for Invex Programs via Penalty Functions J. Zhang Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China X. X. Huang School of Management, Fudan University, Shanghai 200433, China Abstract. In this paper, we apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program....

Nonlinear oscillators with hardening and softening cubic Duffing nonlinearity are considered. Such classical conservative oscillators are known to have an amplitude-dependent period. In this work, we design oscillators with the Duffing-type restoring force but an amplitude-independent period. We present their Lagrangians, equations of motion, conservation laws, as well as solutions for motion.

We describe a new method to introduce constraints in cell-centered Lagrangian schemes in the framework of compressible hydrodynamics. In this paper we apply it to the modeling of contact and sliding on solid wall boundaries. We illustrate our method, which is based on the minimization of a specific objective function, by several basic problems.

Problems with the electroweak theory indicate the need for a consistent weak interactions theory. The analysis presented in this work is restricted to the relatively simple case of elastic scattering of a neutrino on a Dirac particle. The theory presented herein assumes that the neutrino is a massive particle. Furthermore, the dimension 2 L     of the Fermi constant F G as well as its unive...

For each single-parameter Gini social evaluation function, and by using the dual decomposition of the OWA operators, we derive two contributing factors. The …rst one, the self-dual core that can be considered as a positional measure, similar to the mean. The second one, the anti-self dual remainder, that we will prove is an equality measure with balanced sensitivity to both tails.

x (ν) (a) = x (a), x (ν) (b) = x (b), provided that, for every i in {1, . . . ,m}, Liψi is continuous in a neighborhood of x, Li is convex in its second variable, and ψi evaluated along x has positive sign. We discuss the optimality of our assumptions comparing them with an example of Sarychev [J. Dynam. Control Systems, 3 (1997), pp. 565–588]. As a consequence, we obtain the nonoccurrence of t...

We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description. Whether a given set of equations of motion admits or not a Lagrangian formulation has been an interesting issue for a long time. As early as 1887, Helmholtz formulated necessary and sufficient conditions for this to happen, and the problem has a rich history [1]. More recentl...

This study reports the mutual transformations between the third-order Eulerian and Lagrangian solutions for the irrotational progressive gravity waves propagating on the uniform depth. Based on the fundamental principle of kinematics, the instantaneous Eulerian and Lagrangian velocities are identically equal, and using a successive Taylor series expansion to the path and the period of particle ...

I promised a second part. Here it is. I hesitated, because I don’t like being destructive, and unfortunately, to deal with the current state of affairs in quantum theory means just doing this: I show you that the current gauge theory is fundamentally ill-designed, along with it fall Weinberg model and Wightman theory. 1. Continuing with the Lagrangian Formalism Let me continue from where I left...