As preparation for a duality theory for saddle programs, a partial conjugacy correspondence is developed among equivalence classes of saddle functions. Three known conjugacy correspondences, including Fenchel's correspondence among convex functions and Rockafellar's extension of it to equivalence classes of saddle functions, are shown to be degenerate special cases. Additionally, two new corres...

To investigate the effect of increasing velocity within one gait on horse and rider movement and to describe the resulting changes in saddle forces, seven ridden dressage horses were examined on an instrumented treadmill. The speed ranged between 1.3-1.8 m/s at walk and 2.6-3.6 m/s at trot. Kinematics of the horse and rider, vertical ground reaction forces and saddle forces were measured simult...

The harmonic approximation to transition state theory simplifies the problem of calculating a chemical reaction rate to identifying relevant low energy saddle points in a chemical system. Here, we present a saddle point finding method which does not require knowledge of specific product states. In the method, the potential energy landscape is transformed into the square of the gradient, which c...

In this paper we introduce a computational method for proving the existence of generic saddle-to-saddle connections between equilibria of first order vector fields. The first step consists of rigorously computing high order parametrizations of the local stable and unstable manifolds. If the local manifolds intersect, the NewtonKantorovich theorem is applied to validate the existence of a so-cal...

In this paper, we investigate a two-person zero-sum game with fractional loss function, which we call the two-person zero-sum fractional game. We are interested in a game value and a saddle point of the two-person zero-sum game and observe that they exist under various conditions. But, in many cases, it seems to be difficult to search directly for a game value and a saddle point of the fraction...

This paper deals with the saddle-point solution of a class of stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that both players have access to a common noisy linear measurement of the state and they are permitted to utilize only this information in constructing their controls. The saddle-point...

An extension of an existing truncated boundary-value method for the numerical continuation of connecting orbits is proposed to deal with homoclinic orbits to a saddle-node equilibrium. In contrast to previous numerical work by Schecter and Friedman & Doedel, the method is based on (linear) projection boundary conditions. These boundary conditions , with extra deening conditions for a saddle-nod...

Background: Cases of acquired saddle nose have been reported; however, reports of sarcoidosis with acquired saddle nose are very rare. The main cause of sarcoidosis is estimated to be an abnormal immune reaction rather than infection. Aim: Rhinoplasty using an autologous rib was planned and performed without plate fixation. Case Presentation: Our patient was diagnosed with sarcoidosis at the ag...

The theory of second-order epi-derivatives of extended-real-valued functions is applied to convex functions on lR and shown to be closely tied to proto-differentiation of the corresponding subgradient multifunctions, as well as to second-order epi-differentiation of conjugate functions. An extension is then made to saddle functions, which by definition are convex in one argument and concave in ...

Background: Contemporary studies have investigated the effects of bicycle saddle height for optimal performance and injury prevention. A recent review established a dynamic knee flexion angle of 25 ̊-30 ̊ for optimal economy, anaerobic power, and knee tracking (Bini et al., 2011: Sports Medicine, 41, 463-476). Muyor et al, (2011: Journal of Human Kinetics, 29, 15-23), investigated hamstring exten...