For $\mathfrak g$ a Kac-Moody algebra of affine type, we show that there is an $\text{Aut}\, \mathcal O$-equivariant identification between $\text{Fun}\,\text{Op}_{\mathfrak g}(D)$, the functions on space ${\mathfrak g}$-opers disc, and $W\subset \pi_0$, intersection kernels screenings inside vacuum Fock module $\pi_0$. This kernel $W$ generated by two states: conformal vector, state $\delta_{-...

tio2 thin films and ag/tio2 nanoparticles were prepared by cvd and plasma bombardment method. xrd results showed the presence of ag nanoparticles in tio2 matrix. sem image confirmed formation of ag nanoparticles. xps analysis was utilized to study the chemical state of the ag/tio2 nanostructure. statistical surface analysis revealed that since there is a linear relation between logarithmic diag...

the article introduces cyclic dilation groups and finite affine groups for prime integers, and  as an application of this theory it presents a unified group theoretical approach for the  cyclic wavelet transform (cwt) of prime dimensional periodic signals.

1 Affine Morphisms Definition 1. Let f : X −→ Y be a morphism of schemes. Then we say f is an affine morphism or that X is affine over Y , if there is a nonempty open cover {Vα}α∈Λ of Y by open affine subsets Vα such that for every α, fVα is also affine. If X is empty (in particular if Y is empty) then f is affine. Any morphism of affine schemes is affine. Any isomorphism is affine, and the aff...

Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for Lφ affine surface areas are established. 2000 AMS subject classification: Primary 52A20; Secondary 53A15. Finding the right notion of affine surface area was one of the first questions asked within affine differential geometry. At ...

The paper deals with affine selections of affine (both convex and concave) multifunctions acting between finite-dimensional real normed spaces. It is proved that each affine multifunction with compact values possesses an exhaustive family of affine selections and, consequently, can be represented by its affine selections. Moreover, a convex multifunction with compact values possesses an exhaust...