On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.

On Approximation of Nonbounded Continuous Functions

This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.

APPROXIMATION OF CONTINUOUS FUNCTIONS BY GENERALIZED KARAMATA MEANS

A sufficient condition for the order of approximation of a continuous 2π periodic function with a given majorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order is obtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums of their Fourier series to be of Jackson order. The error estimate is shown to be the best possible.

CONTINUOUS AND DISCRETE N-CONVEX APPROXIMATIONS

We show that the best L_p-approximant to continuous functions by n-convex functions is the limit of discrete n-convex approximations.The techniques of the proof are then used to show the existence of near interpolants to discrete n-convex data by continuous n-convex functions if the data points are close.

Dynamics of high-frequency modulated waves in a nonlinear dissipative continuous bi-inductance network

This paper presents intensive investigation of dynamics of high frequency nonlinear modulated excitations in a damped bimodal lattice. The effects of the dissipation are considered through a linear dissipation coefficient whose evolution in terms of the carrier wave frequency is checked. There appears that the dissipation coefficient increases with the carrier wave frequency. In the linear limit and for high frequency waves, study of the asymptotic behavior of plane waves reveals the existence of two additional regions in the dispersion curve where the modulational phenomenon is observed compared to the lossless line. Based on the multiple scales method exploited in the continuum approximation using an appropriate decoupling ansatz for the voltage of the two different cells, it appears that the motion of modulated waves is described by a dissipative complex Ginzburg–Landau equation instead of a Korteweg–de Vries equation. We also show that this amplitude wave equation admits envelope and hole solitons in the high frequency mode. From basic sources, we design a programmable electronic generator of complex signals with desired characteristics, which delivers signals exploited as input waves for all our numerical simulations. These simulations are performed in the LTspice software that uses realistic components and give the results that corroborate perfectly our analytical predictions.

Approximation of conic section by quartic Bzier curve with endpoints continuity condition

A new method for approximation of conic section by quartic B′ezier curve is presented, based on the quartic B′ezier approximation of circular arcs. Here we give an upper bound of the Hausdorff distance between the conic section and the approximation curve, and show that the error bounds have the approximation order of eight. Furthermore, our method yields quartic G2 continuous spline approximation of conic section when using the subdivision scheme,and the effectiveness of this method is demonstrated by some numerical examples.

RATIONAL FUNCTIONS OF BEST UNIFORM APPROXIMATION AND HOLOMORPHIC CONTINUATION OF FUNCTIONS

Let f be a function, continuous and real valued on the segment △,△ (-∞,∞) and {Rn} be the sequence of the rational functions of best uniform approximation to fon △ of order (n,n). In the present work, the convergence of {Rn} in the complex plane is considered for the special caseswhen the poles (or the zeros, respectively) of {Rn} accumulate in the terms of weak convergence of measures to acompact set of zera capacity.As a consequence, sufficient conditions for the holomorphic and the meromorphic continuability of fare given.

Effects of Surface Charges on the Seawater Desalination Using Functionalized Graphene

In this paper, we investigate the selection rule for desalinating seawater using functionalized graphene sheet as a semi-permissible membrane. Both the applied mathematical modeling and MD simulations will be used to determine the acceptance conditions for water molecule or sodium ion permeating into the functionalized graphene. Both the Lennard-Jones potential and Coulomb forces are considered by taking into accounts the major molecular and ionic interactions between molecules, ions and functionalized graphene sheet. The continuous approximation will then be used to coarse grain most significant molecular and ionic interactions so that the multi-body problems could be simplified into several two-body problems and the 3D motions are reduced into degenerated 1D motion. Our mathematical model and simulations show that the negatively charged graphene always accepts sodium ions and water;however the permeability of water molecules and sodium ions becomes very sensitive to the presence of positive charges on the graphene.

L^p CONTINUITY OF HRMANDER SYMBOL OPERATORS OpS_(0,0) ~m AND NUMERICAL ALGORITHM

If we use Littlewood-Paley decomposition, there is no pseudo-orthogonality for Ho¨rmander symbol operators OpS m 0 , 0 , which is different to the case S m ρ,δ （0 ≤δ 〈 ρ≤ 1）. In this paper, we use a special numerical algorithm based on wavelets to study the L p continuity of non infinite smooth operators OpS m 0 , 0 ; in fact, we apply first special wavelets to symbol to get special basic operators, then we regroup all the special basic operators at given scale and prove that such scale operator’s continuity decreases very fast, we sum such scale operators and a symbol operator can be approached by very good compact operators. By correlation of basic operators, we get very exact pseudo-orthogonality and also L 2 → L 2 continuity for scale operators. By considering the influence region of scale operator, we get H 1 （= F 0 , 2 1 ） → L 1 continuity and L ∞→ BMO continuity. By interpolation theorem, we get also L p （= F 0 , 2 p ） → L p continuity for 1 〈 p 〈 ∞ . Our results are sharp for F 0 , 2 p → L p continuity when 1 ≤ p ≤ 2, that is to say, we find out the exact order of derivations for which the symbols can ensure the resulting operators to be bounded on these spaces.

Iterative computational approach to the solution of the Hamilton-Jacobi-Bellman-lsaacs equation in nonlinear optimal control

In this paper, iterative or successive approximation methods for the Hamilton-Jacobi-Bellman-lsaacs equations （HJBIEs） arising in both deterministic and stochastic optimal control for affine nonlinear systems are developed. Convergence of the methods are established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the methods. However, the results presented in the paper are preliminary, and do not yet imply in anyway that the solutions computed will be stabilizing. More improvements and experimentation will be required before a satisfactory algorithm is developed.

Monte Carlo simulations for targeted beta therapy: An optimization for liver lesions and comparison of dose distributions in other organs

Objective:To optimize targeted beta therapy for liver lesions in adult male phantom by comparing the efficacy and safety profiles of five different beta-emitting radionuclides:90Y,166Ho,153Sm,47Sc,and 177Lu.Methods:This study includes Monte Carlo simulations of the behavioral characteristics of five different beta emitters that have current or potential use in targeted beta therapy.The energy loss of beta particles moving within the material through ionization or chemical processes,the energy transferred to the material,the energy lost by beta particles along the distance traveled within the tissue,and consequently,the stopping power are calculated using the Bethe-Bloch formula.The CSDA(continuous slowing-down approximation)range of beta particles within the tissue is examined using ESTAR and GEANT codes,while the stopping power of the tissue is investigated using FLUKA,ESTAR,and GEANT codes.Tissue dose calculations for the target organ are obtained using the IDAC-Dose2.1 and MIRDcalc simulation programs,using parameters such as absorbed dose per accumulated activity(S-factor)and specific absorbed fraction(SAF).Additionally,dose and flux values are obtained using the PHITS program.Results:The behaviors and dose contribution of beta particles in liver tissue have been addressed in various ways.90Y,which has the highest average beta energy,was observed to provide a higher absorbed dose value in the liver compared to other beta-emitting isotopes,while the lowest absorbed dose was observed with 177Lu.In other organs,it has been observed that 90Y and 47Sc contribute to a higher absorbed dose compared to other betaemitting isotopes.Conclusions:This study emphasizes the complexity and significance of targeted beta therapy optimization.

Design Methodology of the Structure of Postal Express Mail Networks of Aviation Channels in China

On the basis of the postal area center office system, the continuous space approximation is used to study the structure of postal express mail networks of aviation channels in China. Tradeoffs among sorting, handling, transportation, administrative and facilities costs are examined. The optimizing design methodology proposed in this paper can be used to analyze and design the postal express mail network. The objective is to minimize the total system cost.

Padéapproximant approach to singular properties of quantum gases:the ideal cases

In this paper,we show how to recover the low-temperature and high-density information of ideal quantum gases from the high-temperature and low-density approximation by the Padéapproximant.The virial expansion is a high-temperature and low-density expansion and in practice,often,only the first several virial coefficients can be obtained.For Bose gases,we determine the BEC phase transition from a truncated virial expansion.For Fermi gases,we recover the low-temperature and high-density result from the virial expansion.