Calculation of the one- and two-loop lamb shift for arbitrary excited hydrogenic states

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)6] and for the two-loop Lamb shift [of order alpha2(Zalpha)6] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of states, defined as Delta N = n3deltaE(nS) - delta E(1S). We present numerical results for one-loop and two-loop corrections for excited S, P, and D states. In particular, the normalized Lamb shift difference of states is calculated with an uncertainty of order 0.1 kHz.     

Transplantation Theorems��A Survey

In this survey article we overview transplantation theorems for several types of continuous and discrete orthogonal expansions. These include: Hankel and Dunkl transforms, and Fourier-Bessel, Jacobi and Laguerre expansions. We also discuss the idea of transference of transplantation and point out how a notion of conjugacy for orthogonal expansions may be interpreted as a generalized transplantation.     

On Connections Between Hankel, Laguerre and Heisenberg Multipliers

We prove two results showing connections between Hankel multipliers,multipliers for a certain kind of Laguerre expansion and multipliersfor the Heisenberg sublaplacian. In their spirit they are closeto the well-known theorems of de Leeuw and Igari relating L^pmultipliers on R and its discrete subgroup Z. Also a conjectureis stated and its consequences are discussed.     

Complexity of some cutting plane methods that use analytic centers

We consider cutting plane methods for minimizing a convex (possibly nondifferentiable) function subject to box constraints. At each iteration, accumulated subgradient cuts define a polytope that localizes the minimum. The objective and its subgradient are evaluated at the analytic center of this polytope to produce one or two cuts that improve the localizing set. We give complexity estimates for several variants of such methods. Our analysis is based on the works of Goffin, Luo and Ye. Research supported by the State Committee for Scientific Research under Grant 8S50502206.     

Erbium–ytterbium co-doped fiber amplifier operating at 1550 nm with stimulated lasing at 1064 nm

A new method of controlling the amplified spontaneous emission (ASE) from Yb^3 + ions in Er^3 +/Yb^3 + co-doped fiber amplifiers is presented. The 1 μm ASE is suppressed by stimulating a laser emission at 1064 nm in a fiber amplifier, due to a positive feedback for the 1 μm signal. The results are compared to a conventional amplifier setup without any ASE control. We have shown, that applying a feedback loop in an Er^3 +/Yb^3 + co-doped fiber amplifier allows higher power scaling and provides operation without unwanted parasitic lasing effects, increasing the stability and robustness of the amplifier.     

The BSM-AI project: SUSY-AI–generalizing LHC limits on supersymmetry with machine learning

A key research question at the Large Hadron Collider is the test of models of new physics. Testing if a particular parameter set of such a model is excluded by LHC data is a challenge: it requires time consuming generation of scattering events, simulation of the detector response, event reconstruction, cross section calculations and analysis code to test against several hundred signal regions defined by the ATLAS and CMS experiments. In the BSM-AI project we approach this challenge with a new idea. A machine learning tool is devised to predict within a fraction of a millisecond if a model is excluded or not directly from the model parameters. A first example is SUSY-AI, trained on the phenomenological supersymmetric standard model (pMSSM). About 300, 000 pMSSM model sets – each tested against 200 signal regions by ATLAS – have been used to train and validate SUSY-AI. The code is currently able to reproduce the ATLAS exclusion regions in 19 dimensions with an accuracy of at least \(93\%\). It has been validated further within the constrained MSSM and the minimal natural supersymmetric model, again showing high accuracy. SUSY-AI and its future BSM derivatives will help to solve the problem of recasting LHC results for any model of new physics. SUSY-AI can be downloaded from http://susyai.hepforge.org/. An on-line interface to the program for quick testing purposes can be found at http://www.susy-ai.org/.     

The method for calculation of carrier concentration in narrow-gap n-type doped Hg<Subscript>1−x</Subscript>Cd<Subscript>x</Subscript>Te structures

A simple method for the computation of carrier concentration in n-type doped Hg_1?xCd_xTe (MCT) structures is proposed. The method is based on the postulate of the existence of donor bands. In our model the donor bands are postulated to have a Gaussian distribution of density of states characterized by two parameters only (mean energy for this distribution and standard deviation). These parameters could be obtained with experimental data, which were comprised of a wide range of doping levels for various kinds of dopants.     

Theoretical evaluation of NMR shifts in polycyclic aromatic hydrocarbons

ABSTRACT

Using computational chemistry methodology, we evaluate the proton magnetic shieldings and the corresponding chemical shifts of 12 polycyclic aromatic hydrocarbons that derive from chrysene, perylene and picene. Due to the large size of the studied compounds, we resort to density functional theory (DFT) and use it together with the B3LYP and the KT1 functionals. After a systematic method and basis set selection study carried out on methane, benzene and anthracene, the DFT(B3LYP) method and the 6-31G*, 6-31G** and 6-311++G** bases are selected to carry out the calculations, because of the efficiency in providing shifts close to the experimental data available. Additionally, we select the DFT(KT1) method together with the aug-pcS-1 basis set, and HF/6-31G* shifts are also calculated. In order to estimate the error in the theoretical results, we take as reference accurate experimental chemical shifts obtained for the molecules under investigation. Extra measurements are needed for this purpose and are included in the present work. The best combination of method and basis set is DFT(B3LYP)/6-31G**, proving to be very efficient in getting shifts close to experiment at a relatively low computational cost, and therefore we recommend it for the evaluation of proton shifts in larger polycyclic aromatic hydrocarbons.     

A volume microstrip RF coil for MRI microscopy

Quantitative magnetic resonance imaging (MRI) studies of small samples such as a single cell or cell clusters require application of radiofrequency (RF) coils that provide homogenous B₁ field distribution and high signal-to-noise ratio (SNR).We present a novel design of an MRI RF volume microcoil based on a microstrip structure. The coil consists of two parallel microstrip elements conducting RF currents in the opposite directions, thus creating homogenous RF field within the space between the microstrips. The construction of the microcoil is simple, efficient and cost-effective.Theoretical calculations and finite element method simulations were used to optimize the coil geometry to achieve optimal B₁ and SNR distributions within the sample and predict parameters of the coil. The theoretical calculations were confirmed with MR images of a 1-mm-diameter capillary and a plant obtained with the double microstrip RF microcoil at 11.7 T. The in-plane resolution of MR images was 24 μm×24 μm.     

The ζ-Determinant and the Additivity of the η-Invariant on the Smooth, Self-Adjoint Grassmannian

In this paper we discuss the existence of the ‘-determinant of a Dirac operator \Dd\Dd on a compact manifold with boundary. We show that the determinant is well defined in the case of the operator \Dd\Dd with a domain determined by a boundary condition from the smooth, self-adjoint Grassmannian \Grass_￥^*(\Dd)\Grass_{\infty}^*(\Dd) discussed in the papers [5, 13, 29]. We prove a generalization of a pasting formula for the m-invariant (see [34]). The results of the paper are used in the recent proof of the projective equality of the ‘-determinant and Quillen determinant on \Grass_￥^*(\Dd)\Grass_{\infty}^*(\Dd) (see [30, 31]).