Infinite horizon H_2/H_\infty optimal control for discrete-time Markov jump systems with (x,u,v)-dependent noise

In this paper, an infinite horizon $H_2/H_\infty $ control problem is addressed for a broad class of discrete-time Markov jump systems with ( $x,u,v$ )-dependent noises. First of all, under the condition of exact detectability, the stochastic Popov–Belevich–Hautus (PBH) criterion is utilized to establish an extended Lyapunov theorem for a generalized Lyapunov equation. Further, a necessary and sufficient condition is presented for the existence of state-feedback $H_2/H_\infty $ optimal controller on the basis of two coupled matrix Riccati equations, which may be solved by a backward iterative algorithm. A numerical example with simulations is supplied to illustrate the proposed theoretical results.     

Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type A 1

The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let Λ _t be the Yoneda algebra of a reconstruction algebra of type A ₁ over a field k. In this paper, a minimal projective bimodule resolution of Λ _t is constructed, and the k-dimensions of all Hochschild homology and cohomology groups of Λ _t are calculated explicitly.     

Congruences of multipartition functions modulo powers of primes

Let p _r (n) denote the number of r-component multipartitions of n, and let S _γ,λ be the space spanned by η(24z) ^γ ?(24z), where η(z) is the Dedekind’s eta function and ?(z) is a holomorphic modular form in \(M_{\lambda}(\mathrm{SL}_{2}(\mathbb{Z}))\) . In this paper, we show that the generating function of \(p_{r}(\frac{m^{k} n +r}{24})\) with respect to n is congruent to a function in the space S _γ,λ modulo m ^k . As special cases, this relation leads to many well known congruences including the Ramanujan congruences of p(n) modulo 5,7,11 and Gandhi’s congruences of p ₂(n) modulo 5 and p ₈(n) modulo 11. Furthermore, using the invariance property of S _γ,λ under the Hecke operator \(T_{\ell^{2}}\) , we obtain two classes of congruences pertaining to the m ^k -adic property of p _r (n).     

Enhanced robustness of zero-line modes in graphene via magnetic field

We systematically studied the influence of magnetic field on zero-line modes (ZLMs) in graphene and demonstrated the physical origin of their enhanced robustness by employing nonequilibrium Green’s functions and the Landauer–Büttiker formula. We found that a perpendicular magnetic field can separate the wavefunctions of the counter-propagating kink states into opposite directions. Specifically, the separation vanishes at the charge neutrality point and increases as the Fermi level deviates from the charge neutrality point and can reach a magnitude comparable to the wavefunction spread at a moderate field strength. Such spatial separation of oppositely propagating ZLMs effectively suppresses backscattering and is more significant under zigzag boundary condition than under armchair boundary condition. Moreover, the presence of magnetic field enlarges the bulk gap and suppresses the bound states, thereby further reducing the scattering. These mechanisms effectively increase the mean free paths of the ZLMs to approximately 1 μm in the presence of a disorder.     

Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the total degree and the vector degree, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.     

Radioanalysis of ultra-low level radionuclides for environmental tracer studies and decommissioning of nuclear facilities

Journal of Radioanalytical and Nuclear Chemistry - Determination of long-lived radionuclides is critical for environmental radioactivity investigation, environmental processes studies and...     

星座旋转及坐标交织在DTMB系统中的应用研究

介绍了一种结合星座旋转和坐标交织的信号空间分集技术。该技术能以较低的实现复杂度为代价,提高信号分集阶数,获得分集增益。仿真结果证明,将这一技术应用于DTMB系统中,能有效地改善DTMB系统在衰落信道下的信号接收质量。     

HC112市内电话维护管理系统

本文介绍了市内电话维护管理系统体系结构的层次模型，讨论了各组成部分的关键技术及层间关系，给出了一种基于局域网和广域网的ＨＣ１１２（Ｈｙｐｏ Ｃｅｎｔｒａｌｉｚｅｄ１１２）的实现。     

连续函数与p幂可和函数的Jackson算子逼近

对f∈X是(X是G2x或D2x.1≤p< ∞)以及Jackson算子证明了如下不等式‖J.（f）-f‖x≤1+2π/3-3/（4π）+89π/24（2n2+1）ω（f·1/n）x,从而改进和推广了文献[1]的工作。