750 GeV Resonance in the Gauged U(1)′U(1)'-Extended MSSM

Recently the ATLAS and CMS collaborations at the LHC announced their observation of a potential 750 GeV di-photon resonance, after analyzing the $\sqrt{s}=13$ TeV LHC data. This observation has significant implications for low-energy supersymmetry. Beyond the MSSM and the NMSSM, we study the MSSM-extensions with an extra $U(1)'$ gauge symmetry. The anomaly cancellation and the spontaneous breaking of the non-decoupled $U(1)'$ generically require introducing vector-like supermultiplets (both colored and color-neutral ones) and singlet supermultiplets, respectively. We illustrate that the potential 750 GeV resonance ($Y$) can be accommodated in various mechanisms, as a singlet-like scalar or pseudoscalar. Three benchmark scenarios are presented: (1) vector-like quarks (VLQ) mediated $pp \to Y \to \gamma \gamma$; (2) scalar VLQ mediated $pp \to Y \to \gamma \gamma$; (3) heavy scalar (pseudo-scalar) $H/A$ associated production $pp \to H^*/A^* \to Y H/h$. Additionally, we notice that the $Z'$-mediated vector boson fusion production and $Z'$-associated production $pp \to Y qq'$, if yielding a signal rate of the observed level, might have been excluded by the searches for $Z'$ via Drell-Yan process at the LHC.Comment: v3, figure update with corresponding modification in discussion, version accepted by PL

On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations

Considered herein are the generalized Camassa-Holm and Degasperis-Procesi equations in the spatially periodic setting. The precise blow-up scenarios of strong solutions are derived for both of equations. Several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established. The exact blow-up rates are also determined. Finally, geometric descriptions of these two integrable equations from non-stretching invariant curve flows in centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are given.Comment: 26 page

An investigation into minimising total energy consumption and total completion time in a flexible job shop for recycling carbon fiber reinforced polymer

The increased use of carbon fiber reinforced polymer (CFRP) in industry coupled with European Union restrictions on landfill disposal has resulted in a need to develop relevant recycling technologies. Several methods, such as mechanical grinding, thermolysis and solvolysis, have been tried to recover the carbon fibers. Optimisation techniques for reducing energy consumed by above processes have also been developed. However, the energy efficiency of recycling CFRP at the workshop level has never been considered before. An approach to incorporate energy reduction into consideration while making the scheduling plans for a CFRP recycling workshop is presented in this paper. This research sets in a flexible job shop circumstance, model for the bi-objective problem that minimise total processing energy consumption and makespan is developed. A modified Genetic Algorithm for solving the raw material lot splitting problem is developed. A case study of the lot sizing problem in the flexible job shop for recycling CFRP is presented to show how scheduling plans affect energy consumption, and to prove the feasibility of the model and the developed algorithm