Body with mirror surface and connected interior invisible from one point
Here we demonstrate existence of a piecewise smooth obstacle having connected interior and invisible from a point in the framework of geometric optics.
math.MG↗
arXiv subjects
Alena Aleksenko
Publications and source records attributed to Alena Aleksenko.
On the sequence $αn!$
We prove that there exists $α\in \mathbb{R}$ such that for any $N$ the dicrepancy $D_N$ of the sequence $\{αn !\} ,\, 1\le n \le N$ satisfies $ D_N = O(\log N)$.
math.NT↗
A spectrum associated with Minkowski diagonal continued fraction
We prove a result on the structure of a Diophantine spectrum associated with Minkowski diagonal continued fraction.
math.NT↗
Examples of Admissible Simplification of Mathematical Theories
"Mathematicians, like physicists, are pushed by a strong fascination. Research in mathematics is hard, it is intellectually painful even if it is rewarding, and you would not do it without some strong urge." [D. Ruelle]. We shall give some examples from our experience, when we were able to simplify some serious mathematical models to make them understandable by children, preserving both aesthetic and intellectual value. The latter is in particularly measured by whether a given simplification allows setting a sufficient list of problems feasible for school students.
math.HO↗
Bodies invisible in one direction and bodies of zero total cross section
We consider a body in a parallel flow of non-interacting particles. One can imagine that the flow is highly rarefied or consists of light rays. The interaction of particles with the body is perfectly elastic. We introduce the notions of a body of zero resistance and an invisible body and prove that all such bodies do exist.
physics.optics↗
Bodies of zero resistance and bodies invisible in one direction
We consider a body in a parallel flow of non-interacting particles. The interaction of particles with the body is perfectly elastic. We introduce the notions of a body of zero resistance, a body that leaves no trace, and an invisible body, and prove that all such bodies do exist.
math.DS↗
The problem of the body of revolution of minimal resistance
Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of {\it convex} axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class of axially symmetric but {\it generally nonconvex} bodies. The infimum in this problem is not attained. We construct a sequence of bodies minimizing the resistance. This sequence approximates a convex body with smooth front surface, while the surface of approximating bodies becomes more and more complicated. The shape of the resulting convex body and the value of minimal resistance are compared with the corresponding results for Newton's problem and for the problem in the intermediate class of axisymmetric bodies satisfying the {\it single impact} assumption \cite{CL1}. In particular, the minimal resistance in our class is smaller than in Newton's problem; the ratio goes to 1/2 as (length)/(width of the body) $\to 0$, and to 1/4 as (length)/(width) $\to +\infty$.
math.OC↗