In 1970s, a methodwas developed for integration of nonlinear equations bymeans of algebraic geometry. Starting froma Lax representationwith spectral parameter, the algebro-geometricmethod allows to solve the system explicitly in terms of theta functions of Riemann surfaces. However, the explicit formulas obtained in this way fail to answer qualitative questions such as whether a given singular ...

In this work, we developed a method which effectively uses subdivision surfaces to fit deformable models to noisy 3–D data. The subdivision models provide a compact low dimensional representation of model parameter space. They also allow a free form deformation of the objects of arbitrary geometry. These two properties make them ideal for fitting deformable models to noisy data. We tested our a...

We introduce the fatness parameter of a 4-dimensional polytope P, defined as φ(P) = ( f1 + f2)/( f0 + f3). It arises in an important open problem in 4-dimensional combinatorial geometry: Is the fatness of convex 4polytopes bounded? We describe and analyze a hyperbolic geometry construction that produces 4-polytopes with fatness φ(P) > 5.048, as well as the first infinite family of 2-simple, 2-s...

The propagator is calculated on a noncommutative version of the flat plane and the Lobachevsky plane with and without an extra (euclidean) time parameter. In agreement with the general idea of noncommutative geometry it is found that the limit when the two ‘points’ coincide is finite and diverges only when the geometry becomes commutative. The flat 4-dimensional case is also considered. This is...

Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establis...

Dendrograms used in data analysis are ultrametric spaces, hence objects of nonarchimedean geometry. It is known that there exist p-adic representations of dendrograms. Completed by a point at infinity, they can be viewed as subtrees of the Bruhat-Tits tree associated to the p-adic projective line. The implications are that certain moduli spaces known in algebraic geometry are in fact p-adic par...

A dipole model is used to simulate incoherent Raman and fluorescent scattering by microspheres. The use of the addition theorem for spherical harmonics circumvents the need to evaluate double sums in the final formulas, thereby drastically reducing computational effort. Special attention is paid to consideration of backscattering geometry, which is important for lidar applications. The formulas...

recently many studies have been done on different issues of using multiple antennas at transmit and receive sides of a radar system in a mimo (multiple input multiple output) configuration. in addition, for the electronic warfare‟s purposes, the utilization of available signals of the environment to detect the targets has gained considerable attention in recent years. such passive radars use th...

The range of neutralino-proton cross sections for R-parity preserving supergravity models with GUT scale unification of the gauge coupling constants is examined. The models considered here are mSUGRA, models with non universal soft breaking and D-brane models. It is found that the current dark matter detectors are sampling significant parts of the SUSY parameter space and future detectors could...

In the verification under uncertainty setting, an algorithm is given, for each input item, an uncertainty area that is guaranteed to contain the exact input value, as well as an assumed input value. An update of an input item reveals its exact value. If the exact value is equal to the assumed value, we say that the update verifies the assumed value. We consider verification under uncertainty fo...