In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
This paper presents a concurrent dual-band branch-line coupler with an independently tunable center frequency. In the proposed architecture, the quarter-wavelength lines, which work at two separated bands concurrently...This paper presents a concurrent dual-band branch-line coupler with an independently tunable center frequency. In the proposed architecture, the quarter-wavelength lines, which work at two separated bands concurrently and can be tuned in one of them, are key components. Based on the analysis of ABCD-matrix, a novel hybrid structure and a pair of varactors topology are utilized to achieve concurrent dual-band operation and independent tunability, respectively. Using this configuration, it is convenient to tune the center frequency of the upper band, while the responses of the lower band remain unaltered. To verify the proposed idea, a demonstration is implemented and the simulated results are presented.展开更多
The independence number of a graph G is the maximum cardinality among all independent sets of G. For any tree T of order n ≥ 2, it is easy to see that . In addition, if there are duplicated leaves in a tree, then the...The independence number of a graph G is the maximum cardinality among all independent sets of G. For any tree T of order n ≥ 2, it is easy to see that . In addition, if there are duplicated leaves in a tree, then these duplicated leaves are all lying in every maximum independent set. In this paper, we will show that if T is a tree of order n ≥ 4 without duplicated leaves, then . Moreover, we constructively characterize the extremal trees T of order n ≥ 4, which are without duplicated leaves, achieving these upper bounds.展开更多
For a graph G=(V,E),a Roman{2}-dominating function f:V→{0,1,2}has the property that for every vertex v∈V with f(v)=0,either v is adjacent to at least one vertex u for which f(u)=2,or at least two vertices u1 and u2 ...For a graph G=(V,E),a Roman{2}-dominating function f:V→{0,1,2}has the property that for every vertex v∈V with f(v)=0,either v is adjacent to at least one vertex u for which f(u)=2,or at least two vertices u1 and u2 for which f(u1)=f(u2)=1.A Roman{2}-dominating function f=(V0,V1,V2)is called independent if V1∪V2 is an independent set.The weight of an independent Roman{2}-dominating function f is the valueω(f)=Σv∈V f(v),and the independent Roman{2}-domination number i{R2}(G)is the minimum weight of an independent Roman{2}-dominating function on G.In this paper,we characterize all trees with i{R2}(T)=γ(T)+1,and give a linear time algorithm to compute the value of i{R2}(T)for any tree T.展开更多
This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate ...This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate random numbers. Based on the fact that the initial state of such setup together with its environment cannot be known, we show that the independence of its generated output cannot be guaranteed. Some consequences of this theoretical limitation are discussed.展开更多
Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I ...Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.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
京津冀地区共同构建面向国际化的开放平台,为外商直接投资(foreign direct investment,FDI)流入和创新活动的开展提供了新的机遇。基于京津冀地区各城市2011-2021年的面板数据,考察京津冀利用FDI影响自主创新的作用及机制。结果表明,京...京津冀地区共同构建面向国际化的开放平台,为外商直接投资(foreign direct investment,FDI)流入和创新活动的开展提供了新的机遇。基于京津冀地区各城市2011-2021年的面板数据,考察京津冀利用FDI影响自主创新的作用及机制。结果表明,京津冀利用FDI对其自主创新能力存在显著的促进作用,该促进作用受到高等教育学生人数的正向调节,并且伴随着地区数字经济的发展呈现非线性影响;产业结构高级化是京津冀利用FDI影响自主创新的途径之一。地区异质性结果显示,外部地区利用FDI对自主创新的促进作用大于中部核心功能区;年份异质性结果显示,伴随着协同战略的实施,京津冀地区利用FDI对自主创新能力的促进作用由不显著转变为显著促进。展开更多
It has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori.To reveal the complexity of the measured vibration signals,and provide the priori inf...It has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori.To reveal the complexity of the measured vibration signals,and provide the priori information for the blind source separation,in this paper,we propose a novel source number estimation based on independent component analysis(ICA)and clustering evaluation analysis,and then carry out experiment studies with typical mechanical vibration signals from a shell structure.The results demonstrate that the proposed ICA based source number estimation performs stably and robustly for the shell structure.展开更多
Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large...Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.展开更多
In this paper, we give the algebraic independence measures for the values ofMahler type functions in complex number field and p-adic number field, respectively.
Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem...Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.展开更多
In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,w...In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,which gets rid of NMM's important defect of rank deficiency when using higher-order local approximation functions.Several techniques are presented.In terms of mesh generation,a relationship between the quadtree structure and the mathematical mesh is established to allow a robust h-refinement.As to the condition number,a scaling based on the physical patch is much better than the classical scaling based on the mathematical patch;an overlapping width of 1%–10%can ensure a good condition number for 2nd,3rd,and 4th order local approximation functions;the small element issue can be overcome after the local approximation on small patch is replaced by that on a regular patch.On numerical accuracy,local approximation using complete polynomials is necessary for the optimal convergence rate.Two issues that may damage the convergence rate should be prevented.The first is to approximate the curved boundary of a higher-order element by overly few straight lines,and the second is excessive overlapping width.Finally,several refinement strategies are verified by numerical examples.展开更多
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
基金Supported by the Provincial Natural Science Foundation of Zhejiang(No.Y1101270)the National Natural Science Foundation of China(No.61171040)+1 种基金Ningbo University Disciplinary Project(No.XKL141038)Agilent Technologies Inc.Research Project(No.3110)
文摘This paper presents a concurrent dual-band branch-line coupler with an independently tunable center frequency. In the proposed architecture, the quarter-wavelength lines, which work at two separated bands concurrently and can be tuned in one of them, are key components. Based on the analysis of ABCD-matrix, a novel hybrid structure and a pair of varactors topology are utilized to achieve concurrent dual-band operation and independent tunability, respectively. Using this configuration, it is convenient to tune the center frequency of the upper band, while the responses of the lower band remain unaltered. To verify the proposed idea, a demonstration is implemented and the simulated results are presented.
文摘The independence number of a graph G is the maximum cardinality among all independent sets of G. For any tree T of order n ≥ 2, it is easy to see that . In addition, if there are duplicated leaves in a tree, then these duplicated leaves are all lying in every maximum independent set. In this paper, we will show that if T is a tree of order n ≥ 4 without duplicated leaves, then . Moreover, we constructively characterize the extremal trees T of order n ≥ 4, which are without duplicated leaves, achieving these upper bounds.
基金Supported by National Natural Science Foundation of China(Grant No.12171440)。
文摘For a graph G=(V,E),a Roman{2}-dominating function f:V→{0,1,2}has the property that for every vertex v∈V with f(v)=0,either v is adjacent to at least one vertex u for which f(u)=2,or at least two vertices u1 and u2 for which f(u1)=f(u2)=1.A Roman{2}-dominating function f=(V0,V1,V2)is called independent if V1∪V2 is an independent set.The weight of an independent Roman{2}-dominating function f is the valueω(f)=Σv∈V f(v),and the independent Roman{2}-domination number i{R2}(G)is the minimum weight of an independent Roman{2}-dominating function on G.In this paper,we characterize all trees with i{R2}(T)=γ(T)+1,and give a linear time algorithm to compute the value of i{R2}(T)for any tree T.
文摘This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate random numbers. Based on the fact that the initial state of such setup together with its environment cannot be known, we show that the independence of its generated output cannot be guaranteed. Some consequences of this theoretical limitation are discussed.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Graph problems of topological parameters based on the spectra of graph matrices”(2021D01C069)the National Natural Science Foundation of the People's Republic of China“The investigation of spectral properties of graph operations and their related problems”(12161085)。
文摘Let G be a connected graph of order n and m_(RD)^(L)_(G)I denote the number of reciprocal distance Laplacian eigenvaluesof G in an interval I.For a given interval I,we mainly present several bounds on m_(RD)^(L)_(G)I in terms of various structuralparameters of the graph G,including vertex-connectivity,independence number and pendant vertices.
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→∞ ).
文摘京津冀地区共同构建面向国际化的开放平台,为外商直接投资(foreign direct investment,FDI)流入和创新活动的开展提供了新的机遇。基于京津冀地区各城市2011-2021年的面板数据,考察京津冀利用FDI影响自主创新的作用及机制。结果表明,京津冀利用FDI对其自主创新能力存在显著的促进作用,该促进作用受到高等教育学生人数的正向调节,并且伴随着地区数字经济的发展呈现非线性影响;产业结构高级化是京津冀利用FDI影响自主创新的途径之一。地区异质性结果显示,外部地区利用FDI对自主创新的促进作用大于中部核心功能区;年份异质性结果显示,伴随着协同战略的实施,京津冀地区利用FDI对自主创新能力的促进作用由不显著转变为显著促进。
基金supported by China Postdoctoral Science Foundation (No. 2013M532032)National Nature Science Foundation of China (No. 51305329, 51035007)+1 种基金the Doctoral Foundation of Education Ministry of China (No. 20130201120040)the Shaanxi Postdoctoral Scientific research project
文摘It has been challenging to correctly separate the mixed signals into source components when the source number is not known a priori.To reveal the complexity of the measured vibration signals,and provide the priori information for the blind source separation,in this paper,we propose a novel source number estimation based on independent component analysis(ICA)and clustering evaluation analysis,and then carry out experiment studies with typical mechanical vibration signals from a shell structure.The results demonstrate that the proposed ICA based source number estimation performs stably and robustly for the shell structure.
文摘Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.
基金Supported by the Natural Science Foundation of Henan University（05ZDZR001）
文摘In this paper, we give the algebraic independence measures for the values ofMahler type functions in complex number field and p-adic number field, respectively.
文摘Both independence and independence-separation problems on chessboard graphs have been studied in detail, with hundreds of papers in the broader independence category, and several on the independence-separation problem variant for chessboard graphs. In this paper, the inde-pendence-separation problem is considered on the d-dimensional rook’s graph. A lower bound of k, for , is found for the independence-separation number on the d-dimensional rook’s graph, denoted by . For the case where , it is found that when n is odd and , . Conjecture and discussion are added.
基金supported by the National Natural Science Foundation of China(Grant Nos.52130905 and 52079002)。
文摘In this paper,strategies are provided for a powerful numerical manifold method(NMM)with h and p refinement in analyses of elasticity and elasto-plasticity.The new NMM is based on the concept of the independent cover,which gets rid of NMM's important defect of rank deficiency when using higher-order local approximation functions.Several techniques are presented.In terms of mesh generation,a relationship between the quadtree structure and the mathematical mesh is established to allow a robust h-refinement.As to the condition number,a scaling based on the physical patch is much better than the classical scaling based on the mathematical patch;an overlapping width of 1%–10%can ensure a good condition number for 2nd,3rd,and 4th order local approximation functions;the small element issue can be overcome after the local approximation on small patch is replaced by that on a regular patch.On numerical accuracy,local approximation using complete polynomials is necessary for the optimal convergence rate.Two issues that may damage the convergence rate should be prevented.The first is to approximate the curved boundary of a higher-order element by overly few straight lines,and the second is excessive overlapping width.Finally,several refinement strategies are verified by numerical examples.
