RECURSIVE UTILITY,PRODUCTIVE GOVERNMENT EXPENDITURE AND OPTIMAL FISCAL POLICY

This paper employs a stochastic endogenous growth model extended to the case of a recursive utility function which can disentangle intertemporal substitution from risk aversion to analyze productive government expenditure and optimal fiscal policy, particularly stresses the importance of factor income. First, the explicit solutions of the central planner＇s stochastic optimization problem are derived, the growth maximizing and welfare-maximizing government expenditure policies are obtained and their standing in conflict or coincidence depends upon intertemporal substitution. Second, the explicit solutions of the representative individual＇s stochastic optimization problem which permits to tax on capital income and labor income separately are derived ,and it is found that the effect of risk on growth crucially depends on the degree of risk aversion,the intertemporal elasticity of substitution and the capital income share. Finally, a flexible optimal tax policy which can be internally adjusted to a certain extent is derived, and it is found that the distribution of factor income plays an important role in designing the optimal tax policy.     

THE OPTIMAL ALLOCATION ABOUT CAPITAL AND LABOR IN THE ECONOMIC GROWTH WITH AN ENDOGENOUS TECHNICAL PROGRESS MODEL

In this paper, the balanced economic growth path was considered in a new growth model with endogenous technical progress. It is not only obtained the optimal allocation about capital and labor between a goods-producing sector and a R&D Sector, but also the optimal value of saving rates. By discussing the effect of parameters, it are also got the following results: When the rate of time preference (discount factor) rising, the fractions of Capital and labor in the goods-producing sector will increase , the fractions in R&D sector and the saving rates will decrease; When the population grows rapidly, the result will be contrary.     

Degenerations of rational Bézier surface with weights in the form of exponential function

Rational Bézier surface is a widely used surface fitting tool in CAD. When all the weights of a rational Bézier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bézier surfaces. In this paper, we study on the degenerations of the rational Bézier surface with weights in the exponential function and indicate the difference of our result and the work of Garc′?a-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bézier surface with weights in the exponential function is defined, which is just the limit of the surface.Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster.     

ALGEBROIDAL FUNCTION AND ITS DERIVED FUNCTION IN UNIT CIRCULAR DISC

In this article,the authors define the derived function of an algeboidal function in the unit disc,prove it is an algabriodal function,and study the order of algebroidal function and that of its derived function in unit circular disc.     

THE AVERAGE ABUNDANCE FUNCTION WITH MUTATION OF THE MULTI-PLAYER SNOWDRIFT EVOLUTIONARY GAME MODEL

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation.The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of the results of numerical simulation on the basis of the intuitive expression of the average abundance function.In addition,the biological background of this research lies in research on the effects of mutation,which is regarded as a biological concept and a disturbance to game behavior on the average abundance function.The mutation will make the evolutionary result get closer to the neutral drift state.It can be deduced that this affection is not only related to mutation,but also related to selection intensity and the gap between payoff and aspiration level.The main research findings contain four aspects.First,we have deduced the concrete expression of the expected payoff function.The asymptotic property and change trend of the expected payoff function has been basically obtained.In addition,the intuitive expression of the average abundance function with mutation has been obtained by taking the detailed balance condition as the point of penetration.It can be deduced that the effect of mutation is to make the average abundance function get close to 1/2.In addition,this affection is related to selection intensity and the gap.Secondly,the first-order Taylor expansion of the average abundance function has been deduced for when selection intensity is sufficiently small.The expression of the average abundance function with mutation can be simplified from a composite function to a linear function because of this Taylor expansion.This finding will play a significant role when analyzing the results of the numerical simulation.Thirdly,we have obtained the approximate expressions of the average abundance function corresponding to small and large selection intensity.The significance of the above approximate analysis lies in that we have grasped the basic characteristics of the effect of mutation.The effect is slight and can be neglected when mutation is very small.In addition,the effect begins to increase when mutation rises,and this effect will become more remarkable with the increase of selection intensity.Fourthly,we have explored the influences of parameters on the average abundance function with mutation through numerical simulation.In addition,the corresponding results have been explained on the basis of the expected payoff function.It can be deduced that the influences of parameters on the average abundance function with mutation will be slim when selection intensity is small.Moreover,the corresponding explanation is related to the first-order Taylor expansion.Furthermore,the influences will become notable when selection intensity is large.     

Singularities of the Radon Transform of a Class of Piecewise Smooth Functions in R2

The Radon transform is the mathematical foundation of Computerized Tomography[1](CT).Its important applications includes medical CT,noninvasive test and etc.If one is specially interested in the places at which the image function changed largely such as the interfaces of two different tissues,tissue and ill tissue and the interfaces of two difierent matters,and want to reconstruct the outlines of the interfaces,one should reconstruct the singularities of the image function.The exact inversion of the Radon transform is valid only for smooth function[2].The singularity places of the reconstructed function should be studied specially.The research includes the propagation and inversion of singularity of the Radon transform.If one use convolutionbackprojection method to reconstruct the image function,the reconstructed function become blurring at the singularity places of the original function.M.Jiang and etc[3]developed a blind deconvolution method deblurring reconstructed image.By[4]and following research,we see that one can use a neighborhood data of the singularities of the Radon transform to inverse the singularity of the Radon transform,and therefore the reconstruction is available for some incomplete data reconstructions.     

无约束全局优化的一个可调参数的填充函数

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.     

ESTIMATES OF N-FUNCTION AND m-FUNCTION OF MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPLEX DIFFERENCE EQUATIONS

We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.     

叙列空间上的二级囿变函数I

The Stieltjes integral and bounded variation function of order 2 were introduced by Min, S. H., Guo Dajun and etc. One of the authors introduced the notion of bounded variation function on the sequence spaces, again. In this paper we consider the variation function of order 2 and the bounded variation function of order 2 from [α, b] to sequence space λ .     

Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.     

A CLASS OF SINGULAR FOURTH-ORDER THREE-POINT BOUNDARY VALUE PROBLEMS

This paper studies the existence of nontrivial solution to a nonlinear fourthorder three-point boundary value problem, where the nonlinear term is a strong Carathodory function and contains all order derivatives of unknown function. By introducing a height function of nonlinear term on some bounded set and considering the integration of the height function, some existence results are obtained.     

The local Hlder exponent for the entropy of real unimodal maps In Memory of Lei Tan

We consider the topological entropy h(θ) of real unimodal maps as a function of the kneading parameter θ(equivalently, as a function of the external angle in the Mandelbrot set). We prove that this function is locally Hlder continuous where h(θ) 0, and more precisely for any θ which does not lie in a plateau the local Hlder exponent equals exactly, up to a factor log 2, the value of the function at that point.This confirms a conjecture of Isola and Politi(1990), and extends a similar result for the dimension of invariant subsets of the circle.     

Uniform convergence and sequence of maps on a compact metric space with some chaotic properties

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f : X → X of a sequence of continuous topologically transitive (in strongly successive way) functions fn : X → X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney’s definition is lost on the limit function.     

A STONE-WEIERSTRASS THEOREM FOR CERTAIN DISCONTINUOUS FUNCTIONS

La Abe point separating uiatal subalgebra. of C(T) where T is a compact metric space. For each bounded function f:T which is continuous on the complement of a meagre subset of T there exists a sequence (wn) of elements of the algebra A such that the sequence (w) converges uniformly to the function f on each compact subset of the interior of the continuity points of the function f.     

Mechanical Deduction of Formulas of Differential Equations

1.IntroductionIn the study of ordinary differential equations,a great deal of labor isinvolved in formula deduction in many crucial steps of making assertions.Forexample,for Hilbert's 16th problem,the problem can be reformed as follows:find the maxinum number N(n)of limit cycles and relative positions for systemof differential equations:     

UNIFORM CONVERGENCE AND SEQUENCE OF MAPS ON A COMPACT METRIC SPACE WITH SOME CHAOTIC PROPERTIES

Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.     

Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.     

The Extremism of Two Variable Function Based on the Positive Definite Property

In this paper we give out a sufficient and solution of quadratic function's maximum with theory of quadratic form and give out the definition of the positive definite property of the following homogeneous polynomials of degree In two variables function, based on the definite of local maximum of two variables function.     

Measure Estimates of Nodal Sets of Polyharmonic Functions

This paper deals with the function u which satisfies△k_u = 0, where k≥2 is an integer. Such a function u is called a polyharmonic function. The author gives an upper bound of the measure of the nodal set of u, and shows some growth property of u.     

ON THE ERROR-SUM FUNCTION OF ALTERNATING LüROTH SERIES

The error-sum function of alternating Luroth series is introduced, which, to some extent, discerns the superior or not of an expansion comparing to other expansions. Some elementary properties of this function are studied. Also, the Hausdorff dimension of graph of such function is determined.