2,150 research outputs found
2D Signal Estimation for Sparse Distributed Target Photon Counting Data
In this study, we explore the utilization of maximum likelihood estimation
for the analysis of sparse photon counting data obtained from distributed
target lidar systems. Specifically, we adapt the Poisson Total Variation
processing technique to cater to this application. By assuming a Poisson noise
model for the photon count observations, our approach yields denoised estimates
of backscatter photon flux and related parameters. This facilitates the
processing of raw photon counting signals with exceptionally high temporal and
range resolutions (demonstrated here to 50 Hz and 75 cm resolutions), including
data acquired through time-correlated single photon counting, without
significant sacrifice of resolution. Through examination involving both
simulated and real-world 2D atmospheric data, our method consistently
demonstrates superior accuracy in signal recovery compared to the conventional
histogram-based approach commonly employed in distributed target lidar
applications
Modular Equations and Distortion Functions
Modular equations occur in number theory, but it is less known that such
equations also occur in the study of deformation properties of quasiconformal
mappings. The authors study two important plane quasiconformal distortion
functions, obtaining monotonicity and convexity properties, and finding sharp
bounds for them. Applications are provided that relate to the quasiconformal
Schwarz Lemma and to Schottky's Theorem. These results also yield new bounds
for singular values of complete elliptic integrals.Comment: 23 page
Permutable entire functions satisfying algebraic differential equations
It is shown that if two transcendental entire functions permute, and if one
of them satisfies an algebraic differential equation, then so does the other
one.Comment: 5 page
Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated,
e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius
of convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not for all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature
rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat
Fabrication and mechanical testing of a new sandwich structure with carbon fiber network core
The aim is the fabrication and mechanical testing of sandwich structures including a new core material known as fiber network sandwich materials. As fabrication norms for such a material do not exist as such, so the primary goal is to reproduce successfully fiber network sandwich specimens. Enhanced vibration testing diagnoses the quality of the fabrication process. These sandwich materials possess low structural strength as proved by the static tests (compression, bending), but the vibration test results give high damping values, making the material suitable for vibro-acoustic applications where structural strength is of secondary importance e.g., internal panelling of a helicopter
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Flexible parameter-sparse global temperature time-profiles that stabilise at 1.5C and 2.0C
The meeting of the United Nations Framework Convention on Climate Change (UNFCCC) in December 2015 committed parties to the Convention to hold the rise in global average temperature to well below 2.0 C above pre-industrial levels. It also committed the parties to pursue efforts to limit warming to 1.5 C. This leads to two key questions. First,what extent of emission reductions will achieve either target? Second, what is the benefit of the reduced climate impacts by keeping warming at or below 1.5 C? To provide answers, climate model simulations need to follow trajectories consistent
with these global temperature limits. It is useful to operate models in an inverse mode to make model-specific estimates of greenhouse gas (GHG) concentration pathways consistent with the prescribed temperature profiles. Further inversion derives related emissions pathways for these concentrations. For this to happen, and to enable climate research centres to compare GHG concentrations and emissions estimates, common temperature trajectory scenarios are required. Here we define algebraic
curves which asymptote to a stabilised limit, while also matching the magnitude and gradient of recent warming levels. The curves are deliberately parameter-sparse, needing prescription of just two parameters plus the final temperature. Yet despite this simplicity, they can allow for temperature overshoot and for generational changes where more effort to decelerate warming
change is needed by future generations. The curves capture temperature profiles from the existing Representative Concentration Pathway (RCP2.6) scenario projections by a range of different earth system models (ESMs), which have warming amounts towards the lower levels of those that society is discussing
The iterated minimum modulus and conjectures of Baker and Eremenko
In transcendental dynamics significant progress has been made by studying points whose iterates escape to infinity at least as fast as iterates of the maximum modulus. Here we take the novel approach of studying points whose iterates escape at least as fast as iterates of the minimum modulus, and obtain new results related to Eremenko's conjecture and Baker's conjecture, and the rate of escape in Baker domains. To do this we prove a result of wider interest concerning the existence of points that escape to infinity under the iteration of a positive continuous function
Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
This paper concerns the dynamics of polynomial automorphisms of .
One can associate to such an automorphism two currents and the
equilibrium measure . In this paper we study some
geometric and dynamical properties of these objects. First, we characterize
as the unique measure of maximal entropy. Then we show that the measure
has a local product structure and that the currents have a
laminar structure. This allows us to deduce information about periodic points
and heteroclinic intersections. For example, we prove that the support of
coincides with the closure of the set of saddle points. The methods used
combine the pluripotential theory with the theory of non-uniformly hyperbolic
dynamical systems
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