Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.     

Ab initio calculations on the spectroscopic constants, vibrational levels and classical turning points for the 21∏u state of dimer 7Li2

The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.     

逼近Banach空间中渐近非扩张映象的不动点

设E是一致凸Banach空间,C是E的非空闭凸子集, T:C→C是具有不动点的渐近非扩张映象. 该文证明了, 在某些适当的条件下, 由下列修改了的Ishikawa迭代程序所定义的序列{x\-n},\$\$x\-\{n+1\}=t\-nT\+n(s\-nT\+nx\-n+(1-s\-n)x\-n)+(1-t\-n)x\-n,\$\$弱收敛到T的不动点, 其中{t\-n},{s\-n}是区间\[0,1\]中满足某些限制的实数列.     

时滞差分方程的吸引性

本文给出了时滞差分方程x_n+1=x_nf(x_n,x_n-1),n=0,1,…解的全局吸引性的一个新的充分条件;作为应用,部分解决了G.Ladas的一个猜想.     

Critical temperatures of elements from their boiling points

A linear relation between critical temperature and boiling point is proposed for elements belonging to the same group in the periodic table. The validity of the relationship is demonstrated for the alkalies and the groups 16, 17 and 18. From this the critical temperature of tellurium is predicted as 2325?K and that for polonium as 2277?K.     

Low density observations of Rb and Cs chains along the liquid–vapour coexistence curves to the critical point in relation to quantum-chemical predictions on the metal-insulator transitions in Li and Na rings

Recent ab initio predictions concerning the metal-insulator (MI) transition in rings of the light alkali atoms, Li and Na, are compared and contrasted with experimental facts concerning diluted Rb and Cs alkalis. The main focus here is on the local coordination number as a function of density as these two heavy alkali metallic fluids are taken along the liquid–vapour coexistence curve towards the critical point, which in these cases coincides with the MI transition. Also recorded are the results of experiments in which Cs chains are observed at large interatomic spacing outside semiconducting substrates of InSb and GaAs.     

Improvement of pour point and oxidative stability of synthetic ester basestocks for biolubricant applications

For environmental reasons, as well as the dwindling source of petroleum, a new class of environmentally acceptable and renewable biolubricants based on plant oils is available. Even though plant oils possess excellent lubricant-related properties, there are some concerns about using it as biolubricant base oil. In this study we present a series of structures derived from oleic acid to be used as synthetic biolubricant basestocks. Measuring of pour point (PP), flash point, viscosity index (VI), oxidation onset temperature (OT) and signal maximum temperature (SMT) was carried out for each compound. Furthermore, the friction and wear properties were measured using a high-frequency reciprocating rig (HFRR). The resulting product structures were confirmed by NMR and FTIR spectroscopic analysis. The results showed that ethylhexyl 9-(octanoyloxy)-10-(behenoxy)octadecanoate with behenyl mid-chain ester exhibited the most favorable low temperature performance (PP ?48 °C) and ethylhexyl 9-(octanoyloxy)-10-(octyloxy)octadecanoate octyl mid-chain ester exhibited higher oxidation stability (OT 142 °C) than the other synthetic ester oils. On the other hand, the highest ball wear scan diameter was obtained for ethylhexyl 9-(octanoyloxy)-10-(behenoxy)octadecanoate while the lowest value was obtained for 9-hydroxy-10-octyloxyoctadecanoic acid. Overall, it was concluded that these synthetic ester oils have potential in formulation of industrial fluids for different temperature applications.     

ℋ︁‐LU factorization in preconditioners for augmented Lagrangian and grad‐div stabilized saddle point systems

The (mixed finite element) discretization of the linearized Navier–Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as ‘grad‐div’ (GD) stabilization, as well as on the discrete side where it is known as an ‘augmented Lagrangian’ (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ??‐LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ??‐LU factorization in the preconditioners. Copyright © 2010 John Wiley & Sons, Ltd.     

Melting heat transfer in the stagnation‐point flow of an upper‐convected Maxwell (UCM) fluid past a stretching sheet

The steady laminar boundary layer flow and heat transfer past a stretching sheet arre considered. Upper‐convected Maxwell (UCM) fluid is treated as a rheological model. The resulting nonlinear differential system is solved by homotopy analysis method (HAM). The influence of melting parameter (M), Prandtl number (Pr), Deborah number (β) and stretching ratio (A = a/c) on the velocity and temperature profiles is thoroughly examined. It is noticed that fields are effected appreciably with the variation of parameters. Furthermore, it is seen that the local Nusselt number is a decreasing function of melting parameter. Copyright © 2011 John Wiley & Sons, Ltd.     

Mixed convection unsteady stagnation point flow over a stretching sheet with heat transfer in the presence of variable free stream

An analysis is performed for the unsteady mixed convection flow of an incompressible viscous fluid about a stagnation point on a stretching sheet in the presence of a variable free stream. The equations of motion and energy are transformed into the ordinary differential equations by using similarity transformations. Homotopy analysis method is used for the solution of the governing problem. The results have been discussed by plots. The present values of the function are shown very close to the previous limiting solutions. Copyright © 2011 John Wiley & Sons, Ltd.