958 research outputs found
Global existence of solutions of semilinear heat equation with nonlinear memory condition
We consider a semilinear parabolic equation with flux at the boundary
governed by a nonlinear memory. We give some conditions for this problem which
guarantee global existence of solutions as well as blow up in finite time of
all nontrivial solutions. The results depend on the behavior of variable
coefficients as $t \to \infty.
An explicit solution for a multimarginal mass transportation problem
We construct an explicit solution for the multimarginal transportation
problem on the unit cube with the cost function and
one-dimensional uniform projections. We show that the primal problem is
concentrated on a set with non-constant local dimension and admits many
solutions, whereas the solution to the corresponding dual problem is unique (up
to addition of constants).Comment: 31 pages, 4 figures. The paper was completely rewritten. Heuristic
considerations to find a solution of the primal problem added. Algorithm to
find the primal problem solution numerically added (arbitrary marginals). The
construction was generalized for a C(ln x + ln y + ln z), C is convex.
Measure on the triangle was found with the support singular with respect to
the Lebesgue measur
Modeling a Sensor to Improve its Efficacy
Robots rely on sensors to provide them with information about their
surroundings. However, high-quality sensors can be extremely expensive and
cost-prohibitive. Thus many robotic systems must make due with lower-quality
sensors. Here we demonstrate via a case study how modeling a sensor can improve
its efficacy when employed within a Bayesian inferential framework. As a test
bed we employ a robotic arm that is designed to autonomously take its own
measurements using an inexpensive LEGO light sensor to estimate the position
and radius of a white circle on a black field. The light sensor integrates the
light arriving from a spatially distributed region within its field of view
weighted by its Spatial Sensitivity Function (SSF). We demonstrate that by
incorporating an accurate model of the light sensor SSF into the likelihood
function of a Bayesian inference engine, an autonomous system can make improved
inferences about its surroundings. The method presented here is data-based,
fairly general, and made with plug-and play in mind so that it could be
implemented in similar problems.Comment: 18 pages, 8 figures, submitted to the special issue of "Sensors for
Robotics
American Depository Receipts As A Way For Russian Companies to Enter The U.S. Capital Market
The international capital market has become more developed in the last two decades because of advances in information technology, increased co-operation among financial regulators and the sophistication of the market players. This paper focuses on depository receipts as an essential element in the market integration process. The paper explores how domestic investors and corporations can acquire, issue and trade in foreign securities on the major stock markets of other countries, especially emerging markets such as the Russian Federation. This paper reviews the development of European Depository Receipts (EDRs), Global Depository Receipts (GDRs) and the American Depository Receipts (ADRs) in the light of establishing a global accommodation for foreign investments. The paper takes a critical look at the ADRs and proposes a regime of regulatory requirements for the acquisition, management and sale of depository receipts in the United States
Blow-up problem for nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition
In this paper we consider initial boundary value problem for nonlinear
nonlocal parabolic equation with absorption under nonlinear nonlocal boundary
condition and nonnegative initial datum. We prove comparison principle, global
existence and blow-up of solutions.Comment: arXiv admin note: text overlap with arXiv:1602.0501
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