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.     

The Closed Subsemigroups of a Clifford Semigroup

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that {∪α∈Y′ Gα | Y′∈ P(Y) } is the set of all closed subsemigroups of a Clifford semigroup S = [Y; Gα; ?α, β], where Y′denotes the subsemilattice of Y generated by Y′. In particular, G is the only closed subsemigroup of itself for a group G and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring P(S) is isomorphic to the semiring P(Y) for a Clifford semigroup S = [Y; Gα; ?α, β].     

可口革囊星虫三种同工酶表达初步分析

应用聚丙烯酰胺凝胶电泳法，对可口革囊星虫的收吻肌、吻、肠、肾管和体壁5种组织或器官进行了同工酶分析．共分析了酯酶、过氧化物酶和超氧化物歧化酶等三种同工酶．结果表明：酯酶具有显著的组织特异性，其余两种酶相对不明显；可口革囊星虫的肠除了行使消化功能外，还和吻、肾管一起在清除自由基方面起着重要作用；提出将EST分析作为星虫动物门的一个分类学依据。     

Influence of thermal stabilization on the solute concentration of the melt in directional solidification

Experiments on Al–25 at%Ni peritectic alloy consisting of melting followed by thermal stabilization ranging from 0 to 2 h were carried out in a Bridgman-type furnace. Temperature distribution, microstructure evolution and solute concentration in the mushy zone are characterized. An analytical model is proposed to evaluate the Ni concentration of the melt after thermal stabilization. Effect of temperature gradient and volume fraction of liquid phase in the mushy zone on the Ni concentration of the melt is discussed. The steady state Ni concentration of the melt is inappropriately below the initial Ni concentration of the sample. The deviation increases with decreasing temperature gradient. Finally, the influence of thermal stabilization on the solute concentration of the melt is discussed based on a comparison of Al–Ni peritectic alloys with Al–Ni hyper-eutectic alloys and Al–Cu hypo-eutectic alloys.     

绘系统状态轨线的一种方法

介绍了一种作系统运动积分曲线的方法，并运用该方法绘出几个常见动力学系统的状态轨线，说明其实用价值。