Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well-known, ...

The problem of locating local maxima and minima of a function from approximate measurement results is vital for many physical applications: in spectral analysis, chemical species are identified by locating local maxima of the spectra; in radioastronomy, sources of celestial radio emission and and their subcomponents are identified by locating local maxima of the measured brightness of the radio...

Let h1, · · · , hn be positive integers. We study new sums m(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 min { r1 h1 , · · · , rn hn } and M(h1, · · · , hn) = h1−1 ∑ r1=0 · · · hn−1 ∑ rn=0 max { r1 h1 , · · · , rn hn } , the first of which times h1 · · ·hn is the number of lattice points in a pyramid of dimension n + 1. We show that m(h1, · · · , hn) (h1 − 1) · · · (hn − 1) = 1 + ∑ ∅6 =I⊆{1...

In this work, we have a proposed an automatic method to brain tumor segmentation using magnetic resonance imaging (MRI) histogram. In our proposed method input is taken from abnormal slice of the MRI volume. Based on image histogram of the abnormal slice, our algorithm automatically detected the local minima and maxima using histogram smoothing techniques. Threshold value obtained from local mi...

The extension of permutation statistics to labelled trees is the subject of a number of articles. Generating functions for the number of labelled trees of several types according to the number of ascents and descents are given in [4]. A functional equation satisfied by the generating function for the number of labelled trees according to the number of descents and leaves is given in [5]. Centra...