For modular elliptic curves over number fields of narrow class one, and with multiplicative reduction at a collection p-adic primes, we define new invariants. Inspired by Nekovář Scholl's plectic conjectures, believe these invariants control the Mordell–Weil group higher rank support our expectations numerical experiments.

The selection of features extracted for image retrieval is quite important. We in this paper choose standard deviation and kurtosis to character texture. Non-subsampled shearlet transform is used to derive texture features. Shearlet is a new sparse representation tool of multidimensional function, which provides a simple and efficient mathematical framework. We firstly decompose the source imag...

In this paper, we study the construction of irregular shearlet systems, i.e., systems of the form SH(ψ,Λ) = {a− 4 ψ(A−1 a S−1 s (x− t)) : (a, s, t) ∈ Λ}, where ψ ∈ L(R), Λ is an arbitrary sequence in R ×R×R2, Aa is a parabolic scaling matrix and Ss a shear matrix. These systems are obtained by appropriately sampling the Continuous Shearlet Transform. We derive sufficient conditions for such a d...