This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such tha...This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such that er=eu for all r∉J(R),where J(R)is the Jacobson radical of ring R.展开更多
A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A r...A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.展开更多
Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 ...Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.展开更多
Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered ...Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm＇s performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O（√N） time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.展开更多
In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly r...In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.展开更多
Strongly regular (α,β)-reguli are a class of incidence structures with given conditions which were introduced by Hamilton and Mathon. We introduce two classes of codes constructed from strongly regular (α,β)-regul...Strongly regular (α,β)-reguli are a class of incidence structures with given conditions which were introduced by Hamilton and Mathon. We introduce two classes of codes constructed from strongly regular (α,β)-reguli within PG(k-1,q). The codes are related with two-weight codes intimately.展开更多
We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility c...We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.展开更多
Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil s...Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].展开更多
A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this paper, we study the regularity of right SF-rings...A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this paper, we study the regularity of right SF-rings and prove that if R is a right SF-ring whose all maximal (essential) right ideals are GW-ideals, then R is regular.展开更多
In this paper, an equivalent condition of a graph G with t （2≤ t ≤n） distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular （necessarily be strongly regular）, an equi...In this paper, an equivalent condition of a graph G with t （2≤ t ≤n） distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular （necessarily be strongly regular）, an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.展开更多
In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups...In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.展开更多
Owing to the large amplitude and nonlinearity of extreme sea waves,sailing ships exhibit obvious large-amplitude motion and green water.For a tumblehome vessel,a low-tumblehome freeboard and wave-piercing bow make gre...Owing to the large amplitude and nonlinearity of extreme sea waves,sailing ships exhibit obvious large-amplitude motion and green water.For a tumblehome vessel,a low-tumblehome freeboard and wave-piercing bow make green water more likely.To study the green water of a wave-facing sailing tumblehome vessel in strong nonlinear regular waves,the computational fluid dynamics software STAR-CCM+was used.The Reynolds-averaged Navier–Stokes method was used for the numerical simulation,and the k-epsilon model was adopted to deal with viscous turbulence.The volume of the fluid method was used to capture the free surface,and overset grids were utilized to simulate the large-amplitude ship motion.This study delves into the influence of wave height on the ship motion response and a tumblehome vessel green water under a large wave steepness(0.033≤H/λ≤0.067)at Fr=0.22.In addition,the dynamic process of green water and the“wave run-up”phenomenon were evaluated.The results suggest that when the wavelength is equal to the ship length and the wave steepness increases to 0.056,the increase in the water height on the deck is obvious.However,the wave height had little effect on the green water duration.The wave steepness and“backwater”have a great impact on the value and number of the peak of the water height on the deck.When the wave steepness exceeded 0.056,the water climbed up,and the plunging-type water body was formed at the top of the wave baffle,resulting in a large water area on the deck.展开更多
A complete classification of the multivalued coset groups of order 3 is given.The proof is based on the classification of rank 3 groups having regular normal subgroups.
In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characteriz...In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.展开更多
Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then th...Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then the m-ary hyperoperations defined on the quotient canonical(m,n)-ary hypermodule[M:N^(*)]are m-ary operations and the relation N^(*)is a strongly regular relation.Further,in this case,it is shown that the scalar hyperoperation is just an operation.展开更多
This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is...This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.展开更多
A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent ...A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.展开更多
In this paper, we construct some families of strongly regular graphs on finite fields by using unions of cyclotomic classes and index 2 Gauss sums. New infinite families of strongly regular graphs are found.
The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly re...The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly regular graphs is revealed,the full group of automorphisms is described,and some other nice properties are given.To each graph a list of interesting subgraphs is provided as well.展开更多
文摘This note is to investigate the properties of strongly semipotent rings.It is proved that every strongly semipotent ring is a idempotent unit regular ring,i.e.,there exist a non-zero idempotent e and a unit u such that er=eu for all r∉J(R),where J(R)is the Jacobson radical of ring R.
文摘A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.
基金Supported by the National Natural Science Foundation of China（11161006, 11171142） Supported by the Natural Science Foundation of Guangxi Province（2011GXNSFA018144, 018139, 2010GXNSFB 013048, 0991102）+2 种基金 Supported by the Guangxi New Century 1000 Talents Project Supported by the Guangxi Graduate Student Education Innovation Project（2011106030701M06） Supported by the SRF of Guangxi Education Committee
文摘In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.
文摘Koetzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongLy-regular self- complementary graph whose order is 4k ＋ 1, where 4k ＋ 1 = x^2 ＋ y^2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k ＋ 1 orders.
基金supported by the National Natural Science Foundation of China(Grant Nos.61502101 and 61170321)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20140651)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110092110024)
文摘Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm＇s performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O（√N） time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.
基金Supported by the National Natural Science Foundation of China(10861007)
文摘In this paper,we introduce and investigate the strongly regular relation.Then we give the relational representations and an intrinsic characterization of strongly algebraic lattices via mapping relation and strongly regular relation.
基金the Scientific Research Start-up Foundation of Qingdao University of Science and Technology in China (No. 0022327)
文摘Strongly regular (α,β)-reguli are a class of incidence structures with given conditions which were introduced by Hamilton and Mathon. We introduce two classes of codes constructed from strongly regular (α,β)-reguli within PG(k-1,q). The codes are related with two-weight codes intimately.
基金supported by the European Regional Development Fund through the program COMPETEby the Portuguese Government through the FCT—Fundacao para a Ciencia e a Tecnologia under the project PEst—C/MAT/UI0144/2013+1 种基金partially supported by Portuguese Funds trough CIDMA—Center for Research and development in Mathematics and Applications,Department of Mathematics,University of Aveiro,3810-193,Aveiro,Portugalthe Portuguese Foundation for Science and Technology(FCT-Fundacao para a Ciencia e Tecnologia),within Project PEst-OE/MAT/UI4106/2014
文摘We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.
基金supported by the Natural Science Foundation of China (No.11901062)the Sichuan Natural Science Foundation (No.2024NSFSC0417)。
文摘Recently,linear codes with a few weights have been extensively studied due to their applications in secret sharing schemes,constant composition codes,strongly regular graphs and so on.In this paper,based on the Weil sums,several classes of two-weight or three-weight linear codes are presented by choosing a proper defining set,and their weight enumerators and complete weight enumerators are determined.Furthermore,these codes are proven to be minimal.By puncturing these linear codes,two classes of two-weight projective codes are obtained,and the parameters of the corresponding strongly regular graph are given.This paper generalizes the results of[7].
文摘A ring R is called a left (right) SF-ring if all simple left (right) R-modules are flat. It is known that von Neumann regular rings are left and right SF-rings. In this paper, we study the regularity of right SF-rings and prove that if R is a right SF-ring whose all maximal (essential) right ideals are GW-ideals, then R is regular.
基金Supported by the Anhui Provincial Natural Science Foundation(050460102)National Natural Science Foundation of China(10601001,10571163)+3 种基金NSF of Department of Education of Anhui Province(2004kj027,2005kj005zd)Foundation of Anhui Institute of Architecture and Industry(200510307)Foundation of Mathematics Innovation Team of Anhui UniversityFoundation of Talents Group Construction of Anhui University
文摘In this paper, an equivalent condition of a graph G with t （2≤ t ≤n） distinct Laplacian eigenvalues is established. By applying this condition to t = 3, if G is regular （necessarily be strongly regular）, an equivalent condition of G being Laplacian integral is given. Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree. Graph G is characterized in the case of its being triangle-free, bipartite and pentagon-free. In both cases, G is Laplacian integral.
基金Supported by the National Natural Science Foundation of China (Grant No. 10961014)the Science and Technology Projects in Guangdong Province (Grant No. 2010B010600039)+3 种基金the Guangdong Provincial Natural Science Foundation of China (Grant No. S2011010003681)the Anhui Provincial Excellent Youth Talent Foundation (Grant No. 2012SQRL115ZD)the University Natural Science Project of Anhui Province (Grant No. KJ2012B133)the Fuyang Normal College Natural Science Foundation (Grant No. 2007LZ01)
文摘In this paper, fuzzy quasi-ideals of ordered semigroups are characterized by the properties of their level subsets. Furthermore, we introduce the notion of completely semiprime fuzzy quasi-ideals of ordered semigroups and characterize strongly regular ordered semigroups in terms of completely semiprime fuzzy quasi-ideals. Finally, we investigate the characterizations and decompositions of left and right simple ordered semigroups by means of fuzzy quasi-ideals.
基金Supported by the Heilongjiang Touyan Project of Chinaand the Frontier Science Center of the Ministry of Education for Extreme Marine Environment Wave Fields
文摘Owing to the large amplitude and nonlinearity of extreme sea waves,sailing ships exhibit obvious large-amplitude motion and green water.For a tumblehome vessel,a low-tumblehome freeboard and wave-piercing bow make green water more likely.To study the green water of a wave-facing sailing tumblehome vessel in strong nonlinear regular waves,the computational fluid dynamics software STAR-CCM+was used.The Reynolds-averaged Navier–Stokes method was used for the numerical simulation,and the k-epsilon model was adopted to deal with viscous turbulence.The volume of the fluid method was used to capture the free surface,and overset grids were utilized to simulate the large-amplitude ship motion.This study delves into the influence of wave height on the ship motion response and a tumblehome vessel green water under a large wave steepness(0.033≤H/λ≤0.067)at Fr=0.22.In addition,the dynamic process of green water and the“wave run-up”phenomenon were evaluated.The results suggest that when the wavelength is equal to the ship length and the wave steepness increases to 0.056,the increase in the water height on the deck is obvious.However,the wave height had little effect on the green water duration.The wave steepness and“backwater”have a great impact on the value and number of the peak of the water height on the deck.When the wave steepness exceeded 0.056,the water climbed up,and the plunging-type water body was formed at the top of the wave baffle,resulting in a large water area on the deck.
基金supported by National Natural Science Foundation of China(Grant No.12361003)supported by the Sobolev Institute of Mathematics State Contract(Grant No.FWNF-2022-0002)National Natural Science Foundation of China(Grant No.12171126)。
文摘A complete classification of the multivalued coset groups of order 3 is given.The proof is based on the classification of rank 3 groups having regular normal subgroups.
文摘In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.
文摘Quotient canonical(m,n)-hypermodules over Krasner(m,n)-hyperrings are studied as a generalization of the well-known algebraic hyperstructures.In this work,we prove that if N is a normal(m,n)-ary subhypermodule,then the m-ary hyperoperations defined on the quotient canonical(m,n)-ary hypermodule[M:N^(*)]are m-ary operations and the relation N^(*)is a strongly regular relation.Further,in this case,it is shown that the scalar hyperoperation is just an operation.
文摘This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system. into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.
基金supported by National Natural Science Foundation of China(No.11571091)Natural Science Foundation of Hebei Province,China(No.F2019205147)Innovation Program of Hebei Normal University,China(No.CXZZSS2020050).
文摘A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.
基金supported by National Natural Science Foundation of China (Grant Nos.10971250 and 11171150)
文摘In this paper, we construct some families of strongly regular graphs on finite fields by using unions of cyclotomic classes and index 2 Gauss sums. New infinite families of strongly regular graphs are found.
文摘The goal of the present paper is to provide a gallery of small directed strongly regular graphs.For each graph of order n≤12 and valency k<n/2,a diagram is depicted,its relation to other small directed strongly regular graphs is revealed,the full group of automorphisms is described,and some other nice properties are given.To each graph a list of interesting subgraphs is provided as well.
