Joseph Halpern and Judea Pearl ([2005]) draw upon structural equation models to develop an attractive analysis of 'actual cause'. Their analysis is designed for the case of deterministic causation. I show that their account can be naturally extended to provide an elegant treatment of probabilistic causation. 1Introduction2Preemption3Structural Equation Models4The Halpern and Pearl Definition of...

This paper reviews some of quantum computation basics: qubit definition, quantum operations, quantum algorithms, measurement and quantum walk, and then applies the discrete quantum hypercube walk to the nonlinear systems over Galois Finite Field GF (2). The modified quantum walk algorithm needs O( mn 2 ) iteration, while the best classical general solution takes O( nm 2 ) iteration. The paper a...

We investigate effectiveness of an acceleration method applied to the modified Picard iteration for simulations of variably saturated flow. We solve nonlinear systems using both unaccelerated and accelerated modified Picard iteration as well as Newton’s method. Since Picard iterations can be slow to converge, the advantage of acceleration is to provide faster convergence while maintaining advan...

Let C be a nonempty closed convex subset of a real Banach space X which has a uniformly Gâteaux differentiable norm. Let T ∈ ΓC and f ∈ΠC. Assume that {xt} converges strongly to a fixed point z of T as t→ 0, where xt is the unique element of C which satisfies xt = t f (xt) + (1− t)Txt. Let {αn} and {βn} be two real sequences in (0,1) which satisfy the following conditions: (C1) limn→∞αn = 0; (C...

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equati...

We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over system T to Spector’s bar recursion, whereas the other is T-equivalent to modified bar recursion. Modified bar recursion itself is show...

In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its comp...