We developed the spacetime-covariant Hamilton principle for barotropic flows of a perfect fluid in external axial-vector potential conjugate to helicity current. Such carry helicity, chiral imbalance, controlled by axial potential. The interest such setting is motivated recent observation that axial-current anomaly quantum field theories with Dirac fermions appears as kinematic property classic...

In this paper, the optimal control of transmission dynamics of hand, foot and mouth disease (HFMD), formulated by a compartmental deterministic SEIPR (Susceptible-Incubation (Exposed)- Infected - Post infection virus shedding - Recovered) model with vaccination and treatment as control parameters is considered. The objective function is based on the combination of minimizing the number of infec...

The development of the equations of motion for a mechanical ystem from Hamilton’s principle can be viewed as a problem in he calculus of variations when the constraints on the system are olonomic and the forces are derivable from a potential function. endering stationary the integral of the Lagrangian over a fixed nterval of time taken between two fixed points in configuration pace, then, yield...

Hamilton’s variation principle can be shown to correspond to Fermat’s Principle for a wave propagation in configuration space (q-space), and the Hamilton-Jacobi equation expresses Huygens’ Principle for this wave propagation. Unfortunately this powerful and momentous conception of Hamilton, is deprived, in most modern reproductions, of its beautiful raiment as a superfluous accessory, in favour...

In this paper we discuss the applications of the Hamilton-Pontryagin variational principle for designing time-adaptive variational integrators. First, we review the multisymplectic formalism of field theories. Next, we review the Hamilton-Pontryagin principle and show how it can be used to handle time reparametrizations in a very natural way. Finally, we derive a time-adaptive variational integ...

This paper interrelates the performance criteria involving path independent curvilinear integrals, the multitime maximum principle, the multitime Hamilton-Jacobi-Bellman PDEs and the multitime dynamic programming, to study the linear-quadratic regulator problems and to characterize the optimal control by means of multitime variant of the Riccati PDE that may be viewed as a feedback law. Section...

in this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. we present some sufficient and necessary conditions for $gbox h$ being hamilton-connected when $g$ is a hamilton-connected graph and $h$ is a tree or $g$ is a hamiltonian graph and $h$ is $k_2$.

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...