A fresh class of superconducting and hard pentaborides

On the basis of the current theoretical understanding of boron-based hard superconductors under ambient conditions,numerous studies have been conducted with the aim of developing superconducting materials with favorable mechanical properties using boron-rich compounds.In this paper,first-principles calculations reveal the existence of an unprecedented family of tetragonal pentaborides MB_(5)(M=Na,K,Rb,Ca,Sr,Ba,Sc,and Y),comprising B_(20)cages and centered metal atoms acting as stabilizers and electron donors to the boron sublattice.These compounds exhibit both superconductivity and high hardness,with the maximum superconducting transition temperature T_(c)of 18.6 K being achieved in RbB5 and the peak Vickers hardness Hv of 35.1 GPa being achieved in KB_(5)at 1 atm.The combination of these properties is particularly evident in KB_(5),RbB5,and BaB5,with Tc values of∼14.7,18.6,and 16.3 K and H_(v)values of∼35.1,32.4,and 33.8 GPa,respectively.The results presented here reveal that pentaborides can provide a framework for exploring and designing novel superconducting materials with favorable hardness at achievable pressures and even under ambient conditions.

ASYMPTOTICS OF THE SOLUTIONS TO STOCHASTIC WAVE EQUATIONS DRIVEN BY A NON-GAUSSIAN LéVY PROCESS

In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Levy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

Diffusion occupation time before exiting

Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c 〈 a 〈 b 〈 d, we find expressions of double Laplace transforms of the form Ex[e--θTd--λ∫o Td1a 〈Xs〈b ds; Td 〈 Tc], where Tx denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein- Uhlenbeck process, respectively. Some known results are also recovered.

Asymptotic analysis parabolic stochastic equations driven by of a kernel estimator for partial differential fractional noises

We study a strongly elliptic partial differential operator with time- varying coefficient in a parabolic diagonalizable stochastic equation driven by fractional noises. Based on the existence and uniqueness of the solution, we then obtain a kernel estimator of time-varying coefficient and the convergence rates. An example is given to illustrate the theorem.

Guaranteed cost sliding mode control for discrete-time looper systems in hot strip finishing mills

A guaranteed cost sliding mode control(SMC)algorithm is investigated to further improve the control accuracy of looper-tension systems in hot strip finishing mills.First,a global sliding mode surface function is designed by linear matrix inequalities and guaranteed cost technique,which can force the system states into switching region initially,and can guarantee the system robustness with a good performance during the whole control process.Then,a novel reaching law is designed,which can satisfy the sliding mode reaching conditions.Simulation results demonstrate that the proposed control scheme has good stability and robustness comparing with traditional SMC.The designed controller can regulate the strip tension and looper angle to ensure better performance,which is very suitable for complex looper systems.