相关论文: Refracting profiles and generalized holodiagrams

A well studied family of random fractals called fractal percolation is discussed. We focus on the projections of fractal percolation on the plane. Our goal is to present stronger versions of the classical Marstrand theorem, valid for almost…

The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…

In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…

Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…

A special formula for the total mean curvature of an ovaloid is derived. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, some integral formula for ovaloids is…

Reconfigurable reflectors have a significant potential in future telecommunication systems, and approaches to the design and realization of full and tunable reflection control are now actively studied. Reflectarrays, being the classical…

Reflection at an interface separating two different media is a rather universal phenomenon which arises because of wave mismatching at the interface. By means of supersymmetric quantum mechanics methods, it is shown that a fully transparent…

Absolute negative refraction regions for both polarizations of electromagnetic wave in two-dimensional photonic crystal have been found through both the analysis and the exact numerical simulation. Especially, absolute all-angle negative…

Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…

We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…

A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…

Artificial gauge fields enable extending the control over dynamics of uncharged particles, by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed…

This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…

Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and…

The document covers the fundamental algorithm of backward propagation from the point of view of reconstructing the wavefield captured by a "screen" in an imaging system. Owing to a property of the Helmholtz equation, wavefields have an…

The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…

We establish propagation of singularities for the semiclassical Schr\"odinger equation, where the potential is conormal to a hypersurface. We show that semiclassical wavefront set propagates along generalized broken bicharacteristics, hence…

We construct an extension of diffusion geometry to multiple modalities through joint approximate diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps…

By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…

Generalizing homogeneous spectra for rings graded by natural numbers, we introduce multihomogeneous spectra for rings graded by abelian groups. Such homogeneous spectra have the same completeness properties as their classical counterparts,…