We classify all linear operators $A:V\to V$ satisfying $(Au,v)=(u,A^rv)$ and $(Au,A^rv)=(u,v)$ with $r=2,3,\dots$ on a complex, real, or quaternion vector space scalar product given by nonsingular symmetric, skew-symmetric, Hermitian, skew-Hermitian form.

Measurements of flux-tubes generated by sources in different representations of SU(2) and U(1) lattice gauge theory in three dimensions are reported. Heavy “quarks” are considered in three representations of SU(2): fundamental (j = 1/2), adjoint (j = 1), and quartet (j = 3/2). Wilson loops are used to introduce a static quark-antiquark (QjQj) pair. Several attributes of the fields generated by ...

We report, for the first time, the dependence of the multiplicity of different fragments on the system size employing a quantum molecular dynamics model. This dependence is extracted from the simulations of symmetric collisions of Ca+Ca, Ni+Ni, Nb+Nb, Xe+Xe, Er+Er, Au+Au and U+U at incident energies between 50 A MeV and 1 A GeV. We find that the multiplicity of different fragments scales with t...

From a set of d-dimensional vectors for some integer d ≥ 1, we obtain a d-dot product graph by letting each vector au correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product au · av ≥ t, for some fixed, positive threshold t. Dot product graphs can be used to model social networks. To understand the position of d-dot product graphs in the land...

The structures and interaction energies of guanine and uracil quartets have been determined by B3LYP hybrid density functional calculations. The total interaction energy ∆E T of the C 4h-symmetric guanine quartet consisting of Hoogsteen type base pairs with two hydrogen bonds between two neighbor bases is-66.07 kcal/mol at the highest level. The uracil quartet with C6-H6...O4 interactions betwe...

*Correspondence: [email protected] 2College of Sciences, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we consider the existence of positive solutions for a second-order discrete boundary value problem (g(k – 1) u(k – 1)) +w(k)f (k,u(k)) = 0 subject to the bounda...