Irreducible Apollonian Configurations and Packings

An Apollonian configuration of circles is a collection of circles in the plane with disjoint interiors such that the complement of the interiors of the circles consists of curvilinear triangles. One well-studied method of forming an Apollonian configuration is to start with three mutually tangent circles and fill a curvilinear triangle with a new circle, then repeat with each newly created curvilinear triangle. More generally, we can start with three mutually tangent circles and a rule (or rules) for how to fill a curvilinear triangle with circles.     

Tiling Polygons with Lattice Triangles

Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinates of the vertices in any tiling are rationals with the possible denominators odd numbers dependent on the cotangents of the angles in the triangles.     

Nuclear Magnetic Resonance (NMR) Spectroscopy: A Review and a Look at Its Use as a Probative Tool in Deamination Chemistry

Abstract

This year (2006) represents the 60th anniversary of nuclear magnetic resonance (NMR) spectroscopy (discovered independently by Nobel laureates Edward Purcell and Felix Bloch). It is therefore appropriate and indeed valuable to reflect on how this versatile methodology has developed, expanded, and evolved into a cornerstone of chemical research since 1946. No doubt multiple reviews discussing various aspects of NMR technology will emerge over the course of this year, but the field has grown so exponentially since its inception that it would be impossible for a single review to meaningfully encompass all features of the NMR methodology. This work, therefore, is not meant to provide a comprehensive review of NMR spectroscopy (such an undertaking would prove unwieldy and is inapt in the current context). Instead, it will provide an overview of NMR spectroscopy including the basic principles of NMR (the NMR phenomenon, instrumentation, and spectral interpretation) the historical development of the field, and a few unique applications of the methodology. Finally, illustrations of the utility and application of NMR spectroscopy as a probative tool in the intriguing field of deamination chemistry will be examined. Among the examples highlighted are the elucidation of the mechanism of N‐nitrosoamide conversion to the trans‐diazotate ester, denitrosation under near‐neutral conditions, elucidation of the bond‐forming step of Friedel‐Crafts benzylation, and the identification of novel electronic (π?‐acceptor agostic‐type interaction) and steric (persisteric) effects.     

Toward an acoustic noninvasive diagnosis of urinary bladder outlet obstruction

On average, in aging males, the prostate enlarges (benign prostatic enlargement or BPE) and may cause bladder outlet obstruction (BOO). The internationally standardized method for diagnosing BOO is based on measurements of urinary flow rate and bladder pressure, using a catheter inserted into the bladder via the urethra. This method is invasive, time-consuming, and uncomfortable for the patient. We are developing a novel diagnostic method based on perineal recording of sound during urinary flow. Although it is known that (some aspects of) the recorded sound are (among others) related to the degree of obstruction, an exact and unique relation allowing derivation of the degree of obstruction from the sound recording is not known. In a biophysical model of the urethra, we found that the weighted average frequency, the standard deviation, and the skewness of the power spectrum are monotonically related to the degree of obstruction. The standard deviation was the most significant predictor of BOO (89% correct). Based on this model study, we are confident that a simple noninvasive acoustic method for diagnosing BOO caused by BPE can be developed. This would lower the threshold for urodynamic testing of patients with lower urinary tract symptoms resulting in higher therapeutic efficacy.     

RF：究竟能否成为插入式Ⅰ?

对于下一代智能手机、移动视频播放器以及Web漫游附件的整合,其含意不仅是要将多用途基带与应用处理器、加速器和内存一起放到同一片SoC(系统单芯片)上,而且还要将许多小信号RF电路整合到SoC上.其中就存在一项重人难题.     

今天的EDA向何处去？

这就是正在没落的电子设计自动化业的现状吗？上月初,每年一次的设计自动化研讨会开幕,据说到场人数低于预期。有些供应商（最著名的是Cadence Design Systems）缺席展会,很多其它厂商的展位也缩水。已有人在议论EDA必须有所变化。本文发表时,Cadence已宣布了对Mentro Graphics的主动出价,而Mentor也迅速加以拒绝,理由是出价过低,以及不可能获得监管批准等。现在有一种论调是EDA业三巨头（Candence、Mentor和Synopsys）的合并,它表示着市场的最终老化。     

流量管理SoC设计者越来越大的梦魇

SoC（系统级芯片）在先于它出现的板级计算机上开始了自己的生命;作为一个中央处理器,其CPU总线连接到本地内存与外设控制器。从此以后,这种以CPU为中心、面向总线的架构一直是很多SoC的优先规划。     

Electronic properties of (3/2 × 3/2)-Na/Cu(1 1 1)

High-resolution electron energy loss spectroscopy was used to study the electronic properties of (3/2 × 3/2)-Na/Cu(1 1 1) at room temperature. Loss spectra showed two-well distinct losses at 114 and 180 meV assigned to not dispersive charge density waves. Mechanisms to explain their existence are proposed. Moreover, the expected 2D plasmon of the Na quantum well state was not observed. The strong influence of the underlying Cu substrate may be responsible for the absence of such mode.     

GLSMs for partial flag manifolds

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to realizations of tangent bundles and other aspects pertinent to (0, 2) models. Second, we review constructions of Calabi–Yau complete intersections within such flag manifolds, and properties of the gauged linear sigma models. We discuss a number of examples of nonabelian GLSMs in which the Kähler phases are not birational, and in which at least one phase is realized in some fashion other than as a complete intersection, extending previous work of Hori–Tong. We also review an example of an abelian GLSM exhibiting the same phenomenon. We tentatively identify the mathematical relationship between such non-birational phases, as examples of Kuznetsov’s homological projective duality. Finally, we discuss linear sigma model moduli spaces in these gauged linear sigma models. We argue that the moduli spaces being realized physically by these GLSMs are precisely Quot and hyperquot schemes, as one would expect mathematically.