Let G be a graph,for any u∈V(G),let N(u) denote the neighborhood of u and d(u)=|N(u)| be the degree of u.For any UV(G),let N(U)=∪_~u∈U N(u), and d(U)=|N(U)|.A graph G is called claw-free if it has no induced subgra...Let G be a graph,for any u∈V(G),let N(u) denote the neighborhood of u and d(u)=|N(u)| be the degree of u.For any UV(G),let N(U)=∪_~u∈U N(u), and d(U)=|N(U)|.A graph G is called claw-free if it has no induced subgraph isomorphic to K_~1,3 .One of the fundamental results concerning cycles in claw-free graphs is due to Tian Feng,et al.: Let G be a 2-connected claw-free graph of order n,and d(u)+d(v)+d(w)≥n-2 for every independent vertex set {u,v,w} of G, then G is Hamiltonian. It is proved that,for any three positive integers s,t and w,such that if G is a (s+t+w-1)-connected claw-free graph of order n,and d(S)+d(T)+d(W)>n-(s+t+w) for every three disjoint independent vertex sets S,T,W with |S|=s,|T|=t,|W|=w,and S∪T∪W is also independent,then G is Hamiltonian.Other related results are obtained too.展开更多
Let G be a graph. An independent set Y in G is called an essential independent set (or essential set for simplicity) if there is {yi , y2} Y such that dist(y1 , y2) - 2. For integer t > 0, let It(G) = {Y| Y is an i...Let G be a graph. An independent set Y in G is called an essential independent set (or essential set for simplicity) if there is {yi , y2} Y such that dist(y1 , y2) - 2. For integer t > 0, let It(G) = {Y| Y is an independent set of G, |Y| = t}, It(G) = {Y|Y is an essential set of G, |Y| = t}. For ∈E It(G), let si(y) = |{v|v ∈V(G), |N(v) n Y| = i}|(i = 0, 1,…, t). Let X, Y g V(G). Define dist(X, Y) = dist(u, v), n(Y) = |{v|v ∈V(G), dist({v}, Y) ≤ 2}|. A non-negative rational sequence (a1，a2,…, ak+1) (k ≥2) is called an LTW-sequence, if it satisfies 1) a1 ≤ 1; 2) for arbitrary i1, i2,…，ih. ∈{2,3,……, k + 1}, The main new results of this paper are as follows: Let (a1， a2，… ak+1) be all LTW-sequence, and k ≥ 2. If G is a k-connected graph, and then G has a Hamilton cycle; if G is a (k + 1)-connected graph and for each then G is Hamilton-connected. The existing results are generalized by these since Ik+1(G) is replaced by I(G). We introduce a new technique of T-insertion in this paper， by using the T-vertex inserting lemmas we give a unified proof for a graph to be hamiltonian or Hamilton-connected.展开更多
BCube is one kind of important data center networks.Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks.So far,there have been many results concerning fault-tolerant Hami...BCube is one kind of important data center networks.Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks.So far,there have been many results concerning fault-tolerant Hamiltonicity and fault-tolerant Hamiltonian connectivity in some data center networks.However,these results only consider faulty edges and faulty servers.In this paper,we study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity of BCube(n,k)under considering faulty servers,faulty links/edges,and faulty switches.For any integers n≥2 and k≥0,let BCn,k be the logic structure of BCube(n,k)and F be the union of faulty elements of BCn,k,Let fv/fe,and fs be the number of faulty servers,faulty edges,and faulty switches of BCiLbe(n,k),respectively.We show that BCnik-F is fault-tolerant Hamiltonian if fv+fe+(n-1)/s≤(n-1)(k+1)-2 and BCn,k-F is fault-tolerant Hamiltonian-connected ifv,+fe+(n-1)fs≤(n-1)(k+1)-3.To the best of our knowledge,this paper is the first work which takes faulty switches into account to study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity in data center networks.展开更多
Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traver...Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.展开更多
BACKGROUND Depression is a common and serious psychological condition,which seriously affects individual well-being and functional ability.Traditional treatment methods include drug therapy and psychological counselin...BACKGROUND Depression is a common and serious psychological condition,which seriously affects individual well-being and functional ability.Traditional treatment methods include drug therapy and psychological counseling;however,these methods have different degrees of side effects and limitations.In recent years,nonconvulsive electrotherapy(NET)has attracted increasing attention as a noninvasive treatment method.However,the clinical efficacy and potential mechanism of NET on depression are still unclear.We hypothesized that NET has a positive clinical effect in the treatment of depression,and may have a regulatory effect on serum inflammatory factors during treatment.AIM To assess the effects of NET on depression and analyze changes in serum inflammatory factors.METHODS This retrospective study enrolled 140 patients undergoing treatment for depression between May 2017 and June 2022,the observation group that received a combination of mindfulness-based stress reduction(MBSR)and NET treatment(n=70)and the control group that only received MBSR therapy(n=70).The clinical effectiveness of the treatment was evaluated by assessing various factors,including the Hamilton Depression Scale(HAMD)-17,self-rating idea of suicide scale(SSIOS),Pittsburgh Sleep Quality Index(PSQI),and levels of serum inflammatory factors before and after 8 wk of treatment.The quality of life scores between the two groups were compared.Comparisons were made using t and χ^(2) tests.RESULTS After 8 wk of treatment,the observation group exhibited a 91.43%overall effectiveness rate which was higher than that of the control group which was 74.29%(64 vs 52,χ^(2)=7.241;P<0.05).The HAMD,SSIOS,and PSQI scores showed a significant decrease in both groups.Moreover,the observation group had lower scores than the control group(10.37±2.04 vs 14.02±2.16,t=10.280;1.67±0.28 vs 0.87±0.12,t=21.970;5.29±1.33 vs 7.94±1.35,t=11.700;P both<0.001).Additionally,there was a notable decrease in the IL-2,IL-1β,and IL-6 in both groups after treatment.Furthermore,the observation group exhibited superior serum inflammatory factors compared to the control group(70.12±10.32 vs 102.24±20.21,t=11.840;19.35±2.46 vs 22.27±2.13,t=7.508;32.25±4.6 vs 39.42±4.23,t=9.565;P both<0.001).Moreover,the observation group exhibited significantly improved quality of life scores compared to the control group(Social function:19.25±2.76 vs 16.23±2.34;Emotions:18.54±2.83 vs 12.28±2.16;Environment:18.49±2.48 vs 16.56±3.44;Physical health:19.53±2.39 vs 16.62±3.46;P both<0.001)after treatment.CONCLUSION MBSR combined with NET effectively alleviates depression,lowers inflammation(IL-2,IL-1β,and IL-6),reduces suicidal thoughts,enhances sleep,and improves the quality of life of individuals with depression.展开更多
Based on the ideas in[9],an integer d<sup>0</sup>（v）,called the implicit degree of v whichsatisfies d<sup>0</sup>（v）≥d（v）,is associated with each vertex v of a graph G.It is proved that ...Based on the ideas in[9],an integer d<sup>0</sup>（v）,called the implicit degree of v whichsatisfies d<sup>0</sup>（v）≥d（v）,is associated with each vertex v of a graph G.It is proved that if theimplicit degree sequence d<sub>1</sub><sup>0</sup>,d<sub>2</sub><sup>0</sup>,…,d<sub>n</sub><sup>0</sup>（where d<sub>1</sub><sup>0</sup>≤d<sub>2</sub><sup>0</sup>≤…≤d<sub>n</sub><sup>0</sup>）of a simple graph G on n≥3vertices satisfiesd<sub>i</sub><sup>0</sup>≤i【n/2（?）d<sub>n-i</sub><sup>0</sup>≥n-i,then G is hamiltonian.This is an improvement of the well-known theorem of Chvatal（[4]）.展开更多
A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show t...A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show that if G is.3-connected claw-free graph and(1)if for each vertex V the set of venices at distance three from v doesn’tcontain and independent subset of size three,then G is hamiltonian;(2) if G contains no induced subgraph with degree sequence(1,1,1,2,2,2,3,3,3),so that ear vertel of degree is adjacent to a vertex of degree i + 1 for i=1,2,then G is hamiltonoan. Furthermore,we obtain a generalization of both(1) and(2),in which the graphs F1 and F2coatain an the known forbidded subgraphs given in[3] as indeced subgraphs.展开更多
In this note, we denote by G a graph with order n, by V and E the vertex set andedge set of G, respectively. V<sub>0</sub>={v∈V|d（v）≥n/2}, V<sub>0</sub>=V\V<sub>0</sub>. Let H b...In this note, we denote by G a graph with order n, by V and E the vertex set andedge set of G, respectively. V<sub>0</sub>={v∈V|d（v）≥n/2}, V<sub>0</sub>=V\V<sub>0</sub>. Let H be a subgraph ofG. For simplicity, we also use H to denote the vertex set of it. For a∈V S, TV,展开更多
文摘Let G be a graph,for any u∈V(G),let N(u) denote the neighborhood of u and d(u)=|N(u)| be the degree of u.For any UV(G),let N(U)=∪_~u∈U N(u), and d(U)=|N(U)|.A graph G is called claw-free if it has no induced subgraph isomorphic to K_~1,3 .One of the fundamental results concerning cycles in claw-free graphs is due to Tian Feng,et al.: Let G be a 2-connected claw-free graph of order n,and d(u)+d(v)+d(w)≥n-2 for every independent vertex set {u,v,w} of G, then G is Hamiltonian. It is proved that,for any three positive integers s,t and w,such that if G is a (s+t+w-1)-connected claw-free graph of order n,and d(S)+d(T)+d(W)>n-(s+t+w) for every three disjoint independent vertex sets S,T,W with |S|=s,|T|=t,|W|=w,and S∪T∪W is also independent,then G is Hamiltonian.Other related results are obtained too.
文摘Let G be a graph. An independent set Y in G is called an essential independent set (or essential set for simplicity) if there is {yi , y2} Y such that dist(y1 , y2) - 2. For integer t > 0, let It(G) = {Y| Y is an independent set of G, |Y| = t}, It(G) = {Y|Y is an essential set of G, |Y| = t}. For ∈E It(G), let si(y) = |{v|v ∈V(G), |N(v) n Y| = i}|(i = 0, 1,…, t). Let X, Y g V(G). Define dist(X, Y) = dist(u, v), n(Y) = |{v|v ∈V(G), dist({v}, Y) ≤ 2}|. A non-negative rational sequence (a1，a2,…, ak+1) (k ≥2) is called an LTW-sequence, if it satisfies 1) a1 ≤ 1; 2) for arbitrary i1, i2,…，ih. ∈{2,3,……, k + 1}, The main new results of this paper are as follows: Let (a1， a2，… ak+1) be all LTW-sequence, and k ≥ 2. If G is a k-connected graph, and then G has a Hamilton cycle; if G is a (k + 1)-connected graph and for each then G is Hamilton-connected. The existing results are generalized by these since Ik+1(G) is replaced by I(G). We introduce a new technique of T-insertion in this paper， by using the T-vertex inserting lemmas we give a unified proof for a graph to be hamiltonian or Hamilton-connected.
基金supported by the National Natural Science Foundation of China under Grant Nos.U1905211,61572337,and 61972272Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No.1701173B+1 种基金Application Foundation Research of Suzhou of China under Grant No.SYG201653a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘BCube is one kind of important data center networks.Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks.So far,there have been many results concerning fault-tolerant Hamiltonicity and fault-tolerant Hamiltonian connectivity in some data center networks.However,these results only consider faulty edges and faulty servers.In this paper,we study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity of BCube(n,k)under considering faulty servers,faulty links/edges,and faulty switches.For any integers n≥2 and k≥0,let BCn,k be the logic structure of BCube(n,k)and F be the union of faulty elements of BCn,k,Let fv/fe,and fs be the number of faulty servers,faulty edges,and faulty switches of BCiLbe(n,k),respectively.We show that BCnik-F is fault-tolerant Hamiltonian if fv+fe+(n-1)/s≤(n-1)(k+1)-2 and BCn,k-F is fault-tolerant Hamiltonian-connected ifv,+fe+(n-1)fs≤(n-1)(k+1)-3.To the best of our knowledge,this paper is the first work which takes faulty switches into account to study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity in data center networks.
基金Project supported by the Heilongjiang Province Natural Science Foundation Joint Guidance Project,China (Grant No.LH2020F022)the Fundamental Research Funds for the Central Universities,China (Grant No.3072022CF0801)。
文摘Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.
基金Supported by Guangdong Provincial Medical Scientific Research Fund Project,No.B2016109.
文摘BACKGROUND Depression is a common and serious psychological condition,which seriously affects individual well-being and functional ability.Traditional treatment methods include drug therapy and psychological counseling;however,these methods have different degrees of side effects and limitations.In recent years,nonconvulsive electrotherapy(NET)has attracted increasing attention as a noninvasive treatment method.However,the clinical efficacy and potential mechanism of NET on depression are still unclear.We hypothesized that NET has a positive clinical effect in the treatment of depression,and may have a regulatory effect on serum inflammatory factors during treatment.AIM To assess the effects of NET on depression and analyze changes in serum inflammatory factors.METHODS This retrospective study enrolled 140 patients undergoing treatment for depression between May 2017 and June 2022,the observation group that received a combination of mindfulness-based stress reduction(MBSR)and NET treatment(n=70)and the control group that only received MBSR therapy(n=70).The clinical effectiveness of the treatment was evaluated by assessing various factors,including the Hamilton Depression Scale(HAMD)-17,self-rating idea of suicide scale(SSIOS),Pittsburgh Sleep Quality Index(PSQI),and levels of serum inflammatory factors before and after 8 wk of treatment.The quality of life scores between the two groups were compared.Comparisons were made using t and χ^(2) tests.RESULTS After 8 wk of treatment,the observation group exhibited a 91.43%overall effectiveness rate which was higher than that of the control group which was 74.29%(64 vs 52,χ^(2)=7.241;P<0.05).The HAMD,SSIOS,and PSQI scores showed a significant decrease in both groups.Moreover,the observation group had lower scores than the control group(10.37±2.04 vs 14.02±2.16,t=10.280;1.67±0.28 vs 0.87±0.12,t=21.970;5.29±1.33 vs 7.94±1.35,t=11.700;P both<0.001).Additionally,there was a notable decrease in the IL-2,IL-1β,and IL-6 in both groups after treatment.Furthermore,the observation group exhibited superior serum inflammatory factors compared to the control group(70.12±10.32 vs 102.24±20.21,t=11.840;19.35±2.46 vs 22.27±2.13,t=7.508;32.25±4.6 vs 39.42±4.23,t=9.565;P both<0.001).Moreover,the observation group exhibited significantly improved quality of life scores compared to the control group(Social function:19.25±2.76 vs 16.23±2.34;Emotions:18.54±2.83 vs 12.28±2.16;Environment:18.49±2.48 vs 16.56±3.44;Physical health:19.53±2.39 vs 16.62±3.46;P both<0.001)after treatment.CONCLUSION MBSR combined with NET effectively alleviates depression,lowers inflammation(IL-2,IL-1β,and IL-6),reduces suicidal thoughts,enhances sleep,and improves the quality of life of individuals with depression.
文摘Based on the ideas in[9],an integer d<sup>0</sup>（v）,called the implicit degree of v whichsatisfies d<sup>0</sup>（v）≥d（v）,is associated with each vertex v of a graph G.It is proved that if theimplicit degree sequence d<sub>1</sub><sup>0</sup>,d<sub>2</sub><sup>0</sup>,…,d<sub>n</sub><sup>0</sup>（where d<sub>1</sub><sup>0</sup>≤d<sub>2</sub><sup>0</sup>≤…≤d<sub>n</sub><sup>0</sup>）of a simple graph G on n≥3vertices satisfiesd<sub>i</sub><sup>0</sup>≤i【n/2（?）d<sub>n-i</sub><sup>0</sup>≥n-i,then G is hamiltonian.This is an improvement of the well-known theorem of Chvatal（[4]）.
文摘A graph is claw-free if it contains no induced subgraph isomorphic to a K1,3.This paper studies hamiltonicity in 3-connected claw-free graphs.Four generation of Shepherd’s result[4] are obtained.For example,we show that if G is.3-connected claw-free graph and(1)if for each vertex V the set of venices at distance three from v doesn’tcontain and independent subset of size three,then G is hamiltonian;(2) if G contains no induced subgraph with degree sequence(1,1,1,2,2,2,3,3,3),so that ear vertel of degree is adjacent to a vertex of degree i + 1 for i=1,2,then G is hamiltonoan. Furthermore,we obtain a generalization of both(1) and(2),in which the graphs F1 and F2coatain an the known forbidded subgraphs given in[3] as indeced subgraphs.
文摘In this note, we denote by G a graph with order n, by V and E the vertex set andedge set of G, respectively. V<sub>0</sub>={v∈V|d（v）≥n/2}, V<sub>0</sub>=V\V<sub>0</sub>. Let H be a subgraph ofG. For simplicity, we also use H to denote the vertex set of it. For a∈V S, TV,
