1,457 research outputs found
A Comprehensive Analysis of Uncertainties Affecting the Stellar Mass - Halo Mass Relation for 0<z<4
We conduct a comprehensive analysis of the relationship between central
galaxies and their host dark matter halos, as characterized by the stellar
mass-halo mass (SM-HM) relation, with rigorous consideration of uncertainties.
Our analysis focuses on results from the abundance matching technique, which
assumes that every dark matter halo or subhalo above a specific mass threshold
hosts one galaxy. We discuss the quantitative effects of uncertainties in
observed galaxy stellar mass functions (GSMFs) (including stellar mass
estimates and counting uncertainties), halo mass functions (including cosmology
and uncertainties from substructure), and the abundance matching technique used
to link galaxies to halos (including scatter in this connection). Our analysis
results in a robust estimate of the SM-HM relation and its evolution from z=0
to z=4. The shape and evolution are well constrained for z < 1. The largest
uncertainties at these redshifts are due to stellar mass estimates; however,
failure to account for scatter in stellar masses at fixed halo mass can lead to
errors of similar magnitude in the SM-HM relation for central galaxies in
massive halos. We also investigate the SM-HM relation to z=4, although the
shape of the relation at higher redshifts remains fairly unconstrained when
uncertainties are taken into account. These results will provide a powerful
tool to inform galaxy evolution models. [Abridged]Comment: 27 pages, 12 figures, updated to match ApJ accepted version
Sufficiency of a Numerical Downstream Continuation
(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by the Navier-Stokes equations indicate that downstream continuation achieved by applying a second derivative boundary condition at a finite location often provides the least restrictive method of closing the flow [3]
Alien Registration- Scott, Charlie H. (Portland, Cumberland County)
https://digitalmaine.com/alien_docs/21978/thumbnail.jp
On the Existence of Strong Solutions to Autonomous Differential Equations with Minimal Regularity
For proving the existence and uniqueness of strong solutions to dY/dt = F(Y), Y(0) = C, the most quoted condition seen in elementary differential equations texts is that F(Y) and its first derivative be continuous. One wonders about the existence of a minimal regularity condition which allows unique strong solutions. In this note, a bizarre example is seen where F(Y) is not differentiable at an equilibrium solution; yet unique non-global strong solutions exist at each point, whereas global non-unique weak solutions are allowed. A characterizing theorem is obtained
Sufficiency of a Numerical Downstream Continuation
(First paragraph) Customarily one does not impose n-th order boundary conditions on the solution of initial/boundary value problems whose characterizing partial differential equations are also n-th order. However, conjecture that such problems are not well-posed, or that a solution might not exist, is not always justified [l]. Perhaps a physically more natural example is provided by problems of computational fluid dynamics. Here boundary conditions which correctly should be applied at an infinite distance downstream from the region of interest are for computational convenience often applied at a finite location [2]. Results of numerical experimentation on viscous flows governed by the Navier-Stokes equations indicate that downstream continuation achieved by applying a second derivative boundary condition at a finite location often provides the least restrictive method of closing the flow [3]
A System Equivalence Related to Dulac\u27s Extension of Bendixson\u27s Negative Theorem for Planar Dynamical Systems
Bendixson\u27s Theorem [H. Ricardo, A Modem Introduction to Differential Equations, Houghton-Mifflin, New York, Boston, 2003] is useful in proving the non-existence of periodic orbits for planar systems dx/dt = F(x, y), dy/dt = G (x, y) in a simply connected domain D, where F, G are continuously differentiable. From the work of Dulac [M. Kot, Elements of Mathematical Ecology, 2nd printing, University Press, Cambridge, 2003] one suspects that system (1) has periodic solutions if and only if the more general system dx/d tau = B(x, y)F(x, y), dy/d tau = B(x, y)G(x, y) does, which makes the subcase (1) more tractable, when suitable non-zero B (x, y) which are C1(D) can be found. Thus, Bendixson\u27s Theorem can be applied to system (2), where otherwise it is unfruitful in establishing the non-existence of periodic solutions for system (1). The object of this note is to give a simple proof justifying this Dulac-related postulate of the equivalence of systems (1) and (2). (c) 2006 Elsevier Ltd. All rights reserved
A System Equivalence Related to Dulac\u27s Extension of Bendixson\u27s Negative Theorem for Planar Dynamical Systems
Bendixson\u27s Theorem [H. Ricardo, A Modem Introduction to Differential Equations, Houghton-Mifflin, New York, Boston, 2003] is useful in proving the non-existence of periodic orbits for planar systems dx/dt = F(x, y), dy/dt = G (x, y) in a simply connected domain D, where F, G are continuously differentiable. From the work of Dulac [M. Kot, Elements of Mathematical Ecology, 2nd printing, University Press, Cambridge, 2003] one suspects that system (1) has periodic solutions if and only if the more general system dx/d tau = B(x, y)F(x, y), dy/d tau = B(x, y)G(x, y) does, which makes the subcase (1) more tractable, when suitable non-zero B (x, y) which are C1(D) can be found. Thus, Bendixson\u27s Theorem can be applied to system (2), where otherwise it is unfruitful in establishing the non-existence of periodic solutions for system (1). The object of this note is to give a simple proof justifying this Dulac-related postulate of the equivalence of systems (1) and (2). (c) 2006 Elsevier Ltd. All rights reserved
On the Existence of Periodic and Eventually Periodic Solutions of a Fluid Dynamic Forced Harmonic Oscillator
For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G\u3e0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from the fan
Probability Models for Blackjack Poker
For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer\u27s seven. Theoretical and experimental methods are used in order to determine whether the calculation can be truncated after the dealer\u27s fifth card without significant loss of accuracy. Less than one tenth of one percent difference is observed between the fifth card truncated expectation and the experimentally obtained expectation
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