In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests mo...In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].展开更多
Traveling is one major theme of Fitzgerald's novel Tender Is the Night. This fashionable activity for the 1920 s Americans is represented in the novel as ostensibly bearing different meanings to the main character...Traveling is one major theme of Fitzgerald's novel Tender Is the Night. This fashionable activity for the 1920 s Americans is represented in the novel as ostensibly bearing different meanings to the main characters, but a deeper look would reveal that it is unanimously resorted to as a weapon against the spiritual barrenness caused by the cult of business, and more importantly, as a way to the experience of rootedness.展开更多
The static drill rooted nodular pile is a new type of pile foundation consisting of precast nodular pile and the surrounding cemented soil.This composite pile has a relatively high bearing capacity and the mud polluti...The static drill rooted nodular pile is a new type of pile foundation consisting of precast nodular pile and the surrounding cemented soil.This composite pile has a relatively high bearing capacity and the mud pollution will be largely reduced during the construction process by using this type of pile.In order to investigate the bearing capacity and load transfer mechanism of this pile,a group of experiments were conducted to provide a comparison between this new pile and the bored pile.The axial force of a precast nodular pile was also measured by the strain gauges installed on the pile to analyze the distribution of the axial force of the nodular pile and the skin friction supported by the surrounding soil,then 3D models were built by using the ABAQUS finite element program to investigate the load transfer mechanism of this composite pile in detail.By combining the results of field tests and the finite element method,the outcome showed that the bearing capacity of a static drill rooted nodular pile is higher than the bored pile,and that this composite pile will form a double stress dispersion system which will not only confirm the strength of the pile,but also make the skin friction to be fully mobilized.The settlement of this composite pile is mainly controlled by the precast nodular pile;meanwhile,the nodular pile and the surrounding cemented soil can be considered as deformation compatibility during the loading process.The nodes on the nodular pile play an important role during the load transfer process,the shear strength of the interface between the cemented soil and the soil of the static drill rooted pile is larger than that of the bored pile.展开更多
It is well known that any kind of exact enumerations of rooted maps on nonplanar surface is quite difficult. This paper presents a functional equation for rooted Eulerian maps on the projective plane. A parametric exp...It is well known that any kind of exact enumerations of rooted maps on nonplanar surface is quite difficult. This paper presents a functional equation for rooted Eulerian maps on the projective plane. A parametric expression, through which an exact enumeration by root-valency and the number of edges of maps may be determined, is obtained.展开更多
The integration of wind turbines(WTs)in variable speed drive systems belongs to the main factors causing lowstability in electrical networks.Therefore,in order to avoid this issue,WTs hybridization with a storage syst...The integration of wind turbines(WTs)in variable speed drive systems belongs to the main factors causing lowstability in electrical networks.Therefore,in order to avoid this issue,WTs hybridization with a storage system is a mandatory.This paper investigates WT system operating at variable speed.The system contains of a permanent magnet synchronous generator(PMSG)supported by a battery storage system(BSS).To enhance the quality of active and reactive power injected into the network,direct power control(DPC)scheme utilizing space-vector modulation(SVM)technique based on proportional-integral(PI)control is proposed.Meanwhile,to improve the rendition of this method(DPC-SVM-PI),the rooted tree optimization technique(RTO)algorithm-based controller parameter identification is used to achieve PI optimal gains.To compare the performance ofRTO-based controllers,they were implemented and tested along with some other popular controllers under different working conditions.The obtained results have shown the supremacy of the suggested PIRTO algorithm compared to competing controllers regarding total harmonic distortion(THD),overshoot percentage,settling time,rise time,average active power value,overall efficiency,and active power steadystate error.展开更多
There are 36 counties affirmed to be aid-poverty-development county in the early 21st century, which distribute around the circumferential mountain of Sichuan Basin, According to the topographic features and the distr...There are 36 counties affirmed to be aid-poverty-development county in the early 21st century, which distribute around the circumferential mountain of Sichuan Basin, According to the topographic features and the distribution of nationality, these aid-poverty-development counties can be classified into 4 depressed-regions. Study shows that regional poverty performance of 4 depressed-regions not only has many commons in the field of regional economic structure and industry structure, which is far behind the average development performance of Sichuan in the field of economic sum per capita such as GDP, farmer net income per capita as well as retail scale consumer goods, it is also quite different related to infrastructure and social development within 4 depressed-regions. Regional Poverty is chronically resulted in interaction of the multi-factors. Natural condition constraint is the basic factor contributed to regional poverty, policy influences play key role, the poor culture is inherent factor to regional poverty and the marginal locations play important role.展开更多
In order to provide theoretical basis and technical support for the afforestation and artificial water supply of P.szechuanica in arid areas,the characteristics of water consumption of P.szechuanica were explored,and ...In order to provide theoretical basis and technical support for the afforestation and artificial water supply of P.szechuanica in arid areas,the characteristics of water consumption of P.szechuanica were explored,and the law of water demand of P.szechuanica was grasped.In this paper,potted seedlings of 1-0 rooted cuttings of P.szechuanica were taken as research objects,and change situation of water consumption under different water control gradients was measured regularly by using weighing method,further analyzing dynamic change of water consumption of P.szechuanica and revealing water demand law of 1-0 rooted cuttings of P.szechuanica.The results showed that total change of water consumption of 1-0 rooted cuttings of P.szechuanica had"slow-fast-slow-fast"double-peak trend in the growth period of the current year,and corresponded with univariate linear relation(R^(2)=0.7137),with significant difference.In whole growth period,water consumption in August was the highest,which was 2.7 times of that in June and July and 1.5 times of that after September.In different water control treatments,the dynamic changes of daily and monthly water consumption were significantly different.In seven water control treatments,monthly water consumption was between(6315.95±1690.70)and(10105.28±3065.30)g/month,and mean was(8211.07±2308.23)g/month.With intensification of water control treatment,water consumption increased,but there was no seedling death due to water shortage.P.szechuanica has great plasticity in water demand,and can survive in both arid and humid environments.Meanwhile,it is revealed that P.szechuanica is the most widely distributed tree species in the region.展开更多
This paper provides a functional equation astisfied by the generating function for enumerating rooted loopless planar maps with vertex partition. A kind of applications in enumerating, by providing explicit formulae, ...This paper provides a functional equation astisfied by the generating function for enumerating rooted loopless planar maps with vertex partition. A kind of applications in enumerating, by providing explicit formulae, a type of rooted loopless planar maps with the maximum valency of vertices given are described. Meanwhile, the functional equation for enumerating rooted loopless planar maps (connected) with the edge number and the valency of root-vertex as the parameters is also derived directly.展开更多
Sixteen one-year-old dogs were used in our experiment.We rotated the maxillary secondincisors of the dogs,applying a force of 100g and a moment of 550g·mm.The duration of theexperiment varied from 72h to 8 weeks....Sixteen one-year-old dogs were used in our experiment.We rotated the maxillary secondincisors of the dogs,applying a force of 100g and a moment of 550g·mm.The duration of theexperiment varied from 72h to 8 weeks.Activation was performed once every 2 weeks and the impressions were taken in order to measure the angles of rotation.The results of our experiment showthat the rotation rate of single-rooted tooth in dogs is 3.04/week.The graph shows the form ofgradual stairs.This paper introduces a new specialized experimental apparatus for tooth rotation.The angles of rotation are measured geometrically.展开更多
This paper focused on the water relations of two halophytes differing in photosynthetic pathway, phe- notype, and life cycle： Karelinia caspica （Pall.） Less. （C3, deep-rooted perennial Asteraceae grass） and Atrip...This paper focused on the water relations of two halophytes differing in photosynthetic pathway, phe- notype, and life cycle： Karelinia caspica （Pall.） Less. （C3, deep-rooted perennial Asteraceae grass） and Atriplex tatarica L. （C4, shallow-rooted annual Chenopodiaceae grass）. Gas exchange, leaf water potential, and growth characteristics were investigated in two growing seasons in an arid area of Xinjiang to explore the physiological adaptability of the two halophytes. Both K. caspica and A. tatarica showed midday depression of transpiration, in- dicating that they were strong xerophytes and weak midday depression types. The roots of A. tatarica were con- centrated mainly in the 0-60 cm soil layer, and the leaf water potential （~L） increased sharply in the 0-20 cm layer due to high soil water content, suggesting that the upper soil was the main water source. On the other hand, K. caspica had a rooting depth of about 1.5 m and a larger root/shoot ratio, which confirmed that this species uptakes water mainly from deeper soil layer. Although A. tatarica had lower transpiration water consumption, higher water use efficiency （WUE）, and less water demand at the same leaf water potential, it showed larger water stress impact than K. caspica, indicating that the growth of A. tatarica was restricted more than that of K. caspica when there was no rainfall recharge. As a shallow-rooted C4 species, A. tatarica displayed lower stomatal conductance, which could to some extent reduce transpiration water loss and maintain leaf water potential steadily. In contrast, the deep-rooted C3 species K. caspica had a larger root/shoot ratio that was in favor of exploiting groundwater. We concluded that C3 species （K. caspica） tapes water and C4 species （A. tatarica） reduces water loss to survive in the arid and saline conditions. The results provided a case for the phenotype theory of Schwinning and Ehleringer on halophytic plants.展开更多
This work analyzes heat transfer through a wall containing triangular fins partially embedded in its volume. The coupled heat diffusion equations governing each constituent are solved numericallyusing an iterative fin...This work analyzes heat transfer through a wall containing triangular fins partially embedded in its volume. The coupled heat diffusion equations governing each constituent are solved numericallyusing an iterative finite volume method. A well bracketed effectiveness of the combined system that suits wide range of applications is analytically derived. Good agreement between the numerical and the analytical results is attained. It is found that the fin-root can act simultaneously as a heat sink and heat source for the wall. The heat transfer rate through the combined system is clearly seen to be maximized at a specific fin-root length. The maximum reported heat transfer rate through the triangular rooted-finned wall is found to be at most 90% above that for the rootless fin case at wall Biot number of 1.54. This percentage is noticed to decrease as the wall Biot number decreases. At that Biot number, the maximum heat transfer rate through the combined system reaches 150% above that through the plain wall. As a result of this work, it is recommended to utilize the triangular rooted-fin as a heat transfer enhancer for high mechanical strength structures exposed to highly convective fluid streams.展开更多
We introduce an algebraic structure allowing us to describe subgraphs of a regular rooted tree. Its elements are called structure polynomials, and they are in a one- to-one correspondence with the set of all subgraphs...We introduce an algebraic structure allowing us to describe subgraphs of a regular rooted tree. Its elements are called structure polynomials, and they are in a one- to-one correspondence with the set of all subgraphs of the tree. We define two operations, the sum and the product of structure polynomials, giving a graph interpretation of them. Then we introduce an equivalence relation between polynomials, using the action of the full automorphism group of the tree, and we count equivalence classes of subgraphs modulo this equivalence. We also prove that this action gives rise to symmetric Gelfand pairs. Finally, when the regularity degree of the tree is a prime p, we regard each level of the tree as a finite dimensional vector space over the finite field Fp, and we are able to completely characterize structure polynomials corresponding to subgraphs whose leaf set is a vector subspace.展开更多
An independent set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial AΣx^(|A|), where the sum is over all independent sets A of G. In 1987, Alavi,Malde, Schwe...An independent set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial AΣx^(|A|), where the sum is over all independent sets A of G. In 1987, Alavi,Malde, Schwenk and Erd os conjectured that the independence polynomial of any tree or forest is unimodal.Although this unimodality conjecture has attracted many researchers’ attention, it is still open. Recently, Basit and Galvin even asked a much stronger question whether the independence polynomial of every tree is ordered log-concave. Note that if a polynomial has only negative real zeros then it is ordered log-concave and unimodal.In this paper, we observe real-rootedness of independence polynomials of rooted products of graphs. We find some trees whose rooted product preserves real-rootedness of independence polynomials. In consequence, starting from any graph whose independence polynomial has only real zeros, we can obtain an infinite family of graphs whose independence polynomials have only real zeros. In particular, applying it to trees or forests, we obtain that their independence polynomials are unimodal and ordered log-concave.展开更多
We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expecte...We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.展开更多
After spinal cord injury,impairment of the sensorimotor circuit can lead to dysfunction in the motor,sensory,proprioceptive,and autonomic nervous systems.Functional recovery is often hindered by constraints on the tim...After spinal cord injury,impairment of the sensorimotor circuit can lead to dysfunction in the motor,sensory,proprioceptive,and autonomic nervous systems.Functional recovery is often hindered by constraints on the timing of interventions,combined with the limitations of current methods.To address these challenges,various techniques have been developed to aid in the repair and reconstruction of neural circuits at different stages of injury.Notably,neuromodulation has garnered considerable attention for its potential to enhance nerve regeneration,provide neuroprotection,restore neurons,and regulate the neural reorganization of circuits within the cerebral cortex and corticospinal tract.To improve the effectiveness of these interventions,the implementation of multitarget early interventional neuromodulation strategies,such as electrical and magnetic stimulation,is recommended to enhance functional recovery across different phases of nerve injury.This review concisely outlines the challenges encountered following spinal cord injury,synthesizes existing neurostimulation techniques while emphasizing neuroprotection,repair,and regeneration of impaired connections,and advocates for multi-targeted,task-oriented,and timely interventions.展开更多
All maps we deal with in this note are rooted planar ones, which, in brief, are called maps. Most of terminologies here come from Refs. [1—3]. The purpose of this note is to determine the asymptotic enumerations base...All maps we deal with in this note are rooted planar ones, which, in brief, are called maps. Most of terminologies here come from Refs. [1—3]. The purpose of this note is to determine the asymptotic enumerations based on the enumerations in [1, 2]. Bender and Richmond gave a survey of the asymptotic enumeration. New asymptotic enumerations here can be considered as a complement and improvement of the survey.展开更多
A summation free formula for enumerating rooted nonseparable outerplanar maps with a face partition given is herein presented. As its corollaries, some summation free formulae for the bipartite and the simple cases ar...A summation free formula for enumerating rooted nonseparable outerplanar maps with a face partition given is herein presented. As its corollaries, some summation free formulae for the bipartite and the simple cases are also derived. Moreover, the formula for planted plane trees according to a given vertex partition is demonstrated in a new way.展开更多
In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two ...In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.展开更多
基金Supported by NSFC(No.12101316)Belt and Road Innovative Talents Exchange Foreign Experts project(No.DL2023014002L)。
文摘In this paper,we show that an ideal generated by matching Rota-Baxter equations is a bideal of a Hopf algebra on decorated rooted forests.We then get a bialgebraic structure on the space of decorated rooted forests modulo this biideal.As an application,a connected graded bialgebra and so a graded Hopf algebra on matching Rota-Baxter algebras are constructed,which simplifies the Hopf algebraic structure proposed by[Pacific J.Math.,2022,317(2):441-475].
文摘Traveling is one major theme of Fitzgerald's novel Tender Is the Night. This fashionable activity for the 1920 s Americans is represented in the novel as ostensibly bearing different meanings to the main characters, but a deeper look would reveal that it is unanimously resorted to as a weapon against the spiritual barrenness caused by the cult of business, and more importantly, as a way to the experience of rootedness.
文摘The static drill rooted nodular pile is a new type of pile foundation consisting of precast nodular pile and the surrounding cemented soil.This composite pile has a relatively high bearing capacity and the mud pollution will be largely reduced during the construction process by using this type of pile.In order to investigate the bearing capacity and load transfer mechanism of this pile,a group of experiments were conducted to provide a comparison between this new pile and the bored pile.The axial force of a precast nodular pile was also measured by the strain gauges installed on the pile to analyze the distribution of the axial force of the nodular pile and the skin friction supported by the surrounding soil,then 3D models were built by using the ABAQUS finite element program to investigate the load transfer mechanism of this composite pile in detail.By combining the results of field tests and the finite element method,the outcome showed that the bearing capacity of a static drill rooted nodular pile is higher than the bored pile,and that this composite pile will form a double stress dispersion system which will not only confirm the strength of the pile,but also make the skin friction to be fully mobilized.The settlement of this composite pile is mainly controlled by the precast nodular pile;meanwhile,the nodular pile and the surrounding cemented soil can be considered as deformation compatibility during the loading process.The nodes on the nodular pile play an important role during the load transfer process,the shear strength of the interface between the cemented soil and the soil of the static drill rooted pile is larger than that of the bored pile.
文摘It is well known that any kind of exact enumerations of rooted maps on nonplanar surface is quite difficult. This paper presents a functional equation for rooted Eulerian maps on the projective plane. A parametric expression, through which an exact enumeration by root-valency and the number of edges of maps may be determined, is obtained.
文摘The integration of wind turbines(WTs)in variable speed drive systems belongs to the main factors causing lowstability in electrical networks.Therefore,in order to avoid this issue,WTs hybridization with a storage system is a mandatory.This paper investigates WT system operating at variable speed.The system contains of a permanent magnet synchronous generator(PMSG)supported by a battery storage system(BSS).To enhance the quality of active and reactive power injected into the network,direct power control(DPC)scheme utilizing space-vector modulation(SVM)technique based on proportional-integral(PI)control is proposed.Meanwhile,to improve the rendition of this method(DPC-SVM-PI),the rooted tree optimization technique(RTO)algorithm-based controller parameter identification is used to achieve PI optimal gains.To compare the performance ofRTO-based controllers,they were implemented and tested along with some other popular controllers under different working conditions.The obtained results have shown the supremacy of the suggested PIRTO algorithm compared to competing controllers regarding total harmonic distortion(THD),overshoot percentage,settling time,rise time,average active power value,overall efficiency,and active power steadystate error.
基金Supported by Youth Funding of Sichuan Academy of Soclal Scienccs in 2003(YFSASS03-13)
文摘There are 36 counties affirmed to be aid-poverty-development county in the early 21st century, which distribute around the circumferential mountain of Sichuan Basin, According to the topographic features and the distribution of nationality, these aid-poverty-development counties can be classified into 4 depressed-regions. Study shows that regional poverty performance of 4 depressed-regions not only has many commons in the field of regional economic structure and industry structure, which is far behind the average development performance of Sichuan in the field of economic sum per capita such as GDP, farmer net income per capita as well as retail scale consumer goods, it is also quite different related to infrastructure and social development within 4 depressed-regions. Regional Poverty is chronically resulted in interaction of the multi-factors. Natural condition constraint is the basic factor contributed to regional poverty, policy influences play key role, the poor culture is inherent factor to regional poverty and the marginal locations play important role.
基金Supported by Natural Science Foundation of Tibet Autonomous Region(XZ2019ZRG-58)Forestry Discipline Innovation Team Construction Project of Tibet Agriculture&Animal Husbandry University(Tibet Financial Forecast:2020-001).
文摘In order to provide theoretical basis and technical support for the afforestation and artificial water supply of P.szechuanica in arid areas,the characteristics of water consumption of P.szechuanica were explored,and the law of water demand of P.szechuanica was grasped.In this paper,potted seedlings of 1-0 rooted cuttings of P.szechuanica were taken as research objects,and change situation of water consumption under different water control gradients was measured regularly by using weighing method,further analyzing dynamic change of water consumption of P.szechuanica and revealing water demand law of 1-0 rooted cuttings of P.szechuanica.The results showed that total change of water consumption of 1-0 rooted cuttings of P.szechuanica had"slow-fast-slow-fast"double-peak trend in the growth period of the current year,and corresponded with univariate linear relation(R^(2)=0.7137),with significant difference.In whole growth period,water consumption in August was the highest,which was 2.7 times of that in June and July and 1.5 times of that after September.In different water control treatments,the dynamic changes of daily and monthly water consumption were significantly different.In seven water control treatments,monthly water consumption was between(6315.95±1690.70)and(10105.28±3065.30)g/month,and mean was(8211.07±2308.23)g/month.With intensification of water control treatment,water consumption increased,but there was no seedling death due to water shortage.P.szechuanica has great plasticity in water demand,and can survive in both arid and humid environments.Meanwhile,it is revealed that P.szechuanica is the most widely distributed tree species in the region.
基金This research was partially supported by the U. S. National Science Foundation under Grant Number ECS 85-03212 and by the National Natural Science Foundation of China as well. And, it was completed during the author's stay at RUTCOR, The State Univerity
文摘This paper provides a functional equation astisfied by the generating function for enumerating rooted loopless planar maps with vertex partition. A kind of applications in enumerating, by providing explicit formulae, a type of rooted loopless planar maps with the maximum valency of vertices given are described. Meanwhile, the functional equation for enumerating rooted loopless planar maps (connected) with the edge number and the valency of root-vertex as the parameters is also derived directly.
文摘Sixteen one-year-old dogs were used in our experiment.We rotated the maxillary secondincisors of the dogs,applying a force of 100g and a moment of 550g·mm.The duration of theexperiment varied from 72h to 8 weeks.Activation was performed once every 2 weeks and the impressions were taken in order to measure the angles of rotation.The results of our experiment showthat the rotation rate of single-rooted tooth in dogs is 3.04/week.The graph shows the form ofgradual stairs.This paper introduces a new specialized experimental apparatus for tooth rotation.The angles of rotation are measured geometrically.
基金supported by the National Basic Research Program of China(2009CB825101)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20110008110035)
文摘This paper focused on the water relations of two halophytes differing in photosynthetic pathway, phe- notype, and life cycle： Karelinia caspica （Pall.） Less. （C3, deep-rooted perennial Asteraceae grass） and Atriplex tatarica L. （C4, shallow-rooted annual Chenopodiaceae grass）. Gas exchange, leaf water potential, and growth characteristics were investigated in two growing seasons in an arid area of Xinjiang to explore the physiological adaptability of the two halophytes. Both K. caspica and A. tatarica showed midday depression of transpiration, in- dicating that they were strong xerophytes and weak midday depression types. The roots of A. tatarica were con- centrated mainly in the 0-60 cm soil layer, and the leaf water potential （~L） increased sharply in the 0-20 cm layer due to high soil water content, suggesting that the upper soil was the main water source. On the other hand, K. caspica had a rooting depth of about 1.5 m and a larger root/shoot ratio, which confirmed that this species uptakes water mainly from deeper soil layer. Although A. tatarica had lower transpiration water consumption, higher water use efficiency （WUE）, and less water demand at the same leaf water potential, it showed larger water stress impact than K. caspica, indicating that the growth of A. tatarica was restricted more than that of K. caspica when there was no rainfall recharge. As a shallow-rooted C4 species, A. tatarica displayed lower stomatal conductance, which could to some extent reduce transpiration water loss and maintain leaf water potential steadily. In contrast, the deep-rooted C3 species K. caspica had a larger root/shoot ratio that was in favor of exploiting groundwater. We concluded that C3 species （K. caspica） tapes water and C4 species （A. tatarica） reduces water loss to survive in the arid and saline conditions. The results provided a case for the phenotype theory of Schwinning and Ehleringer on halophytic plants.
文摘This work analyzes heat transfer through a wall containing triangular fins partially embedded in its volume. The coupled heat diffusion equations governing each constituent are solved numericallyusing an iterative finite volume method. A well bracketed effectiveness of the combined system that suits wide range of applications is analytically derived. Good agreement between the numerical and the analytical results is attained. It is found that the fin-root can act simultaneously as a heat sink and heat source for the wall. The heat transfer rate through the combined system is clearly seen to be maximized at a specific fin-root length. The maximum reported heat transfer rate through the triangular rooted-finned wall is found to be at most 90% above that for the rootless fin case at wall Biot number of 1.54. This percentage is noticed to decrease as the wall Biot number decreases. At that Biot number, the maximum heat transfer rate through the combined system reaches 150% above that through the plain wall. As a result of this work, it is recommended to utilize the triangular rooted-fin as a heat transfer enhancer for high mechanical strength structures exposed to highly convective fluid streams.
基金Supported by the Science Fund of the Republic of Serbiagrant number 7749676:Spectrally Constrained Signed Graphs with Applications in Coding Theory and Control Theory-SCSG-ctct.
文摘We give the explicit formula for the characteristic polynomial of the Laplacian matrix of every rooted balanced k-ary tree of depth r.
文摘We introduce an algebraic structure allowing us to describe subgraphs of a regular rooted tree. Its elements are called structure polynomials, and they are in a one- to-one correspondence with the set of all subgraphs of the tree. We define two operations, the sum and the product of structure polynomials, giving a graph interpretation of them. Then we introduce an equivalence relation between polynomials, using the action of the full automorphism group of the tree, and we count equivalence classes of subgraphs modulo this equivalence. We also prove that this action gives rise to symmetric Gelfand pairs. Finally, when the regularity degree of the tree is a prime p, we regard each level of the tree as a finite dimensional vector space over the finite field Fp, and we are able to completely characterize structure polynomials corresponding to subgraphs whose leaf set is a vector subspace.
基金supported by the National Natural Science Foundation of China (Nos.11971206, 12022105)the Natural Science Foundation of Distinguished Young Scholars of Jiangsu Province (No.BK20200048)Postgraduate Research Practice&Innovation Program of Jiangsu Province (No.KYCX21-2565)。
文摘An independent set in a graph G is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial AΣx^(|A|), where the sum is over all independent sets A of G. In 1987, Alavi,Malde, Schwenk and Erd os conjectured that the independence polynomial of any tree or forest is unimodal.Although this unimodality conjecture has attracted many researchers’ attention, it is still open. Recently, Basit and Galvin even asked a much stronger question whether the independence polynomial of every tree is ordered log-concave. Note that if a polynomial has only negative real zeros then it is ordered log-concave and unimodal.In this paper, we observe real-rootedness of independence polynomials of rooted products of graphs. We find some trees whose rooted product preserves real-rootedness of independence polynomials. In consequence, starting from any graph whose independence polynomial has only real zeros, we can obtain an infinite family of graphs whose independence polynomials have only real zeros. In particular, applying it to trees or forests, we obtain that their independence polynomials are unimodal and ordered log-concave.
基金Supported by the National Natural Science Foundation of China(No:6087206011071158)+1 种基金the Science Foundation of Shanghai Education Committee(No:12ZZ193)the Natural Science Foundation of Shanghai city(No:12ZR1421000)
文摘We propose a new expected value of rooted graph in this article,that is, when G is a rooted graph that each vertex may independently succeed with probability p when catastrophic thing happened, we consider the expected number of edges in the operational component of G which containing the root. And we get a very important and useful compute formula which is called deletion-contraction edge formula. By using this formula, we get the computational formulas of expected value for some special graphs. We also discuss the mean of expected value when parameter p has certain prior distribution. Finally, we propose mean-variance optimality when rooted graph has the equilibrium point which has larger mean and smaller variance.
基金supported by the National Key Research and Development Program of China,No.2023YFC3603705(to DX)the National Natural Science Foundation of China,No.82302866(to YZ).
文摘After spinal cord injury,impairment of the sensorimotor circuit can lead to dysfunction in the motor,sensory,proprioceptive,and autonomic nervous systems.Functional recovery is often hindered by constraints on the timing of interventions,combined with the limitations of current methods.To address these challenges,various techniques have been developed to aid in the repair and reconstruction of neural circuits at different stages of injury.Notably,neuromodulation has garnered considerable attention for its potential to enhance nerve regeneration,provide neuroprotection,restore neurons,and regulate the neural reorganization of circuits within the cerebral cortex and corticospinal tract.To improve the effectiveness of these interventions,the implementation of multitarget early interventional neuromodulation strategies,such as electrical and magnetic stimulation,is recommended to enhance functional recovery across different phases of nerve injury.This review concisely outlines the challenges encountered following spinal cord injury,synthesizes existing neurostimulation techniques while emphasizing neuroprotection,repair,and regeneration of impaired connections,and advocates for multi-targeted,task-oriented,and timely interventions.
基金Project supported by the National Natural Science Foundation of China.
文摘All maps we deal with in this note are rooted planar ones, which, in brief, are called maps. Most of terminologies here come from Refs. [1—3]. The purpose of this note is to determine the asymptotic enumerations based on the enumerations in [1, 2]. Bender and Richmond gave a survey of the asymptotic enumeration. New asymptotic enumerations here can be considered as a complement and improvement of the survey.
基金Project supported by the National Natural Science Foundation of China.
文摘A summation free formula for enumerating rooted nonseparable outerplanar maps with a face partition given is herein presented. As its corollaries, some summation free formulae for the bipartite and the simple cases are also derived. Moreover, the formula for planted plane trees according to a given vertex partition is demonstrated in a new way.
文摘In this article, the authors discuss two kinds of new planar maps： pan-fan maps and circuit boundary maps, and provide explicit expressions about their enumerating functions with different parameters. Meanwhile, two explicit counting formulas for circuit cubic boundary maps with two parameters; the size and the valency of the root-face, are also extracted.
