Related papers: Geometrical joke(r?)s for SETI
Sequences whose terms are equal to the number of functions with specified properties are considered. Properties are based on the notion of derangements in a more general sense. Several sequences which generalize the standard notion of…
This paper investigates the derived and spectral analogs of logarithmic geometry. We develop the deformation theory for animated log rings and $\mathbb{E}_\infty$-log rings and examine the corresponding theories of derived and spectral log…
The solution of the geodesic problem for an oblate ellipsoid is developed in terms of series. Tables are provided to simplify the computation. [This is an English translation of F. W. Bessel, Astronomische Nachrichten 4(86), 241-254 (1825).…
We establish a link between the behavior of length functions on Teichm\"uller space and the geometry of certain anti de Sitter 3-manifolds. As an application, we give new purely anti de Sitter proofs of results of Teichm\"uller theory such…
One of the oldest methods for constructing integrable Hamiltonian systems, proposed by Jacobi, recently is being presented as a novel St\"{a}ckel lift construction related with Haantjes geometry. It may cause some confusion.
By a perturbation approach, we construct geometric solitons with various vortex structures(vortex pairs, vortex rings) for some geometric flows(Wave maps, Shr\"odinger flows) from Minkowski spaces to ${\mathbb S}^2\subset\R^3$.
A mixture of an historical article, and of a survey of recent developments, containing also a couple of new results.
Some aspects of the multidimensional soliton geometry are considered.
We consider the application of stable marginally outer trapped surfaces to problems concerning the size of material bodies and the area of black holes. The results presented extend to general initial data sets (V,g,K) previous results…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…
In this paper, the dynamical attractor and heteroclinic orbit have been employed to make the late-time behaviors of the model insensitive to the initial condition and thus alleviate the fine-tuning problem in the torsion cosmology. The…
A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained…
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
We study topology of configuration spaces of planar linkages having one leg of variable length. Such telescopic legs are common in modern robotics where they are used for shock absorbtion and serve a variety of other purposes. Using a Morse…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.
We explore the usefulness of the existing relations between the $S$-matrix and time delay in characterizing baryon resonances in pion-nucleon scattering. We draw attention to the fact that the existence of a positive maximum in time delay…
In this paper we make an overview of results relating the recent "discoveries" in differential geometry, such as higher structures and differential graded manifolds with some natural problems coming from mechanics. We explain that a lot of…
Replaced by a shorter version which appeared in press.