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Do Redistributive Policies Affect Economic Growth?  [PDF]
Zheng Liu
Technology and Investment (TI) , 2013, DOI: 10.4236/ti.2013.41B011
Abstract: To reduce income inequality, redistributive policies are widely adopted by both federal and provincial governments in Canada. Quebec and Canada have a fairer society in OECD countries. However, their economic growth is slower than many other countries. This paper studies how these redistributive policies affect economic growth based on Canadian data for the first time. The growth model is based on standard augmented Solow model and includes several different self-defined policy indexes. Using high quality panel data spanning the period 1982 to 2009 calculated from statistic Canada’s website and Arellano-Bond panel technique, empirical analyses show that redistributive policy is negatively and significantly associated with economic growth. These findings are in accordance with many former literatures and may have important policy significance.
Modified LS Method for Unconstrained Optimization  [PDF]
Jinkui Liu, Li Zheng
Applied Mathematics (AM) , 2011, DOI: 10.4236/am.2011.26104
Abstract: In this paper, a new conjugate gradient formula and its algorithm for solving unconstrained optimization problems are proposed. The given formula satisfies with satisfying the descent condition. Under the Grippo-Lucidi line search, the global convergence property of the given method is discussed. The numerical results show that the new method is efficient for the given test problems.
On the Minimal Polynomial of a Vector  [PDF]
Dabin Zheng, Heguo Liu
Advances in Linear Algebra & Matrix Theory (ALAMT) , 2012, DOI: 10.4236/alamt.2012.24008
Abstract: It is well known that the Cayley-Hamilton theorem is an interesting and important theorem in linear algebras, which was first explicitly stated by A. Cayley and W. R. Hamilton about in 1858, but the first general proof was published in 1878 by G. Frobenius, and numerous others have appeared since then, for example see [1,2]. From the structure theorem for finitely generated modules over a principal ideal domain it straightforwardly follows the Cayley-Hamilton theorem and the proposition that there exists a vector v in a finite dimensional linear space V such that and a linear transformation of V have the same minimal polynomial. In this note, we provide alternative proofs of these results by only utilizing the knowledge of linear algebras.
Non-Lie Symmetry Groups and New Exact Solutions to the (2 + 1)-Dimensional Broer-Kaup System  [PDF]
Bin Zheng, Xiqiang Liu
Advances in Pure Mathematics (APM) , 2013, DOI: 10.4236/apm.2013.31020
Abstract:

For the (2 + 1)-dimensional Broer-Kaup system, we study the corresponding Lie symmetry groups, and obtain the symmetry group theorem and the Backlund transformation formula of solutions finding. At the same time, we find some new exact solutions of the (2 + 1)-dimensional Broer-Kaup system and extend the results in the papers [1-4].

Semi-Automatic Modeling Technique of Torque Converter Flow Passage  [PDF]
Shiping Liu, Shujuan Zheng
Modern Mechanical Engineering (MME) , 2013, DOI: 10.4236/mme.2013.32009
Abstract:

The modeling technique of hydrodynamic torque converter flow passage was investigated. The semi-automatic modeling technique of torque converter flow passage was proposed. The flow passage model of each converter wheel is considered as a revolution entity sliced by two curved surfaces. In order to generate the revolution entity, a new approximation method, condition optimum arc approximation, was proposed. The method was used to approximate the meridional streamlines of the inner and outer wall. As a result, the three-dimensional revolution entity can be conveniently generated. In order to create slice surfaces, the central stream surface of flow passage was approximated with a quadric surface. The normal vector of the quadric surface and the thickness/thickness-function of bade were used to calculate the discrete point coordinates of blade surfaces. Via the rotation transformation to the coordinates, the discrete point coordinates of slice surfaces were obtained. A parameterized program code used for the hydrodynamic torque converter design and semi-automatic modeling was developed. Modeling errors were calculated and analyzed. The flow passage model was generated in several minutes with the help of the program code, Auto CAD and Solidworks software. Finally, the model was inputted into Gambit, and the pre-processing task used for the numerical simulation of torque converter flow field was successfully completed. The investigation results show that the semi-automatic modeling not only can ensure the accuracy of modeling, but also librates the research and design workers of torque converter from the time-consuming modeling work, which paves the way for the numerical simulation of the complex flow field of the hydrodynamic torque converter.

Intracranial aneurysm with neck indistinguishable from surrounding artery branches by cerebral angiography  [PDF]
Zheng Liu, Bangqing Yuan
World Journal of Neuroscience (WJNS) , 2013, DOI: 10.4236/wjns.2013.34040
Abstract:

The aim of this study is to examine morphology of intracranial aneurysm with neck indistinguishable from surrounding artery branches by cerebral angiography and discuss whether such aneurysms can be treated by interventional embolization. 6 patients who had not been treated by embolization due to irregular wide-necked aneurysms indistinguishable from surrounding artery branches by cerebral angiography received craniotomy for aneurysm clipping. The operations succeeded. Morphologically, neck width and location of the aneurysms were carefully observed and photographed from different directions and multi-angles during operation. The intraoperative findings were compared with the preoperative CTA and DSA images. Walls of the 6 patients’ aneurysms tightly clung to or adhered to surrounding branches and oppressed the branches into arcs, similar to the aneurysm walls in shape, and arterial branches and aneurysm walls suffered from segmental adhesion. In addition, abnormalities of communicating arteries to vary degrees were observed in 4 patients. However, after successful surgical clipping, it was revealed that the aneurysms would have been better treated by embolization since they are basically saccular aneurysms with regular sizes. Deformations in preoperative angiography may be due to anatomical variations of surrounding vessels near the aneurysms, aneurysm wall oppression or incomplete adhesion of surrounding arterial branches. Such deformations can be recognized by careful observation in preoperative angiography from different directions and multi-angles.

 

A simple proof of the discrete Steffensen's inequality
Zheng Liu
Tamkang Journal of Mathematics , 2004, DOI: 10.5556/j.tkjm.35.2004.281-283
Abstract: sum_{i=n-k_2+1}^n x_ilesum_{i=1}^n x_iy_ilesum_{i=1}^{k_1} x_i.
On sharp perturbed midpoint inequalities
Zheng Liu
Tamkang Journal of Mathematics , 2005, DOI: 10.5556/j.tkjm.36.2005.131-136
Abstract: The main purpose of this paper is to use a variant of Gr"uss inequality to obtain some perturbed midpoint inequalities. Moreover, we show that our results are sharp and precisely characterize the functions for which equality holds. Thus we provide improvements of some recent results for perturbed midpoint inequalities.
On a trapezoidal type rule for weighted integrals
Zheng Liu
Tamkang Journal of Mathematics , 2004, DOI: 10.5556/j.tkjm.35.2004.227-234
Abstract: An error runs through a paper by Cerone and Dragomir [1] is corrected. Thus enable us to get a right form of a trapezoidal type rule for weighted integrals and its applications in numerical integration.
A refinement of Holder's integral inequality
Zheng Liu
Tamkang Journal of Mathematics , 2003, DOI: 10.5556/j.tkjm.34.2003.383-386
Abstract: The purpose of this note is to show that there is monotonic continuous function $ p(t)$ such that $$ int_a^b left(prod_{i=1}^n f_i(x) ight) dxle p(t)le prod_{i=1}^n left(int_a^b f_i^{r_i}(x)dx ight)^{1over r_i},$$ where $ f_1$, $ f_2,ldots,f_n$ are real positive continuous functions on $ [a,b]$ and $ r_1$, $ r_2,ldots,r_n$ are real positive numbers with $ sum_{i=1}^n {1over r_i}=1$.
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