Presents a way to construct orthogonal piece-wise polynomials on an arbitrary triangular domain via barycentric coordinates. Solution of a boundary value problem for Laplace equation; Methodology; Results and discussion.
In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satis...In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility,and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal;they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.展开更多
Iterated function system （IFS） models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 （R is the set of real numbers）. In this paper, the piece-wi...Iterated function system （IFS） models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 （R is the set of real numbers）. In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn （n is an integer greater than 3）, which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a ＂mapping partial derivative＂, and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in R^n. Therefore, the result is very general. The class of functions obtained is much more diverse because their values depend continuously on all of the variables, with all the coefficients of the possible multi-dimensional affine maps determining the functions.展开更多
The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and th...The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.展开更多
A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “...A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “Dynamic ” Networks is considered in this study. Although shortest path (SP) for dynamic networks have been studied/documented by various researchers, contributions from this present work consists of a sparse matrix storage scheme for efficiently storing large scale sparse network’s connectivity, a concept of Time Delay Factor (TDF) combining with a “general piece- wise linear function” to describe the link cost as a function of time for Non-FIFO links’ costs, and Backward Dijkstra SP Algorithm with simple heuristic rules for rejecting unwanted solutions during the backward search algorithm. Both small-scale (academic) networks as well as large- scale (real-life) networks are investigated in this work to explain and validate the proposed dynamic algorithms. Numerical results obtained from this research work have indicated that the newly proposed dynamic algorithm is reliable, and efficient. Based on the numerical results, the calculated departure time at the source node(s), for a given/specified arrival time at the destination node(s), can be non-unique, for some Non-FIFO networks’ connectivity.展开更多
We have studied the influence of hot-carrier degradation effects on the drain current of a gate-stack double-gate （GS DG） MOSFET device. Our analysis is carried out by using an accurate continuous current-voltage （...We have studied the influence of hot-carrier degradation effects on the drain current of a gate-stack double-gate （GS DG） MOSFET device. Our analysis is carried out by using an accurate continuous current-voltage （I-V） model, derived based on both Poisson＇s and continuity equations without the need of charge-sheet approxi- mation. The developed model offers the possibility to describe the entire range of different regions （subthreshold, linear and saturation） through a unique continuous expression. Therefore, the proposed approach can bring consid- erable enhancement at the level of multi-gate compact modeling including hot-carrier degradation effects.展开更多
We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form（X（t） ＋px（t - 1））″′, = a0x（...We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form（X（t） ＋px（t - 1））″′, = a0x（[t]） ＋ a1x（[t - 1]） ＋ f（t）,where [.] is the greatest integer function, p, a0 and al are nonzero constants, and f（t） is almost automorphic.展开更多
We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(local...We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(locally)integrable wire billiards,for finding surfaces in R^(3)with a first integral of degree one in velocities,and for finding a piece-wise smooth surface in R^(3)homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.展开更多
基金Project supported by the Major Basic Project of China (No.G19990328) and National Natural ScienceFoundation of China.
文摘Presents a way to construct orthogonal piece-wise polynomials on an arbitrary triangular domain via barycentric coordinates. Solution of a boundary value problem for Laplace equation; Methodology; Results and discussion.
基金Supported by the Natural Science Foundation of China(11171221)
文摘In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility,and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal;they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.
文摘Iterated function system （IFS） models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 （R is the set of real numbers）. In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn （n is an integer greater than 3）, which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a ＂mapping partial derivative＂, and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in R^n. Therefore, the result is very general. The class of functions obtained is much more diverse because their values depend continuously on all of the variables, with all the coefficients of the possible multi-dimensional affine maps determining the functions.
基金Support provided by Department of Science and Technology(DST),Government of India vide Grant No.DST/INSPIRE Fellowship/2020/IF200538。
文摘The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.
文摘A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “Dynamic ” Networks is considered in this study. Although shortest path (SP) for dynamic networks have been studied/documented by various researchers, contributions from this present work consists of a sparse matrix storage scheme for efficiently storing large scale sparse network’s connectivity, a concept of Time Delay Factor (TDF) combining with a “general piece- wise linear function” to describe the link cost as a function of time for Non-FIFO links’ costs, and Backward Dijkstra SP Algorithm with simple heuristic rules for rejecting unwanted solutions during the backward search algorithm. Both small-scale (academic) networks as well as large- scale (real-life) networks are investigated in this work to explain and validate the proposed dynamic algorithms. Numerical results obtained from this research work have indicated that the newly proposed dynamic algorithm is reliable, and efficient. Based on the numerical results, the calculated departure time at the source node(s), for a given/specified arrival time at the destination node(s), can be non-unique, for some Non-FIFO networks’ connectivity.
文摘We have studied the influence of hot-carrier degradation effects on the drain current of a gate-stack double-gate （GS DG） MOSFET device. Our analysis is carried out by using an accurate continuous current-voltage （I-V） model, derived based on both Poisson＇s and continuity equations without the need of charge-sheet approxi- mation. The developed model offers the possibility to describe the entire range of different regions （subthreshold, linear and saturation） through a unique continuous expression. Therefore, the proposed approach can bring consid- erable enhancement at the level of multi-gate compact modeling including hot-carrier degradation effects.
基金supported by National Natural Science Foundation of China(Grant Nos.11271380,11501238)Natural Science Foundation of Guangdong Province(Grant Nos.2014A030313641,2016A030313119,S2013010013212)the Major Project Foundation of Guangdong Province Education Department(No.2014KZDXM070)
文摘We present some conditions for the existence and uniqueness of almost automorphic solutions of third order neutral delay-differential equations with piecewise constant of the form（X（t） ＋px（t - 1））″′, = a0x（[t]） ＋ a1x（[t - 1]） ＋ f（t）,where [.] is the greatest integer function, p, a0 and al are nonzero constants, and f（t） is almost automorphic.
基金partially supported by Russian Science Foundation(Grant No.21-41-00018)VD by the Science Fund of Serbia(Grant Integrability and Extremal Problems in Mechanics,Geometry and Combinatorics,MEGIC,Grant No.7744592)the Simons Foundation(Grant No.854861)。
文摘We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(locally)integrable wire billiards,for finding surfaces in R^(3)with a first integral of degree one in velocities,and for finding a piece-wise smooth surface in R^(3)homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.
