An energy-based a posteriori error bound is proposed for the physics-informed neural network solutions of elasticity problems. admissible displacement-stress solution pair obtained from mixed form networks, and formulated as constitutive relation defined by pair. Such an estimator provides upper global discretization. The bounding property, well asymptotic behavior solutions, are studied in dem...

Artificial Intelligence search algorithms search discrete systems. To apply such algorithms to continuous systems, such systems must first be discretized, i.e. approximated as discrete systems. Action-based discretization requires that both action parameters and action timing be discretized. We focus on the problem of action timing discretization. After describing an -admissible variant of Korf...

rupture and wrinkling are two prevalent phenomena that happen in hydro-forming process. many efforts have been made to achieve the upper and lower bounds for the pressure related to rupture and wrinkling of sheet, respectively. the aim of this investigation is to improve the upper bound of fluid pressure in hydro-forming process by hemispherical punch. in this article, analytical study of the u...

In this paper we present a general logical framework for (weighted)MAX-SAT problem, and study properties of inference rules for branch and bound MAX-SAT solver. Several rules, which are not equivalent but Λ-equivalent, are proposed, and we show that Λ-equivalent rules are also sound. As an example, we show how to exploit inference rules to achieve a new lower bound function for a MAX2-SAT solve...

1≤i≤m yibi. Now let P = {x ∈ (R) | Ax ≤ b and x ≥ 0}. Suppose x is a feasible point for our primal linear programming problem, so x ∈ P , i.e., Ax ≤ b and x ≥ 0. Also suppose we can choose y1, . . . , ym defining an m-covector y such that (yA)i ≥ ci and yi ≥ 0 for i = 1, . . . , n. Then c x ≤ yAx, and we have yAx ≤ yb, so altogether we have cx ≤ yAx ≤ yb. We see that yAx and yb are both upper-b...

Abstract The aim of this paper is to prove a blow-up result the solution for semilinear scale invariant damped wave equation under suitable decay condition on radial initial data. admissible range power nonlinear term depends both damping coefficient and pointwise order In addition, we give an upper bound estimate lifespan solution. It not only exponent but also size rate

Let MaxCut(G) be the value of the maximum cut of a graph G. Let f(x, n) be the expectation of MaxCut(G)/xn for random graphs with n vertices and xn edges and let r(x, n) be the expectation of MaxCut(G)/xn for random 2x-regular graphs with n vertices. We prove, for sufficiently large x: 1. limn→∞ f(x, n) ≤ 12 + √ ln 2 2x , 2. limn→∞ r(x, n) ≤ 12 + 1 √ x + 1 2 ln x x .