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Two Proofs of the Farkas-Minkowski Theorem by Tandem Method and by Use of an Orthogonal Complement
This note presents two proofs of the Farkas-Minkowski theorem. The first one is analytical, and this does not presuppose the closedness of a finitely generated cone. We do not employ separationExpand
A family of stochastic differential equation (SDE) models is derived and studied for the aging of biological organisms. The SDE aging models give meaningful mathematical interpretations of the agingExpand
Predator-prey model with fuzzy initial conditions
Predator-prey model, an initial value problem which is found in real life describes the relationship between predators and preys in an ecosystem, consisting of two nonlinear, autonomous differentialExpand
Eisenberg's Duality in Homogeneous Programming, Shephard's Duality and Economic Analysis
This note is to reintroduce to the reader Eisenberg's symmetric duality theorem in homogeneous programming problems as a useful tool in economic analysis, and thereby to pay a due tribute to him forExpand
Proof of Fermat’s Last Theorem for n = 3 Using Tschirnhaus Transformation
This paper gives a proof on Fermat’s last theorem (FLT) for n = 3 by firstly reducing the Fermat’s equation to a cubic equation of one variable and then using Tschirnhaus transformation to reduce itExpand
A proof of the Farkas–Minkowski theorem by a tandem method
This note presents a proof of the Farkas–Minkowski theorem. Our proof does not presuppose the closedness of a finitely generated cone, nor employs separation theorems either. Even the concept ofExpand
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Useful identities in finding a simple proof for Fermat’s last theorem
Fermat’s last theorem, very famous and difficult theorem in mathematics, has been proved by Andrew Wiles and Taylor in 1995 after 358 years later the theorem was stated However, their proof isExpand