相关论文: Multiresolution approximation of the vector fields…

Let $M$ be either the 2-sphere $\SS^2 \subset\RR^3$ or the hyperbolic plane $\HH^2 \subset \RR^3$. If $\Delta(abc)$ is a geodesic triangle on $M$ with corners at $a,b,c\in M$, we denote by $\alpha, \beta, \gamma\in M$ the midpoints of their…

The present article is devoted to developing the Legendre wavelet operational matrix method (LWOMM) to find the numerical solution of two-dimensional hyperbolic telegraph equations (HTE) with appropriate initial time boundary space…

To some braiding R of Hecke type (a Hecke symmetry) we put into correspondence an associative algebra called the modified Reflection Equation Algebra (mREA). We construct a series of matrices L_(m), m=1,2,... with entries belonging to mREA…

This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated…

Polarization has proved an invaluable tool for probing magnetic fields in relativistic jets. Maps of the intrinsic polarization vectors have provided the best evidence to date for uniform, toroidally dominated magnetic fields within jets.…

For a single crystal of TmGa3, two-dimensional angular correlation of positron annihilation radiation spectra were measured and subjected to a deconvolution algorithm based on the Van Citter iterative method. The three-dimensional…

We present a constructive derivation of holographic four-point correlators of arbitrary half-BPS operators for all maximally supersymmetric conformal field theories in $d>2$. This includes holographic correlators in 3d ${\cal N}=8$ ABJM…

Three-dimensional segmentation in magnetic resonance images (MRI), which reflects the true shape of the objects, is challenging since high-resolution isotropic MRIs are rare and typical MRIs are anisotropic, with the out-of-plane dimension…

We described a wide class of $p$-adic refinable equations generating $p$-adic multiresolution analysis. A method for the construction of $p$-adic orthogonal wavelet bases within the framework of the MRA theory is suggested. A realization of…

Within a holographic framework, we consider vector mesons riding on a gravity-dilaton background. The latter one is determined directly from a Schr\"odinger equivalent potential which delivers a proper $\rho$ meson Regge trajectory. The…

In many astronomical works, the structure of vector fields is analyzed, such as the differences in the celestial object coordinates in catalogs or the celestial object velocities, by decomposition into vector spherical harmonics (VSH). This…

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace…

The multi-scale entanglement renormalization ansatz (MERA) is a tensor network representation for ground states of critical quantum spin chains, with a network that extends in an additional dimension corresponding to scale. Over the years…

We study a solenoidal-potential type decomposition of a symmetric $m$-tensor field in $\Rb^2$, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition…

Vector Symbolic Architectures (VSAs) provide a well-defined algebraic framework for compositional representations in hyperdimensional spaces. We introduce HyperSpace, an open-source framework that decomposes VSA systems into modular…

Object recognition and reconstruction is of great interest in many research fields. Detecting pedestrians or cars in traffic cameras or tracking seismic waves in geophysical exploration are only two of many applications. Recently, the…

In (d+1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the…

A K3 surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and a rigidity of curve of genus eleven and gives two kind of descriptions of…

In this work, we investigate the system formed by the equations $\text{div } \vec w=g_0$ and $\text{curl } \vec w=\vec g$ in bounded star-shaped domains of $\mathbb{R}^3$. A Helmholtz-type decomposition theorem is established based on a…

We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a "foliation" of $\mathbb{R}^3$ into fuzzy spheres. We first construct a natural matrix base adapted to…