This paper summarizes the force generated by gastrocnemius muscle for the analysis of muscoskeletal simulation in human locomotion using Hill‟s muscle model. Biomechanics of Hill‟s equation describes the study of physical phenomenon by means of mathematical model that relates force and muscle length with the help of a partial differential equation. To calculate maximum fatigue in the muscle and...

The contraction of a muscle generates a force that decreases when increasing the contraction velocity. This "hyperbolic" force-velocity relationship has been known since the seminal work of A. V. Hill in 1938 [Hill AV (1938) Proc R Soc Lond B Biol Sci 126(843):136-195]. Hill's heuristic equation is still used, and the sliding-filament theory for the sarcomere [Huxley H, Hanson J (1954) Nature 1...

We develop some techniques to prove analytically the existence and stability of long period oscillations of stem cell populations in the case of periodic chronic myelogenous leukemia. Such a periodic oscillation $p_\infty $ can be analytically constructed when the hill coefficient involved in the nonlinear feedback is infinite, and we show it is possible to obtain a contractive returning map (f...

Asymptotics at large time of the Green function to the wave equation with periodic coefficients are found. A particular attention is given to its asymptotics near the wave front. It is shown that the spectral band (with number n = 0, 1, 2, ..) of the corresponding Hill operator is associated with a wave having the front velocity cn < 1. Estimates for cn in the terms of the gap lengths, the effe...

The MWC (Monod-Wyman-Changeux) allosteric model postulates concerted conformational changes between two states: the intrinsically more stable T state with relatively weak ligand binding and the R state with relatively strong ligand binding. The model distinguishes between Y¯ (the fractional occupation of the binding sites) and R¯ (the fraction of molecules in the R state). Cooperativity (measur...

Asymptotics at large time of the Green function to the wave equation with periodic coeecients are found. A particular attention is given to its asymptotics near the wave front. It is shown that the spectral band (with number n = 0; 1; 2; ::) of the corresponding Hill operator is associated with a wave having the front velocity c n < 1. Estimates for c n in the terms of the gap lengths, the eeec...

Let H be the Hill operator and let G n = (A ? n ; A + n) and M n ; n 1; be the corresponding gaps and the eeective masses for the Hill operator. Denote by F(E) the Lyapunov function for the Hill operator. Let n 2 A ? n ; A + n ] be such that F 0 (n) = 0 and h n 0 be the solution of the equation cosh h n = (?1) n F(n): We prove some identities for the eeective masses M n : Then we nd "second ord...

We report a statistical analysis of some highly infected countries by the novel coronavirus (COVID-19). The cumulative data were fitted with various growth models (e.g. Logistic equation, Weibull equation and Hill equation) obtained power index top ten countries. newly Gaussian distribution peak at ~40 days for whose infection curves are seem to be saturated. similarity in kinetics people diffe...