Pin structures on vector bundles are the natural generalization of Spin structures to the case of nonoriented bundles. Spin(n) is the central Z/2Z extension (or double cover) of SO(n) and Pin−(n) and Pin(n) are two different central extensions of O(n), although they are topologically the same. The obstruction to putting a Spin structure on a bundle ξ (= R → E → B) is w2(ξ) H(B;Z/2Z); for Pin it...

40 is a near branch, an analogous argument again shows that Pin(b) is q's lower-right quadrant. Thus, q is the closest connection between p, Pin(a) and Pin(b). Except for redundancies and pruning of sub-optimal trees, BB-SORT-C searches over all possible ways to construct a Steiner tree sequentially, such that each sink is added by a closest connection to some edge in the current tree. Thus, we...

The nanosecond transient response between a pin of a large-scale integrated circuit (LSI) held by a charged person and the ground plane showed a very sharp impulse and high peak current. This response could not be represented using the human body model (HBM), and it was caused by the parasitic capacity between an inner conductor in the LSI and the ground plane. However, the conventional HBM tes...

We show that friction anisotropy is an intrinsic property of the atomic structure of Al–Ni–Co decagonal quasicrystals and not only of clean and well-ordered surfaces that can be prepared in vacuum [ J.Y. Park et al., Science 309,1354 (2005)]. Friction anisotropy is manifested in both nanometer-size contacts obtained with sharp atomic force microscope tips and macroscopic contacts produced in pi...

PURPOSE The purpose of this study was to evaluate the accuracy of a 3.5-mm-diameter anterior cruciate ligament (ACL) tibial retrograde socket drilling pin versus a standard, 2.4-mm drill-tipped guide pin. A secondary purpose was to evaluate surgeon precision in identifying the true (anatomic) center of the ACL tibial footprint using arthroscopic visualization. METHODS Six matched pairs of cad...

A simple, but not widely known, mathematical fact concerning the coverings of the full Lorentz group sheds light on parity and time reversal transformations of fermions. Whereas there is, up to an isomorphism, only one Spin group which double covers the orientation preserving Lorentz group, there are two essentially different groups, called Pin groups, which cover the full Lorentz group. Pin(1,...

OBJECTIVES To validate with an independent study that simple atrophy/postatrophic hyperplastic lesions (proliferative inflammatory atrophy [PIA]) often merge directly with high-grade prostatic intraepithelial neoplasia (PIN). METHODS Using radical prostatectomies (n =14), all high-grade PIN and adenocarcinoma lesions were identified. We examined the two-dimensional topographic relationship be...

Ledeburitic tool steel X210Cr12 was processed by passing through a semi-solid state with subsequent forming on hydraulic press, thus achieving fine-grained martensitic matrix, uniformly dispersed fine precipitates, and removal of sharp-edged primary chromium carbides. The hardness value over 700 HV10. decomposition austenite the promotion further carbide precipitation were carried out cryogenic...