The Essential Component of the Solution Set for Vector Equilibrium Problems

In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector equilibrium problem satisfying some conditions. Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China.     

Effects of microstructure on the temperature dependence of relative initial permeability of NiCuZn ferrites

In the present work, ferrites with compositions of (Ni_0.27Zn_0.64Cu_x)Fe_1.98O₄ (x=0.1, 0.2) were prepared by conventional ceramic methods. The relationship between the microstructure and the temperature dependence of relative initial permeability was investigated. It was found that intergranular pores in the ferrites generate large demagnetizing fields, reducing the temperature dependence of the effective anisotropy field H_eff, and decreasing the temperature dependence of the relative initial permeability accordingly. However, intragranular pores pin the movement of domain walls. Compared with the permeability induced by domain wall motion, the permeability that resulted from the spin rotation is more sensitive to temperature. As a result, the relative initial permeability of ferrites becomes more sensitive to temperature with increasing micropores within grains.     

Robust stabilization of internally delayed uncertain systems via sliding mode control

Summary The problem of robust stabilization of internally delayed uncertain systems via sliding mode controllers (SMC's) is studied in this paper. The robustness property and assymptotic stability of the system are discussed. Some sufficient conditions for the design of SMC and the switching hyperplane are given. Further generalization results, which lead to a simple design and implementation, are made for the system being described in companion form. A method is suggested for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.     

The pH-dependent role of superoxide in riboflavin-catalyzed photooxidation of 8-oxo-7,8-dihydroguanosine

[reaction: see text]. The riboflavin-catalyzed photooxidation of 2',3',5'-tri-O-acetyl-8-oxo-7,8-dihydroguanosine generates a radical intermediate that is competitively trapped by H(2)O, O2(-)(*), or O(2). The products of H(2)O trapping have been previously described as the spiroiminodihydantoin (pH >or= 7) and iminoallantoin/guanidinohydantoin (pH < 7) nucleosides. Trapping by O2(-)(*) leads to the oxaluric acid (pH or= 8.6) pathways (R' ', R' ' = H or 2,3,5-tri-O-Ac-ribofuranosyl). The pH-dependent role of superoxide was probed using Mn-SOD and compared to guanosine and 8-methoxyguanosine photooxidation.     

A note of a modular equation of Ramanujan–Selberg continued fraction

The Ramanujan Journal - We show that if $$E/\mathbb {Q}$$ is an elliptic curve with a rational p-torsion for $$p=2$$ or 3, then there is a congruence relation between Ramanujan’s tau function...     

Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.