The set of toric minimal log discrepancies

We describe the set of minimal log discrepancies of toric log varieties, and study its accumulation points. This work is supported by a 21st Century COE Kyoto Mathematics Fellowship, and a JSPS Grant-in-Aid No 17740011.     

Achievable sets, brambles, and sparse treewidth obstructions

One consequence of the graph minor theorem is that for every k there exists a finite obstruction set Obs(TW?k). However, relatively little is known about these sets, and very few general obstructions are known. The ones that are known are the cliques, and graphs which are formed by removing a few edges from a clique. This paper gives several general constructions of minimal forbidden minors which are sparse in the sense that the ratio of the treewidth to the number of vertices n does not approach 1 as n approaches infinity. We accomplish this by a novel combination of using brambles to provide lower bounds and achievable sets to demonstrate upper bounds. Additionally, we determine the exact treewidth of other basic graph constructions which are not minimal forbidden minors.     

Asymmetry in the Multiprotein Systems of Molecular Biology

Signaling in living systems needs to achieve high specificity, to be reversible, and to achieve high signal to noise. Signaling mediated by multiprotein systems has evolved that avoids the requirement for high-affinity binary complexes that would be difficult to reverse and which, in the overcrowded cell, would lead to excessive noise in the system. Symmetrical structures are only occasionally formed. When they are, it is principally to colocate components, for example, the tyrosyl kinases of growth factors, where dimers form. Symmetry is, however, often broken, presumably to create more sensitivity and specificity in the signaling system by assembling other components, into higher-order multiprotein systems. The binding of a single heparin to two 1:1 FGF:FGFR complexes is an example, as is the binding of a single ligase to the Xrcc4 dimer, perhaps so creating a further DNA-binding site.     

“Optimization of aircraft maintenance/support infrastructure using genetic algorithms—level of repair analysis”

Level of repair analysis (LORA) is an approach used during the design stage of complex equipment for analysis of the cost effectiveness of competing maintenance strategies. LORA is carried as a part of the life cycle cost and cost of ownership analysis and plays a significant role in minimizing the life cycle cost and cost of ownership of the capital equipment. Since many purchasing decisions of complex equipment are based on cost of ownership, it has become essential to carry out LORA to compete in the market. In this paper, we develop a mathematical model for LORA and propose a solution methodology based on genetic algorithms. The concept is illustrated using a hypothetical aircraft engine.     

Codimension-one minimal projections onto Haar subspaces

Let H_n be an n-dimensional Haar subspace of and let H_n−1 be a Haar subspace of H_n of dimension n−1. In this note we show (Theorem 6) that if the norm of a minimal projection from H_n onto H_n−1 is greater than 1, then this projection is an interpolating projection. This is a surprising result in comparison with Cheney and Morris (J. Reine Angew. Math. 270 (1974) 61 (see also (Lecture Notes in Mathematics, Vol. 1449, Springer, Berlin, Heilderberg, New York, 1990, Corollary III.2.12, p. 104) which shows that there is no interpolating minimal projection from C[a,b] onto the space of polynomials of degree n, (n2). Moreover, this minimal projection is unique (Theorem 9). In particular, Theorem 6 holds for polynomial spaces, generalizing a result of Prophet [(J. Approx. Theory 85 (1996) 27), Theorem 2.1].     

Maximum principle at infinity for complete minimal surfaces in flat 3-manifolds

The main result of this paper is the following maximum principle at infinity:Theorem.Let M ₁ and M ₂ be two disjoint properly embedded complete minimal surfaces with nonempty boundaries, that are stable in a complete flat 3-manifold. Then dist(M ₁,M ₂)=min(dist(M ₁,M ₂), dist(M ₂,M ₁)).In case one boundary is empty, e.g. M ₁,then dist(M ₁,M ₂)=dist(M ₂,M ₁).If both boundaries are empty, then M ₁ and M ₂ are flat.     

All-glass open-split interface for capillary GC/MS

This paper describes a design for an all-glass GC/MS interface. The design has advantages due to low dead volume, lack of column effluent adsorption and degradation, simple interface production and installation, and ease of column mounting/dismounting.     

Synthesis of oligonucleotides containing an O-G-alkyl-O-G interstrand cross-link

A methodology to synthesize oligonucleotides containing an alkyl interstrand cross-link between the two O6 atoms of deoxyguanosine has been developed. This cross-link is designed to serve as a stable structural mimic of the lesion formed in duplex DNA with the bifunctional alkylating agent hepsulfam. The O6-alkyl coupling is performed via a Mitsunobu reaction between a nucleoside and mono-protected 1,7-heptanediol. Solid-phase oligonucleotide synthesis using a nucleoside bis-phosphoramidite allows for the assembly of the cross-linked duplex. Sufficient quantities of this cross-linked duplex were obtained for various structural and biological investigations.     

激光沉积修复BT20合金的显微组织和力学性能

针对BT20钛合金锻件当量孔损伤进行激光沉积修复试验,考察了修复试样的组织和力学特点。修复区与基材之间形成了致密冶金结合,Al,Zr,Mo,V合金元素由锻件基体到激光修复区均匀分布,无宏观偏析,硬度分布从基材到修复区依次提高。热影响区组织是由基材的双态组织过渡到网篮组织;修复区组织为粗大的原始柱状晶,晶粒内为/网篮组织,晶内片层取向随机, 宽0.4~0.5 m。修复过程中发现,激光加工工艺参数选择不当、坡度过大等原因会造成修复区组织形成气孔和熔合不良等缺陷,但是通过优化工艺参数可以获得无缺陷修复试样。修复试样的室温静拉伸结果表明,试样的抗拉强度接近锻件基体强度,但修复件的韧性比锻件稍有提高。