In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are dif...In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].展开更多
Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_...Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.展开更多
Ⅰ. INTRODUCTION K. Mahler, Th. Schneider, P. Bundschuh, J. Browkin and Wang Lianxiang considered the question of p-adic number which is approximated by rational numbers and tbe question of the algebraic independence ...Ⅰ. INTRODUCTION K. Mahler, Th. Schneider, P. Bundschuh, J. Browkin and Wang Lianxiang considered the question of p-adic number which is approximated by rational numbers and tbe question of the algebraic independence and transcendence in various ways. However, there are only a few results on the simultaneous approxi-展开更多
In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkow...In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkowski,van der Waerden,Hadwiger,Swinnerton-Dyer,Watson,Levenshtein,Odlyzko,Sloane and Musin.In this paper,we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results,in particular for balls in dimensions three,four and eight.展开更多
A Gallai k-coloring is a k-edge-coloring of a complete graph in which there are no rainbow triangles.For given graphs G_(1),G_(2),G_(3)and nonnegative integers r,s,t with k=r+s+t,the k-colored Gallai-Ramsey number grk...A Gallai k-coloring is a k-edge-coloring of a complete graph in which there are no rainbow triangles.For given graphs G_(1),G_(2),G_(3)and nonnegative integers r,s,t with k=r+s+t,the k-colored Gallai-Ramsey number grk(K_(3):r·G_(1),s·G_(2),t·G_(3))is the minimum integer n such that every Gallai k-colored Kncontains a monochromatic copy of G_(1)colored by one of the first r colors or a monochromatic copy of G_(2)colored by one of the middle s colors or a monochromatic copy of G_(3)colored by one of the last t colors.In this paper,we determine the value of GallaiRamsey number in the case that G_(1)=B_(3)^(+),G_(2)=S_(3)^(+)and G_(3)=K_(3).Then the Gallai-Ramsey numbers grk(K_(3):B_(3)^(+)),grk(K_(3):S_(3)^(+))and grk(K_(3):K_(3))are obtained,respectively.Furthermore,the Gallai-Ramsey numbers grk(K_(3):r·B_(3)^(+),(k-r)·S_(3)^(+)),grk(K_(3):r·B_(3)^(+),(k-r)·K_(3))and grk(K_(3):s·S_(3)^(+),(k-s)·K_(3))are obtained,respectively.展开更多
Given a graph F and a positive integer r,the size Ramsey number R(F,r)is defined as the smallest integer m such that there exists a graph G with m edges where every r-color edge coloring of G results in a monochromati...Given a graph F and a positive integer r,the size Ramsey number R(F,r)is defined as the smallest integer m such that there exists a graph G with m edges where every r-color edge coloring of G results in a monochromatic copy of F.Let P_(n)and C_(n)represent a path and a cycle on n vertices,respectively.In this paper,we establish that for sufficiently large n,R(P_(n),P_(n),P_(n))<772n.Furthermore,we demonstrate that for sufficiently large even integers n,R(P_(n),P_(n),C_(n))≤17093n.For sufficiently large odd integer n,we show that R(P_(n),P_(n),C_(n))≥(7.5-o(1))n.展开更多
A piggyback pipeline is a special configuration of offshore pipelines for offshore oil and gas exploration and is characterized by the coupling of a large-diameter pipe with a small-diameter pipe. This study conducts ...A piggyback pipeline is a special configuration of offshore pipelines for offshore oil and gas exploration and is characterized by the coupling of a large-diameter pipe with a small-diameter pipe. This study conducts a numerical investigation of the transverse VIV characteristics of a piggyback pipeline at low Reynolds numbers, as the vortex shedding modes and vibration characteristics can be accurately represented under laminar flow conditions with minimal computational expense. The effects of influential factors, such as the mass ratio, position angle of the small pipe relative to the main pipe, and Reynolds number, on the VIV amplitude, frequency, vibration center, and mean lift coefficient are specifically examined. The results indicate that the mass ratio has a limited effect on the maximum VIV amplitude. However, as the mass ratio decreases, the lock-in region expands, and the vibration center of the piggyback pipeline deviates further from its original position. The VIV amplitude is minimized, and the lock-in region is the narrowest at a position angle of 45°, whereas the vibration center reaches its maximum displacement at a position angle of 135°. As the Reynolds number increases, the VIV amplitude slightly increases, accompanied by convergence of the vibration center toward its initial position. The mean lift coefficient and wake vortices are also analyzed to establish a connection with the vibration characteristics of the piggyback pipeline. The optimal configuration of the piggyback pipeline is also proposed on the basis of the present numerical results.展开更多
By combining experimental α-decay energies and half-lives, the α-particle preformation factor for nuclei around neutron magic numbers N of 126, 152, and 162 were extracted using the two-potential approach. The nucle...By combining experimental α-decay energies and half-lives, the α-particle preformation factor for nuclei around neutron magic numbers N of 126, 152, and 162 were extracted using the two-potential approach. The nuclei around the shell closure were more tightly bound than adjacent nuclei. Additionally, based on the WS4 mass model (Wang et al., Phys. Lett.B 734, 215 (2014)), we extended the two-potential approach to predict the α-decay half-lives of nuclei around N values of178 and 184 with Z of 119 and 120. We believe that our findings will serve as guidelines for future experimental studies.展开更多
In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub>...In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub> and R<sub>n</sub>(x). We also give relation between the Stirling numbers, the Bell numbers, the R<sub>n</sub> and R<sub>n</sub>(x).展开更多
In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the ...In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.展开更多
We study the production of the X(6900)in the ultra-peripheral heavy ion collisions at the LHC energy region.The potential quantum numbers of X(6900)could be 0^(±+)and 2^(±+).We find that the transverse momen...We study the production of the X(6900)in the ultra-peripheral heavy ion collisions at the LHC energy region.The potential quantum numbers of X(6900)could be 0^(±+)and 2^(±+).We find that the transverse momentum and the polar angle distributions of X(6900)can be used to distinguish these four potential quantum numbers.These characteristic distributions originate from linearly polarized photons emitted by relativistic nuclei and can be measured by further LHC experiments.展开更多
Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the progressive degeneration of upper and lower motor neurons in the brainstem and spinal cord,leading to muscle weakness,para...Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the progressive degeneration of upper and lower motor neurons in the brainstem and spinal cord,leading to muscle weakness,paralysis,and respiratory failure (Morgan and Orrell,2016).展开更多
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The resu...A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.展开更多
To extend the traditional generalized grey incidence model, a novel grey incidence model based on inter- val grey numbers is constructed. Considering the numerical information of indexes cannot be accurately obtained ...To extend the traditional generalized grey incidence model, a novel grey incidence model based on inter- val grey numbers is constructed. Considering the numerical information of indexes cannot be accurately obtained and can be defined as interval grey numbers, the interval grey numbers are defined as standard interval grey num- bers which are split in white part and grey part. The absolute degree of incidence and relative degree of incidence based on the interval grey numbers are constructed and their arithmetic are given. Finally, an example about commercial aircraft index selection illuminates the effectiveness of the model. The results show that the model can sort indexes better and can extend the grey incidence models significantly.展开更多
In this paper, we use a combinatorial analysis method. In the complete graph K N with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by t...In this paper, we use a combinatorial analysis method. In the complete graph K N with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by the neighborhood of some vertex in V(K N). Inspired by the main results of Jayawardene and Rousseau (Ars Combinatoria, 2000, 163-173), we determine the Ramsey numbers of r(K 1, 4, G), where G is the three-partite graph of order six without isolate vertex.展开更多
It is shown that r(W_m, K_n)≤(1+o(1))C_1n log n 2m-2m-2 for fixed even m≥4 and n→∞, and r(W_m, K_n)≤(1+o(1))C_2n 2mm+1 log n m+1m-1 for fixed odd m≥5 and n→∞, wher...It is shown that r(W_m, K_n)≤(1+o(1))C_1n log n 2m-2m-2 for fixed even m≥4 and n→∞, and r(W_m, K_n)≤(1+o(1))C_2n 2mm+1 log n m+1m-1 for fixed odd m≥5 and n→∞, where C_1=C_1(m)>0 and C_2=C_2(m)>0, in particular, C_2=12 if m=5 . It is obtained by the analytic method and using the function f_m(x)=∫ 1 _ 0 (1-t) 1m dtm+(x-m)t , x≥0 , m≥1 on the base of the asymptotic upper bounds for r(C_m, K_n) which were given by Caro, et al. Also, cn log n 52 ≤r(K_4, K_n)≤(1+o(1)) n 3 ( log n) 2 (as n→∞ ). Moreover, we give r(K_k+C_m, K_n)≤(1+o(1))C_5(m)n log n k+mm-2 for fixed even m≥4 and r(K_k+C_m, K_n)≤(1+o(1))C_6(m)n 2+(k+1)(m-1)2+k(m-1) log n k+2m-1 for fixed odd m≥3 (as n→∞ ).展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11671145)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).
文摘In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].
基金supported by the National Key Research and Development Program of China(2023YFA1010200,2020YFA0713100)the National Natural Science Foundation of China(12071453)the Innovation Program for Quantum Science and Technology(2021ZD0302902).
文摘Given two graphs G and H,the Ramsey number R(G,H)is the smallest positive integer N such that every 2-coloring of the edges of K_(N)contains either a red G or a blue H.Let K_(N-1)■K_(1,k)be the graph obtained from K_(N-1)by adding anew vertexνconnecting k vertices of K_(N-1).A graph G withχ(G)=k+1 is called edge-critical if G contains an edge e such thatχ(G-e)=k.A considerable amount of research has been conducted by previous scholars on Ramsey numbers ofgraphs.In this study,we show that for an edge-critical graph G with x(G)=k+1,when k≥2,1≥2,and n is sufficiently large,R(G,K_(1)+nK_(t))=knt+1 and r,(G,K_(1)+nK_(t))=(k-1)nt+1.
基金Project supported by the National Natural Science Foundation of China
文摘Ⅰ. INTRODUCTION K. Mahler, Th. Schneider, P. Bundschuh, J. Browkin and Wang Lianxiang considered the question of p-adic number which is approximated by rational numbers and tbe question of the algebraic independence and transcendence in various ways. However, there are only a few results on the simultaneous approxi-
基金supported by the National Natural Science Foundation of China(12226006,11921001)the Natural Key Research and Development Program of China(2018YFA0704701).
文摘In 1694,Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball.This problem and its higher dimensional generalization have been studied by many mathematicians,including Minkowski,van der Waerden,Hadwiger,Swinnerton-Dyer,Watson,Levenshtein,Odlyzko,Sloane and Musin.In this paper,we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results,in particular for balls in dimensions three,four and eight.
基金Supported by the National Natural Science Foundation of China(12161073)。
文摘A Gallai k-coloring is a k-edge-coloring of a complete graph in which there are no rainbow triangles.For given graphs G_(1),G_(2),G_(3)and nonnegative integers r,s,t with k=r+s+t,the k-colored Gallai-Ramsey number grk(K_(3):r·G_(1),s·G_(2),t·G_(3))is the minimum integer n such that every Gallai k-colored Kncontains a monochromatic copy of G_(1)colored by one of the first r colors or a monochromatic copy of G_(2)colored by one of the middle s colors or a monochromatic copy of G_(3)colored by one of the last t colors.In this paper,we determine the value of GallaiRamsey number in the case that G_(1)=B_(3)^(+),G_(2)=S_(3)^(+)and G_(3)=K_(3).Then the Gallai-Ramsey numbers grk(K_(3):B_(3)^(+)),grk(K_(3):S_(3)^(+))and grk(K_(3):K_(3))are obtained,respectively.Furthermore,the Gallai-Ramsey numbers grk(K_(3):r·B_(3)^(+),(k-r)·S_(3)^(+)),grk(K_(3):r·B_(3)^(+),(k-r)·K_(3))and grk(K_(3):s·S_(3)^(+),(k-s)·K_(3))are obtained,respectively.
基金Supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.24KJD110008)the National Natural Science Foundation of China(Grant No.12401469)。
文摘Given a graph F and a positive integer r,the size Ramsey number R(F,r)is defined as the smallest integer m such that there exists a graph G with m edges where every r-color edge coloring of G results in a monochromatic copy of F.Let P_(n)and C_(n)represent a path and a cycle on n vertices,respectively.In this paper,we establish that for sufficiently large n,R(P_(n),P_(n),P_(n))<772n.Furthermore,we demonstrate that for sufficiently large even integers n,R(P_(n),P_(n),C_(n))≤17093n.For sufficiently large odd integer n,we show that R(P_(n),P_(n),C_(n))≥(7.5-o(1))n.
基金financially supported by the National Natural Science Foundation of China (Grant Nos. 52371289 and 51979192)。
文摘A piggyback pipeline is a special configuration of offshore pipelines for offshore oil and gas exploration and is characterized by the coupling of a large-diameter pipe with a small-diameter pipe. This study conducts a numerical investigation of the transverse VIV characteristics of a piggyback pipeline at low Reynolds numbers, as the vortex shedding modes and vibration characteristics can be accurately represented under laminar flow conditions with minimal computational expense. The effects of influential factors, such as the mass ratio, position angle of the small pipe relative to the main pipe, and Reynolds number, on the VIV amplitude, frequency, vibration center, and mean lift coefficient are specifically examined. The results indicate that the mass ratio has a limited effect on the maximum VIV amplitude. However, as the mass ratio decreases, the lock-in region expands, and the vibration center of the piggyback pipeline deviates further from its original position. The VIV amplitude is minimized, and the lock-in region is the narrowest at a position angle of 45°, whereas the vibration center reaches its maximum displacement at a position angle of 135°. As the Reynolds number increases, the VIV amplitude slightly increases, accompanied by convergence of the vibration center toward its initial position. The mean lift coefficient and wake vortices are also analyzed to establish a connection with the vibration characteristics of the piggyback pipeline. The optimal configuration of the piggyback pipeline is also proposed on the basis of the present numerical results.
基金supported in part by the National Natural Science Foundation of China(Nos.12175100 and 11975132)Construct Program of the Key Discipline in Hunan Province,Research Foundation of Education Bureau of Hunan Province,China(Nos.21B0402,18A237 and 22A0305)+3 种基金Natural Science Foundation of Hunan Province,China(No.2018JJ2321)Innovation Group of Nuclear and Particle Physics in USC,Shandong Province Natural Science Foundation,China(No.ZR2022JQ04)Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment,University of South China(No.2019KFZ10)Hunan Provincial Innovation Foundation for Postgraduate(No.CX20230962).
文摘By combining experimental α-decay energies and half-lives, the α-particle preformation factor for nuclei around neutron magic numbers N of 126, 152, and 162 were extracted using the two-potential approach. The nuclei around the shell closure were more tightly bound than adjacent nuclei. Additionally, based on the WS4 mass model (Wang et al., Phys. Lett.B 734, 215 (2014)), we extended the two-potential approach to predict the α-decay half-lives of nuclei around N values of178 and 184 with Z of 119 and 120. We believe that our findings will serve as guidelines for future experimental studies.
文摘In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub> and R<sub>n</sub>(x). We also give relation between the Stirling numbers, the Bell numbers, the R<sub>n</sub> and R<sub>n</sub>(x).
基金the financial support of the European Union under the REFRESH-Research Excellence for Region Sustainability and High-tech Industries project number CZ.10.03.01/00/22_003/0000048 via the Operational Programme Just Transition and has been done in connection with project Students Grant Competition SP2025/062"specific research on progressive and sustainable production technologies"and SP2025/063"specific research on innovative and progressive manufacturing technologies"financed by the Ministry of Education,Youth and Sports and Faculty of Mechanical Engineering VSB-TUOThe authors would like to extend their sincere appreciation to Researchers Supporting Project number(RSP2025R472)King Saud University,Riyadh,Saudi Arabia.
文摘In a world where supply chains are increasingly complex and unpredictable,finding the optimal way to move goods through transshipment networks is more important and challenging than ever.In addition to addressing the complexity of transportation costs and demand,this study presents a novel method that offers flexible routing alternatives to manage these complexities.When real-world variables such as fluctuating costs,variable capacity,and unpredictable demand are considered,traditional transshipment models often prove inadequate.To overcome these challenges,we propose an innovative fully fuzzy-based framework using LR flat fuzzy numbers.This framework allows for more adaptable and flexible decision-making in multi-objective transshipment situations by effectively capturing uncertain parameters.To overcome these challenges,we develop an innovative,fully fuzzy-based framework using LR flat fuzzy numbers to effectively capture uncertainty in key parameters,offering more flexible and adaptive decision-making in multi-objective transshipment problems.The proposed model also presents alternative route options,giving decisionmakers a range of choices to satisfy multiple requirements,including reducing costs,improving service quality,and expediting delivery.Through extensive numerical experiments,we demonstrate that the model can achieve greater adaptability,efficiency,and flexibility than standard approaches.This multi-path structure provides additional flexibility to adapt to dynamic network conditions.Using ranking strategies,we compared our multi-objective transshipment model with existing methods.The results indicate that,while traditional methods such as goal and fuzzy programming generate results close to the anti-ideal value,thus reducing their efficiency,our model produces solutions close to the ideal value,thereby facilitating better decision making.By combining dynamic routing alternatives with a fully fuzzybased approach,this study offers an effective tool to improve decision-making and optimize complex networks under real-world conditions in practical settings.In this paper,we utilize LINGO 18 software to solve the provided numerical example,demonstrating the effectiveness of the proposed method.
基金supported by the Guangdong Major Project of Basic and Applied Basic Research(Grant Nos.2020B0301030008 and 2023A1515010416)the National Natural Science Foundation of China(Grant Nos.12375073,12275091,12147128,and 12035007).
文摘We study the production of the X(6900)in the ultra-peripheral heavy ion collisions at the LHC energy region.The potential quantum numbers of X(6900)could be 0^(±+)and 2^(±+).We find that the transverse momentum and the polar angle distributions of X(6900)can be used to distinguish these four potential quantum numbers.These characteristic distributions originate from linearly polarized photons emitted by relativistic nuclei and can be measured by further LHC experiments.
文摘Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the progressive degeneration of upper and lower motor neurons in the brainstem and spinal cord,leading to muscle weakness,paralysis,and respiratory failure (Morgan and Orrell,2016).
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
基金Supported by the National Nature Science Foundation of China(10472046)the Scientific Innova-tion Research of College Graduate in Jiangsu Province(CX08B-035Z)the Innovation and Excellence Foundation of Doctoral Dissertation of Nanjing University of Aeronautics and Astronautics(BCXJ08-01)~~
文摘A two-dimensional（2-D） incompressible plane jet is investigated using the lattice Boltzmann method（LBM） for low Reynolds numbers of 42 and 65 based on the jet-exit-width and the maximum jet-exit-velocity. The results show that the mean centerline velocity decays as x-1/3 and the jet spreads as x2/3 in the self-similar region, which are consistent with the theoretical predictions and the experimental data. The time histories and PSD analyses of the instantaneous centerline velocities indicate the periodic behavior and the interaction between periodic components of velocities should not be neglected in the far field region, although it is invisible in the near field region.
基金Supported by the National Natural Science Foundation of China(70901041,71171113)the Joint Research Project of National Natural Science Foundation of China and Royal Society of UK(71111130211)+3 种基金the Major Program of National Funds of Social Science of Chinathe Doctoral Fund of Ministry of Education of China(20093218120032,200802870020)the Qinglan Project for Excellent Youth Teacher in Jiangsu Province(China)the Research Funding of Nanjing University of Aeronautics and Astronautics(NR2011002,NJ2011009)~~
文摘To extend the traditional generalized grey incidence model, a novel grey incidence model based on inter- val grey numbers is constructed. Considering the numerical information of indexes cannot be accurately obtained and can be defined as interval grey numbers, the interval grey numbers are defined as standard interval grey num- bers which are split in white part and grey part. The absolute degree of incidence and relative degree of incidence based on the interval grey numbers are constructed and their arithmetic are given. Finally, an example about commercial aircraft index selection illuminates the effectiveness of the model. The results show that the model can sort indexes better and can extend the grey incidence models significantly.
文摘In this paper, we use a combinatorial analysis method. In the complete graph K N with edges colored arbitrarily by red or blue, we consider the proposition of the subgraph of the red graph or blue graph induced by the neighborhood of some vertex in V(K N). Inspired by the main results of Jayawardene and Rousseau (Ars Combinatoria, 2000, 163-173), we determine the Ramsey numbers of r(K 1, 4, G), where G is the three-partite graph of order six without isolate vertex.
文摘It is shown that r(W_m, K_n)≤(1+o(1))C_1n log n 2m-2m-2 for fixed even m≥4 and n→∞, and r(W_m, K_n)≤(1+o(1))C_2n 2mm+1 log n m+1m-1 for fixed odd m≥5 and n→∞, where C_1=C_1(m)>0 and C_2=C_2(m)>0, in particular, C_2=12 if m=5 . It is obtained by the analytic method and using the function f_m(x)=∫ 1 _ 0 (1-t) 1m dtm+(x-m)t , x≥0 , m≥1 on the base of the asymptotic upper bounds for r(C_m, K_n) which were given by Caro, et al. Also, cn log n 52 ≤r(K_4, K_n)≤(1+o(1)) n 3 ( log n) 2 (as n→∞ ). Moreover, we give r(K_k+C_m, K_n)≤(1+o(1))C_5(m)n log n k+mm-2 for fixed even m≥4 and r(K_k+C_m, K_n)≤(1+o(1))C_6(m)n 2+(k+1)(m-1)2+k(m-1) log n k+2m-1 for fixed odd m≥3 (as n→∞ ).
