Related papers: How do difference bodies in complex vector spaces …
This article is a survey of recent results on slicing inequalities for convex bodies. The focus is on the setting of arbitrary measures in place of volume.
Some aspects of the development of physics and the mathematics set one think about relation between complex numbers and reality around us. If number to spot as the relation of two quantities, from the fact of existence of complex numbers…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
We consider a generalization of the notion of a natural mechanical system to the case of additional forces of gyroscopic type. Such forces appear, for example, as a result of global reduction of a natural system with symmetry. We study…
We describe the canonical correspondence between set of all finite metric spaces and set of special symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…
High proved the following theorem. If the intersections of any two congruent copies of a plane convex body are centrally symmetric, then this body is a circle. In our paper we extend the theorem of High to the sphere and the hyperbolic…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
I discuss the influence of adding the air resistance and the kinetic friction to the classical mechanics homework-problem: finding the motion of a body sliding down a hemispherical hill. For a physically realistic ($\propto v^2$) form of…
This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
The purpose of this paper is to answer the following question: If all hyperplane sections through the origin of a convex body are "equal", is the convex body "equal" to the ball? The meaning of the notion "equal" will change in the course…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
We investigate point arrangements $v_i\in\mathbb R^d,i\in \{1,...,n \}$ with certain prescribed symmetries. The arrangement space of $v$ is the column span of the matrix in which the $v_i$ are the rows. We characterize properties of $v$ in…
In this paper we introduce and study a topological abelian group of convex bodies, analogous to the scissors congruence group and McMullen's polytope algebra, with the universal property that continuous valuations on convex bodies…
We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly non-smooth, points in its boundary. We estimate the $L^{p}$ norm of…
We give an effective characterisation of the walls in the variation of geometric invariant theory problem associated to a quiver and a dimension vector.
Let us have in S^2, R^2 or H^2 a pair of convex bodies, for S^2 different from S^2, such that the intersections of any congruent copies of them are centrally symmetric. Then our bodies are congruent circles. If the intersections of any…
For a finite partially ordered set we calculate the dimension of the variety of its subspace representations having fixed dimension vector. The dimension is given in terms of the Euler quadratic form associated with a partially ordered set,…