Mathematical and Numerical Studies on Meshless Methods for Exterior Unbounded Domain Problems

The method of fundamental solution (MFS) is an efficient meshless method for solving a boundary value problem in an exterior unbounded domain. The numerical solution obtained by the MFS is accurate, while the corresponding matrix equation is ill-conditioned. A modified MFS (MMFS) with the proper basis functions is proposed by the introduction of the modified Trefftz method (MTM). The concrete expressions of the corresponding condition numbers and the solvability by these methods are mathematically proven. Thereby, the optimal parameter minimizing the condition number is also mathematically given. Numerical experiments show that the condition numbers of the matrices corresponding to the MTM and the MMFS are reduced and that the numerical solution by the MMFS is more accurate than the one by the conventional method.Comment: 25 pages, 11 figure

Analysis of Basis Pursuit Via Capacity Sets

Finding the sparsest solution $\alpha$ for an under-determined linear system of equations $D\alpha=s$ is of interest in many applications. This problem is known to be NP-hard. Recent work studied conditions on the support size of $\alpha$ that allow its recovery using L1-minimization, via the Basis Pursuit algorithm. These conditions are often relying on a scalar property of $D$ called the mutual-coherence. In this work we introduce an alternative set of features of an arbitrarily given $D$, called the "capacity sets". We show how those could be used to analyze the performance of the basis pursuit, leading to improved bounds and predictions of performance. Both theoretical and numerical methods are presented, all using the capacity values, and shown to lead to improved assessments of the basis pursuit success in finding the sparest solution of $D\alpha=s$

Fatigue properties of laser welded dual-phase steel joints

AbstractThe aim of this study was to evaluate the effect of laser welding on fatigue properties of DP600 and DP980 steels in relation to the microstructural change and softening in the heat-affected zone. The degree of softening was found to be stronger in the DP980 welded joints than in the the DP600 welded joints. While the severity of the soft zone in the welded DP980 joints led to a significant decrease in the fatigue limit, the mild soft zone present in the DP600 welded joints had little or only a minor effect on the fatigue resistance. Despite the strong effect of the soft zone, the DP980 welded joints showed a similar or even longer fatigue life than that of both the DP600 welded joints and DP600 base metal at higher stress amplitudes. Fatigue crack initiation was observed to occur from the specimen surface, and crack propagation was characterized by the characteristic fatigue striations coupled with secondary cracks

Young children's social withdrawal and teacher–child relationship quality: A cross-cultural comparison between the Netherlands and China

The present study investigated how young children's (5-to-8-year-olds) social inhibition and solitary behavior were associated with teacher–child relationship quality and whether these associations differed across the Netherlands and China. The Dutch sample included 35 teachers and 201 children (49% girls). The Chinese sample consisted of 19 teachers and 152 children (50% girls). Teachers rated children's social inhibition and solitary behavior, and their relationship (closeness, conflict) with each child. Multilevel linear modeling revealed that in both countries, social inhibition was associated negatively with closeness and solitary behavior was associated positively with conflict. These associations were equally strong in China and the Netherlands. One association differed across countries: Social inhibition was associated negatively with conflict in the Netherlands, whereas this association was not significant in China. As such, cultural values could affect how social inhibition links to teacher–child relationships. Caution is recommended when generalizing findings from one country to another country

Simple choreographies of the planar Newtonian NN-body Problem

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.Comment: 31pages, 6 figures. Refinements in notations and proof

Intermittent suckling in combination with an older weaning age improves growth, feed intake and aspects of gastrointestinal tract carbohydrate absorption in pigs after weaning

This study tested the hypothesis that intermittent suckling (IS) with or without an older weaning age would improve post-weaning gastrointestinal tract (GIT) carbohydrate absorptive capacity in pigs while reducing post-weaning stress and aspects of the inflammatory response. Three weaning regimes using primiparous sows were compared: (1) conventional weaning (CW28) (n = 22), where piglets were weaned conventionally at day 28; (2) IS28 (n = 21), where IS started at day 21 until weaning at day 28; and (3) IS35 (n = 21), where IS started at day 28 until weaning at day 35. Sugar absorption tests (10% mannitol or 10% galactose) were used to measure GIT absorptive capacity. All measured parameters were compared in relation to weaning across treatments (i.e., different physiological ages were compared). The IS35 pigs grew fastest in the 12 days after weaning (p < 0.01) and had the highest solid feed intake before and after weaning (p < 0.05). Irrespective of treatment, pre-weaning mannitol levels were higher than post-weaning levels (p < 0.01), whereas post-weaning galactose levels were highest in IS35 pigs (p < 0.01). Cytokine data did not show any treatment effects. In conclusion, these data suggest that IS in combination with an older weaning age (day 35) improved post-weaning adaptation as evidenced by improvements in performance measures and galactose absorption. However, IS28 did not improve post-weaning performance

Experimental observation of the hot electron equilibrium in a minimum-B mirror plasma

(12.06. – 18.06.2017