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In this note new properties for the Gossez example are presented in regard to its representability, closedness, and maximal monotonicity with respect to the two dual systems it naturally inhabits., Keywords: monotone operator, dual system, Fitzpatrick function

Equivalent conditions that make the convex subdifferential maximal monotone are investigated in the general settings of locally convex spaces.

In the context of general Banach spaces characterizations for the maximal monotonicity of operators with non-empty domain interior as well as stronger continuity properties for such operators are provided.

In this note we prove that a recent result stated by D.Y. Gao and R.W. Ogden on global minimizers and local extrema in a phase transition problem is false. Our goal is achieved by providing a thorough analysis of the context and result in question and counter-examples., Comment: This paper has been submitted to QJMAM (The Quarterly Journal of Mechanics and Applied Mathematics) on February 19, 2010 and was rejected on October 19, 2010. The reason for the rejection was that "the paper is more like a pure math paper" and this decision was taken mainly after the editor investigated our web-pages. For more details see http://www.math.uaic.ro/~zalinesc/

The aim of this short note is to give counterexamples to two results by D. Y. Gao [5, Th. 16], [4, Th. 2] and to improve a related result by S.-C. Fang, D. Y. Gao, R.-L. Sheu and S.-Y. Wu [1, Th. 3]., Comment: This paper has been submitted to JIMO (Journal of Industrial and Management Optimization) on September 24, 2009 and rejected in May, 2010. The reason for the rejection was that " The authors' view on this issue is known to people in the field". See also http://www.math.uaic.ro/~zalinesc/

The goal of this article is to give a positive answer to Rockafellar's maximality of the sum conjecture in the linear multi-valued operator case., 3 pages