Symplectic Geometry has seen a rapid development since the 80's with the discovery of rigidity phenomena like the non-squeezing theorem based on Gromov's seminal theory of pseudo-holomorphic curves. A directly related development was Floer's method of using Morse theory in a new way, known as Floer homology, in order to solve the Arnold conjecture. In the 60's Arnold formulated his conjecture b...

serenade op. 24 from arnold schoenberg has been written in 7 movements for 7- person ensemble between 1921-1923 including clarinet and bass clarinet (woodwinds), mandolin, guitar, violin, alto and cello(stringed instrument). movements of this work have some been arranged symmetrically by composer.  the 4th movement of this collection named sonnet has features such as singer accompanied with orc...

The Arnold-Chiari type I malformation has many symptoms such as headache, neck pain, gait impairment, abnormal movements or postures. But a few cases reported association of specific symptom including headache, neck pain, vertigo or ataxia. We report a case of 12 year-old boy presenting with tip-toe gait. Magnetic resonance imaging (MRI) study of brain and spine revealed underlying Arnold-Chiar...

We study numerically the regularity of Arnold tongues corresponding to Diophantine rotation numbers of circle maps at the edge of validity of KAM theorem. This serves as a good test for the numerical stability of two different algorithms. We conclude that Arnold tongues are only finitely differentiable and we also provide a renormalization group explanation of the borderline regularity. Further...