In 1965, T. J. Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in R is at least 2π. We prove this conjecture using the min-max theory of minimal surfaces.

We assess the behaviour of 5 different feature extraction methods for an acoustic event classification task—built using the same SVM underlying technology—by means of two different techniques: accuracy and the entropy triangle. The entropy triangle is able to find a classifier instance whose relatively high accuracy stems from an attempt to specialize in some classes to the detriment of the ove...

In this paper, existence and uniqueness of solution to two-point boundary value for two-sided fractional differential equations involving Caputo fractional derivative is discussed, by means of the Min-Max Theorem.

A new technique named as Intuitionistic fuzzy max-min average composition method is proposed to study the Medical Diagnosis. In Sanchez's approach for decision making is studied and the concept is generalized by the application of IFS theory. Through a survey the relations between the symptoms and diseases are discussed. The proposed method is compared with max-min composition method.

In the general max-min fair allocation, also known as Santa Claus problem, there are m players and n indivisible resources, each player has his/her own utilities for goal is to find an assignment that maximizes minimum total utility of resources assigned a player. We introduce over-estimation strategy help overcome challenges resource having different players. When all positive, we transform it...