We prove duality between the left and right fractional derivatives, independently on the type of fractional operator. Main result asserts that the right derivative of a function is the dual of the left derivative of the dual function or, equivalently, the left derivative of a function is the dual of the right derivative of the dual function. Such duality between left and right fractional operat...

Let Gp be p -series field. We prove the restricted two-parameter Sunouchi operator T χ h is bounded from H q to Lq for 0 < q 1 . By means of interpolation and duality argument, this theorem can be extended to Hardy-Lorentz spaces. As a consequence, we prove the restricted Sunouchi operator is of weak type (L1,L1) . Mathematics subject classification (2010): 42C10.

We describe various structures of algebraic nature on the space of continuous valuations on convex sets, their properties (like versions of Poincaré duality and hard Lefschetz theorem), and their relations and applications to integral geometry. 2000 Mathematics Subject Classification: 46, 47.

The purpose of this study is to apply composition duality methods in the qualitative analysis of evolution linear mixed variational problems. Primal and dual evolution mixed formulations are considered, as well as corresponding macro-hybrid variational models for parallel computing. The well-posedness, stability and convergence analysis of macro-hybrid mixed semi-discrete approximations is perf...

The paper recalls the concept of duality in Mathematics and extends it to Solid Mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical formulation of boundary value problems (Finite Element Method). Usually, Cons...

Firms maximize profits and consumers maximize preferences. This is the core of microeconomics, and under conventional assumptions about decreasing returns it is an application of convex programming. The paradigm of convex optimization, however, runs even deeper through economic analysis. The idea that competitive markets perform well, which dates back at least to Adam Smith, has been interprete...

We develop a duality theory for unbounded Hermitian operators with dense domain in Hilbert space. As is known, the obstruction for a Hermitian operator to be selfadjoint or to have selfadjoint extensions is measured by a pair of deficiency indices, and associated deficiency spaces; but in practical problems, the direct computation of these indices can be difficult. Instead, in this paper we ide...

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of (sub)contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for ...

Mock theta functions were introduced by Ramanujan in 1920 but a proper understanding of mock modularity has emerged only recently with the work Zwegers 2002. In these lectures we describe three manifestations this apparently exotic mathematics important physical contexts holography, topology and duality where come to play an role.