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
In this paper, we ?rst consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete...In this paper, we ?rst consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete hypersemilattice strongly regular relations on ordered semihypergroups, and investigate their related properties.Furthermore, the properties of hyper?lters of an ordered semihypergroup are studied,and several related applications are given. Especially, we prove that the equivalence relation N on an ordered semihypergroup S is the least complete hypersemilattice strongly regular relation on S.展开更多
?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent sem...?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.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
Let G be a primitive strongly regular graph of order n and A is adjacency matrix. In this paper we first associate to A a real 3-dimensional Euclidean Jordan algebra? with rank three spanned by In and the natural powe...Let G be a primitive strongly regular graph of order n and A is adjacency matrix. In this paper we first associate to A a real 3-dimensional Euclidean Jordan algebra? with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of order n. Next we consider a basis? that is a Jordan frame of . Finally, by an algebraic asymptotic analysis of the second spectral decomposition of some Hadamard series associated to A we establish some inequalities over the spectra and over the parameters of a strongly regular graph.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
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
We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and...We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.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
We report on the properties of strong pulses from PSR B0656＋14 by analyzing the data obtained using the Urumqi 25-m radio telescope at 1540 MHz from August 2007 to September 2010.In 44 h of observational data,a total...We report on the properties of strong pulses from PSR B0656＋14 by analyzing the data obtained using the Urumqi 25-m radio telescope at 1540 MHz from August 2007 to September 2010.In 44 h of observational data,a total of 67 pulses with signal-to-noise ratios above a 5σthreshold were detected.The peak flux densities of these pulses are 58 to 194 times that of the average profile,and their pulse energies are 3 to 68 times that of the average pulse.These pulses are clustered around phases about 5-ahead of the peak of the average profile.Compared with the width of the average profile,they are relatively narrow,with the full widths at half-maximum ranging from 0.28 ° to 1.78 °.The distribution of pulse-energies follows a lognormal distribution.These sporadic strong pulses detected from PSR B0656＋14 have different characteristics from both typical giant pulses and its regular pulses.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
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
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The NSF(11801081,11701504) of Chinathe University Natural Science Project(KJ2018A0329) of Anhui Province
文摘In this paper, we ?rst consider the regular and strongly regular relations on ordered semihypergroups in detail. In particular, we introduce the concepts of the hypersemilattice strongly regular relations and complete hypersemilattice strongly regular relations on ordered semihypergroups, and investigate their related properties.Furthermore, the properties of hyper?lters of an ordered semihypergroup are studied,and several related applications are given. Especially, we prove that the equivalence relation N on an ordered semihypergroup S is the least complete hypersemilattice strongly regular relation on S.
文摘?The multiplication semigroup of strongly regular ring R in the light of semigroup is researched,hence some properties of strongly regular rings are obtained. The non-division strongly regular ring R is anilpotent semisimple ring without identity element. It is neither the Artin ring nor the Noether ring. The setidempotents of ring R is an infinite set without the maximum and minimal conditions,it is a unions of someorder sets and hai a non-well-ordered order set at least.
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.
文摘Let G be a primitive strongly regular graph of order n and A is adjacency matrix. In this paper we first associate to A a real 3-dimensional Euclidean Jordan algebra? with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of order n. Next we consider a basis? that is a Jordan frame of . Finally, by an algebraic asymptotic analysis of the second spectral decomposition of some Hadamard series associated to A we establish some inequalities over the spectra and over the parameters of a strongly regular graph.
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 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].
基金supported by the guidance project of scientific research plan of Educational Adminstration of Hubei Province,China(B2016162)the plan of science and technology innovation team of excellent young and middle-age of Hubei province(T201731)
文摘We study when exchange rings are von Neumann regular. An exchange ring R with primitive factors Artinian is von Neumann regular, if the Jacobson radical of any indecomposable homomorphic image of R is T-nilpotent, and if any indecomposable homomorphic image of R is semiprime. Every indecomposable semiprimitive factor ring of R is regular, if R is an exchange ring such that every left primitive factor ring of R is a ring of index at most n and if R has nil-property.
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funded by the National Natural Science Foundation of China(Grant No.10973026)
文摘We report on the properties of strong pulses from PSR B0656＋14 by analyzing the data obtained using the Urumqi 25-m radio telescope at 1540 MHz from August 2007 to September 2010.In 44 h of observational data,a total of 67 pulses with signal-to-noise ratios above a 5σthreshold were detected.The peak flux densities of these pulses are 58 to 194 times that of the average profile,and their pulse energies are 3 to 68 times that of the average pulse.These pulses are clustered around phases about 5-ahead of the peak of the average profile.Compared with the width of the average profile,they are relatively narrow,with the full widths at half-maximum ranging from 0.28 ° to 1.78 °.The distribution of pulse-energies follows a lognormal distribution.These sporadic strong pulses detected from PSR B0656＋14 have different characteristics from both typical giant pulses and its regular pulses.
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 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.
