L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assig...L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assignment of integers to the vertices of G such that adjacent vertices receive integers which differ by at least s, and vertices that are at distance of two receive integers which differ by at least t. Given an L（s, t） -labeling f of a graph G, the L（s, t） edge span of f, βst （ G, f） = max { ｜f（u） -f（v）｜： （ u, v） ∈ E（G） } is defined. The L（ s, t） edge span of G, βst（G）, is minβst（G,f）, where the minimum runs over all L（s, t）-labelings f of G. Let T be any tree with a maximum degree of △≥2. It is proved that if 2s≥t≥0, then βst（T） =（ [△/2 ] - 1）t ＋s; if 0≤2s 〈 t and △ is even, then βst（T） = [ （△ - 1） t/2 ] ; and if 0 ≤2s 〈 t and △ is odd, then βst（T） = （△ - 1） t/2 ＋ s. Thus, the L（s, t） edge spans of the Cartesian product of two paths and of the square lattice are completely determined.展开更多
It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order...It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order to determine the initial collapse span. In the light of principal of virtual work, the simple expression of deflection, bending moment of elastic clamped plate were deduced under the condition of vertical uniform distributed load, horizontal pressure and supporting by elastic foundation, and then, the maximal bending moment expression was derived too. At the same time, the influence degree on square clamped plate by adding horizontal pressure and elastic foundation were analyzed. The results show that the effect of horizontal pressure on maximal bending moment can be ignored when the value of horizontal pressure is two orders of magni- tude less than that of coeificient of elastic stiffness existing elastic foundation.展开更多
The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equa...The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of tile problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green＇s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.展开更多
Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology...Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology of hepatitis C virus(HCV)infection.On the other hand,Kemeny’s constant(Ω)is a beneficial quantifier characterizing the universal average activities of a Markov chain.This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state si.Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues.Motivated by Levene and Loizou,we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial.Based on the achieved results,entirely results are obtained for the M鯾ius hexagonal ring network.展开更多
In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundam...In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.展开更多
BACKGROUND： Induced differentiation strategies and cytochemical properties of human embryonic stem ceils （hESCs） have been investigated. However, the electrophysiological functions of tyrosine hydroxylase （TH）-po...BACKGROUND： Induced differentiation strategies and cytochemical properties of human embryonic stem ceils （hESCs） have been investigated. However, the electrophysiological functions of tyrosine hydroxylase （TH）-positive cells dedved from hESCs remain unclear. OBJECTIVE： To investigate the differentiation efficiency of TH-positive cells from hESCs in vitro using modified four-step culture methods, including embryoid body formation, and to examine the functional characteristics of the differentiated TH-positive cells using electrophysiological techniques. DESIGN, TIME AND SETTING： Neuroelectrophysiology was performed at the Reproductive Medicine Center and Stem Cell Research Center, Peking University Third Hospital, and the Neuroscience Research Institute and Department of Neurobiology, Peking University, from September 2004 to August 2008. MATERIALS： The hESC line, PKU-1.1, a monoclonal cell line derived from a pre-implantation human blastocyst in the Reproductive Medical Center of Peking University Third Hospital. The patch clamp recording system was provided by the Neuroscience Research Institute and Department of Neurobiology, Peking University. METHODS： The hESC line was induced to differentiate into TH-positive cells in vitro using a modified four-step culture method, including the formation of embryoid body, as well as the presence of sonic hedgehog and fibroblast growth factor 8. The cell karyotype was assessed by G-banding karyotype analysis techniques and specific markers were detected immunocytochemically. Whole-cell configuration was obtained after obtaining a tight seal of over 1 GΩ. Ionic currents were detected by holding the cells at -70 mV and stepping to test voltages between -80 and 40 mV in 10-mV increments in voltage-clamp configuration. MAIN OUTCOME MEASURES： We measured the cell karyotype, specific cell markers, and the electrophysiological properties of the voltage-gated ion channels on the cell membrane of TH-positive dopaminergic cells differentiated from our hESCs line in vitro. RESULTS： The differentiated cells had a consistent appearance, and the majority of cells （〉 90%） expressed TH and β-tubulion, as well as the neural progenitor marker, nestino Cell karyotype analysis demonstrated that all of the hESCs had a stable and normal karyotype （46, XX） after differentiation. In addition, patch clamp recording showed that the 10 recorded TH-positive cells exhibited a fast inward current when the test voltage depolarized to -30 mV, and a delayed outward current when the test voltage depolarized to -10 mV. The peak of inward current was obtained at voltage between 10 mV and 0 mV, while the peak of outward current was obtained at 40 mV. The average peak of inward current density was （ -50.05 ± 15.50） pA/pF, and the average peak of outward current density was （41.98 ± 13.55） pA/pE CONCLUSION： More than 90% of the differentiated hESC-derived cells induced by the modified four-step culture method exhibit dopaminergic neuronal properties, including general electrophysiological functional properties, such as functional potassium and sodium channels.展开更多
Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, ...Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of Fk?(G)? , Rk?(G) , r-iterative graph ,Frk?(G)? and r-iterative graph , where k?≥2 and r?≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.展开更多
Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution...Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.展开更多
基金The National Natural Science Foundation of China(No10671033)Southeast University Science Foundation ( NoXJ0607230)
文摘L（ s, t）-labeling is a variation of graph coloring which is motivated by a special kind of the channel assignment problem. Let s and t be any two nonnegative integers. An L （s, t）-labeling of a graph G is an assignment of integers to the vertices of G such that adjacent vertices receive integers which differ by at least s, and vertices that are at distance of two receive integers which differ by at least t. Given an L（s, t） -labeling f of a graph G, the L（s, t） edge span of f, βst （ G, f） = max { ｜f（u） -f（v）｜： （ u, v） ∈ E（G） } is defined. The L（ s, t） edge span of G, βst（G）, is minβst（G,f）, where the minimum runs over all L（s, t）-labelings f of G. Let T be any tree with a maximum degree of △≥2. It is proved that if 2s≥t≥0, then βst（T） =（ [△/2 ] - 1）t ＋s; if 0≤2s 〈 t and △ is even, then βst（T） = [ （△ - 1） t/2 ] ; and if 0 ≤2s 〈 t and △ is odd, then βst（T） = （△ - 1） t/2 ＋ s. Thus, the L（s, t） edge spans of the Cartesian product of two paths and of the square lattice are completely determined.
基金Supported by the National Natural Science Foundation of China （41071273） the Special Research Fund for the Doctoral Program of Higher Education of China （200090095110002）
文摘It is critical for the material to be of active supporting capacity before initial collapse ot mare root wltn supermgn water material backfill mining, and the maximum bending moment should be first calculated in order to determine the initial collapse span. In the light of principal of virtual work, the simple expression of deflection, bending moment of elastic clamped plate were deduced under the condition of vertical uniform distributed load, horizontal pressure and supporting by elastic foundation, and then, the maximal bending moment expression was derived too. At the same time, the influence degree on square clamped plate by adding horizontal pressure and elastic foundation were analyzed. The results show that the effect of horizontal pressure on maximal bending moment can be ignored when the value of horizontal pressure is two orders of magni- tude less than that of coeificient of elastic stiffness existing elastic foundation.
文摘The quasi-Green＇s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green＇s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of tile problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green＇s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.
文摘Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology of hepatitis C virus(HCV)infection.On the other hand,Kemeny’s constant(Ω)is a beneficial quantifier characterizing the universal average activities of a Markov chain.This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state si.Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues.Motivated by Levene and Loizou,we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial.Based on the achieved results,entirely results are obtained for the M鯾ius hexagonal ring network.
文摘In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.
基金the National Natural Science Foundation of China, No. 30672239
文摘BACKGROUND： Induced differentiation strategies and cytochemical properties of human embryonic stem ceils （hESCs） have been investigated. However, the electrophysiological functions of tyrosine hydroxylase （TH）-positive cells dedved from hESCs remain unclear. OBJECTIVE： To investigate the differentiation efficiency of TH-positive cells from hESCs in vitro using modified four-step culture methods, including embryoid body formation, and to examine the functional characteristics of the differentiated TH-positive cells using electrophysiological techniques. DESIGN, TIME AND SETTING： Neuroelectrophysiology was performed at the Reproductive Medicine Center and Stem Cell Research Center, Peking University Third Hospital, and the Neuroscience Research Institute and Department of Neurobiology, Peking University, from September 2004 to August 2008. MATERIALS： The hESC line, PKU-1.1, a monoclonal cell line derived from a pre-implantation human blastocyst in the Reproductive Medical Center of Peking University Third Hospital. The patch clamp recording system was provided by the Neuroscience Research Institute and Department of Neurobiology, Peking University. METHODS： The hESC line was induced to differentiate into TH-positive cells in vitro using a modified four-step culture method, including the formation of embryoid body, as well as the presence of sonic hedgehog and fibroblast growth factor 8. The cell karyotype was assessed by G-banding karyotype analysis techniques and specific markers were detected immunocytochemically. Whole-cell configuration was obtained after obtaining a tight seal of over 1 GΩ. Ionic currents were detected by holding the cells at -70 mV and stepping to test voltages between -80 and 40 mV in 10-mV increments in voltage-clamp configuration. MAIN OUTCOME MEASURES： We measured the cell karyotype, specific cell markers, and the electrophysiological properties of the voltage-gated ion channels on the cell membrane of TH-positive dopaminergic cells differentiated from our hESCs line in vitro. RESULTS： The differentiated cells had a consistent appearance, and the majority of cells （〉 90%） expressed TH and β-tubulion, as well as the neural progenitor marker, nestino Cell karyotype analysis demonstrated that all of the hESCs had a stable and normal karyotype （46, XX） after differentiation. In addition, patch clamp recording showed that the 10 recorded TH-positive cells exhibited a fast inward current when the test voltage depolarized to -30 mV, and a delayed outward current when the test voltage depolarized to -10 mV. The peak of inward current was obtained at voltage between 10 mV and 0 mV, while the peak of outward current was obtained at 40 mV. The average peak of inward current density was （ -50.05 ± 15.50） pA/pF, and the average peak of outward current density was （41.98 ± 13.55） pA/pE CONCLUSION： More than 90% of the differentiated hESC-derived cells induced by the modified four-step culture method exhibit dopaminergic neuronal properties, including general electrophysiological functional properties, such as functional potassium and sodium channels.
文摘Given a simple connected graph G, we consider two iterated constructions associated with G: Fk (G) and Rk (G) . In this paper, we completely obtain the normalized Laplacian spectrum of Fk (G) and Rk (G) , with k ≥2, respectively. As applications, we derive the closed-formula of the multiplicative degree-Kirchhoff index, the Kemeny’s constant, and the number of spanning trees of Fk?(G)? , Rk?(G) , r-iterative graph ,Frk?(G)? and r-iterative graph , where k?≥2 and r?≥1 . Our results extend those main results proposed by Pan et al. (2018), and we provide a method to characterize the normalized Laplacian spectrum of iteratively constructed complex graphs.
文摘Solving for currents of an electrical circuit with resistances and batteries has always been the ultimate test of proper understanding of Kirchoff’s rules. Yet, it is hardly ever emphasized that a systematic solution of more complex cases requires good understanding of the relevant part of Graph theory. Even though this is usually not covered by Physics’ curriculum, it may still be of interest to some teachers and their mathematically inclined students, who may want to learn details of the rigorous approach. The purpose of this article is to provide a concise derivation of a linear set of equations leading to a unique solution of the problem at hand. We also present a simple computer program which builds such a solution for circuits of any textbook size.
