In this paper we present the N-norms/Nconorms in neutrosophic logic and set as extensions of Tnorms/T-conorms in fuzzy logic and set. Then we show some applications of the neutrosophic logic to robotics. I. DEFINITION OF NEUTROSOPHIC SET Let T, I, F be real standard or non-standard subsets of ]0, 1[, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf I = i_inf, sup F = f_sup, inf F = f_inf, ...

This article presents a problem on model uncertainties in stochastic control, which an agent assumes best case scenario one risk and at the same time worst another risk. Particularly, maximizes its view Brownian motion, simultaneously minimizing motion choice of probability measure. selection method measure generalizes approach to considers scenarios for views motions, such as robust control. S...

Necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics. This work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure. Application to problems in incompressible fluid mechanics employing...

We consider the behavior of inf-sup stabilization in the context of transient problems with multiple time scales. Our motivation for studying this setting is provided by reacting flows problems for which small time steps are necessary in the integration process. We show that for algorithms defined through a process wherein spatial and temporal discretizations are separated, the coupling of impl...

di(x,A) = inf{di(x,A) : a ∈ A}, i ∈ I Hi(A,B) = max{sup di(a,B), sup di(A, b)} = sup{|di(x,A) − di(x,B)|} where a ∈ A, b ∈ B and x ∈ X It is well known that on 2 , Hi is a pseudometric, called the induced Hausdorff pseudometric induced by di, i ∈ I. Let (X,U) be a unifrom space with an augumented associated family p∗. p∗ also induces a uniformity U∗ on 2 defined by the base β∗ = {V ∗(i, ε) : i ...

Proof. Let g(x) = u(x) − sup∂Br(y) u − r2 − |x − y|2 2n supBr(y) f . We have ∆g = ∆u + supBr(y) f ≥ − f + supBr(y) f ≥ 0, that is, g is subharmonic in Br(y). Then supBr(y) g = sup∂Br(y) g = 0, so g ≤ 0 in Br(y) and the lemma follows. Lemma 2. If u is a solution to ∆u = f in Br(y) and v solves ∆v = 0 and v = u on ∂Br(y), then r2 − |x − y|2 2n inf Br(y) f ≤ v(x) − u(x) ≤ r 2 − |x − y|2 2n sup Br(...

In this work we present and analyse new inf-sup stable, and stabilised, finite element methods for the Oseen equation in anisotropic quadrilateral meshes. The meshes are formed of closed parallelograms, and the analysis is restricted to two space dimensions. Starting with the lowest order Q1 × P0 pair, we first identify the pressure components that make this finite element pair to be non-inf-su...