The existence of two non-contractible closed geodesics on every bumpy Finsler compact space form

Let $M=S^n/ \Gamma$ and $h$ be a nontrivial element of finite order $p$ in $\pi_1(M)$, where the integer $n\geq2$, $\Gamma$ is a finite group which acts freely and isometrically on the $n$-sphere and therefore $M$ is diffeomorphic to a compact space form. In this paper, we establish first the resonance identity for non-contractible homologically visible minimal closed geodesics of the class $[h]$ on every Finsler compact space form $(M, F)$ when there exist only finitely many distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$. Then as an application of this resonance identity, we prove the existence of at least two distinct non-contractible closed geodesics of the class $[h]$ on $(M, F)$ with a bumpy Finsler metric, which improves a result of Taimanov in [Taimanov 2016] by removing some additional conditions. Also our results extend the resonance identity and multiplicity results on $\mathcal{R}P^n$ in [arXiv:1607.02746] to general compact space forms.Comment: 33 pages, All comments are welcome. arXiv admin note: substantial text overlap with arXiv:1607.0274

The minimal periodic solutions for superquadratic autonomous Hamiltonian systems without the Palais-Smale condition

In this paper, we prove the existence of periodic solutions with any prescribed minimal period $T>0$ for even second order Hamiltonian systems and convex first order Hamiltonian systems under the weak Nehari condition instead of Ambrosetti-Rabinowitz's. To this end, we shall develop the method of Nehari manifold to directly deal with a frequently occurring problem where the Nehari manifold is not a manifold

Research on Chaotic Firefly Algorithm and the Application in Optimal Reactive Power Dispatch

Firefly algorithm (FA) is a newly proposed swarm intelligence optimization algorithm. The original version of FA usually traps into local optima like many other general swarm intelligence optimization algorithm. In order to overcome this drawback, the chaotic firefly algorithm(CFA) is proposed. The methods of chaos initialization, chaos population regeneration and linear decreasing inertia weight have been introduced into the original version of FA so as to increase its global search mobility for robust global optimization. The CFA is calculated in Matlab and is examined on six benchmark functions. In order to evaluate the engineering application of the algorithm, the reactive power optimization problem in IEEE 30 bus system is solved by CFA. The outcomes show that the CFA has better performance compared to the original version of FA and PS

Pressure-resistant intermediate valence in Kondo insulator SmB6

Resonant x-ray emission spectroscopy (RXES) was used to determine the pressure dependence of the f-electron occupancy in the Kondo insulator SmB6. Applied pressure reduces the f-occupancy, but surprisingly, the material maintains a significant divalent character up to a pressure of at least 35 GPa. Thus, the closure of the resistive activation energy gap and onset of magnetic order are not driven by stabilization of an integer valent state. Over the entire pressure range, the material maintains a remarkably stable intermediate valence that can in principle support a nontrivial band structure

Magnetic and vibrational properties of high-entropy alloys

The magnetic properties of high-entropy alloys based on equimolar FeCoCrNi were investigated using vibrating sample magnetometry to determine their usefulness in high-temperature magnetic applications. Nuclear resonant inelastic x-ray scattering measurements were performed to evaluate the vibrational entropy of the ^(57)Fe atoms and to infer chemical order. The configurational and vibrational entropy of alloying are discussed as they apply to these high-entropy alloys

Structure of shock compressed model basaltic glass: Insights from O K-edge X-ray Raman scattering and high-resolution ^(27)Al NMR spectroscopy

The detailed atomic structures of shock compressed basaltic glasses are not well understood. Here, we explore the structures of shock compressed silicate glass with a diopside–anorthite eutectic composition (Di_(64)An_(36)), a common Fe-free model basaltic composition, using oxygen K-edge X-ray Raman scattering and high- resolution ^(27)Al solid-state NMR spectroscopy and report previously unknown details of shock-induced changes in the atomic configurations. A topologically driven densification of the Di_(64)An_(36) glass is indicated by the increase in oxygen K-edge energy for the glass upon shock compression. The first experimental evidence of the increase in the fraction of highly coordinated Al in shock compressed glass is found in the ^(27)Al NMR spectra. This unambiguous evidence of shock-induced changes in Al coordination environments provides atomistic insights into shock compression in basaltic glasses and allows us to microscopically constrain the magnitude of impact events or relevant processes involving natural basalts on Earth and planetary surfaces