We find an invariant characterization of planar webs of maximum rank. For 4-webs, we prove that a planar 4-web is of maximum rank three if and only if it is linearizable and its curvature vanishes. This result leads to the direct web-theoretical proof of the Poincar´e’s theorem: a planar 4- web of maximum rank is linearizable. We also find an invariant intrinsic characterization of planar 4-webs ...

We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar ...

This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different thresholding procedures are introduced for the estimation of the ambiguity function. Such estimation methods are suitable if the ambiguity function is only non-negligible ...

All points on the surface of the Earth are moving. To define the velocity of a given point, we can place a GPS receiver there and measure the coordinates every day. After collecting enough data, we can generate a time series of three coordinates, North, East and Height directions. The most used technique to determine such displacements, is the linear model. The main objective of this thesis ...

We demonstrate how to model the toppling activity in avalanching systems by stochastic differential equations (SDEs). The theory is developed as a generalization of the classical mean field approach to sandpile dynamics by formulating it as a generalization of Itoh’s SDE. This equation contains a fractional Gaussian noise term representing the branching of an avalanche into small active clusters, ...

In the present paper we study geometric structures associated with webs of hypersurfaces. We prove that with any geodesic (n + 2)-web on an n-dimensional manifold there is naturally associated a unique projective structure and, provide that one of web foliations is pointed, there is also associated a unique affine structure. The projective structure can be chosen by the claim that the leaves of all ...

The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.

We give a detailed study of dynamical properties of the Zhang model, including evaluation of topological entropy and estimates for the Lyapunov exponents and the dimension of the attractor. In the thermodynamic limit the entropy goes to zero and the Lyapunov spectrum collapses.1

In this article we want to present the EISCAT Svalbard Radar (ESR) in some detail, as well as some of the instruments of interest for ionospheric and magnetospheric research that are located in the vicinity of it. We particularly describe how this instrument cluster, close to the geomagnetic conjugate point of the Chinese Antarctic Zhongshan station, can contribute to inter-hemispheric coordinated ...

The production of proteins in a cell is a regulated process. This means that the cell will only produce a type of protein when that type is needed. A fundamental step where this regulation occurs is at gene transcription. It is observed that transcription is regulated differently for different genes, and the question is therefore asked: why has evolution come up with different modes of transcriptional ...