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...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.展开更多
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 ...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.展开更多
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 obt...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.展开更多
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...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.展开更多
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 coeffic...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.展开更多
The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined.We show the existence of two frequency modes and carry out intensive investigations on the low freq...The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined.We show the existence of two frequency modes and carry out intensive investigations on the low frequency mode.Thanks to the multiple scales method,the behavior of these waves is investigated and the dissipative effects are analyzed.It appears that the dissipation coefficient increases with the carrier wave frequency.In the continuous approximation,we derive that the propagation of these waves is governed by the complex Ginzburg-Landau equation instead of the Korteweg-de-Vries equation as previously established.Asymptotic studies of the dynamics of plane waves in the line reveal the existence of three additional regions in the dispersion curve where the modulational phenomenon is observed.In the low frequency mode,we demonstrate that the network allows the propagation of dark and bright solitons.Numerical findings are in perfect agreement with the analytical predictions.展开更多
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 c...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.展开更多
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 converg...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.展开更多
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 ...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.展开更多
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 de...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.展开更多
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 ...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.展开更多
This paper proposes three new attacks. In the first attack we consider the class of the public exponents satisfying an equation e X-N Y ＋（ap^r＋ bq^r）Y = Z for suitably small positive integers a, b. Applying contin...This paper proposes three new attacks. In the first attack we consider the class of the public exponents satisfying an equation e X-N Y ＋（ap^r＋ bq^r）Y = Z for suitably small positive integers a, b. Applying continued fractions we show thatY/Xcan be recovered among the convergents of the continued fraction expansion of e/N. Moreover, we show that the number of such exponents is at least N^（2/（r＋1）-ε）where ε≥ 0 is arbitrarily small for large N. The second and third attacks works upon k RSA public keys（N_i, e_i） when there exist k relations of the form e_ix-N_iy_i ＋（ap_i^r ＋ bq_i^r ）y_i = z_i or of the form e_ix_i-N_iy ＋（ap_i^r ＋ bq_i^r ）y = z_i and the parameters x, x_i, y, y_i, z_i are suitably small in terms of the prime factors of the moduli. We apply the LLL algorithm, and show that our strategy enables us to simultaneously factor k prime power RSA moduli.展开更多
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 spec...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.展开更多
The e-commerce industry has experienced significant growth in the past decade,particu-larly post-COVID.To accommodate such growth,the parcel delivery sector has also grown rapidly.However,there is a lack of study that...The e-commerce industry has experienced significant growth in the past decade,particu-larly post-COVID.To accommodate such growth,the parcel delivery sector has also grown rapidly.However,there is a lack of study that properly evaluates its social and environ-mental impacts at a large scale.A model is proposed to analyze such impacts.A parcel gen-eration process is presented to convert public data into parcel volumes and stops.A continuous approximation model is fitted to estimate the length of parcel service tours.A case study is conducted using New York City(NYC)data.The parcel generation is shown to be a valid fit.The continuous approximation model parameters have R2 values of 98%or higher.The model output is validated against UPS truck trips.Application of the model to 2021 suggests residential parcel deliveries contributed to 0.05%of total daily vehicle-kilometer-traveled(VKT)in NYC corresponding to 14.4 metric tons of carbon equivalent(MTCE)emissions per day.COVID-19 contributed to an increase in parcel deliveries that led to up to 1064.3 MTCE of annual greenhouse gas(GHG)emissions in NYC(which could power 532 standard US households for a year).The existing bike lane infrastructure can support the substitution of 17%of parcel deliveries by cargo bikes,which would reduce VKT by 11%.Adding 3 km of bike lanes to connect Amazon facilities can expand their cargo bike substitution benefit from a VKT reduction of 5%up to 30%.If 28 km of additional bike lanes are made,parcel delivery substitution citywide could increase from 17%to 34%via cargo bike and save an additional 2.3 MTCE per day.Cargo bike priorities can be set to reduce GHG emissions for lower-income neighborhoods including Harlem,Sunset Park,and Bushwick.展开更多
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:Th...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.展开更多
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,...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.展开更多
文摘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.
文摘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.
文摘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.
文摘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.
文摘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.
文摘The dynamics of modulated waves in a nonlinear bi-inductance transmission line with dissipative elements are examined.We show the existence of two frequency modes and carry out intensive investigations on the low frequency mode.Thanks to the multiple scales method,the behavior of these waves is investigated and the dissipative effects are analyzed.It appears that the dissipation coefficient increases with the carrier wave frequency.In the continuous approximation,we derive that the propagation of these waves is governed by the complex Ginzburg-Landau equation instead of the Korteweg-de-Vries equation as previously established.Asymptotic studies of the dynamics of plane waves in the line reveal the existence of three additional regions in the dispersion curve where the modulational phenomenon is observed.In the low frequency mode,we demonstrate that the network allows the propagation of dark and bright solitons.Numerical findings are in perfect agreement with the analytical predictions.
基金Supported by the NSF of China(11101230 and 11371209)
文摘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.
基金The work is supported by Project 69 with Ministry of ScienceEducation, Bulgaria.
文摘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.
文摘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.
文摘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.
基金supported in part by The Fundamental Research Funds for the Central Universities under Grant No.2020JKF306Special Funds for theoretical physics Research Program of the NSFC under Grant No.11947124,and NSFC under Grant Nos.11575125 and 11675119。
文摘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.
文摘This paper proposes three new attacks. In the first attack we consider the class of the public exponents satisfying an equation e X-N Y ＋（ap^r＋ bq^r）Y = Z for suitably small positive integers a, b. Applying continued fractions we show thatY/Xcan be recovered among the convergents of the continued fraction expansion of e/N. Moreover, we show that the number of such exponents is at least N^（2/（r＋1）-ε）where ε≥ 0 is arbitrarily small for large N. The second and third attacks works upon k RSA public keys（N_i, e_i） when there exist k relations of the form e_ix-N_iy_i ＋（ap_i^r ＋ bq_i^r ）y_i = z_i or of the form e_ix_i-N_iy ＋（ap_i^r ＋ bq_i^r ）y = z_i and the parameters x, x_i, y, y_i, z_i are suitably small in terms of the prime factors of the moduli. We apply the LLL algorithm, and show that our strategy enables us to simultaneously factor k prime power RSA moduli.
基金Supported by the Doctoral programme foundation of National Education Ministry of China
文摘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.
基金support from C2SMART University Transportation Center(USDOT#69A3551747124).
文摘The e-commerce industry has experienced significant growth in the past decade,particu-larly post-COVID.To accommodate such growth,the parcel delivery sector has also grown rapidly.However,there is a lack of study that properly evaluates its social and environ-mental impacts at a large scale.A model is proposed to analyze such impacts.A parcel gen-eration process is presented to convert public data into parcel volumes and stops.A continuous approximation model is fitted to estimate the length of parcel service tours.A case study is conducted using New York City(NYC)data.The parcel generation is shown to be a valid fit.The continuous approximation model parameters have R2 values of 98%or higher.The model output is validated against UPS truck trips.Application of the model to 2021 suggests residential parcel deliveries contributed to 0.05%of total daily vehicle-kilometer-traveled(VKT)in NYC corresponding to 14.4 metric tons of carbon equivalent(MTCE)emissions per day.COVID-19 contributed to an increase in parcel deliveries that led to up to 1064.3 MTCE of annual greenhouse gas(GHG)emissions in NYC(which could power 532 standard US households for a year).The existing bike lane infrastructure can support the substitution of 17%of parcel deliveries by cargo bikes,which would reduce VKT by 11%.Adding 3 km of bike lanes to connect Amazon facilities can expand their cargo bike substitution benefit from a VKT reduction of 5%up to 30%.If 28 km of additional bike lanes are made,parcel delivery substitution citywide could increase from 17%to 34%via cargo bike and save an additional 2.3 MTCE per day.Cargo bike priorities can be set to reduce GHG emissions for lower-income neighborhoods including Harlem,Sunset Park,and Bushwick.
文摘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.
文摘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.
