Existence of Positive Solutions for Operator Equations and Applications to Semipositone Problems

In this paper we study the existence of positive solutions of the following operator equation in a Banach space E: where G(x, λ) = λKFx+e₀, K: E↦ E is a linear completely continuous operator, F: P↦ E is a nonlinear continuous , bounded operator, e₀∈ E, λ is a parameter and P is a cone of Banach space E. Since F is not assumed to be positive and e₀ may be a negative element, the operator equation is a so-called semipositone problem. We prove that under certain super-linear conditions on the operator F the operator equation has at least one positive solution for λ > 0 sufficiently small, and that under certain sub-linear conditions on the operator F the operator equation has at least one positive solution for λ > 0 sufficiently large. In addition, we briefly outline an application of our results which simplify previous theorems in the literature.     

Mǒsbauer study of the field induced uniaxial anisotropy in electro-deposited FeCo alloy films

Thin ferromagnetic films with in-plane magnetic anisotropy are promising materials for obtaining high microwave permeability.The paper reports a Mo¨ssbauer study of the field induced in-plane uniaxial anisotropy in electro-deposited FeCo alloy films.The FeCo alloy films were prepared by the electro-deposition method with and without an external magnetic field applied parallel to the film plane during deposition.Vibrating sample magnetometry and Mo¨ssbauer spectroscopy measurements at room temperature indicate that the film deposited in external field shows an in-plane uniaxial anisotropy with an easy direction coinciding with the external field direction and a hard direction perpendicular to the field direction,whereas the film deposited without external field does not show any in-plane anisotropy.Mo¨ssbauer spectra taken in three geometric arrangements show that the magnetic moments are almost constrained in the film plane for the film deposited with applied magnetic field.Also,the magnetic moments tend to align in the direction of the applied external magnetic field during deposition,indicating that the observed anisotropy should be attributed to directional ordering of atomic pairs.     

p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions

In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.     

Characterization of gadolinium oxide film by pulse laser deposition

In this work, Gd-oxide dielectric films were deposited on Si by pulse laser deposition method (PLD), moreover, the micro-structures and electrical properties were reported. High-resolution transmission electron microscopy (HRTEM) and X-ray diffraction (XRD) indicated that Gd-oxide was polycrystalline Gd₂O₃ structure, and no Gd metal phase was detected. In addition, both interface at Si and Ni fully silicide (FUSI) gate were smooth without the formation of Si-oxide. X-ray photoelectron spectroscopy (XPS) confirmed the formation of Gd₂O₃ and gave an atom ratio of 1:1 for Gd:O, indicating O vacancies existed in Gd₂O₃ polycrystal matrix even at O₂ partial pressure of 20 mTorr. Electrical measurements indicated that the dielectric constant of Gd-oxide film was 6 and the leakage current was 0.1 A/cm² at gate bias of 1 V.     

Some results on controllability of a nonlinear degenerate parabolic system by bilinear control

In this paper, we discuss the controllability of a nonlinear degenerate parabolic system with bilinear control. Based on the shrinking property of the solutions, we prove that the system is not globally approximately controllable. Furthermore, we give an approximate null controllability result. We also prove that the system is not globally exactly null controllable by a comparison principle.     

Positive solutions and eigenvalue regions of two-delay singular systems with a twin parameter

The paper is concerned with a two-delay singular differential system with a twin parameter. Applying fixed-point index theory, we show the relationship between the asymptotic behaviors of nonlinearities (at zero and infinity) and the open regions (eigenvalue regions) of parameters, which are correlated with delays, such that the system has zero, one and two positive solution(s).     

High-power 1.5 and 3.4 μm intracavity KTA OPO driven by a diode-pumped Q-switched Nd:YAG laser

With a non-critically phase-matched KTA crystal, a high-power intracavity optical parametric oscillator (IOPO) driven by a diode-side-pumped acousto-optically Q-switched Nd:YAG laser has been realized. The maximum average output power of 13.6 W at the signal wavelength of 1534 nm and 3 W at the idler wavelength of 3472.7 nm were obtained with the repetition rate of 18 kHz, giving the optical-optical conversion efficiency of about 5.7% from diode-power at 808 nm to OPO signal output, which was the highest conversion efficiency for intracavity KTA OPO with diode-side-pumping configurations to our best knowledge. At the highest output power of 13.6 W, the signal pulse duration of 5.46 ns was obtained, corresponding to the single pulse energy of 756 μJ and peak power of 138 kW, respectively.     

Optimized temperature measurement with time-of-flight method

Driven by resonance probe light background Rubidium gas can emit fluorescence, which interacts with the falling atomic cloud in the temperature measurement with the time-of-flight (TOF) method and influence the experimental results. The dependencies of the acceleration and the temperature of the atomic cloud on the detuning of the probe beams were studied. We propose that the deviation of the acceleration from the gravity acceleration can be taken as a criterion of the accuracy of the temperature measurement using TOF method. Moreover, using the principle of the radiation force on the cold atomic cloud, one may measure the considerably weak intensity of the fluorescence.     

Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

预应力对熔石英损伤的影响

采用ANSYS进行形变-应力模拟。对不同应力状态下的熔石英表面进行三倍频激光损伤测试,结果发现,预加压应力为0~50 MPa时损伤阈值有明显提高的趋势,用应力耦合作用对此给出了解释：0~50 MPa的预加压应力可以降低和抵消激光辐照产生的张应力破坏,大于50 MPa预应力的耦合作用会使得该处机械性能下降,另外,损伤增长在预应力存在时更容易发生。因此,0~50 MPa预加压应力时的表面预应力可以提高熔石英的抗激光辐照能力。