Titlebook: Exploring Mathematical Analysis, Approximation Theory, and Optimization; 270 Years Since A.-M Nicholas J. Daras,Michael Th. Rassias,Nikolao

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On the Application of Ergodic Theory to an Alternating Series Expansion for Real Numbers,ernating series representations in terms of rationals we present some important results arising from the application of ergodic theory to an alternating series expansion for real numbers in terms of rationals generating from another algorithm called . which gives generalized versions of the correspo

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Finite Element Methods with Higher Order Polynomials,uations’ non-linearities. For this reason, novel formulations of FEM were introduced, including the use of orthogonal polynomials and high-order polynomials. In this review, the focus rests on studying and analysing the aforementioned formulations and describing their improvements over the classical

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On a Reverse Hilbert-Type Inequality in the Whole Plane with Multi-Parameters,ality in the whole plane with multi-parameters. The corresponding constant factor of the inequality is proved to be the best possible. Moreover, we also consider equivalent forms and a few particular inequalities.

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On Ergodic States, Spontaneous Symmetry Breaking and Quasi-Averages,es include quantum spin systems and many-body boson systems. As a consequence, we elucidate the problem of equivalence between Bose-Einstein condensation and the quasi-average spontaneous symmetry breaking of the gauge invariance recently discussed for continuous boson systems. The multi-mode extend