A Note on an Economic Lot-sizing Problem with Perishable Inventory and Economies of Scale Costs:Approximation Solutions and Worst Case Analysis

This paper presents an economic lot-sizing problem with perishable inventory and general economies of scale cost functions. For the case with backlogging allowed, a mathematical model is formulated, and several properties of the optimal solutions are explored. With the help of these optimality properties, a polynomial time approximation algorithm is developed by a new method. The new method adopts a shift technique to obtain a feasible solution of subproblem and takes the optimal solution of the subproblem as an approximation solution of our problem. The worst case performance for the approximation algorithm is proven to be （4√2 ＋ 5）/7. Finally, an instance illustrates that the bound is tight.

Spatial Agglomeration of Exhibition Enterprises on a Regional Scale in China

During the past two decades, the exhibition industry in China has been developing rapidly and has become an important part of the modern service industry, particularly the agglomeration characteristics of exhibition enterprises highlighted on the regional scale. Although the development of theoretical research on the western exhibition industry has taken place over time, the spatial perspective has not been at the centre of attention so far. This paper aims to fill this gap and report on the agglomeration characteristics of exhibition enterprises and their influential factors. Based on data about exhibition enterprises in the Pearl River Delta(PRD) during 1991–2013, using the Ripley K function analysis and kernel density estimation, this research identifies that: 1) the exhibition enterprise on the regional scale is significantly characterized by spatial agglomeration, and the agglomeration density and scale are continuously increasing; 2) the spatial pattern of agglomeration has developed from a single-center to multi-center form. Meanwhile, this paper profiles the factors influencing the spatial agglomeration of exhibition enterprises by selecting the panel data of nine cities in the PRD in 1999, 2002, 2006 and 2013. The results show that market capacity, urban informatization level and exhibition venues significantly influence the location choice of exhibition enterprises. Among them, the market capacity is a variable that exerts a far greater impact than other factors do.

PARAMETERIZATION OF SYMMETRIC SCALING FUNCTIONS

In this paper,the factorization for filters with length Km of scaling functions into simple blocks is considered.

CHARACTERIZATIONS OF FUNDAMENTAL SCALING FUNCTIONS AND WAVELETS

The objective of Ibis paper is to establish precise characterizations of scaling functions which are orthonormal or fundamental.A criterion for the corresponding wavelets is also given.

A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional （1D） strongly attractive Fermi gases with SU（w） symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent v= 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU （ w） and non-SU （ w ） symmetries in one dimension.

Approximation to NLAR(p) with Wavelet Neural Networks

Recently, wavelet neural networks have become a popular tool for non-linear functional approximation. Wavelet neural networks, which basis functions are orthonormal scalling functions, are more suitable in approximating to function. Based on it, approximating to NLAR(p) with wavelet neural networks is studied.

APPLICATIONS OF WAVELET GALERKIN FEM TO BENDING OF PLATE STRUCTURE

A kind of calculating method for high order differential expandedby the wavelet scal- ing functions and the of their product used inGalerkin FEM is proposed, so that we can use the wavelet Galerkin FEMto solve boundary-value differential equations with orders higherthan two. To combine this method with the Generalized Gaussianintegral method in wavelt theory, we can find That this method hasmany merits in solving mechanical problems, such as the bending ofplates and Those with variable thickness. The numerical results showthat this method is accurate.

APPLICATIONS OF WAVELET GALERKIN FEM TO BENDING OF BEAM AND PLATE STRUCTURES

In this paper, an approach is proposed for taking calculations of high order differentials of scaling functions in wavelet theory in order to apply the wavelet Galerkin FEM to numerical analysis of those boundary-value problems with order higher than 2. After that, it is realized that the wavelet Galerkin FEM is used to solve mechanical problems such as bending of beams and plates. The numerical results show that this method has good precision.

Notes on the Scaling Function

Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.

2-D NONSEPARABLE SCALING FUNCTIONINTERPOLATION AND APPROXIMATION

The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are also given. In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.

A CLASS OF COMPACTLY SUPPORTED ORTHOGONAL SYMMETRIC COMPLEX WAVELETS WITH DILATION FACTOR 3

When approximation order is an odd positive integer, a simple method is given to construct compactly supported orthogonal symmetric complex scaling function with dilation factor 3. Two corresponding orthogonal wavelets, one is symmetric and the other is antisymmetric about origin, are constructed explicitly. Additionally, when approximation order is an even integer 2, we also give a method to construct compactly supported orthogonal symmetric complex that illustrate the corresponding results. wavelets. In the end, there are several examples

Wavelet-Based Fractal Function Approximation

In this paper, we study on the application of radical B-spline wavelet scaling function in fractal function approximation system. The paper proposes a wavelet-based fractal function approximation algorithm in which the coefficients can be determined by solving a convex quadraticprogramming problem. And the experiment result shows that the approximation error of this algorithm is smaller than that of the polynomial-based fractal function approximation. This newalgorithm exploits the consistency between fractal and scaling function in multi-scale and multiresolution, has a better approximation effect and high potential in data compression, especially inimage compression.

AN MRA YIELDS AN ORTHONORMAL WAVELET BASIS——AN OPERATOR THEORETIC PROOF

In this paper we show how to construct a scaling function and an orthonor-mal wavelet basis from a multiresolution approximation using an operator theoreticmethod.

Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets

The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.

A CLASS OF BIDIMENSIONAL NONSEPARABLEWAVELET PACKETS

2-band wavelet packets in L-2 (R-s) were constructed in [3]. In this note, a way to construct bidimensional orthonormal wavelet packets related to the dilation matrix M = ((1)(1) (1)(-1)) is obtained. M-wavelets are used ill quincunx subsampling in two dimensions for image processing. What is more., the approach of this paper can be generalized to construct wavelet packets in L-2 (R-s) related to a general diltion matrix.

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point; a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle＇s invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.

Corrections to the scaling of the second-order structure function in isotropic turbulence

The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov＇s 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed.

Prognostic factors and its predictive value in patients with metastatic spinal cancer

BACKGROUND The spine is the most common location of metastatic diseases.Treating a metastatic spinal tumor depends on many factors,including patients’overall health and life expectancy.The present study was conducted to investigate prognostic factors and clinical outcomes in patients with vertebral metastases.AIM To investigate prognostic factors and their predictive value in patients with metastatic spinal cancer.METHODS A retrospective analysis of 109 patients with metastatic spinal cancer was conducted between January 2015 and September 2017.The prognoses and survival were analyzed,and the effects of factors such as clinical features,treatment methods,primary lesions and affected spinal segments on the prognosis of patients with metastatic spinal cancer were discussed.The prognostic value of Frankel spinal cord injury functional classification scale,metastatic spinal cord compression(MSCC),spinal instability neoplastic score(SINS)and the revised Tokuhashi score for prediction of prognosis was explored in patients with metastatic spinal tumors.RESULTS Age,comorbidity of metastasis from elsewhere,treatment methods,the number of spinal tumors,patient’s attitude toward tumors and Karnofsky performance scale score have an effect on the prognosis of patients(all P<0.05).With respect to classification of spinal cord injury,before operation,the proportion of grade B and grade C was higher in the group of patients who died than in the group of patients who survived,and that of grade D and grade E was lower in the group of patients who died than in the group of patients who survived(all P<0.05).At 1 mo after operation,the proportion of grade A,B and C was higher in the group of patients who died than in the group of patients who survived,and that of grade E was lower in patients in the group of patients who died than in the group of patients who survived(all P<0.05).MSCC occurred in four(14.3%)patients in the survival group and 17(21.0%)patients in the death group(P<0.05).All patients suffered from intractable pain,dysfunction in spinal cord and even paralysis.The proportion of SINS score of 1 to 6 points was lower in the death group than in the survival group,and the proportion of SINS score of 7 to 12 points was higher in the death group than in the survival group(all P<0.05).The proportion of revised Tokuhashi score of 0 to 8 points and 9 to 11 points were higher in the death group than in the survival group,and the proportion of revised Tokuhashi score of 12 to 15 points was lower in the death group than in the survival group(all P<0.05).Frankel spinal cord injury functional classification scale,MSCC,SINS and revised Tokuhashi score were important factors influencing the surgical treatment of patients with metastatic spinal cancer(all P<0.05).CONCLUSION Frankel spinal cord injury functional classification scale,MSCC,SINS and revised Tokuhashi score were helpful in predicting the prognosis of patients with metastatic spinal cancer.

Function projective synchronization in partially linear drive-response chaotic systems

This paper gives the definition of function projective synchronization with less conservative demand for a scaling function, and investigates the function projective synchronization in partially linear drive-response chaotic systems. Based on the Lyapunov stability theory, it has been shown that the function projective synchronization with desired scaling function can be realized by simple control law. Moreover it does not need scaling function to be differentiable, bounded and non-vanished. The numerical simulations are provided to verify the theoretical result.

WAVELET-NUMERICAL METHOD IN CRACK ANALYSIS

Properties of wavelet of good localization were used to approximate displacement fields near the crack tip. Wavelet-numerical algorithm and simulation singularity problem of the crack tip,cere established. As an example, stress intensity factors were obtained. The numerical results show that this algorithm has good precision.