Рассмотрены слоистые изотропные структуры, включающие слои метаматериала. Двухслойные и многослойные симметричные структуры, а также структура с непрерывным изменением параметров материала были исследованы. Впервые условия прозрачности таких конструкций и сооружений выведены из них представлены. Показано, что границы областей непрохождения волны соответствуют условиям прозрачности таких конструкций. Показано, что для симметричных структур прозрачности и четности-времени (ПП) в электродинамике и оптике требуются дополнительные условия, в отличие от представленных структур.

In the paper, a delayed control for an even-order chain of integrators is proposed. It is known that for many differential models, in particular, for models of mechanical systems, the control problem is reduced to the stabilization of chain of integrators. The proposed method use a simple inductive design and cascade systems’ asymptotic stability property. For any order of the integrator the control is a linear combination of delayed state coordinates with odd indices, and it depends on three numerical parameters. The parameters are selected from the stability region of a second-order linear delayed system and they can vary within a wide range. The result obtained can be applied to the stabilization problem for systems with incomplete measurements. In particular, for some class of mechanical systems, the proposed control can be a derivative-free alternative of stabilizing control.

This paper discusses whether laser technology holds promise for use in marking steel billets in a continuous-production environment. A laser-marking experiment was performed on “dull metal” and “bright metal,” which have different oxidation layers. The experiment was performed on rolled-shape samples produced using a wide variety of carbon steels and differing scale produced by using different cooling rates during heat treatment (in water, or in a furnace). A QR code or bar code was applied to the heat-treated samples using laser markers where the laser exposure and laser power used for application of the code were varied. The experimental results revealed significant technical difficulties preventing use of this technology with “dull metal” (application of the code to areas coated with scale causes the corresponding areas to change color — gray instead of bronze resulting in the code being impossible to read using standard equipment). Delamination of the oxide coating on the billet will lead to loss of code, and make the code impossible to subsequently read. Successful laser marking of “dull metal” requires initial preparation of the surface for marking in order to remove scale inclusions, so that the code will have uniform color and contrast. A clean surface requires less time to laser mark and lower laser-marker power because of the high contrast between the code and the surface. The code remained intact and readable after long storage (on the order of 9 months) under standard conditions.

An optimization approach to linear control systems has recently become very popular. For example, the linear feedback matrix in the classical linear-quadratic regulator problem can be viewed as a variable, and the problem can be reduced to the minimization of the performance indicator for this variable. To this end, one can apply the gradient method and obtain a justification of the convergence. This approach has been successfully applied to a number of problems, including output feedback optimization. The present paper is the first to apply this approach to the peak-to-peak gain minimization problem. A gradient method for finding a static state or output feedback is written out and justified. A number of examples are considered, including the single and double pendulums.

We propose a test procedure for distinguishing between two separable classes of arbitrary distribution tails and, moreover, prove its consistency. The method is based on the goodness-of-fit test for an arbitrary distribution tail, and properties of this test are also discussed. This is the first goodness-of-fit test for distribution tails proposed in the literature that can be applied for testing the goodness-of-fit hypothesis with a discrete distribution tail. In contrast to the overwhelming majority of works related to statistics of extremes, we do not assume that the distributions belong to any of maximum domains of attraction.