Parametric polynomial surface is a fundamental element in CAD systems. Since the most of the classic minimal surfaces are represented by non-parametric polynomial, it is interesting to study the minimal surfaces repre...Parametric polynomial surface is a fundamental element in CAD systems. Since the most of the classic minimal surfaces are represented by non-parametric polynomial, it is interesting to study the minimal surfaces represented in parametric polynomial form. Recently,Ganchev presented the canonical principal parameters for minimal surfaces. The normal curvature of a minimal surface expressed in these parameters determines completely the surface up to a position in the space. Based on this result, in this paper, we study the bi-quintic isothermal minimal surfaces. According to the condition that any minimal isothermal surface is harmonic,we can acquire the relationship of some control points must satisfy. Follow up, we obtain two holomorphic functions f（z） and g（z） which give the Weierstrass representation of the minimal surface. Under the constrains that the minimal surface is bi-quintic, f（z） and g（z） can be divided into two cases. One case is that f（z） is a constant and g（z） is a quadratic polynomial, and another case is that the degree of f（z） and g（z） are 2 and 1 respectively. For these two cases,we transfer the isothermal parameter to canonical principal parameter, and then compute their normal curvatures and analyze the properties of the corresponding minimal surfaces. Moreover,we study some geometric properties of the bi-quintic harmonic surfaces based on the B′ezier representation. Finally, some numerical examples are demonstrated to verify our results.展开更多
With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the perfor...With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation（IOSGD）,FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.展开更多
In this paper, the problem of computing zeros of a general degree bivariate Bernstein polynomial is considered. An efficient and robust algorithm is presented that takes into full account particular properties of the ...In this paper, the problem of computing zeros of a general degree bivariate Bernstein polynomial is considered. An efficient and robust algorithm is presented that takes into full account particular properties of the function considered. The algorithm works for rectangular as well as triangular domains. The outlined procedure can also be applied for the computation of the intersection of a Bezier patch and a plane as well as in the determination of an algebraic curve restricted to a compact domain. In particular, singular points of the algebraic curve are reliably detected.展开更多
This paper discusses the makespan minimization of a production batch within a specific concurrent system,seru production system.A seru production system consists of multiple independent serus.A seru is a compact assem...This paper discusses the makespan minimization of a production batch within a specific concurrent system,seru production system.A seru production system consists of multiple independent serus.A seru is a compact assembly origination in which products are assembled from-the-beginning-to-the-end without disruptions.One capability of a seru production system is its responsiveness.A performance measure used to evaluate a seru system’s responsiveness is the makespan of production batches assembled within the seru system.This study addresses the makespan minimization problem through an optimal seru loading policy.The problem is formulated as a min-max integer optimization model.An exact dimension-reduction Algorithm is developed to obtain the optimal allocation that minimizes the makespan.We show that the solution space increases very quickly.In contrast,our algorithm is efficient with a polynomial computational complexity of,where is the total number of serus in a seru system.To verify the usefulness of the developed exact dimension-reduction algorithm,we compare it with a widely practiced greedy algorithm through experiments.We find that our optimal algorithm is robust in most cases and the greedy algorithm is efficient when variability in production efficiencies is high.This result can guide us to adopt different algorithms in different business environments.If the variability in production efficiencies is high,e.g.,new employees and/or new products assembly,the greedy algorithm is efficient.For other cases,our optimal algorithm should be adopted to obtain the minimum makespan.We also extend the method to the application of a rotating seru.展开更多
基金Supported by the National Natural Science Foundation of China(11401077,11671068,11271060)the Fundamental Research of Civil Aircraft of China(MJ-F-2012-04)the Fundamental Research Funds for the Central Universities of China(DUT16LK38)
文摘Parametric polynomial surface is a fundamental element in CAD systems. Since the most of the classic minimal surfaces are represented by non-parametric polynomial, it is interesting to study the minimal surfaces represented in parametric polynomial form. Recently,Ganchev presented the canonical principal parameters for minimal surfaces. The normal curvature of a minimal surface expressed in these parameters determines completely the surface up to a position in the space. Based on this result, in this paper, we study the bi-quintic isothermal minimal surfaces. According to the condition that any minimal isothermal surface is harmonic,we can acquire the relationship of some control points must satisfy. Follow up, we obtain two holomorphic functions f（z） and g（z） which give the Weierstrass representation of the minimal surface. Under the constrains that the minimal surface is bi-quintic, f（z） and g（z） can be divided into two cases. One case is that f（z） is a constant and g（z） is a quadratic polynomial, and another case is that the degree of f（z） and g（z） are 2 and 1 respectively. For these two cases,we transfer the isothermal parameter to canonical principal parameter, and then compute their normal curvatures and analyze the properties of the corresponding minimal surfaces. Moreover,we study some geometric properties of the bi-quintic harmonic surfaces based on the B′ezier representation. Finally, some numerical examples are demonstrated to verify our results.
基金supported by Science and Technology Commission of Shanghai Municipality (No.14142201400)
文摘With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation（IOSGD）,FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.
文摘In this paper, the problem of computing zeros of a general degree bivariate Bernstein polynomial is considered. An efficient and robust algorithm is presented that takes into full account particular properties of the function considered. The algorithm works for rectangular as well as triangular domains. The outlined procedure can also be applied for the computation of the intersection of a Bezier patch and a plane as well as in the determination of an algebraic curve restricted to a compact domain. In particular, singular points of the algebraic curve are reliably detected.
基金This research is funded by OMRON research project of Doshisha Business SchoolJSPS KAKENHI[grant number 20K01897,20K01909,20K01639]+1 种基金The National Natural Science Foundation of China[grant number 71420107028,71501032,71871064]Science Research project of Liao Ning Province[grant number LN2019J06]。
文摘This paper discusses the makespan minimization of a production batch within a specific concurrent system,seru production system.A seru production system consists of multiple independent serus.A seru is a compact assembly origination in which products are assembled from-the-beginning-to-the-end without disruptions.One capability of a seru production system is its responsiveness.A performance measure used to evaluate a seru system’s responsiveness is the makespan of production batches assembled within the seru system.This study addresses the makespan minimization problem through an optimal seru loading policy.The problem is formulated as a min-max integer optimization model.An exact dimension-reduction Algorithm is developed to obtain the optimal allocation that minimizes the makespan.We show that the solution space increases very quickly.In contrast,our algorithm is efficient with a polynomial computational complexity of,where is the total number of serus in a seru system.To verify the usefulness of the developed exact dimension-reduction algorithm,we compare it with a widely practiced greedy algorithm through experiments.We find that our optimal algorithm is robust in most cases and the greedy algorithm is efficient when variability in production efficiencies is high.This result can guide us to adopt different algorithms in different business environments.If the variability in production efficiencies is high,e.g.,new employees and/or new products assembly,the greedy algorithm is efficient.For other cases,our optimal algorithm should be adopted to obtain the minimum makespan.We also extend the method to the application of a rotating seru.
