In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomi...In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplic...In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D.展开更多
We first propose the normal Pythagorean neutrosophic set(NPNS)in this paper,which synthesizes the distribution of the incompleteness,indeterminacy,and inconsistency of the Pythagorean neutrosophic set(PNS)and normal f...We first propose the normal Pythagorean neutrosophic set(NPNS)in this paper,which synthesizes the distribution of the incompleteness,indeterminacy,and inconsistency of the Pythagorean neutrosophic set(PNS)and normal fuzzy number.We also define some properties of NPNS.For solving the decision-making problem of the nonstrictly independent and interacting attributes,two kinds of NPNS Choquet integral operators are proposed.First,the NPNS Choquet integral average(NPNSCIA)operator and the NPNS Choquet integral geometric(NPNSCIG)operator are proposed.Then,their calculating formulas are derived,their properties are discussed,and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied.Finally,the two kinds of operators are applied to validate the stability of the new method.展开更多
In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f h...In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m > 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results展开更多
This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment met...This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.展开更多
The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit desi...The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.展开更多
We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind o...This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.展开更多
In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of none...In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.展开更多
The PLIC/SN method that combines the second-order volume tracking method (PLIC-VOF) with the equation of surface normal (SN) vector was recently proposed (M. Sun, “Volume Tracking of Subgrid Particles,” Internationa...The PLIC/SN method that combines the second-order volume tracking method (PLIC-VOF) with the equation of surface normal (SN) vector was recently proposed (M. Sun, “Volume Tracking of Subgrid Particles,” International Journal for Numerical Methods in Fluids, Vol. 66, No. 12, 2011, pp. 1530-1554). The method is able to track the motion of a subgrid particle, but the accuracy is not as good as expected on high resolution grids for vortical flows. In this paper, a simple unsplit multidimensional advection algorithm is coupled with the equation of SN vector. The advection algorithm is formulated as the finite volume method, so that it can be used readily for both structured and unstructured grids while maintaining the exact mass conservation. The new method improves the accuracy significantly for high resolution grids. In the well-known test of the time-resolved vortex problem of T = 2, the circular interface is resolved with an accuracy better than ever using the equation of SN vector.展开更多
The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extende...The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.展开更多
基于3~6岁学龄前132个男童的测量数据,分析得出三类体型,确定研究对象为最普遍的第2类正常体型;以第2类正常体男童的基本裤型为例,利用CLO3D进行虚拟仿真试验,结合髋关节、膝关节活动范围确定五种动态模拟,进行不同动态下基本裤型的虚...基于3~6岁学龄前132个男童的测量数据,分析得出三类体型,确定研究对象为最普遍的第2类正常体型;以第2类正常体男童的基本裤型为例,利用CLO3D进行虚拟仿真试验,结合髋关节、膝关节活动范围确定五种动态模拟,进行不同动态下基本裤型的虚拟压力和虚拟应力探究。结果显示:髋、膝关节角度较大时,后臀部位的B2点以及膝盖部位的F5点等虚拟压力和应力也较大;由于面料拉伸,大腿外侧的S2、S3点有较大的应力以及较小的压力,而膝盖以下几乎没有服装虚拟压力和应力。在此基础上进行版型优化,优化效果最好的是B2点,其平均虚拟压力和应力分别下降了5.59 k Pa和8.73%;使用汗布、毛圈布、珠地布三种针织面料进行模拟试穿,以及真人试穿测试,进一步验证了版型优化的有效性。展开更多
基金supported partially by the National Natural Science Foundation of China under Grant Nos.11771034 and 11401018
文摘In this paper it is shown how to transform a regular triangular set into a normal triangular set by computing the W-characteristic set of their saturated ideal and an algorithm is proposed for decomposing any polynomial set into ?nitely many strong characteristic pairs, each of which is formed with the reduced lexicographic Gr?bner basis and the normal W-characteristic set of a characterizable ideal.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
基金Supported by the NSF of China(10771220)Supported by the Doctorial Point Fund of National Education Ministry of China(200810780002)
文摘In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D.
基金This research was funded by the National Natural Science Foundation of China,Grant No.61703280Zhejiang Provincial Natural Science Foundation of China,Grant No.LY20F020011+3 种基金Social Sciences and Humanities Youth Foundation of Ministry of Education,Grant No.21YJCZH039Natural Science Foundation of Zhejiang Province,Grant No.TY22F025548the Public Welfare Technology Research Project of Zhejiang Province,Grant No.GG22F015473Key scientific research project of Shaoxing University,Grant No.2020LG1004.
文摘We first propose the normal Pythagorean neutrosophic set(NPNS)in this paper,which synthesizes the distribution of the incompleteness,indeterminacy,and inconsistency of the Pythagorean neutrosophic set(PNS)and normal fuzzy number.We also define some properties of NPNS.For solving the decision-making problem of the nonstrictly independent and interacting attributes,two kinds of NPNS Choquet integral operators are proposed.First,the NPNS Choquet integral average(NPNSCIA)operator and the NPNS Choquet integral geometric(NPNSCIG)operator are proposed.Then,their calculating formulas are derived,their properties are discussed,and an approach for solving the interacting multi-attribute decision making based on the NPNS is studied.Finally,the two kinds of operators are applied to validate the stability of the new method.
基金Supported by the National Natural Science Foundation of China（l1461070, 11271090） Supported by the Natural Science Foundation of Guangdong Province（S2012010010121）
文摘In this paper,we study the normality criterion for families of meromorphic functions concerning shared set depending on f∈F.Let F be a family of meromorphic functions in the unit disc A.For each f∈F,all zeros of f have multiplicity at least 2 and there exist nonzero complex numbers b_f,c_f satisfying(i) b_f/c_f is a constant;(ii) min{σ(0,b_f),σ(0,c_f),σ(b_f,c_f)} ≥m for some m > 0;(iii) E_f'(S_f)■ E_f(S_f),where S_f = {b_f,c_f}.Then F is normal in A.At the same time,the corresponding results are also proved.The results in this paper improve and generalize the related results
基金funded by the Korean Government(MSIT)Grant NRF-2022R1C1C1006671.
文摘This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.
文摘The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.
文摘We studied the normality criterion for families of meromorphic functions which related to One-way sharing set, and obtain two normal criterions, which improve the previous results.
基金supported in part by the National Natural Science Foundation of China(11626214,11571309)the General Research Project of Zhejiang Provincial Department of Education(Y201635378)+3 种基金the Zhejiang Provincial Natural Science Foundation of China(LY17F020011)J.Peng is supported by the National Natural Science Foundation of China(11771160)the Research Promotion Program of Huaqiao University(ZQN-PY411)Natural Science Foundation of Fujian Province(2015J01254)
文摘This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.
文摘In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.
文摘The PLIC/SN method that combines the second-order volume tracking method (PLIC-VOF) with the equation of surface normal (SN) vector was recently proposed (M. Sun, “Volume Tracking of Subgrid Particles,” International Journal for Numerical Methods in Fluids, Vol. 66, No. 12, 2011, pp. 1530-1554). The method is able to track the motion of a subgrid particle, but the accuracy is not as good as expected on high resolution grids for vortical flows. In this paper, a simple unsplit multidimensional advection algorithm is coupled with the equation of SN vector. The advection algorithm is formulated as the finite volume method, so that it can be used readily for both structured and unstructured grids while maintaining the exact mass conservation. The new method improves the accuracy significantly for high resolution grids. In the well-known test of the time-resolved vortex problem of T = 2, the circular interface is resolved with an accuracy better than ever using the equation of SN vector.
文摘The study of fuzzy sets is specifically designed to mathematically represent uncertainty and vagueness by assigning values of membership to objects that belong to a particular set. This notion has been broadly extended to other areas of topology where various topological concepts have been shown to hold on fuzzy topology. Some notions naturally extend to closure spaces without requiring a lot of modification of the underlying topological ideas. This work investigates the variants of normality on fuzzy isotone spaces.
文摘基于3~6岁学龄前132个男童的测量数据,分析得出三类体型,确定研究对象为最普遍的第2类正常体型;以第2类正常体男童的基本裤型为例,利用CLO3D进行虚拟仿真试验,结合髋关节、膝关节活动范围确定五种动态模拟,进行不同动态下基本裤型的虚拟压力和虚拟应力探究。结果显示:髋、膝关节角度较大时,后臀部位的B2点以及膝盖部位的F5点等虚拟压力和应力也较大;由于面料拉伸,大腿外侧的S2、S3点有较大的应力以及较小的压力,而膝盖以下几乎没有服装虚拟压力和应力。在此基础上进行版型优化,优化效果最好的是B2点,其平均虚拟压力和应力分别下降了5.59 k Pa和8.73%;使用汗布、毛圈布、珠地布三种针织面料进行模拟试穿,以及真人试穿测试,进一步验证了版型优化的有效性。
