An upper bound for the crossing number of augmented cubes

A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing. The {\it crossing number} of a graph $G$ is the minimum number of pairwise intersections of edges in a good drawing of $G$ in the plane. The {\it $n$-dimensional augmented cube} $AQ_n$, proposed by S.A. Choudum and V. Sunitha, is an important interconnection network with good topological properties and applications. In this paper, we obtain an upper bound on the crossing number of $AQ_n$ less than $26/324^{n}-(2n^2+7/2n-6)2^{n-2}$.Comment: 39 page

Numerical analysis of dynamic characteristics in the ultra-high speed grinding spindle system

In this paper, the dynamic characteristics of ultra-high speed grinding spindle system is analyzed by using digital analysis methods. The spindle system is the key components of the machine tool, and its performance directly determines the machining stability and accuracy. Liquid hybrid bearing, with its superior performance has been widely applied to high speed and heavy machine tools. In order to study the spindle system, Fluent software was used to analyze the dynamic characteristics of liquid hybrid bearing. With the increase of the rotational speed, the capacity of liquid hybrid bearing changes significantly, and the relationship between the capacity and rotational is linear in intermediate stage. At the same time, the stiffness and damping of the liquid hybrid bearing has a corresponding increase with the increase of rotational speed. When the rotational speed increase to a certain extent, the dynamic performance of the spindle system will improve. Finally, the concentrated mass method and the finite element analysis method were used to analyze the dynamic characteristics of the spindle system, respectively. The results obtained by the both methods have good consistency, and the critical speed is about 14000 rve/min

Section thickness-dependent tensile properties of squeeze cast magnesium alloy AM60

The development of alternative casting processes is essential for the high demand of light weight magnesium components to be used in the automotive industry, which often contain different section thicknesses. Squeeze casting with its inherent advantages has been approved for the capability of minimizing the gas porosity in magnesium alloys. For advanced engineering design of light magnesium automotive applications, it is critical to understand the effect of section thickness on mechanical properties of squeeze cast magnesium alloys. In this study, magnesium alloy AM60 with different section thicknesses of 6, 10 and 20 mm squeeze cast under an applied pressure of 30 MPa was investigated. The prepared squeeze cast AM60 specimens were tensile tested at room termperature. The results indicate that the mechanical properties including yield strength (YS), ultimate tensile strength (UTS) and elongation (A) decrease with an increase in section thickness of squeeze cast AM60. The microstructure analysis shows that the improvement in the tensile behavior of squeeze cast AM60 is primarily attributed to the low-gas porosity level and fine grain strucuture which result from the variation of cooling rate of different section thickness. The numerical simulation (Magmasoft? was employed to determine the solidification rates of each step, and the simulated results show that the solidification rate of the alloy decreases with an increase in the section thickness. The computed solidification rates support the experimental observation on grain structural development

The autophagic degradation of cytosolic pools of peroxisomal proteins by a new selective pathway.

Damaged or redundant peroxisomes and their luminal cargoes are removed by pexophagy, a selective autophagy pathway. In yeasts, pexophagy depends mostly on the pexophagy receptors, such as Atg30 for Pichia pastoris and Atg36 for Saccharomyces cerevisiae, the autophagy scaffold proteins, Atg11 and Atg17, and the core autophagy machinery. In P. pastoris, the receptors for peroxisomal matrix proteins containing peroxisomal targeting signals (PTSs) include the PTS1 receptor, Pex5, and the PTS2 receptor and co-receptor, Pex7 and Pex20, respectively. These shuttling receptors are predominantly cytosolic and only partially peroxisomal. It remains unresolved as to whether, when and how the cytosolic pools of peroxisomal receptors, as well as the peroxisomal matrix proteins, are degraded under pexophagy conditions. These cytosolic pools exist both in normal and mutant cells impaired in peroxisome biogenesis. We report here that Pex5 and Pex7, but not Pex20, are degraded by an Atg30-independent, selective autophagy pathway. To enter this selective autophagy pathway, Pex7 required its major PTS2 cargo, Pot1. Similarly, the degradation of Pex5 was inhibited in cells missing abundant PTS1 cargoes, such as alcohol oxidases and Fox2 (hydratase-dehydrogenase-epimerase). Furthermore, in cells deficient in PTS receptors, the cytosolic pools of peroxisomal matrix proteins, such as Pot1 and Fox2, were also removed by Atg30-independent, selective autophagy, under pexophagy conditions. In summary, the cytosolic pools of PTS receptors and their cargoes are degraded via a pexophagy-independent, selective autophagy pathway under pexophagy conditions. These autophagy pathways likely protect cells from futile enzymatic reactions that could potentially cause the accumulation of toxic cytosolic products.Abbreviations: ATG: autophagy related; Cvt: cytoplasm to vacuole targeting; Fox2: hydratase-dehydrogenase-epimerase; PAGE: polyacrylamide gel electrophoresis; Pot1: thiolase; PMP: peroxisomal membrane protein; Pgk1: 3-phosphoglycerate kinase; PTS: peroxisomal targeting signal; RADAR: receptor accumulation and degradation in the absence of recycling; RING: really interesting new gene; SDS: sodium dodecyl sulphate; TCA, trichloroacetic acid; Ub: ubiquitin; UPS: ubiquitin-proteasome system Vid: vacuole import and degradation