0 −−−−→ O s −−−−→ E0 s∗ −−−−→ I −−−−→ 0. As usual, s is the distinguished nonzero global section of E0. The determinant line bundle of E0 is trivial, while the second Chern class is equal to the integer k. If X is in particular an algebraic surface, and H a fixed ample line bundle, then we can talk about slope-stability with respect to H. The bundle E0 is only slopesemistable, of slope 0, but t...

The effects of reactive and sputtering oxygen partial pressure on the structure, stoichiometry optical properties hafnium oxide (HfO2) thin films have been systematically investigated. electron cyclotron resonance ion beam deposition (ECR-IBD) technique was used to fabricate JGS-3 fused silica substrates. amorphous structure HfO2 were determined by X-ray Diffraction. Energy-dispersive Spectrosc...

The observed clustering of ultra-high energy cosmic rays suggests the existence of a neutral component. The models with violation of Lorentz invariance may explain this component by neutrons becoming stable above some threshold energy E0. The protons, in turn, may become unstable above some energy E1 > E0. We calculate the dependence of the threshold energies E0 and E1 on the parameters of the ...

Let Fe be the set of faulty edges of Sn and E0 be the edge set of some pairwise vertex-disjoint paths of Sn. In [5], the authors showed that E0 lies on a Hamiltonian path P (u, v) of Sn−Fe where d(u, v) is odd, |Fe| ≤ n− 3, |E0| ≤ 2n− 7− 2|Fe|. In this paper we improve the previous result as follows: E0 lies on a Hamiltonian path P (u, v) of Sn − Fe where d(u, v) is odd, Fe ≤ n− 3, |E0| ≤ 2n− 6...

It is known that every semigroup of normal completely positive maps of a von Neumann can be “dilated” in a particular way to an E0-semigroup acting on a larger von Neumann algebra. The E0-semigroup is not uniquely determined by the completely positive semigroup; however, it is unique (up to conjugacy) provided that certain conditions of minimality are met. Minimality is a subtle property, and i...

Given an edge-weighted graph G = (V,E) and a set E0 ⊂ E, the incremental network design problem with minimum spanning trees asks for a sequence of edges e1, . . . , e ′ r ∈ E \ E0 minimizing ∑T t=1 w(Xt) where w(Xt) is the weight of a minimum spanning tree Xt for the subgraph (V,E0 ∪ {e1, . . . , et}) and T = |E \ E0|. We prove that this problem can be solved by a greedy algorithm.

The apoE knockout (E0) mouse is one of the most widely used animal models of atherosclerosis, and there may be similarities to chylomicron remnant–induced atherosclerosis in humans. Although the lesions of these mice contain large numbers of cholesteryl ester (CE)-laden macrophages (foam cells), E0 plasma lipoproteins are relatively weak inducers of cholesterol esterification in macrophages. Pr...

We study the extremality of the BEC and the BSC for Gallager’s reliability function E0 evaluated under the uniform input distribution for binary input DMCs from the aspect of channel polarization. In particular, we show that amongst all B-DMCs of a given E0(ρ) value, for a fixed ρ ≥ 0, the BEC and BSC are extremal in the evolution of E0 under the one-step polarization transformations.