The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$. In this paper, we prove that $\log {\rm lcm}_{mn<i\le ln}\{ai+b\} =An+o(n)$, where $A$ is a constant depending on $l, m$ and $a$.Comment: 8 pages. To appear in Archiv der Mathemati

A comparative study of benchmarking approaches for non-domestic buildings: Part 1 – Top-down approach

Benchmarking plays an important role in improving energy efficiency of non-domestic buildings. A review of energy benchmarks that underpin the UK’s Display Energy Certificate (DEC) scheme have prompted necessities to explore the benefits and limitations of using various methods to derive energy benchmarks. The existing methods were reviewed and grouped into top-down and bottom-up approaches based on the granularity of the data used. In the study, two top-down methods, descriptive statistics and artificial neural networks (ANN), were explored for the purpose of benchmarking energy performances of schools. The results were used to understand the benefits of using these benchmarks for assessing energy efficiency of buildings and the limitations that affect the robustness of the derived benchmarks. Compared to the bottom-up approach, top-down approaches were found to be beneficial in gaining insight into how peers perform. The relative rather than absolute feedback on energy efficiency meant that peer pressure was a motivator for improvement. On the other hand, there were limitations with regard to the extent to which the energy efficiency of a building could be accurately assessed using the top-down benchmarks. Moreover, difficulties in acquiring adequate data were identified as a key limitation to using the top-down approach for benchmarking non-domestic buildings. The study suggested that there are benefits in rolling out of DECs to private sector buildings and that there is a need to explore more complex methods to provide more accurate indication of energy efficiency in non-domestic buildings

Quantum Speed Limit for Perfect State Transfer in One Dimension

The basic idea of spin chain engineering for perfect quantum state transfer (QST) is to find a set of coupling constants in the Hamiltonian, such that a particular state initially encoded on one site will evolve freely to the opposite site without any dynamical controls. The minimal possible evolution time represents a speed limit for QST. We prove that the optimal solution is the one simulating the precession of a spin in a static magnetic field. We also argue that, at least for solid-state systems where interactions are local, it is more realistic to characterize the computation power by the couplings than the initial energy.Comment: 5 pages, no figure; improved versio

Superfluid pairing in a mixture of a spin-polarized Fermi gas and a dipolar condensate

We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We show that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. We formulate, in the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory which allows us to estimate the critical temperature when the anisotropic Fock potential is taken into consideration and to determine the system parameters that optimize the critical temperature at which such a superfluid emerges before the system begins to phase separate.Comment: 10 pages, 3 figure

1.57 μm InGaAsP/InP surface emitting lasers by angled focus ion beam etching

The characteristics of 1.57 μm InGaAsP/InP surface emitting lasers based on an in-plan ridged structure and 45° beam deflectors defined by angled focused ion beam (FIB) etching are reported. With an externally integrated beam deflector, threshold currents and emission spectra identical to conventional edge emitting lasers are achieved. These results show that FIB etching is a very promising technique for the definition of high quality mirrors and beam deflectors on semiconductor heterostructures for a variety of integrated optoelectronic devices

Higher Dimensional Operators in the MSSM

The origin and the implications of higher dimensional effective operators in 4-dimensional theories are discussed in non-supersymmetric and supersymmetric cases. Particular attention is paid to the role of general, derivative-dependent field redefinitions which one can employ to obtain a simpler form of the effective Lagrangian. An application is provided for the Minimal Supersymmetric Standard Model extended with dimension-five R-parity conserving operators, to identify the minimal irreducible set of such operators after supersymmetry breaking. Among the physical consequences of this set of operators are the presence of corrections to the MSSM Higgs sector and the generation of "wrong"-Higgs Yukawa couplings and fermion-fermion-scalar-scalar interactions. These couplings have implications for supersymmetry searches at the LHC.Comment: Contribution to the proceedings of the "Susy 2008" conference; (6 pages

Fluxon analogues and dark solitons in linearly coupled Bose-Einstein condensates

Two effectively one-dimensional parallel coupled Bose-Einstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled Gross-Pitaevskii equations. In particular, grey-soliton-like solutions representing analogues of superconducting Josephson fluxons as well as coupled dark solitons are discussed. Theoretical approximations based on variational formulations are derived. It is found that the presence of a magnetic trap can destabilize the fluxon analogues. However, stabilization is possible by controlling the effective linear coupling between the condensates.Comment: 14 pages, 7 figures, The paper is to appear in Journal of Physics

Interrater Reliability in Toxicity Identification: Limitations of Current Standards.

PurposeThe National Cancer Institute Common Terminology Criteria for Adverse Events (CTCAE) v5.0 is the standard for oncology toxicity encoding and grading, despite limited validation. We assessed interrater reliability (IRR) in multireviewer toxicity identification.Methods and materialsTwo reviewers independently reviewed 100 randomly selected notes for weekly on-treatment visits during radiation therapy from the electronic health record. Discrepancies were adjudicated by a third reviewer for consensus. Term harmonization was performed to account for overlapping symptoms in CTCAE. IRR was assessed based on unweighted and weighted Cohen's kappa coefficients.ResultsBetween reviewers, the unweighted kappa was 0.68 (95% confidence interval, 0.65-0.71) and the weighted kappa was 0.59 (0.22-1.00). IRR was consistent between symptoms noted as present or absent with a kappa of 0.6 (0.66-0.71) and 0.6 (0.65-0.69), respectively.ConclusionsSignificant discordance suggests toxicity identification, particularly retrospectively, is a complex and error-prone task. Strategies to minimize IRR, including training and simplification of the CTCAE criteria, should be considered in trial design and future terminologies