Path-Independent Consideration

In the context of choice with limited consideration, where the decision-maker may not pay attention to all available options, the consideration function of a decision maker is path-independent if her choice cannot be manipulated by the presentation of the choice set. This paper characterizes a model of choice with limited consideration with path independence, which is equivalent to a consideration function that satisfies both the attention filter and consideration filter properties from Masatlioglu et al. (2012) and Lleras et al. (2017), respectively. Despite the equivalence of path-independent consideration with the consideration structures from these two papers, we show that, to have a choice with limited consideration that is path-independent, satisfying both axioms on the choice function that characterize choice limited consideration with attention and consideration filters unilaterally (from Masatlioglu et al. (2012) and Lleras et al. (2017)) is necessary but not sufficient.

Path independence of the additive functionals for McKean–Vlasov stochastic differential equations with jumps

In this paper, the path independent property of additive functionals of McKean–Vlasov stochastic differential equations with jumps is characterized by nonlinear partial integro-differential equations involving [Formula: see text]-derivatives with respect to probability measures introduced by Lions. Our result extends the recent work16 by Ren and Wang where their concerned McKean–Vlasov stochastic differential equations are driven by Brownian motions.

Choice resolutions

We describe a process to compose and decompose choice behavior, called resolution. In the forward direction, resolutions amalgamate simple choices to create a complex one. In the backward direction, resolutions detect when and how a primitive choice can be deconstructed into smaller choices. A choice is resolvable if it is the resolution of smaller choices. Rationalizability, rationalizability by a preorder, and path independence are all preserved (backward and forward) by resolutions, whereas rationalizability by a weak order (equivalently, ) is not. We characterize resolvable choices, and show that resolvability generalizes .

Space-distribution PDEs for path independent additive functionals of McKean–Vlasov SDEs

Let [Formula: see text] be the space of probability measures on [Formula: see text] with finite second moment. The path independence of additive functionals of McKean–Vlasov SDEs is characterized by PDEs on the product space [Formula: see text] equipped with the usual derivative in space variable and Lions’ derivative in distribution. These PDEs are solved by using probabilistic arguments developed from Ref. 2. As a consequence, the path independence of Girsanov transformations is identified with nonlinear PDEs on [Formula: see text] whose solutions are given by probabilistic arguments as well. In particular, the corresponding results on the Girsanov transformation killing the drift term derived earlier for the classical SDEs are recovered as special situations.

Evaluation of surface energy for formation of multiple edge cracks using Medg-integral

A novel contour integral approach termed Medg is introduced for computation of the surface energy required for the formation of multiple edge cracks. The method is developed by reinterpretation of the conventional M-integral with deliberate delimitation of integration contour and selection of coordinate origin. Due to path independence, this method is efficient, easy to implement by using finite elements, and does not require a complicated mesh around the crack tips for good accuracy. Attention is also addressed to discussion of the size effects on proper interpretation of its physical meaning. The adequacy of the numerical results computed for the finite size corrections has been validated by using some of the available empirical formulations. It is observed that the size effect can be neglected when the crack size remains under one-tenth of the structure size. The results of a specific multi-cracked geotechnical structure suggest that, the damage state such as degradation of the structural stiffness due to the presence of edge cracks can be properly inspected by using Medg.

A M-theta Method on Mode I and II Failure of Two Cameroonian Hardwoods in Bending

This work deals with the numerical simulation on bending test to characterize two Cameroonian hardwoods under mode I and II loading for different crack lengths. The finite element analysis for fracture in orthotropic medium is developed. The algorithm of fracture is introduced in a finite element software Cast3M. According to the Mtheta method, the calculation of the stress intensity factors and the energy release rate for pure mode I and II fracture are deduced using a SENB (Single Edge Notch Bending) specimen. The path independence of Mθ-method on the specimen is confirmed.