First-principles study on the electronic structure, magnetic properties and phase stability of alloyed cementite with Cr or Mn

Using the first-principles technique, the electronic structures, magnetic properties and phase stability of alloyed cementite with Cr or Mn were investigated. The calculations show that the chemical and mechanical stability of alloyed cementite can be strengthened by the use of Cr/Mn-doped method. The Magnetic Moments (Ms) of Mn₁Fe₂C, Mn₂Fe₁C, Cr₁Fe₂C and Cr₂Fe₁C are 5.274, 0.941, 1.864 and 0.736 μ_B/f.u, respectively. The Ms of Cr in Fe₂CrC (−1.374 μ_B) and Cr₂FeC (−0.032 μ_B) are different due to replacing different sites Fe atoms. The magnetic behaviors of Mn are different from Cr in alloyed cementite. The Ms of Mn in Fe₂MnC and Mn₂FeC are 2.300 μ_B and −0.147 μ_B, respectively.     

Rectifying and photovoltage characteristics of Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>Co<Subscript>2</Subscript>O<Subscript>y</Subscript>/Nb-doped SrTiO<Subscript>3</Subscript> heterojunction

A heterojunction was fabricated by growing a layer of Bi₂Sr₂Co₂O _y thin film on the 0.7 wt% Nb-doped SrTiO₃ substrate. Such heterojunction showed good rectifying characteristics over a wide temperature range, and its transport mechanism under the forward bias can be attributed to a space charge limited conduction mechanism via defects near the interface of the heterojunction. Photovoltaic properties of the heterojunction were studied by using both continuous-wave and pulsed irradiations and the results can be well explained by the photovoltaic effect of a p–n junction.     

基于多级微反射镜的傅里叶变换红外光谱仪中准直误差的分析

通过对基于多级微反射镜的空间调制傅里叶变换红外光谱仪准直误差的分析,模拟了准直误差的存在而导致的干涉图大光程差处对比度反转和光谱图边频噪声的产生。讨论了在不同的误差系数下复原光谱图的信噪比和分辨率,并且分析了干涉图大光程差处对比反转以及光谱图边频分量的产生原因。仿真结果表明,在误差系数α=0.15°.mm-1时,光谱的信噪比会下降到6 dB,同时光谱分辨率会退化到13.4cm-1。本文的结论将应用于微型光谱仪系统的光学设计与装调。     

Portfolio optimization in a regime-switching market with derivatives

We consider the optimal asset allocation problem in a continuous-time regime-switching market. The problem is to maximize the expected utility of the terminal wealth of a portfolio that contains an option, an underlying stock and a risk-free bond. The difficulty that arises in our setting is finding a way to represent the return of the option by the returns of the stock and the risk-free bond in an incomplete regime-switching market. To overcome this difficulty, we introduce a functional operator to generate a sequence of value functions, and then show that the optimal value function is the limit of this sequence. The explicit form of each function in the sequence can be obtained by solving an auxiliary portfolio optimization problem in a single-regime market. And then the original optimal value function can be approximated by taking the limit. Additionally, we can also show that the optimal value function is a solution to a dynamic programming equation, which leads to the explicit forms for the optimal value function and the optimal portfolio process. Furthermore, we demonstrate that, as long as the current state of the Markov chain is given, it is still optimal for an investor in a multiple-regime market to simply allocate his/her wealth in the same way as in a single-regime market.     

Genetic-algorithm-based simulation optimization considering a single stochastic constraint

In this paper, we consider the discrete optimization via simulation problem with a single stochastic constraint. We present two genetic-algorithm-based algorithms that adopt different sampling rules and searching mechanisms, and thus deliver different statistical guarantees. The first algorithm offers global convergence as the simulation effort goes to infinity. However, the algorithm’s finite-time efficiency may be sacrificed to maintain this theoretically appealing property. We therefore propose the second heuristic algorithm that can take advantage of the desirable mechanics of genetic algorithm, and might be better able to find near-optimal solutions in a reasonable amount of time. Empirical studies are performed to compare the efficiency of the proposed algorithms with other existing ones.     

Relaxation in nonconvex optimal control problems described by fractional differential equations

We consider the minimization problem of an integral functional with integrand that is not convex in the control on solutions of a control system described by fractional differential equation with mixed nonconvex constraints on the control. A relaxation problem is treated along with the original problem. It is proved that, under general assumptions, the relaxation problem has an optimal solution, and that for each optimal solution there is a minimizing sequence of the original problem that converges to the optimal solution with respect to the trajectory, the control, and the functional in appropriate topologies simultaneously.     

Well-posedness,wave breaking and peakons for a modified μ-Camassa–Holm equation

Considered herein is a modified periodic Camassa–Holm equation with cubic nonlinearity which is called the modified μ-Camassa–Holm equation. The proposed equation is shown to be formally integrable with the Lax pair and bi-Hamiltonian structure. Local well-posedness of the initial-value problem to the modified μ-Camassa–Holm equation in the Besov space is established. Existence of peaked traveling-wave solutions and formation of singularities of solutions for the equation are then investigated. It is shown that the equation admits a single peaked soliton and multi-peakon solutions with a similar character of the μ-Camassa–Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and several wave-breaking mechanisms for solutions with certain initial profiles are described in detail.     

The classification of golden shaped hypersurfaces in Lorentz space forms

In this paper, we will study the golden shaped hypersurfaces in Lorentz space forms. Based on the classification of isoparametric hypersurfaces, we obtain the whole families of the golden shaped hypersurfaces in Minkowski space, de Sitter space and anti-de Sitter space, respectively.     

Real Paley-Wiener theorems for the Clifford Fourier transform

Associated with the Dirac operator and partial derivatives, this paper establishes some real Paley-Wiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform (CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT, the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin.     

New sets of frequency-hopping sequences with optimal Hamming correlation

Frequency-hopping spread spectrum and direct-sequence spread spectrum are two main spread coding technologies in communication systems. Frequency-hopping sequences are needed in FH-CDMA systems. In this paper, a construction of optimal sets of frequency-hopping sequences using cyclotomy and the Chinese remainder theorem is introduced. It generalizes some earlier constructions, and produces new optimal sets of frequency-hopping sequences.