Inverse problem of the Holling-Tanner model and its solution

In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Differentiation and integration methods of the problem solution are implemented and it is shown that the integration method produces more accurate results and uses less number of points on the given time interval

The 2020 UV emitter roadmap

Solid state UV emitters have many advantages over conventional UV sources. The (Al,In,Ga)N material system is best suited to produce LEDs and laser diodes from 400 nm down to 210 nm—due to its large and tuneable direct band gap, n- and p-doping capability up to the largest bandgap material AlN and a growth and fabrication technology compatible with the current visible InGaN-based LED production. However AlGaN based UV-emitters still suffer from numerous challenges compared to their visible counterparts that become most obvious by consideration of their light output power, operation voltage and long term stability. Most of these challenges are related to the large bandgap of the materials. However, the development since the first realization of UV electroluminescence in the 1970s shows that an improvement in understanding and technology allows the performance of UV emitters to be pushed far beyond the current state. One example is the very recent realization of edge emitting laser diodes emitting in the UVC at 271.8 nm and in the UVB spectral range at 298 nm. This roadmap summarizes the current state of the art for the most important aspects of UV emitters, their challenges and provides an outlook for future developments

Differential branching fraction and angular analysis of the decay B0s→ ϕμ+μ−

The determination of the differential branching fraction and the first angular analysis of the decay B[superscript 0][subscript 0] → ϕμ[superscript +]μ[subscript −] are presented using data, corresponding to an integrated luminosity of 1.0 fb[superscript −1], collected by the LHCb experiment at s√=7s=7 TeV. The differential branching fraction is determined in bins of q[superscript 2], the invariant dimuon mass squared. Integration over the full q[superscript 2] range yields a total branching fraction of B(B[superscript 0][subscript s]→ϕμ[superscript +]μ[subscript −])=(7.07[superscript +0.64][subscript −0.59]±0.71±0.71)) × 10[subscript −7], where the first uncertainty is statistical, the second systematic, and the third originates from the branching fraction of the normalisation channel. An angular analysis is performed to determine the angular observables F[subscript L], S[subscript 3], A[subscript 6], and A[subscript 9]. The observables are consistent with Standard Model expectations.National Science Foundation (U.S.

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements