Frequency conditions for the global stability of nonlinear delay equations with several equilibria

In our adjacent work, we developed a spectral comparison principle for compound cocycles generated by delay equations. In particular, this principle allows to derive frequency conditions (inequalities) for the uniform exponential stability of such cocycles by means of their comparison with stationary problems. Such inequalities are hard to verify analytically since they contain resolvents of additive compound operators and to compute the resolvents it is required solving a first-order PDEs with boundary conditions involving both partial derivatives and delays. In this work, we develop approximation schemes to verify some of the arising frequency inequalities. Beside some general results, we mainly stick to the case of scalar equations. By means of the Suarez-Schopf delayed oscillator and the Mackey-Glass equations, we demonstrate applications of the theory to reveal regions in the space of parameters where the absence of closed invariant contours can be guaranteed. Since our conditions are robust, so close systems also satisfy them, we expect them to actually imply the global stability, as in known finite-dimensional results utilizing variants of the Closing Lemma which is still awaiting developments in infinite dimensions

Double Refinement Network for Efficient Indoor Monocular Depth Estimation

Monocular depth estimation is the task of obtaining a measure of distance for each pixel using a single image. It is an important problem in computer vision and is usually solved using neural networks. Though recent works in this area have shown significant improvement in accuracy, the state-of-the-art methods tend to require massive amounts of memory and time to process an image. The main purpose of this work is to improve the performance of the latest solutions with no decrease in accuracy. To this end, we introduce the Double Refinement Network architecture. The proposed method achieves state-of-the-art results on the standard benchmark RGB-D dataset NYU Depth v2, while its frames per second rate is significantly higher (up to 18 times speedup per image at batch size 1) and the RAM usage per image is lower

Possibilities of use of industrial waste in road construction on the territory of the leningrad region

The main results of the joint international project №2006/123-438 “ECOROAD” (South-East Finland - Russia Neighborhood Programme) are presented in this paper. Coordinator of the project is Lappeenranta University of Technology, main partners are Saint-Petersburg State Polytechnical University and Saint Petersburg State Technological University of Plant Polymers. The project was implemented with support of the Committee of Natural Resources and Environmental Protection of the Leningrad Region, Committee of Road Maintenance and Transport of the Leningrad Region, and some enterprises of the Leningrad Region. Important data and recommendations for practical use of industrial waste of enterprises of the Leningrad Region (fly ashes, metallurgic slag, etc.) were received during implementation of the project