Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group Zn of arbitrary order n = 2, 3, . . ., but as its symmetry group a larger group — the non-Abelian dihedral group Dn — is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our appr...

For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered D-module along the zero-section of the cotangent bundle. This follows from a similar assertion for coherent graded modules over a polynomial algebra over the ...

[1] The current satellite magnetic missions offer new opportunities to determine the electrical conductivity of the Earth. However, satellites are nearly stationary in local time and therefore sample the inducing and induced fields quite differently than geomagnetic observatories, which rotate with the Earth. We show that estimates of induction transfer functions obtained from CHAMP magnetic da...

It should be possible to observe coherent synchrotron radiation at millimeter wavelengths in a compact electron storage ring, provided that the bunch can be made su ciently short. On the other hand, for a short bunch the radiation reaction is so strong that it could cause a longitudinal instability if the current exceeded some threshold. This might cause bunch lengthening, and cut o or reduce t...

Chimera states is a fascinating phenomenon of coexisting synchronized and desynchronized behavior discovered in networks of nonlocally coupled identical phase oscillators. In this work, we consider a generic model for a saddlenode bifurcation on a limit cycle representative for neuron excitability type-I. It is given by N nonlocally coupled SNIPER oscillators in the oscillatory regime arranged ...

The ability of photorefractive crystals such as barium titanate and strontium barium niobate to record spatially phase shifted real time holograms with high diffraction efficiency is the basis of many new optical devices involving coherent amplification. Some examples are unidirectional ring resonators, passive phase conjugate mirrors and coherent image amplifiers. 1 While in the past, most att...

We show that Krause's recollement exists for any locally coherent Grothendieck category whose derived is compactly generated. As a source of such categories, we consider the hearts intermediate and restrictable t-structures in commutative noetherian ring. induced tilting object over heart gives rise to an equivalence between two recollements, particular, singular equivalence.

We demonstrated the monolithic integration of reusable and wavelength reconfigurable ring resonator lasers and waveguides of arbitrary shapes to out-couple and guide laser emission on the same fused-silica chip. The ring resonator hosts were patterned by a single-mask standard lithography, whereas the waveguides were inscribed in the proximity of the ring resonator by using 3-dimensional femtos...