General mathematical theory of large deflections of thin plates with some holes

The theoretical analysis and the numerical computations for the problem of a thin plate with large deflection and some holes become much more difficult due to the multi-valued properties of the stress functionF and the single-valued demands on the displacements. The necessary and sufficient conditions which can assureF to be single-valued are obtained in this paper. At the same time, we prove that the single-valued demands on the displacements are equivalent to 3m functional constraint equationsDC(w,F)=0, wherem is the number of holes. From these conclusions, the single-valued governing-equations of the problem of plates with large deflection and some holes are derived. It is a system of fourth order partial differential equations with 3m unknown constants and constrained equations. A numerical method for solving this problem is presented. The problem of the critical load is considered and an iterative scheme for computing the buckled states is given when a critical load λ is ‘single’.     

Thermoelectroelastic state of a multiply connected anisotropic plate

Generalized complex potentials in a plane problem of thermoelectroelasticity are introduced. Expressions for the basic characteristics of the thermoelectroelastic state are derived. Boundary conditions for determining the complex potentials and the general form of these functions for a multiply connected plate are obtained. The potentials are used to solve a specific problem __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 116–126, November 2005.     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

Bohr-Coster diagrams for multiply ionized states of light elements in the rangeZ = 10 to 20

Calculations in the L-S coupling approximation of the average total energies of various defect electron configurations with single or doubleK shell and varying number ofL shell vacancies for some light elements in the rangeZ = 10 to 20 are reported. The calculations show that the linear trend observed for normal Bohr-Coster diagrams (√E vsZ curves for the usual X-ray energy states) persists in the case of multiply ionized atomic states as well.     

多重栾晶钯颗粒的可见光简易合成及对乙醇的电催化氧化

以氯化钯(PdCl₂)为金属前驱体,乙醇为还原剂,聚乙烯吡咯烷酮(PVP)为稳定剂和导向剂,利用普通市售节能灯产生的光热作用,辅助制备多重栾晶钯纳米颗粒.用HRTEM、FFT、PXRD、XPS、UV-Vis和FT-IR等技术对产品的形貌、晶体结构、光学性质和稳定性进行了表征,并通过循环伏安法研究了多重栾晶Pd修饰玻碳电极对乙醇的电催化氧化活性.结果表明,多重栾晶钯结构的形成依赖于光和热的协同作用.该材料的表面等离子共振吸收峰在可见光区域,对乙醇有较好的电催化活性和抗中毒能力.     

Lead‐enhanced gas‐phase stability of multiply charged EDTA anions: a combined experimental and theoretical study

Besides their fundamental importance, multiply charged anions (MCAs) are considered as promising molecular capacitors for which their intrinsic stabilities are of great significance. Herein, the gas‐phase stabilities of ethylenediaminetetraacetic acid (EDTA) anions (i.e. [EDTA‐nH]^n?, n = 1–4) and their Pb(II) complexes (i.e. [EDTA + Pb‐nH]^(2‐n)?, n = 3, 4) have been investigated using an approach that combines extractive electrospray ionization mass spectrometry (EESI‐MS) measurements, Car–Parrinello molecular dynamics simulations and density functional theory/Tao–Perdew–Staroverov–Scuseria calculations. The EESI‐MS data showed that the doubly charged EDTA anions in the form of [EDTA‐2H]^2? and [EDTA + Pb‐4H]^2? were much more abundantly observed than the singly charged species such as [EDTA‐H]^? and [EDTA + Pb‐3H]^?, respectively. The calculation results indicated that [EDTA‐2H]^2? and [EDTA + Pb‐4H]^2? anions were thermodynamically more stable than the [EDTA‐H]^? and [EDTA + Pb‐3H]^? species in the gas phase, respectively. The [EDTA + Pb‐3H]^? anions preferred five‐coordinated structure, whereas [EDTA + Pb‐4H]^2? anions formed either five‐coordinated or six‐coordinated structures. The calculations further revealed that significant electron clouds drifting from the ligand EDTA to the metal Pb(II) ions and the large distances between the carboxylic groups reduced the Coulomb repulsion among the excess electrons of these MCAs. Our data demonstrated that EESI‐MS combined with theoretic calculations were able to provide a deep insight into the fundamental behavior of stability of MCAs in the gas phase and, thus, might be useful tools for studying MCAs for potential molecular capacitors. Copyright © 2012 John Wiley & Sons, Ltd.     

Cluster-assisted generation of multiply charged ions in nanosecond laser ionization of seeded furan beam at 532 and 1064 nm

The multiply charged ions of C ^{q +} (q ≤ 4), O ^{q +} (q ≤ 6) were produced when a furan cluster beam interacted with nanosecond 1064 and 532 nm lasers at intensities of 10¹⁰–10¹² W/cm². It is shown that O⁶⁺ and C⁴⁺ ions were the dominant multiply charged species at 1064 nm, while C²⁺, C³⁺, O²⁺, O³⁺ ions were the main multiply charged species at 532 nm. By varying the electric field in the extraction region of the time of flight mass spectrometer (TOFMS), two types of ions were extracted, one of which had large kinetic energy and narrow space distribution, and the other had small kinetic energy and broad space distribution. The formation channels for He-like ions of C⁴⁺ and O⁶⁺ are discussed.     

Ellipticity-dependent of multiple ionisation methyl iodide cluster using 532 nm nanosecond laser

The dependence of multiply charged ions on laser ellipticity in methyl iodide clusters with 532 nm nanosecond laser was measured using a time-of-flight mass spectrometer. The intensities of multiply charged ions I^q+(q = 2–4) with circularly polarised laser pulse were clearly higher than those with linearly polarised laser pulse but the intensity of single charged ions I⁺ was inverse. And the dependences of ions on the optical polarisation state were investigated and a flower petal and square distribution for single charged ions (I⁺, C⁺) and multiply charged ions (I²⁺, I³⁺, I⁴⁺, C²⁺) were observed, respectively. A theoretical calculation was also proposed to simulate the distributions of ions and theoretical results fitted well with the experimental ones. It indicated that the high multiphoton ionisation probability in the initial stage would result in the disintegration of big clusters into small ones and suppress the production of multiply charged ions.     

The Discontinuous Riemann–Hilbert Problem for Elliptic Complex Equations of First Order

In this article, we first transform the general uniformly elliptic systems of first order equations with certain conditions into the complex equations, and propose the discontinuous Riemann- Hilbert problem and its modified well-posedness for the complex equations. Then we give a priori estimates of solutions of the modified discontinuous Riemann-Hilbert problem for the complex equations and verify its solvability. Finally the solvability results of the original discontinuous Riemann-Hilbert boundary value problem can be derived. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.     

Oblique derivative problems for second order nonlinear equations of mixed type in multiply connected domains

In this paper, the unique solvability of oblique derivative boundary value problems for second order nonlinear equations of mixed (elliptic-hyperbolic) type in multiply connected domains is proved, which mainly is based on the representation of solutions for the above boundary value problem, and the uniqueness and existence of solutions of the above problem for the equation u_xx + sgn y u_yy = 0.