Related papers: Internal split opfibrations and cofunctors
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
Fibrations over a category $B$, introduced to category theory by Grothendieck, encode pseudo-functors $B^{op} \rightsquigarrow {\bf Cat}$, while the special case of discrete fibrations encode presheaves $B^{op} \to {\bf Set}$. A two-sided…
We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…
For a category B with finite products, we first characterize pseudofunctors from B to Cat whose corresponding opfibration is cartesian monoidal. Among those, we then characterize the ones which extend to pseudofunctors from internal groups…
Excitonic fine structure splitting in quantum dots is closely related to the lateral shape of the wave functions. We have studied theoretically the fine structure splitting in InAs quantum dots with a type-II confinement imposed by a GaAsSb…
Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional…
All-optical computing has recently emerged as a vibrant research field in response to the energy crisis and the growing demand for information processing. However, the efficiency of subwavelength-scale all-optical devices remains relatively…
In this paper, we introduce a new combinatorial operation, called a flip, on arbitrary partially ordered sets. We define a mutation to be a flip that maps a lattice to a lattice. We study properties of flips, and give a necessary and…
Ou et al. (2022) introduce the problem of learning set functions from data generated by a so-called optimal subset oracle. Their approach approximates the underlying utility function with an energy-based model, whose parameters are…
Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorpism. We note that this gluing procedure does not guarantee that the building pieces,…
The spectral properties of one exciton trapped in a self-assembled multi-layered quantum dot is obtained using a high precision variational numerical method. The exciton Hamiltonian includes the effect of the polarization charges, induced…
Exceptional points (EPs) represent a distinct type of spectral singularity in non-Hermitian systems, and intriguing physics concepts have been studied with optical EPs recently. As a system beyond photonics, the mechanical oscillators…
We apply differential operators to modular forms on orthogonal groups $\mathrm{O}(2, \ell)$ to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are…
The contraction is applied to obtaining of integrable systems associated with nonsemisimple algebras. The effect of contraction is splitting off some components from initial system without loss of integrability.
In this paper we introduce the notion of Hurewicz fibrations in the class of embedding maps of orbifold charts by giving the concept of E-fibration embedding. We study the fundamental properties of this concept such as the restriction,…
Interlaced Spin Grating is a scheme for the preparation of spectro-spatial periodic absorption gratings in a inhomogeneously broadened absorption profile. It relies on the optical pumping of atoms in a nearby long-lived ground state…
On-chip optical isolators play a key role in optical communications and computing based on silicon integrated photonic structures. Recently there have raised great attentions and hot controversies upon isolation of light via linear and…
Ultracold bosons in optical superlattices are expected to exhibit fractional-filling insulating phases for sufficiently large repulsive interactions. On strictly 1D systems, the exact mapping between hard-core bosons and free spinless…
We give sufficient conditions for F-injectivity to deform. We show these conditions are met in two common geometrically interesting setting, namely when the special fiber has isolated CM-locus or is F-split.
We observe fine structure in the resonance spectra of optical microcavities. We identify the polarization-resolved modes in the spectrum and find that resonance frequencies split in accordance with the theoretical prediction. The observed…