The Solution of the Second Peskin Conjecture and Developments

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processesIncludes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiologyIntroduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modeling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in mechanics, astronomy, and physicsDemonstrates mathematic modeling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in mechanics, astronomy, and physic

Extended Crystal PDE's

In this paper we show that between PDE's and crystallographic groups there is an unforeseen relation. In fact we prove that integral bordism groups of PDE's can be considered extensions of crystallographic subgroups. In this respect we can consider PDE's as {\em extended crystals}. Then an algebraic-topological obstruction ({\em crystal obstruction}), characterizing existence of global smooth solutions for smooth boundary value problems, is obtained. Applications of this new theory to the Ricci-flow equation and Navier-Stokes equation are given that solve some well-known fundamental problems. These results, are also extended to singular PDE's, introducing ({\em extended crystal singular PDE's}). An application to singular MHD-PDE's, is given following some our previous results on such equations, and showing existence of (finite times stable smooth) global solutions crossing critical nuclear energy production zone

Learning to discriminate interaural time differences at low and high frequencies

This study investigated learning, in normal-hearing adults, associated with training (i.e. repeated practice) on the discrimination of ongoing interaural time difference (ITD). Specifically, the study addressed an apparent disparity in the conclusions of previous studies, which reported training-induced learning at high frequencies but not at low frequencies. Twenty normal-hearing adults were trained with either low- or high-frequency stimuli, associated with comparable asymptotic thresholds, or served as untrained controls. Overall, trained listeners learnt more than controls and over multiple sessions. The magnitudes and time-courses of learning with the lowand high-frequency stimuli were similar. While this is inconsistent with the conclusion of a previous study with low-frequency ITD, this previous conclusion may not be justified by the results reported. Generalization of learning across frequency was found, although more detailed investigations of stimulus-specific learning are warranted. Overall, the results are consistent with the notion that ongoing ITD processing is functionally uniform across frequency. These results may have implications for clinical populations, such as users of bilateral cochlear implants