The two basic linear time Planarity algorithms: Are they the same?

We compare the two most widely known planarity testing algorithms, the one due to Hoperoft and Tarjan, and the other to Lempel. Even, and Cederbaum. These two algorithms are generally viewed as very different approaches to the problems of planarity testing and graph embedding. In this paper, however, by utilizing previously unnoticed freedoms of choice in the order in which the operations of the Hoperoft-Tarjan algorithm can be performed, we create a variation of this algorithm which, in terms of the order in which vertices are processed, is indistinguishable on all planar graph inputs from the Lempel -Even-Cederbaum algorithm. This allows one to create hybridized algorithms which, when interpreted as embedding algorithms, combine all of the features of both procedures.     

Specific heat and anisotropic superconducting and normal-state magnetization of HoNi2B2C

The magnetization of single-crystal HoNi₂B₂C has been measured as a function of applied field (H) and temperature in order to probe the interplay between superconductivity and magnetism in this complex layered system. The normal-state magnetic susceptibility of HoNi₂B₂C is highly anisotropic with a Curie-Weiss-like temperature dependence for H applied perpendicular to the c-axis and with a much weaker temperature dependence for H applied parallel to the c-axis, indicating that the Ho⁺³ magnetic moments lie predominately in the tetragonal a−b plane below 20 K. High-field magnetization (2000 Oe), low-field magnetization (20 Oe) and zero-field specific heat all give an antiferromagnetic ordering temperature of T_N=5.0 K. Remarkably, in 20 Oe applied field both superconductivity (T_c=8.0 K) and antiferromagnetism (T_N=5.0 K) clearly make themselves manifest in the magnetization data. From these magnetization data a phase diagram in the H−T plane was constructed for both directions of applied field. This phase diagram shows a non-monotonic temperature dependence of H_c2 with a deep minimum at T_N=5 K. The high-field magnetization data for H applied perpendicular to the c-axis also reveal a cascade of three phase transitions for T < 5 K and H < 15 000 Oe, contributing to the rich H versus T phase diagram for HoNi₂B₂C at low temperatures.     

Relation between the Superconducting Transition Temperature and the Axial Ratio in R Ni 2 B 2 C ( R =Y,Ho, Er,Tm, Lu) Under High Pressure

The effect of pressure on the lattice parameters of R Ni 2 B 2 C ( R = Y, Ho, Er, Tm, Lu) has been measured in order to investigate the relation of T C to axial ratio c/a in the tetragonal lattice or the cohesive properties of these materials. The large anisotropies are observed in the lattice compression curves especially for R =Ho and Tm; the c -axis is more compressible than the a -axis. On the other hand, the anisotropy in the lattice compression is found to be relatively small for R =Y and Lu. The close relation between T C and c/a is pointed out particularly for R =Ho.     

Symmetry analysis of the interplay between local moment anisotropies and propagation vectors in the borocarbides

Representational analysis is used to examine the interplay between Fermi surface nesting and local moment effects in the formation of the magnetically ordered states of the rare-earth nickel borocarbides, RNi₂B₂C. We derive compatibility tables for the propagation wavevector k, the local moment anisotropy and the ordered moment direction μ _k for materials with this tetragonal crystal structure. The magnetic structures observed in the rare-earth nickel borocarbides are discussed in this context.     

Large antichains in the partition lattice

Consider the partially ordered set of all partitions of an n-element set, ordered by refinement. The sizes of the various ranks within this poset are the Stirling numbers of the second kind. We show that the ratio of the size of the largest antichain to the size of the largest rank exceeds n^1/35 for all n sufficiently large.     

基于可靠性的工程设计

现代结构要求更危险和更复杂的设计，需要精确地了解结构的载荷、几何、材料性能、制造过程和运行环境等的不确定性。可靠性评估技术可用来发展安全设计，并确定在结构系统中的不确定性所产生影响，然而通过进一步的研究、试验和质量控制来提高结构的安全性和功效。     

Density-functional geometry optimization of the 150,000-atom photosystem-I trimer

We present a linear-scaling method based on the use of density-functional theory (DFT) for the system-wide optimization of x-ray structural coordinates and apply it to optimize the 150,000 atoms of the photosystem-I (PS-I) trimer. The method is based on repetitive applications of a multilevel ONIOM procedure using the PW916-31G(d) DFT calculations for the high level and PM3 for the lower level; this method treats all atoms in the structure equivalently, a structure in which the majority of the atoms can be considered as part of some internal "active site." To obtain a realistic single structure, some changes to the original protein model were necessary but these are kept to a minimum in order that the optimized structure most closely resembles the original x-ray one. Optimization has profound effects on the perceived electronic properties of the cofactors, with, e.g., optimization lowering the internal energy of the chlorophylls by on average 53 kcal mol(-1) and eliminates the enormous 115 kcal mol(-1) energy spread depicted by the original x-ray heavy-atom coordinates. A highly precise structure for PS-I results that is suitable for analysis of device function. Significant qualitative features of the structure are also improved such as correction of an error in the stereochemistry of one of the chlorophylls in the "special pair" of the reaction center, as well as the replacement of a water molecule with a metal cation in a critical region on the C3 axis. The method also reveals other unusual features of the structure, leading both to suggestions concerning device functionality and possible mutations between gene sequencing and x-ray structure determination. The optimization scheme is thus shown to augment the molecular modeling schemes that are currently used to add medium-resolution structural information to the raw scattering data in order to obtain atomically resolved structures. System-wide optimization is now a feasible process and its use within protein x-ray data refinement should be considered.