A purpose of critical point theory is the counting of critical points of functions. Principal theorems in the subject state in precise terms that topological complexity of the underlying space is reflected in the existence and nature of critical points of any smooth real-valued function defined on the space. The initial development of critical point theory is peculiarly the work of one man, Mar...

In this note we prove the following theorem. For any three sets of points in the plane, each of n ≥ 2 points such that any three points (from the union of three sets) are not collinear and the convex hull of 3n points is monochromatic, there exists an integer k ∈ {1, 2, . . . , n− 1} and an open half-plane containing exactly k points from each set.

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the central limit theorem and a vector-valued almost sure invariance principle. We also obtain results on decay of correlations.

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...

Abstract We prove a Central Limit Theorem for the critical points of random spherical harmonics, in high-energy limit. The result is consequence deeper characterization total number points, which are shown to be asymptotically fully correlated with sample trispectrum, i.e. integral fourth Hermite polynomial evaluated on eigenfunctions themselves. As consequence, and nodal length

Generalized Geraghty type fuzzy mappings oncomplete metric spaces are introduced and a fixed point theorem thatgeneralizes some recent comparable results for fuzzy mappings incontemporary literature is obtained. Example is provided to show thevalidity of obtained results over comparable classical results for fuzzymappings in fixed point theory. As an application, existence of coincidencefuzzy p...

Kelly’s theorem states that a set of n points affinely spanning C3 must determine at least one ordinary complex line (a line passing through exactly two of the points). Our main theorem shows that such sets determine at least 3n/2 ordinary lines, unless the configuration has n − 1 points in a plane and one point outside the plane (in which case there are at least n− 1 ordinary lines). In additi...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

Despite the acknowledged contribution of Small and Medium Enterprises (SMEs) to the food industry, there is increasing evidence that Hazard Analysis Critical Control Point (HACCP) implementation is limited in this sector, with the burden of implementation perceived as potentially insurmountable. The purpose of this study was to modify the generic HACCP model for Tunisian ricotta cheese producti...