Actually, we could have even applied the PCA to the entire observation vector (reflectance + DLP). This topic is slightly controversial, and conflicting opinions can be encountered in literature on this topic. We decided to apply the PCA separately in order not to mix two physically “inhomogeneous” quantities, because we feel that this approach is more “traceable” from a physical standpoint, ev...

A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl’s electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the conformal connection. By showing that every one-particle Hamiltonian generates the structure equations we establish a correspondence between phase space and the 8-d...

A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some ap...

The problem of construction of fiber bundle over the moduli space of the Skyrme model is considered. We analyse an extension of the original Skyrme model which includes the minimal interaction with fermions. An analogy with modili space of the fermion-monopole system is used to construct a fiber bundle structure over the skyrmion moduli space. The possibility of the non-trivial holonomy appeara...

Let V be a vector space with inner product (u, v) and norm u = (u, u) 1/2. We are given u ∈ V and a subspace˜V = span v (n) are linearly independent. We want to find p ∈ ˜ V such that u − p is minimal.

We find a full strongly exceptional collection for the Cayley plane OP, the simplest rational homogeneous space of the exceptional group E6. This collection, closely related to the one given by the second author in [Man11], consists of 27 vector bundles which are homogeneous for the group E6, and is a Lefschetz collection with respect to the minimal equivariant embedding of OP.

let $t$ be a bounded operator on the banach space $x$ and $ph$ be an analytic self-map of the unit disk $bbb{d}$‎. ‎we investigate some operator theoretic properties of‎ ‎bilateral composition operator $c_{ph‎, ‎t}‎: ‎f ri t circ f circ ph$ on the vector-valued hardy space $h^p(x)$ for $1 leq p leq‎ ‎+infty$.‎ ‎compactness and weak compactness of $c_{ph‎, ‎t}$ on $h^p(x)$‎ ‎are characterized an...

This paper shows that the general hypersurface of degree ≥ 6 in projective four space cannot support an indecomposable rank two vector bundle which is Arithmetically CohenMacaulay and four generated. Equivalently, the equation of the hypersurface is not the Pfaffian of a four by four minimal skewsymmetric matrix.