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Mathematician reveals world’s oldest example of applied geometry
land survey Creating right angles Si.427 trigonometric function
2021/8/10
A scientist has revealed that an ancient clay tablet could be the oldest and most complete example of applied geometry. The surveyor's field plan from the Old Babylon period shows that ancient mathema...
An Example of a Nearly Integrable Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension
Nearly Integrable Hamiltonian System Trajectory Dense Maximal Hausdorff Dimension
2015/9/25
The famous ergodic hypothesis suggests that for a typical Hamiltonian on a typical energy surface nearly all trajectories are dense. KAM theory disproves it.Ehrenfest (The Conceptual Foundations of th...
Normally Hyperbolic Invariant Laminations and diffusive behaviour for the generalized Arnold example away from resonances
Hyperbolic Invariant Laminations generalized Arnold away from resonances
2015/9/25
In this paper we study existence of Normally Hyperbolic Invariant Laminations (NHIL) for a nearly integrable system given by the product of the pendulum and the rotator perturbed with a small coupling...
Analysis of Belief Propagation for Non-Linear Problems: The Example of CDMA (or: How to Prove Tanaka’s Formula)
Binary signal and white gaussian noise spread sequence scheme of linear time
2015/8/21
We consider the CDMA (code-division multipleaccess) multi-user detection problem for binary signals and additive white gaussian noise. We propose a spreading sequences scheme based on random sparse si...
Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework
Schwarz Christoffel conformal mapping numerical integration extended finite element method quadrature generalized finite element method
2011/9/20
Abstract: Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be...
Logarithmic Poisson cohomology: example of calculation and application to prequantization
Logarithmic Poisson cohomology application prequantization
2011/2/24
In this paper, we introduce the notions of logarithmic Poisson structure
and logarithmic principal Poisson structure; we prove that the latter
induces a representation by logarithmic derivation of t...
Example of a 6-by-6 Matrix with Different Tropical and Kapranov Ranks
matrix theory tropical semiring tropical rank Kapranov rank
2011/2/28
We provide an example of a 6-by-6 matrix A such that rkt(A) = 4, rkK(A) = 5. This answers a question asked by M. Chan, A. Jensen, and E. Rubei.
A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set
Sierpinki Gasket harmonic function
2011/6/2
Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on an...
In this note we show that the restriction of the cotangent bundle $\Omega_{\mathbb P}^2$ of the projective plane to a Fermat curve $C$ of degree $d$ in characteristic $p \equiv -1 \mod 2d$ is, up to t...
The concept of quasi-integrability: a concrete example
The concept quasi-integrability concrete example
2010/11/10
We use the deformed sine-Gordon models recently presented by Bazeia et al to discuss possible definitions of quasi-integrability. We present one such definition and use it to calculate an infinite num...
An example of Melkersson subcategory which is not closed under injective hulls
Melkersson subcategory injective hulls
2010/11/12
The Melkersson subcategory is a special Serre subcategory. It was proved that a Serre subcategory which is closed under injective hulls is a Melkersson subcategory. However, it has been an open quest...
Mathematical justification of spectral/covariance techniques: On the example of arc detection
arcing faults Fourier transform power spectrum
2010/9/13
Detecting arcing faults is an important but difficult-to-solve practical problem. Many existing methods of arc detection are based upon acquiring a signal that is proportional to current and then maki...
An example of non-homeomorphic conjugate varieties
example non-homeomorphic conjugate varieties
2010/12/13
We give examples of smooth quasi-projective varieties over complex numbers, in the context of connected Shimura varieties, which are not homeomor-phic to a conjugate of itself by an automorphism of th...
The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a cons...
An Example of Lie Group with Sasakian Structure of Constant $\Phi-$sectional Curvature
sasakian manifold lie group
2009/1/13
An Example of Lie Group with Sasakian Structure of Constant $\Phi-$sectional Curvature。