Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Some integral inequalities on time scales

In this paper, some new integral inequalities on time scales are presented by using elementarily analytic methods in calculus of time scales.Comment: 8 page

Transport properties and anisotropy in rare earth doped CaFe2As2 single crystals with Tc above 40 K

In this paper we report the superconductivity above 40 K in the electron doping single crystal Ca1-xRexFe2As2 (Re = La, Ce, Pr). The x-ray diffraction patterns indicate high crystalline quality and c-axis orientation. the resistivity anomaly in the parent compound CaFe2As2 is completely suppressed by partial replacement of Ca by rare earth and a superconducting transition reaches as high as 43 K, which is higher than the value in electron doping FeAs-122 compounds by substituting Fe ions with transition metal, even surpasses the highest values observed in hole doping systems with a transition temperature up to 38 K. The upper critical field has been determined with the magnetic field along ab-plane and c-axis, yielding the anisotropy of 2~3. Hall-effect measurements indicate that the conduction in this material is dominated by electron like charge carriers. Our results explicitly demonstrate the feasibility of inducing superconductivity in Ca122 compounds via electron doping using aliovalent rare earth substitution into the alkaline earth site, which should add more ingredients to the underlying physics of the iron-based superconductors.Comment: 21 pages, 7 figure

Dynamical Axion Field in Topological Magnetic Insulators

Axions are very light, very weakly interacting particles postulated more than 30 years ago in the context of the Standard Model of particle physics. Their existence could explain the missing dark matter of the universe. However, despite intensive searches, they have yet to be detected. In this work, we show that magnetic fluctuations of topological insulators couple to the electromagnetic fields exactly like the axions, and propose several experiments to detect this dynamical axion field. In particular, we show that the axion coupling enables a nonlinear modulation of the electromagnetic field, leading to attenuated total reflection. We propose a novel optical modulators device based on this principle.Comment: 5 pages, 3 figure

Effects of tai chi on postural control during dual-task stair negotiation in knee osteoarthritis : a randomised controlled trial protocol

Stair ascent and descent require complex integration between sensory and motor systems; individuals with knee osteoarthritis (KOA) have an elevated risk for falls and fall injuries, which may be in part due to poor dynamic postural control during locomotion. Tai chi exercise has been shown to reduce fall risks in the ageing population and is recommended as one of the non-pharmocological therapies for people with KOA. However, neuromuscular mechanisms underlying the benefits of tai chi for persons with KOA are not clearly understood. Postural control deficits in performing a primary motor task may be more pronounced when required to simultaneously attend to a cognitive task. This single-blind, parallel design randomised controlled trial (RCT) aims to evaluate the effects of a 12-week tai chi programme versus balance and postural control training on neuromechanical characteristics during dual-task stair negotiation. Sixty-six participants with KOA will be randomised into either tai chi or balance and postural control training, each at 60 min per session, twice weekly for 12 weeks. Assessed at baseline and 12 weeks (ie, postintervention), the primary outcomes are attention cost and dynamic postural stability during dual-task stair negotiation. Secondary outcomes include balance and proprioception, foot clearances, self-reported symptoms and function. A telephone follow-up to assess symptoms and function will be conducted at 20 weeks. The findings will help determine whether tai chi is beneficial on dynamic stability and in reducing fall risks in older adults with KOA patients in community. Ethics approval was obtained from the Ethics Committee of the Affiliated Rehabilitation Hospital of Fujian University of Traditional Chinese Medicine (#2018KY-006-1). Study findings will be disseminated through presentations at scientific conferences or publications in peer-reviewed journals. ChiCTR1800018028. [Abstract copyright: © Author(s) (or their employer(s)) 2020. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.

Alternate proof of the Rowe-Rosensteel proposition and seniority conservation

For a system with three identical nucleons in a single-$j$ shell, the states can be written as the angular momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these non-orthonormal states form a matrix which coincides with the one derived by Rowe and Rosensteel [Phys. Rev. Lett. {\bf 87}, 172501 (2001)]. The propositions they state are related to the eigenvalue problems of the matrix and dimensions of the associated subspaces. In this work, the propositions will be proven from the symmetric properties of the $6j$ symbols. Algebraic expressions for the dimension of the states, eigenenergies as well as conditions for conservation of seniority can be derived from the matrix.Comment: 9 pages, no figur

Coexistence of Itinerant Electrons and Local Moments in Iron-Based Superconductors

In view of the recent experimental facts in the iron-pnictides, we make a proposal that the itinerant electrons and local moments are simultaneously present in such multiband materials. We study a minimal model composed of coupled itinerant electrons and local moments to illustrate how a consistent explanation of the experimental measurements can be obtained in the leading order approximation. In this mean-field approach, the spin-density-wave (SDW) order and superconducting pairing of the itinerant electrons are not directly driven by the Fermi surface nesting, but are mainly induced by their coupling to the local moments. The presence of the local moments as independent degrees of freedom naturally provides strong pairing strength for superconductivity and also explains the normal-state linear-temperature magnetic susceptibility above the SDW transition temperature. We show that this simple model is supported by various anomalous magnetic properties and isotope effect which are in quantitative agreement with experiments.Comment: 7 pages, 4 figures; an expanded versio

Entanglement detection beyond the CCNR criterion for infinite-dimensions

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.Comment: 11 page