Simplified system displays complex curves corresponding to input data

Cathode ray oscilloscope displays curves or contours of complex shapes corresponding to sets of x,y coordinates. It requires few storage facilities and produces a rapid display of complex curves with a fewer number of commands than previous systems

Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space \sM_{\dd}^n of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, ACC-coordinates, as those $(n+2) \times (n+2)$ real matrices \bW with \bW^T \bQ_{D,n} \bW = \bQ_{W,n} where $Q_{D,n} = x_1^2 +... + x_{n+2}^2 - \frac{1}{n}(x_1 +... + x_{n+2})^2$ is the $n$-dimensional Descartes quadratic form, $Q_{W,n} = -8x_1x_2 + 2x_3^2 + ... + 2x_{n+2}^2$, and \bQ_{D,n} and \bQ_{W,n} are their corresponding symmetric matrices. There are natural actions on the parameter space \sM_{\dd}^n. We introduce $n$-dimensional analogues of the Apollonian group, the dual Apollonian group and the super-Apollonian group. These are finitely generated groups with the following integrality properties: the dual Apollonian group consists of integral matrices in all dimensions, while the other two consist of rational matrices, with denominators having prime divisors drawn from a finite set $S$ depending on the dimension. We show that the the Apollonian group and the dual Apollonian group are finitely presented, and are Coxeter groups. We define an Apollonian cluster ensemble to be any orbit under the Apollonian group, with similar notions for the other two groups. We determine in which dimensions one can find rational Apollonian cluster ensembles (all curvatures rational) and strongly rational Apollonian sphere ensembles (all ACC-coordinates rational).Comment: 37 pages. The third in a series on Apollonian circle packings beginning with math.MG/0010298. Revised and extended. Added: Apollonian groups and Apollonian Cluster Ensembles (Section 4),and Presentation for n-dimensional Apollonian Group (Section 5). Slight revision on March 10, 200

Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)$\times$(center) is an integer vector. This series of papers explain such properties. A {\em Descartes configuration} is a set of four mutually tangent circles with disjoint interiors. We describe the space of all Descartes configurations using a coordinate system \sM_\DD consisting of those $4 \times 4$ real matrices \bW with \bW^T \bQ_{D} \bW = \bQ_{W} where \bQ_D is the matrix of the Descartes quadratic form $Q_D= x_1^2 + x_2^2+ x_3^2 + x_4^2 -{1/2}(x_1 +x_2 +x_3 + x_4)^2$ and \bQ_W of the quadratic form $Q_W = -8x_1x_2 + 2x_3^2 + 2x_4^2$. There are natural group actions on the parameter space \sM_\DD. We observe that the Descartes configurations in each Apollonian packing form an orbit under a certain finitely generated discrete group, the {\em Apollonian group}. This group consists of $4 \times 4$ integer matrices, and its integrality properties lead to the integrality properties observed in some Apollonian circle packings. We introduce two more related finitely generated groups, the dual Apollonian group and the super-Apollonian group, which have nice geometrically interpretations. We show these groups are hyperbolic Coxeter groups.Comment: 42 pages, 11 figures. Extensively revised version on June 14, 2004. Revised Appendix B and a few changes on July, 2004. Slight revision on March 10, 200

Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. It observed there exist infinitely many types of integral Apollonian packings in which all circles had integer curvatures, with the integral structure being related to the integral nature of the Apollonian group. Here we consider the action of a larger discrete group, the super-Apollonian group, also having an integral structure, whose orbits describe the Descartes quadruples of a geometric object we call a super-packing. The circles in a super-packing never cross each other but are nested to an arbitrary depth. Certain Apollonian packings and super-packings are strongly integral in the sense that the curvatures of all circles are integral and the curvature$\times$centers of all circles are integral. We show that (up to scale) there are exactly 8 different (geometric) strongly integral super-packings, and that each contains a copy of every integral Apollonian circle packing (also up to scale). We show that the super-Apollonian group has finite volume in the group of all automorphisms of the parameter space of Descartes configurations, which is isomorphic to the Lorentz group $O(3, 1)$.Comment: 37 Pages, 11 figures. The second in a series on Apollonian circle packings beginning with math.MG/0010298. Extensively revised in June, 2004. More integral properties are discussed. More revision in July, 2004: interchange sections 7 and 8, revised sections 1 and 2 to match, and added matrix formulations for super-Apollonian group and its Lorentz version. Slight revision in March 10, 200

The profitability and risk effects of allowing bank holding companies to merge with other financial firms: a simulation study

Bank mergers ; Bank holding companies ; Nonbank activities

Investigating the banking consolidation trend

This paper examines whether the U.S. banking industry's recent consolidation trend--toward fewer and bigger firms--is a natural result of market forces. The paper finds that it is not: The evidence does not support the popular claims that large banking firms are more efficient and less risky than smaller firms or the notion that the industry is consolidating in order to eliminate excess capacity. The paper suggests, instead, that public policies are encouraging banks to merge, although it acknowledges that other forces may be at work as well.Bank mergers

Independent Orbiter Assessment (IOA): Analysis of the crew equipment subsystem

The results of the Independent Orbiter Assessment (IOA) of the Failure Modes and Effects Analysis (FMEA) and Critical Items List (CIL) are presented. The IOA approach features a top-down analysis of the hardware to determine failure modes, criticality, and potential critical (PCIs) items. To preserve independence, this analysis was accomplished without reliance upon the results contained within the NASA FMEA/CIL documentation. The independent analysis results coresponding to the Orbiter crew equipment hardware are documented. The IOA analysis process utilized available crew equipment hardware drawings and schematics for defining hardware assemblies, components, and hardware items. Each level of hardware was evaluated and analyzed for possible failure modes and effects. Criticality was assigned based upon the severity of the effect for each failure mode. Of the 352 failure modes analyzed, 78 were determined to be PCIs

Biomechanical comparison of the track start and the modified one-handed track start in competitive swimming: an intervention study

This study compared the conventional track and a new one-handed track start in elite age group swimmers to determine if the new technique had biomechanical implications on dive performance. Five male and seven female GB national qualifiers participated (mean ± SD: age 16.7 ± 1.9 years, stretched stature 1.76 ± 0.8 m, body mass 67.4 ± 7.9 kg) and were assigned to a control group (n = 6) or an intervention group (n = 6) that learned the new onehanded dive technique. All swimmers underwent a 4-week intervention comprising 12 ± 3 thirty-minute training sessions. Video cameras synchronized with an audible signal and timing suite captured temporal and kinematic data. A portable force plate and load cell handrail mounted to a swim starting block collected force data over 3 trials of each technique. A MANCOVA identified Block Time (BT), Flight Time (FT), Peak Horizontal Force of the lower limbs (PHF) and Horizontal Velocity at Take-off (Vx) as covariates. During the 10-m swim trial, significant differences were found in Time to 10 m (TT10m), Total Time (TT), Peak Vertical Force (PVF), Flight Distance (FD), and Horizontal Velocity at Take-off (Vx) (p < .05). Results indicated that the conventional track start method was faster over 10 m, and therefore may be seen as a superior start after a short intervention. During training, swimmers and coaches should focus on the most statistically significant dive performance variables: peak horizontal force and velocity at take-off, block and flight time

DETERMINANTS OF BORROWER DROPOUT IN MICROFINANCE: AN EMPIRICAL INVESTIGATION IN MALI

Repeat borrowing is critical for the long-term financial viability of microfinance institutions (MFIs), which provide financial services to low-income households in developing countries. Repeat borrowers reduce MFI administrative costs, lower risks, and increase institutional productivity. In this paper we study the determinants of borrower dropout of an MFI operating in an urban center in Mali. Specifically, we quantify the explicit and implicit costs that a borrower must incur in obtaining loans from an MFI.Financial Economics,

Random l-colourable structures with a pregeometry

We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: 1. A zero-one law. 2. The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. 3. There is a formula $\xi(x,y)$ (not directly speaking about colours) such that, with asymptotic probability 1, the relation "there is an $l$-colouring which assigns the same colour to $x$ and $y$" is defined by $\xi(x,y)$. 4. With asymptotic probability 1, an $l$-colourable structure has a unique $l$-colouring (up to permutation of the colours).Comment: 35 page