way of representing them. If the ordinals are sufficiently small, there is a standard way (e.g. Cantor normal forms for ordinals less than ε0); in general, representations are often found by using functions on initial segments of the ordinals: Each term
openaire   +1 more source

A Geometric Construction of Continuous, Strictly Increasing Singular Functions

Proceedings of the Japan Academy Series A: Mathematical Sciences, 2007
Hisashi Okamoto, Marcus Wunsch
exaly  

Correct Formulation of Gradient Characteristics for Adaptive Notch Filters Based on Monotonically Increasing Gradient Algorithm

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2017
Shunsuke Koshita   +2 more
exaly  

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