Classical designs and their (projective) q-analogs can both be viewed as designs in matroids, using the matroid of all subsets of a set and the matroid of linearly independent subsets of a vector space, respectively. Another natural matroid is given by the point sets in general position of an affine space, leading to the concept of an affine design. Accordingly, a t-(n, k, λ) affine design of o...

DOI: 10.1002/adom.201600356 of the local environment. [ 5 ] Confi nement of plasmon modes to a surface of metal nanostructures under the constraints imposed by the fi nite boundaries of the nanostructure alters their dispersion, only allowing for discrete solutions. In the quasi-static limit, where the wavelength of the excitation light is much larger than the size of the nanostructure, the nan...

In this paper we extend the discussion on Homological Mirror Symmetry for Fano toric varieties presented in [HV] to more general case of monotone symplectic manifolds with real polarizations. We claim that the Hori – Vafa prediction, proven in [CO] for toric Fano varieties, can be checked in much more wider context. Then the notion of Bohr Sommerfeld with respect to the canonical class lagrangi...

We define an extension of matroid rank submodularity called R-submodularity, and introduce a minor-closed class of matroids called extended submodular matroids that are well-behaved with respect to R-submodularity. We apply R-submodularity to study a class of matroids with negatively correlated multivariate Tutte polynomials called the Z-Rayleigh matroids. First, we show that the class of exten...

Transition of surface-plasmon resonance from out-of-plane photonic crystal effect is observed in a semiconductor array of subwavelength holes by optical pump-terahertz probe measurements. The dielectric properties of the photoexcited array are essentially altered by the intense optical excitation due to photogenerated free carriers. As a result, the array becomes metallic and favors the couplin...

We introduce a new concept of Fano-like resonances for the extinction cross-section at light scattering by small (relative to the light wavelength) particles. The resonances occur beyond the applicability of the Rayleigh approximation, when the interference of different electromagnetic modes excited in the particle with the same multipole moment is crucial, while the partition of the incident w...

In this paper, a type of compact nanosensor based on a metal-insulator-metal structure is proposed and investigated through cascading double asymmetric cavities, in which their metal cores shift along different axis directions. The cascaded asymmetric structure exhibits high transmission and sharp Fano resonance peaks via strengthening the mutual coupling of the cavities. The research results s...

We investigate birational boundedness of Fano varieties and Fano fibrations. We establish an inductive step towards birational boundedness of Fano fibrations via conjectures related to boundedness of Fano varieties and Fano fibrations. As corollaries, we provide approaches towards birational boundedness and boundedness of anti-canonical volumes of varieties of -Fano type. Furthermore, we show b...

We construct new subvarieties in the varieties of power sums for certain quartic hypersurfaces. This provides a generalization of Mukai’s description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. In fact in [TZ08] we show that these quartics are exactly the Scorza quartics associated to general pairs of trigonal curves and ineffective theta c...

A single metallic nanodisk is the simplest plasmonic nanostructure, but it robust enough to generate a Fano resonance in forward and backward scattering spectra by increment of height symmetric asymmetric dielectric environment. Thanks phase retardation effect, non-uniform distribution electric field along aluminum (Al) generates out-of-plane higher-order modes, which interfere with dipolar mod...