43,922 research outputs found
Information of Interest
A pricing formula for discount bonds, based on the consideration of the
market perception of future liquidity risk, is established. An
information-based model for liquidity is then introduced, which is used to
obtain an expression for the bond price. Analysis of the bond price dynamics
shows that the bond volatility is determined by prices of certain weighted
perpetual annuities. Pricing formulae for interest rate derivatives are
derived.Comment: 12 pages, 3 figure
Aeroelastic effects in multi-rotor vehicles with application to a hybrid heavy lift system. Part 1: Formulation of equations of motion
This report presents a set of governing coupled differential equations for a model of a hybrid aircraft. The model consists of multiple rotor systems connected by an elastic interconnecting structure, with options to add any combination of or all of the following components; i.e., thrusters, a buoyant hull, and an underslung weight. The dynamic equations are written for the individual blade with hub motions, for the rigid body motions of the whole model, and also for the flexible modes of the interconnecting structure. One of the purposes of this study is to serve as the basis of a numerical study aimed at determining the aeroelastic stability and structural response characteristics of a Hybrid Heavy Lift Airship (HHLA). It is also expected that the formulation may be applicable to analyzing stability and responses of dual rotor helicopters such as a Heavy Lift Helicopter (HLH). Futhermore, the model is capable of representing coupled rotor/body aeromechanical problems of single rotor helicopters
Innovation Rate Sampling of Pulse Streams with Application to Ultrasound Imaging
Signals comprised of a stream of short pulses appear in many applications
including bio-imaging and radar. The recent finite rate of innovation
framework, has paved the way to low rate sampling of such pulses by noticing
that only a small number of parameters per unit time are needed to fully
describe these signals. Unfortunately, for high rates of innovation, existing
sampling schemes are numerically unstable. In this paper we propose a general
sampling approach which leads to stable recovery even in the presence of many
pulses. We begin by deriving a condition on the sampling kernel which allows
perfect reconstruction of periodic streams from the minimal number of samples.
We then design a compactly supported class of filters, satisfying this
condition. The periodic solution is extended to finite and infinite streams,
and is shown to be numerically stable even for a large number of pulses. High
noise robustness is also demonstrated when the delays are sufficiently
separated. Finally, we process ultrasound imaging data using our techniques,
and show that substantial rate reduction with respect to traditional ultrasound
sampling schemes can be achieved.Comment: 14 pages, 13 figure
Crime In 2016: A Preliminary Analysis
Earlier this year, the Brennan Center analyzed crime data from the 30 largest cities in 2015, finding that crime overall remained the same as in 2014. It also found that murder increased by 14 percent, with just three cities — Baltimore, Chicago, and Washington, D.C. — responsible for half that increase. All told, 2015's murder rate was still near historic lows. The authors concluded that reports of a national crime wave were premature and unfounded, and that "the average person in a large urban area is safer walking on the street today than he or she would have been at almost any time in the past 30 years."This report updates those findings. It collects midyear data from police departments to project overall crime, violent crime, and murder for all of 2016
Crime Trends: 1990-2016
This report examines crime trends at the national and city level during the last quarter century. It covers the years 1990 through 2016, as crime rates peaked in 1991. It analyzes data from the Federal Bureau of Investigation and from police departments from the nation's 30 largest cities. Data for 2016 are estimated, as full year data was not available at the time of publication.This report concludes that although there are some troubling increases in crimes in specific cities, there is no evidence of a national crime wave
Covariant Uniform Acceleration
We show that standard Relativistic Dynamics Equation F=dp/d\tau is only
partially covariant. To achieve full Lorentz covariance, we replace the
four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By
taking this tensor to be constant, we obtain a covariant definition of
uniformly accelerated motion. We compute explicit solutions for uniformly
accelerated motion which are divided into four types: null, linear, rotational,
and general. For null acceleration, the worldline is cubic in the time. Linear
acceleration covariantly extends 1D hyperbolic motion, while rotational
acceleration covariantly extends pure rotational motion.
We use Generalized Fermi-Walker transport to construct a uniformly
accelerated family of inertial frames which are instantaneously comoving to a
uniformly accelerated observer. We explain the connection between our approach
and that of Mashhoon. We show that our solutions of uniformly accelerated
motion have constant acceleration in the comoving frame. Assuming the Weak
Hypothesis of Locality, we obtain local spacetime transformations from a
uniformly accelerated frame K' to an inertial frame K. The spacetime
transformations between two uniformly accelerated frames with the same
acceleration are Lorentz. We compute the metric at an arbitrary point of a
uniformly accelerated frame.
We obtain velocity and acceleration transformations from a uniformly
accelerated system K' to an inertial frame K. We derive the general formula for
the time dilation between accelerated clocks. We obtain a formula for the
angular velocity of a uniformly accelerated object. Every rest point of K' is
uniformly accelerated, and its acceleration is a function of the observer's
acceleration and its position. We obtain an interpretation of the
Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.Comment: 36 page
Expansions of the real field by open sets: definability versus interpretability
An open set U of the real numbers R is produced such that the expansion
(R,+,x,U) of the real field by U defines a Borel isomorph of (R,+,x,N) but does
not define N. It follows that (R,+,x,U) defines sets in every level of the
projective hierarchy but does not define all projective sets. This result is
elaborated in various ways that involve geometric measure theory and working
over o-minimal expansions of (R,+,x). In particular, there is a Cantor subset K
of R such that for every exponentially bounded o-minimal expansion M of
(R,+,x), every subset of R definable in (M,K) either has interior or is
Hausdorff null.Comment: 14 page
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