‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

comNode classification within Membrane Residue Curves (M-RCMs) currently hinges on Lyapunov’s Theorem and therefore the computation of mathematically complex eigenvalues. This paper presents an alternative criterion for the classification of nodes within M-RCMs based on the total membrane flux at node compositions. This paper demonstrates that for a system exhibiting simple permeation behaviour...

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prim...

Liouville closed $H$-fields are ordered differential fields whose ordering and derivation interact in a natural way where every linear equation of order $1$ has nontrivial solution. (The introduction gives precise definition.) For $H$-field $K$ with small we show: the Intermediate Value Property for polynomials iff is elementarily equivalent to field transseries. We also indicate how this appli...

We study analytically the initial value problem for a self-interacting (massive) scalar-field on a Reissner-Nordström spacetime. Following the no-hair theorem we examine the dynamical physical mechanism by which the selfinteracting (SI) hair decays. We show that the intermediate asymptotic behaviour of SI perturbations is dominated by an oscillatory inverse power-law decaying tail. We show that...

Let κ be an uncountable cardinal with κ = κ. In this paper we introduce Rκ, a Cauchy-complete real closed field of cardinality 2. We will prove that Rκ shares many features with R which have a key role in real analysis and computable analysis. In particular, we will prove that the Intermediate Value Theorem holds for a non-trivial subclass of continuous functions over Rκ. We propose Rκ as a can...

A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson, D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent ...

Inductive characterizations of words containing the same number of 'a' and 'b' can easily be given. However, formally proving the completeness of some of them turns out to be trickier than one may expect. We discuss and compare two Coq developments relating such balanced words to their inductive characterizations. One is based on auxiliary inductive structures and elementary arguments. The othe...