The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. ...The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.展开更多
This paper deals with a multi-objective parameter optimization framework for energy saving in injection molding process.It combines an experimental design by Taguchi's method,a process analysis by analysis of vari...This paper deals with a multi-objective parameter optimization framework for energy saving in injection molding process.It combines an experimental design by Taguchi's method,a process analysis by analysis of variance(ANOVA),a process modeling algorithm by artificial neural network(ANN),and a multi-objective parameter optimization algorithm by genetic algorithm(GA)-based lexicographic method.Local and global Pareto analyses show the trade-off between product quality and energy consumption.The implementation of the proposed framework can reduce the energy consumption significantly in laboratory scale tests,and at the same time,the product quality can meet the pre-determined requirements.展开更多
A lexicographic image hash method based on space and frequency features was proposed. At first, the image database was constructed, and then color and texture features were extracted from the image blocks including in...A lexicographic image hash method based on space and frequency features was proposed. At first, the image database was constructed, and then color and texture features were extracted from the image blocks including information for every image in the database, which formed feature vectors. The feature vectors were clustered to form dictionary. In hash generation, the image was preproc^ssed and divided into blocks firstly. Then color and texture features vectors were extracted from the blocks. These feature vectors were used to search the dictionary, and the nearest word in dictionary for each block was used to form the space features. At the same time. frequency feature was extracted from each block. The space and frequency features were connected to form the intermediate hash. Lastly, the final hash sequence was obtained by pseudo-randomly permuting the intermediate hash. Experiments show that the method has a very low probability of collision and a good perception of robustness. Compared with other methods, this method has a low collision rate.展开更多
In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w 【n ≤ 10. Computer search of lexic...In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w 【n ≤ 10. Computer search of lexicographic constant-weight equidistant codes is performed. Tables with bounds on the size of lexicographic constant-weight equidistant codes are presented.展开更多
Efficient values from Game Theory are used, in order to find out a fair allocation for a scheduling game associated with the problem of scheduling jobs with a common due date. A four person game illustrates the basic ...Efficient values from Game Theory are used, in order to find out a fair allocation for a scheduling game associated with the problem of scheduling jobs with a common due date. A four person game illustrates the basic ideas and the computational difficulties.展开更多
In this paper, a fish farm was modeled using the Lexicographic linear goal programming approach due to incommensurability in objectives. The study considered the fish farming plan with two sizes of catfish from stocki...In this paper, a fish farm was modeled using the Lexicographic linear goal programming approach due to incommensurability in objectives. The study considered the fish farming plan with two sizes of catfish from stocking to harvesting at four-month intervals. The multi-objective goals developed are required raw materials feed, water, light (resource utilization), sales revenue, profit realized, labor utilization, production costs, and pond utilization. The developed model was tested using related data collected from the farm records with the use of TORA 2007 software. The compromised solution from the results showed that the developed model is an efficient tool for decision-making process in the fish farm business organization.展开更多
We study CFG parse tree enumeration in this paper. By dividing the set of all parse trees into infinite hierarchies according to height of parse tree, the hierarchical lexicographic order on the set of parse trees is ...We study CFG parse tree enumeration in this paper. By dividing the set of all parse trees into infinite hierarchies according to height of parse tree, the hierarchical lexicographic order on the set of parse trees is established. Then grammar-based algorithms for counting and enumerating CFG parse trees in this order are presented. To generate a parse tree of height n, the time complexity is O（n）. If τ is a lowest parse tree for its yield, then O（n） =O（｜｜τ｜｜ ＋ 1）, where ｜｜τ｜｜ is the length of the sentence （yield） generated by τ. The sentence can be obtained as a by-product of the parse tree. To compute sentence from its parse tree （needn＇t be lowest one）, the time complexity is O（node）＋O（｜｜τ｜｜ ＋ 1）, where node is the number of non-leaf nodes of parse tree τ. To generate both a complete lowest parse tree and its yield at the same time, the time complexity is O（｜｜τ｜｜ ＋ 1）.展开更多
One of the basic issues in the study of hybrid systems is the well-posedness(existence and uniqueness of solutions)problem of discontinuous dynamical systems.This paper addresses this problem for a class of piecewise ...One of the basic issues in the study of hybrid systems is the well-posedness(existence and uniqueness of solutions)problem of discontinuous dynamical systems.This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of Carathéodory solutions in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions.Furthermore,it is clear that when carrier signal h(t)=0,closed-loop pulse-width modulation(PWM)DC–DC converters are not well posed,and when some condition is satisfied,the closed-loop PWM DC–DC converters with a P controller are well posed.展开更多
In this paper, minimax theorems and saddle points for a class of vector-valued mappings f（x, y） = u（x） ＋ β（x）v（y） are first investigated in the sense of lexicographic order, where u, v are two general vector...In this paper, minimax theorems and saddle points for a class of vector-valued mappings f（x, y） = u（x） ＋ β（x）v（y） are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.展开更多
Let K be a field and let A = K[X1,...,Xn] be the polynomial ring in X1, ..., Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics c...Let K be a field and let A = K[X1,...,Xn] be the polynomial ring in X1, ..., Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics computing some invariants. Moreover, we study the link between such a special class of squarefree lexsegment ideals and the so-called s-sequences.展开更多
Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.Since then,many classes of graphs have been proved to be antimagic.But few is known about the antimagicness of lexicographic prod...Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.Since then,many classes of graphs have been proved to be antimagic.But few is known about the antimagicness of lexicographic product graphs.In this paper,via the construction of a directed Eulerian circuit,the Siamese method,and some modification on graph labeling,the antimagicness of lexicographic product graph G[Pn]is obtained.展开更多
It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Gro...It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Grobner basis.In this context,Eisenbud,Peeva and Sturmfels defined a mapγfrom the noncommutative polynomial ring k〈X_(1),...,X_(n)〉to the commutative one k[x_(1),...,x_(n)]and proved that any ideal J of k〈X_(1),...,X_(n)〉,written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)],amits a finite Grobner basis with respect to a special monomial ordering on k〈X_(1),...,X_(n)〉.In this work,we approach the opposite problem.We prove that under some conditions,any ideal J of k〈X_(1),...,X_(n)〉admitting a finite Grobner basis can be written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)].展开更多
We consider particular compatible orders on a given completely simple semi- group Sx= M（（x）; I, A; P） where （x） is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace ...We consider particular compatible orders on a given completely simple semi- group Sx= M（（x）; I, A; P） where （x） is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.展开更多
Robustness in most of the literature is associated with rain-max or min-max regret criteria. However, these criteria of robustness are conservative and therefore recently new criteria called, lexicographic a- robust m...Robustness in most of the literature is associated with rain-max or min-max regret criteria. However, these criteria of robustness are conservative and therefore recently new criteria called, lexicographic a- robust method has been introduced in literature which defines the robust solution as a set of solutions whose quality orjth largest cost is not worse than the best possible jth largest cost in all scenarios. These criteria might be significant for robust optimization of single objective optimization problems. However, in real optimization problems, two or more than two conflicting objectives are desired to optimize concurrently and solution of multi objective optimization problems exists in the form of a set of solutions called Pareto solutions and from these solutions it might be difficult to decide which Pareto solution can satisfy rain-max, min-max regret or lexico- graphic a-robust criteria by considering multiple objectives simultaneously. Therefore, lexicographic a-robust method which is a recently introduced method in literature is extended in the current research for Pareto solutions. The proposed method called Pareto lexicographic a-robust approach can define Pareto lexicographic a-robust solu- tions from different scenarios by considering multiple objectives simultaneously. A simple example and an application of the proposed method on a simple problem of multi objective optimization of simple assembly line balancing problem with task time uncertainty is presented to get their robust solutions. The presented method can be significant to implement on different multi objective robust optimization problems containing uncertainty.展开更多
In this paper, lexicographic vector equilibrium problems are investigated. By using the idea of sequential process, the upper semicontinuity and closedness of the solution set map are established for a parametric lexi...In this paper, lexicographic vector equilibrium problems are investigated. By using the idea of sequential process, the upper semicontinuity and closedness of the solution set map are established for a parametric lexicographic strong vector equilibrium problem.展开更多
In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection f...In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.展开更多
Survival of a company in today's competitive business environment depends mainly on its supply chain.An adequate supply chain gives a competitive edge to a com-pany.Sourcing,which is the initial stage of a supply ...Survival of a company in today's competitive business environment depends mainly on its supply chain.An adequate supply chain gives a competitive edge to a com-pany.Sourcing,which is the initial stage of a supply chain,can be made efficient by making an appropriate selection of vendors.Appropriate vendor selection results not only in reduced purchasing costs,decreased production lead time,increased customer satisfaction but also in improved corporate competitiveness.In general,the vendor selection problem is a multi-objective decision-making problem that involves some quantitative and qualitative factors.So,we have considered a multi-objective ven-dor selection problem(MOV SP)with three multiple objective goals:minimization of net ordering price,minimization of rejected units and minimization of late delivered units.In most of the cases,information about the price of a unit,percentage of rejected units,percentage of late delivered units,vendor rating value and vendor quota flexibil-ity may not be known precisely due to some reasons.In this paper,imprecision in input information is handled by the concept of a simulation technique,where the parameter follows the uniform distribution.Deterministic,stochastic,a-cut and ranking function approaches are used to get the crisp value of the simulated data sets.The four differ-ent algorithms,namely-fuzzy programming,goal programming,lexicographic goal programming and D1-distance algorithm,have been used for solving the MOVSP.In last,three different types of simulated data sets have been used to illustrate the work.展开更多
文摘The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively.
基金(Nos. 20806040,61073059 and 61034005) supported by the National Natural Science Foundation of China
文摘This paper deals with a multi-objective parameter optimization framework for energy saving in injection molding process.It combines an experimental design by Taguchi's method,a process analysis by analysis of variance(ANOVA),a process modeling algorithm by artificial neural network(ANN),and a multi-objective parameter optimization algorithm by genetic algorithm(GA)-based lexicographic method.Local and global Pareto analyses show the trade-off between product quality and energy consumption.The implementation of the proposed framework can reduce the energy consumption significantly in laboratory scale tests,and at the same time,the product quality can meet the pre-determined requirements.
基金Natural Science Foundations of Shanghai,China(Nos.15ZR1418500,15ZR1418400)the Training Program of Shanghai University of Electric Power for Academic Backbone Teachers,China
文摘A lexicographic image hash method based on space and frequency features was proposed. At first, the image database was constructed, and then color and texture features were extracted from the image blocks including information for every image in the database, which formed feature vectors. The feature vectors were clustered to form dictionary. In hash generation, the image was preproc^ssed and divided into blocks firstly. Then color and texture features vectors were extracted from the blocks. These feature vectors were used to search the dictionary, and the nearest word in dictionary for each block was used to form the space features. At the same time. frequency feature was extracted from each block. The space and frequency features were connected to form the intermediate hash. Lastly, the final hash sequence was obtained by pseudo-randomly permuting the intermediate hash. Experiments show that the method has a very low probability of collision and a good perception of robustness. Compared with other methods, this method has a low collision rate.
文摘In this paper we consider the problem of finding bounds on the size of lexicographic constant-weight equidistant codes over the alphabet of three, four and five elements with 2 ≤ w 【n ≤ 10. Computer search of lexicographic constant-weight equidistant codes is performed. Tables with bounds on the size of lexicographic constant-weight equidistant codes are presented.
文摘Efficient values from Game Theory are used, in order to find out a fair allocation for a scheduling game associated with the problem of scheduling jobs with a common due date. A four person game illustrates the basic ideas and the computational difficulties.
文摘In this paper, a fish farm was modeled using the Lexicographic linear goal programming approach due to incommensurability in objectives. The study considered the fish farming plan with two sizes of catfish from stocking to harvesting at four-month intervals. The multi-objective goals developed are required raw materials feed, water, light (resource utilization), sales revenue, profit realized, labor utilization, production costs, and pond utilization. The developed model was tested using related data collected from the farm records with the use of TORA 2007 software. The compromised solution from the results showed that the developed model is an efficient tool for decision-making process in the fish farm business organization.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60273023, 60721061)
文摘We study CFG parse tree enumeration in this paper. By dividing the set of all parse trees into infinite hierarchies according to height of parse tree, the hierarchical lexicographic order on the set of parse trees is established. Then grammar-based algorithms for counting and enumerating CFG parse trees in this order are presented. To generate a parse tree of height n, the time complexity is O（n）. If τ is a lowest parse tree for its yield, then O（n） =O（｜｜τ｜｜ ＋ 1）, where ｜｜τ｜｜ is the length of the sentence （yield） generated by τ. The sentence can be obtained as a by-product of the parse tree. To compute sentence from its parse tree （needn＇t be lowest one）, the time complexity is O（node）＋O（｜｜τ｜｜ ＋ 1）, where node is the number of non-leaf nodes of parse tree τ. To generate both a complete lowest parse tree and its yield at the same time, the time complexity is O（｜｜τ｜｜ ＋ 1）.
基金supported by the Postdoctoral Foundation of China (17th).
文摘One of the basic issues in the study of hybrid systems is the well-posedness(existence and uniqueness of solutions)problem of discontinuous dynamical systems.This paper addresses this problem for a class of piecewise affine discontinuous systems with affine inequalities such as systems with pulse-width modulator under the definition of Carathéodory solutions in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions.Furthermore,it is clear that when carrier signal h(t)=0,closed-loop pulse-width modulation(PWM)DC–DC converters are not well posed,and when some condition is satisfied,the closed-loop PWM DC–DC converters with a P controller are well posed.
基金Supported by the National Natural Science Foundation of China(No.11171362,11571055)
文摘In this paper, minimax theorems and saddle points for a class of vector-valued mappings f（x, y） = u（x） ＋ β（x）v（y） are first investigated in the sense of lexicographic order, where u, v are two general vector-valued mappings and β is a non-negative real-valued function. Then, by applying the existence theorem of lexicographic saddle point, we investigate a lexicographic equilibrium problem and establish an equivalent relationship between the lexicographic saddle point theorem and existence theorem of a lexicographic equilibrium problem for vector-valued mappings.
文摘Let K be a field and let A = K[X1,...,Xn] be the polynomial ring in X1, ..., Xn with coefficients in K. In this paper we study the universal squarefree lexsegment ideals, and put our attention on their combinatorics computing some invariants. Moreover, we study the link between such a special class of squarefree lexsegment ideals and the so-called s-sequences.
基金supported by the National Natural Science Foundation of China (Nos. 11401430)
文摘Hartsfield and Ringel conjectured that every connected graph other than K2 is antimagic.Since then,many classes of graphs have been proved to be antimagic.But few is known about the antimagicness of lexicographic product graphs.In this paper,via the construction of a directed Eulerian circuit,the Siamese method,and some modification on graph labeling,the antimagicness of lexicographic product graph G[Pn]is obtained.
文摘It is well known that in the noncommutative polynomial ring in serveral variables Buchberger's algorithm does not always terminate.Thus,it is important to characterize noncommutative ideals that admit a finite Grobner basis.In this context,Eisenbud,Peeva and Sturmfels defined a mapγfrom the noncommutative polynomial ring k〈X_(1),...,X_(n)〉to the commutative one k[x_(1),...,x_(n)]and proved that any ideal J of k〈X_(1),...,X_(n)〉,written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)],amits a finite Grobner basis with respect to a special monomial ordering on k〈X_(1),...,X_(n)〉.In this work,we approach the opposite problem.We prove that under some conditions,any ideal J of k〈X_(1),...,X_(n)〉admitting a finite Grobner basis can be written as J=γ^(-1)(L)for some ideal L of k[x_(1),...,x_(n)].
文摘We consider particular compatible orders on a given completely simple semi- group Sx= M（（x）; I, A; P） where （x） is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.
文摘Robustness in most of the literature is associated with rain-max or min-max regret criteria. However, these criteria of robustness are conservative and therefore recently new criteria called, lexicographic a- robust method has been introduced in literature which defines the robust solution as a set of solutions whose quality orjth largest cost is not worse than the best possible jth largest cost in all scenarios. These criteria might be significant for robust optimization of single objective optimization problems. However, in real optimization problems, two or more than two conflicting objectives are desired to optimize concurrently and solution of multi objective optimization problems exists in the form of a set of solutions called Pareto solutions and from these solutions it might be difficult to decide which Pareto solution can satisfy rain-max, min-max regret or lexico- graphic a-robust criteria by considering multiple objectives simultaneously. Therefore, lexicographic a-robust method which is a recently introduced method in literature is extended in the current research for Pareto solutions. The proposed method called Pareto lexicographic a-robust approach can define Pareto lexicographic a-robust solu- tions from different scenarios by considering multiple objectives simultaneously. A simple example and an application of the proposed method on a simple problem of multi objective optimization of simple assembly line balancing problem with task time uncertainty is presented to get their robust solutions. The presented method can be significant to implement on different multi objective robust optimization problems containing uncertainty.
基金Supported in part by Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant numbers:KJ1501503 and KJ1601102)Chongqing Research Program of Basic Research and Frontier Technology(Grant numbers:cstc2016jcyjA0270 and cstc2016jcyjA0141)+1 种基金the National Natural Science Foundation of China(Grant number:11301418)the Foundation for High-level Talents of Chongqing University of Art and Sciences(Grant number:R2016SC13)
文摘In this paper, lexicographic vector equilibrium problems are investigated. By using the idea of sequential process, the upper semicontinuity and closedness of the solution set map are established for a parametric lexicographic strong vector equilibrium problem.
文摘In this paper we use a compromise approach to identify a lexicographic optimal solution of a multiple objective programming (MOP) problem. With this solution concept, we first find the maximization of each objection function as the ideal value. Then, we construct a lexicographic order for the compromise (differences) between the ideal values and objective functions. Based on the usually lexicographic optimality structure, we discuss some theoretical properties about our approach and derive a constructing algorithm to compute such a lexicographic optimal solution.
文摘Survival of a company in today's competitive business environment depends mainly on its supply chain.An adequate supply chain gives a competitive edge to a com-pany.Sourcing,which is the initial stage of a supply chain,can be made efficient by making an appropriate selection of vendors.Appropriate vendor selection results not only in reduced purchasing costs,decreased production lead time,increased customer satisfaction but also in improved corporate competitiveness.In general,the vendor selection problem is a multi-objective decision-making problem that involves some quantitative and qualitative factors.So,we have considered a multi-objective ven-dor selection problem(MOV SP)with three multiple objective goals:minimization of net ordering price,minimization of rejected units and minimization of late delivered units.In most of the cases,information about the price of a unit,percentage of rejected units,percentage of late delivered units,vendor rating value and vendor quota flexibil-ity may not be known precisely due to some reasons.In this paper,imprecision in input information is handled by the concept of a simulation technique,where the parameter follows the uniform distribution.Deterministic,stochastic,a-cut and ranking function approaches are used to get the crisp value of the simulated data sets.The four differ-ent algorithms,namely-fuzzy programming,goal programming,lexicographic goal programming and D1-distance algorithm,have been used for solving the MOVSP.In last,three different types of simulated data sets have been used to illustrate the work.
