Rational approximations to the solution of the second order Ricatti equation Technical report, 15 Jan. - 14 Oct. 1965

Rational approximations to solution of second order nonlinear Ricatti equation, using linear transformations - differential equations and operational calculu

Generalized rational approximations with applications to problems in control theory Interim technical report

Rational approximations and solution of control theory problems involving Ricatti equation

Analysis of the coupled frequencies and mode shapes of vehicle control systems Final report, 15 Apr. 1965 - 14 Apr. 1966

Coupled frequencies and mode shapes of vehicle control syste

Rational approximations to the generalized Duffing equation Final report, 15 Jan. - 1965 - 14 Jan. 1966

Linear transformation to obtain rational approximation to response of physical system described by nonlinear differential equation including Duffing equation as special cas

Numerical integration of nonlinear differential equations by use of rational approximation Final report, 15 Jan. 1965 - 14 Jul. 1967

Numerical integration of nonlinear differential equations by use of rational approximatio

Analytical Expression for the RKKY Interaction in Doped Graphene

We obtain an analytical expression for the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction $J$ in electron or hole doped graphene for linear Dirac bands. The results agree very well with the numerical calculations for the full tight-binding band structure in the regime where the linear band structure is valid. The analytical result, expressed in terms of the Meijer G-function, consists of a product of two oscillatory terms, one coming from the interference between the two Dirac cones and the second coming from the finite size of the Fermi surface. For large distances, the Meijer G-function behaves as a sinusoidal term, leading to the result $J \sim R^{-2} k_F \sin (2 k_F R) {1 + \cos[(K-K').R]}$ for moments located on the same sublattice. The $R^{-2}$ dependence, which is the same for the standard two-dimensional electron gas, is universal irrespective of the sublattice location and the distance direction of the two moments except when $k_F =0$ (undoped case), where it reverts to the $R^{-3}$ dependence. These results correct several inconsistencies found in the literature.Comment: 5 pages, 5 figure

Constraining weak annihilation using semileptonic D decays

The recently measured semileptonic D_s decay rate can be used to constrain weak annihilation (WA) effects in semileptonic D and B decays. We revisit the theoretical predictions for inclusive semileptonic D_{(s)} decays using a variety of quark mass schemes. The most reliable results are obtained if the fits to B decay distributions are used to eliminate the charm quark mass dependence, without using any specific charm mass scheme. Our fit to the available data shows that WA is smaller than commonly assumed. There is no indication that the WA octet contribution (which is better constrained than the singlet contribution) dominates. The results constrain an important source of uncertainty in the extraction of |Vub| from inclusive semileptonic B decays.Comment: 5 pages, 2 figures, published versio

The Use of Code-Mixing Among Pamonanese in Parata Ndaya Closed-Group Facebook

Research intended to figure out why Pamonanes did code-mixing in Parata Ndaya, a Facebook closed-group site. The research applied qualitative method to get the types of code-mixing and reasons for doing code-mixing, while the analysis used Hoffman\u27s theory. Data were taken from comments of three active members of Parata Ndaya. Comments selected were mainly focused on political issues that happened during Regional House Representative Election in 2014. Data analysis reveals that code-mixing is mostly found in jokes and some comments about political leaders. Thus, the results can provide insights for Parata Ndaya members to build awareness on preserving their local language (i.e. Pamona language) as well as to enhance solidarity among members of the group site