Third harmonics of cosmic ray intensity on quiet days at Deep River Neutron Monitoring Station

The cosmic ray (CR) intensity data recorded in Deep River Neutron Monitoring Station have been investigated on quietest days (QD) for third harmonics of daily variation during solar cycles 21 and 22. It has been observed that in spite of abrupt change in the amplitude and phase of tri-diurnal anisotropy in CR intensity, the amplitude is quite significant throughout the period of investigation with larger amplitude during the years 1980 and 1985. Thus, tri-diurnal anisotropy clearly shows 11-year variation at the mid latitude neutron monitoring station.      

Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

Improved scales of spaces and elliptic boundary-value problems. III

We study elliptic boundary-value problems in improved scales of functional Hilbert spaces on smooth manifolds with boundary. The isotropic Hörmander-Volevich-Paneyakh spaces are elements of these scales. The local smoothness of a solution of an elliptic problem in an improved scale is investigated. We establish a sufficient condition under which this solution is classical. Elliptic boundary-value problems with parameter are also studied.     

Some results of the local theory of smooth functions

We present results of the investigation of the local behavior of smooth functions in neighborhoods of their regular and critical points and prove theorems on the mean values of the functions considered similar to the Lagrange finite-increments theorem. We also study the symmetry of the derivative of an analytic function in the neighborhood of its multiple zero, prove new statements of the Weierstrass preparation theorem related to the critical point of a smooth function with finite smoothness, determine a nongradient vector field of a function in the neighborhood of its critical point, and consider one critical case of stability of an equilibrium position of a nonlinear system. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 231–267, February, 2007.     

Orbifold fibrations of Eschenburg spaces

Most of the few known examples of compact Riemannian manifolds with positive sectional curvature are the total space of a Riemannian submersion. In this article we show that this is true for all known examples, if we enlarge the category to orbifold fibrations. For this purpose we study all almost free isometric circle actions on positively curved Eschenburg spaces, which give rise to principle orbifold bundle structures, and we examine in detail their geometric properties. In particular, we obtain a new family of 6-dimensional orbifolds with positive sectional curvature whose singular locus consists of just two points.      

Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets

We study the dynamics of magnetic bubble solitons in a two-dimensional isotropic antiferromagnetic spin lattice in the case where the exchange integral J(x, y) is position dependent. In the near-continuum regime, this system is described by the relativistic O(3) sigma model on a space-time with a spatially inhomogeneous metric determined by J. We use the geodesic approximation to describe the low-energy soliton dynamics in this system: the n-soliton motion is approximated by geodesic motion in the moduli space M _n of static n-solitons equipped with the L ² metric γ. We obtain explicit formulas for γ for various natural choices of J(x, y). Based on these, we show that single soliton trajectories are refracted with J⁻¹ being analogous to the refractive index and that this refraction effect allows constructing simple bubble lenses and bubble guides. We consider the case where J has a disk inhomogeneity (with the value J ₊ outside a disk and J ₋ < J ₊ inside) in detail. We argue that for sufficiently large J ₊/J ₋, this type of antiferromagnet supports approximate quasibreathers: two or more coincident bubbles confined within the disk spin internally while their shape oscillates with a generically incommensurate period. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 1, pp. 191–208, July, 2007.     

On the use of the multifrequency method for studying scattered fields during the antenna measurements in an anechoic chamber

We consider a method of far-zone wideband antenna measurements performed at discrete frequencies with subsequent synthesis of the tested-antenna response in the time domain for separating the useful signal and interference due to scattering. Experimental results of a study of the scattered fields arising during the measurements of characteristics of centimeter-wave horn antennas on a standard facility in an anechoic chamber are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 47, No. 12, pp. 1066–1077, December, 2004.