Robinson’s implicit function theorem has played a mayor role in the analysis of stability of optimization problems in the last two decades. In this paper we take a new look at this theorem, and with an updated terminology go back to the roots and present some extensions.

ly, a~l implicit invocation mechanism can be modelled as a collection of components, each of which has an interface that specifies a set of methods and a set of events. As is traditionally the case, the methods define operations that other components can explicitly invoke. The events, however, define actions that the component promises to announce to other components in the system. The implicit...

This article presents a method for the explicit construction of limit state functions using Support Vector Machines (SVM). Specifically, the approach aims at handling the difficulties associated with the reliability assessment of problems exhibiting discontinuous responses and disjoint failure domains. The SVM-based explicit construction of limit state functions allows for an easy calculation o...

limit to the tension reinforcement ratio ( ρ) in flexural high strength reinforced concrete (hsrc) members is based on the requirement that tension failure as sufficient rotation capacity are ensured at ultimate limit state. however, the provisions for the total amount of longitudinal reinforcement ratio ( ρ and ρ’) are not associated with any rational derivation. in this paper, a quantitative ...

It is proved for fermi systems that each translationally invariant state co with square integrable correlation functions approaches a limit under the free time evolution. The limit state is the gauge invariant quasi-free state with the same two-point function as co and it is characterized by a maximum entropy principle. Various properties of the limit are discussed, and the extension of the res...

In this paper we consider a passive scalar transported in two-dimensional flow. The governing equation is that of the convection–diffusion–reaction equation. For purposes of computational efficiency, we apply an alternating-direction implicit scheme akin to that proposed by Polezhaev. Use of this implicit operator-splitting scheme allows the application of a tridiagonal Thomas solver to obtain ...

This paper discusses the features and applications of interface tracking techniques for modeling deroplet-based microfluidics. The paper reviews the state of the art of methods for tracking and capturing the interface. These methods are categorized as the implicit and the explicit methods. The implicit methods need to reconstruct the interface by reconnecting the markers on the interface. The i...