90,717 research outputs found
Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
We prove several differential Harnack inequalities for positive solutions to
nonlinear backward heat equations with different potentials coupled with the
Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear
heat equation under the -Ricci flow on a closed surface. These new
Harnack inequalities extend the previous differential Harnack inequalities for
linear heat equations with potentials under the Ricci flow.Comment: 17 pages. New explanations added; Final versio
Analysis of dynamic system optimal assignment with departure time choice
Most analyses on dynamic system optimal (DSO) assignment are done by using the
control theory with an outflow traffic model. On the one hand, this control theoretical
formulation provides some attractive mathematical properties for analysis. On the
other hand, however, this kind of formulation often ignores the importance of
ensuring proper flow propagation. Moreover, the outflow models have also been
extensively criticized for their implausible traffic behaviour. This paper aims to
provide another framework for analysing a DSO assignment problem based upon
sound traffic models. The assignment problem we considered aims to minimize the
total system cost in a network by seeking an optimal inflow profile within a fixed
planning horizon. This paper first summarizes the requirements on a plausible traffic
model and reviews three common traffic models. The necessary conditions for the
optimization problem are then derived using a calculus of variations technique.
Finally, a simple working example and some concluding remarks are given
System optimizing flow and externalities in time-dependent road networks
This paper develops a framework for analysing and calculating system optimizing flow and
externalities in time-dependent road networks. The externalities are derived by using a novel
sensitivity analysis of traffic models. The optimal network flow is determined by solving a
state-dependent optimal control problem, which assigns traffic such that the total system cost
of the network system is minimized. This control theoretic formulation can work with general
travel time models and cost functions. Deterministic queue is predominantly used in dynamic
network models. The analysis in this paper is more general and is applied to calculate the
system optimizing flow for Frieszâs whole link traffic model. Numerical examples are
provided for illustration and discussion. Finally, some concluding remarks are given
Departure from the onset-onset rule
Using a signal-detection task, the generality of Turvey's (1973) onset-onset rule was tested in four experiments. After seeing, in succession, (1) one or two letters (target display), (2) a multiletter detection display, and (3) a mask display, subjects decided whether or not the letter or letters in the target display reappeared in the succeeding detection display at different levels of detection-display duration in various situations. The subjects' sensitivity was inconsistent with the onset-onset rule. More specifically, sensitivity increased with increases in display duration within a fixed stimulus onset asynchrony of 150 msec. Display duration, however, had no effect on response bias. Nor was there any interaction between display duration and display size in terms of either sensitivity or response bias. The more complicated relationship between display duration and display size does not invalidate the departure from the onset-onset rule
Analysis of dynamic system optimum and externalities with departure time choice
This paper aims to analyse the dynamic system optimal assignment with departure time choice, which is an
important, yet underdeveloped area. The main contribution of this paper is the necessary conditions and the
sensitivity analysis for dynamic system optimizing flow. Following this, we revisit the issue of dynamic
externality in a more plausible way. We showed that how the externality can be derived and interpreted from
the control theoretic formulation and the sensitivity analysis of traffic flow. To solve the system optimal
assignment, we propose a dynamic programming solution approach. We present numerical calculations and
discuss the characteristics of the results. In particular, we contrast the system optimal assignment with its
equilibrium counterpart in terms of the amount of travel generated, flow profiles, and travel costs
The Distribution of Integral Points on the Wonderful Compactification by Height
We study the asymptotic distribution of S-integral points of bounded height
on partial bi-equivariant compactifications of semi-simple groups of adjoint
type.Comment: arXiv admin note: text overlap with arXiv:1102.2162 by other author
Recommended from our members
Continuity and change: Challenging the disposable Chinese city
The newly outwardâlooking economic stance that China adopted in the 1980s was reflected by a Westernâstyle building boom. As widely spaced towers replaced traditional courtyardâbased environments, urban legibility was lost â and the new buildings were not designed to last. In recent years there has been a backlash: adaptive reuse is now encouraged, as are looseâfit approaches to new design for greater durability. Californiaâbased architect Renee Y Chow traces these shifts, and highlights projects that have sought to redress the balance â including one by her own practice, Studio URBIS
- âŠ