We present a mixed finite element method for the thin film epitaxy problem. Comparing to the primal formulation which requires C2 elements in the discretization, the mixed formulation only needs to use C1 elements, by introducing proper dual variables. The dual variable in our method is defined naturally from the nonlinear term in the equation, and its accurate approximation will be essential f...

In this paper, we present a dual representation for the multiple stopping problem, hence multiple exercise options. As such, it is a natural generalization of the method in Rogers (Math. Finance 12:271–286, 2002) and Haugh and Kogan (Oper. Res. 52:258–270, 2004) for the standard stopping problem for American options. We term this representation a ‘pure martingale’ dual as it is solely expressed...

In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

We explore here the issue of duality versus spectrum equivalence in abelian vector theories in 2 + 1 dimensions. Specifically we examine a generalized self-dual (GSD) model where a Maxwell term is added to the self-dual model. A gauge embedding procedure applied to the GSD model leads to a Maxwell-Chern-Simons (MCS) theory with higher derivatives. We show that the latter contains a ghost mode c...

We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a random subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all local curvature information contained in the examples, which leads to striking impr...

We perform the dimensional reduction of a uniaxial planar ferromagnet system coupled to an Abelian Chern-Simons gauge field in the self-dual limit, and investigate the soliton and domain wall solutions of the emerging 1+1 dimensional self-dual system. This self-dual ferromagnet is the usual inhomogeneous Landau-Lifshitz system with an extra non-local term supplementing the anisotropic potential...

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the val...

the aim of this study was to compare the effects of three types of balancetraining: single task, dual task under fixed priority instructional set (fp) and dualtask under a variable priority instructional set (vp) on the balance of the elderly.the participants were 36 elderly over 65 years old from kerman province whowere randomly divided into three groups (each 12 subjects) based on burg pretes...

AIMS To evaluate the feasibility and follow-up results of atrial lead implantation and a change to dual chamber pacing following long-term treatment with single chamber ventricular stimulation. METHODS AND RESULTS During a 30-month period, 70 consecutive patients with ventricular pacemakers were referred for pulse generator exchange or lead reoperation. Using defined criteria, an upgrade proc...

Uniqueness typing and affine (or linear) typing are dual type systems. Uniqueness gives a guarantee that an term has not been shared, while affinity imposes a restriction that a term may not be shared. We show that we can unify both concepts through polymorphism.