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 $[0,1]^3$ with the cost function $xyz$ 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