Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the progressive degeneration of upper and lower motor neurons in the brainstem and spinal cord,leading to muscle weakness,para...Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the progressive degeneration of upper and lower motor neurons in the brainstem and spinal cord,leading to muscle weakness,paralysis,and respiratory failure (Morgan and Orrell,2016).展开更多
We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their ...We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.展开更多
A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the preci...A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;M<sub>N</sub>]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.展开更多
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
Rice grain yield is primarily determined by three key agronomic traits:panicle number,grain number per panicle,and grain weight(GW).However,the inherent tradeoffs among these yield components remain a persistent chall...Rice grain yield is primarily determined by three key agronomic traits:panicle number,grain number per panicle,and grain weight(GW).However,the inherent tradeoffs among these yield components remain a persistent challenge in rice breeding programs.Notably,compared with GW,brown rice weight(BRW)provides a more direct metric associated with actual grain yield potential.In this study,we conducted a two-year replicated genome-wide association study to elucidate the genetic architecture of BRW and identify new loci regulating GW.Among seven consistently detected loci across experimental replicates,four were not co-localized with previously reported genes associated with BRW or GW traits.BRW1.1,one of the four newly identified loci,was found to encode a novel RNA-binding protein.Functional characterization revealed that BRW1.1 acts as a negative regulator of BRW,potentially through modulating mRNA translation processes.Intriguingly,through integrated analysis of mutant phenotypes and haplotype variations,we demonstrated that BRW1.1 mediates the physiological tradeoff between GW and panicle number.This study not only delineates the genetic determinants of BRW but also identifies BRW1.1 as a promising molecular target for breaking the yield component tradeoff in precision rice breeding.展开更多
The COVID-19 lockdown was a typical example of extreme emission reduction,providing an opportunity to study the impact of lockdown measures on air pollution.Particle number concentrations(PNC)originate from direct emi...The COVID-19 lockdown was a typical example of extreme emission reduction,providing an opportunity to study the impact of lockdown measures on air pollution.Particle number concentrations(PNC)originate from direct emissions or through new particle formation events.However,their variations during the lockdown period are under investigation.This study focuses on Luohe,a city on the southern edge of the North China Plain,analyzing the changes in PNC and its sources before,during,and after the COVID-19 lockdown.From March 25^(th)to May 31^(st),2022,real-time PNC measurements were conducted using a Scanning Mobility Particle Sizer for particle size.Results showed an 11.2%decrease in PNC during the lockdown compared to pre-lockdown and a 3.6%decrease compared to post-lockdown,indicating reduced local emissions and weakened regional transportation during the lockdown.Positive Matrix Factorization analysis identified six sources contributing to the total PNC,including photochemical nucleation,aged photochemical nucleation,gasoline vehicle emissions,diesel vehicle emissions,coal and biomass combustion,and secondary aerosols.The significant changes in source emissions indicate a substantially reduced traffic volume after the implementation of lockdown measures(2644.8#/cm^(3),2202.2#/cm^(3),2792.7#/cm^(3)).Concurrently,photochemical nucleation(310.1#/cm^(3),306.3#/cm^(3),393.1#/cm^(3))and photochemical nucleation aging(592.8#/cm^(3),744.1#/cm^(3),810.7#/cm^(3))exhibited increasing trends,while coal/biomass combustion(1656.6#/cm^(3),1586.2#/cm^(3),980.0#/cm^(3))and secondary sources(999.4#/cm^(3),791.1#/cm^(3),804.1#/cm^(3))showed decreasing trends.In summary,the contributions of traffic emissions to PNC highlight the potential for targeted traffic management strategies to improve urban air quality.展开更多
This work is devoted to the theory of prime numbers. Firstly it introduced the concept of matrix primes, which can help to generate a sequence of prime numbers. Then it proposed a number of theorems, which together wi...This work is devoted to the theory of prime numbers. Firstly it introduced the concept of matrix primes, which can help to generate a sequence of prime numbers. Then it proposed a number of theorems, which together with theorem of Dirichlet, Siegel and Euler allow to prove the infinity of twin primes.展开更多
This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.
The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it ...The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.展开更多
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler...The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.展开更多
In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setti...In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.展开更多
Subtropical evergreen broad-leaved trees are usually vulnerable to freezing stress,while hexaploid wild Camellia oleifera shows strong freezing tolerance.As a valuable genetic resource of woody oil crop C.oleifera,wil...Subtropical evergreen broad-leaved trees are usually vulnerable to freezing stress,while hexaploid wild Camellia oleifera shows strong freezing tolerance.As a valuable genetic resource of woody oil crop C.oleifera,wild C.oleifera can serve as a case for studying the molecular bases of adaptive evolution to freezing stress.Here,47 wild C.oleifera from 11 natural distribution sites in China and 4 relative species of C.oleifera were selected for genome sequencing.“Min Temperature of Coldest Month”(BIO6)had the highest comprehensive contribution to wild C.oleifera distribution.The population genetic structure of wild C.oleifera could be divided into two groups:in cold winter(BIO6≤0℃)and warm winter(BIO6>0℃)areas.Wild C.oleifera in cold winter areas might have experienced stronger selection pressures and population bottlenecks with lower N_(e) than those in warm winter areas.155 singlenucleotide polymorphisms(SNPs)were significantly correlated with the key bioclimatic variables(106 SNPs significantly correlated with BIO6).Twenty key SNPs and 15 key copy number variation regions(CNVRs)were found with genotype differentiation>50%between the two groups of wild C.oleifera.Key SNPs in cis-regulatory elements might affect the expression of key genes associated with freezing tolerance,and they were also found within a CNVR suggesting interactions between them.Some key CNVRs in the exon regions were closely related to the differentially expressed genes under freezing stress.The findings suggest that rich SNPs and CNVRs in polyploid trees may contribute to the adaptive evolution to freezing stress.展开更多
We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of plana...We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.展开更多
For k given graphs H_(1),...,H_(k) with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors...For k given graphs H_(1),...,H_(k) with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors,then there exists some i with 1≤i≤k such that K_(N) has a subgraph in color i isomorphic to H_(i).Let C_(m) be a cycle of length m and K_(1,n) a star of order n+1.In this paper,we systematically introduce the latest research progress on star-quadrilateral Ramsey numbers and provide an overview of Ramsey numbers concerning quadrilaterals,including multicolor cases.展开更多
TENORM Regulation in the United States of America post-West Virginia vs.EPA Spenser Lynn,Charles Wilson,Emily Caffrey1(1.University of Alabama at Birmingham,School of Health Professions,Clinical and Diagnostic Science...TENORM Regulation in the United States of America post-West Virginia vs.EPA Spenser Lynn,Charles Wilson,Emily Caffrey1(1.University of Alabama at Birmingham,School of Health Professions,Clinical and Diagnostic Sciences,Health Physics Program,1720 University Blvd,Birmingham,AL 35294)Abstract:The regulation of technologically enhanced naturally occurring radioactive materials(TENORM)in the United States of America consists of fragmentary rules split between the federal and state governments.展开更多
In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are dif...In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].展开更多
Determining the crossing number of a given graph is NP-complete. The cycle of length m is denoted by Cm = v1v2…vmv1. G^((1))_(m) (m ≥ 5) is the graph obtained from Cm by adding two edges v1v3 and vlvl+2 (3 ≤ l ≤ m...Determining the crossing number of a given graph is NP-complete. The cycle of length m is denoted by Cm = v1v2…vmv1. G^((1))_(m) (m ≥ 5) is the graph obtained from Cm by adding two edges v1v3 and vlvl+2 (3 ≤ l ≤ m−2), G^((2))m (m ≥ 4) is the graph obtained from Cm by adding two edges v1v3 and v2v4. The famous Zarankiewicz’s conjecture on the crossing number of the complete bipartite graph Km,n states that cr(Km,n)=Z(m,n)=[m/2][m-1/2][n/2[n-1/2].Based on Zarankiewicz’s conjecture, a natural problem is to study the change in the crossingnumber of the graphs obtained from the complete bipartite graph by adding certain edge sets.If Zarankiewicz’s conjecture is true, this paper proves that cr(G^((1))_(m)+Kn)=Z(m,n)+2[n/2] and cr(G^((2))_(m)+Kn)=Z(m,n)+n.展开更多
The Turan number of a graph H,denoted by ex(n,H),is the maximum number of edges in any graph on n vertices containing no H as a subgraph.Let P_(ι)denote the path onιvertices,S_(ι-1)denote the star onιvertices and ...The Turan number of a graph H,denoted by ex(n,H),is the maximum number of edges in any graph on n vertices containing no H as a subgraph.Let P_(ι)denote the path onιvertices,S_(ι-1)denote the star onιvertices and k_(1)P_(ι)∪k_(2)S_(ι-1)denote the path-star forest with disjoint union of k_(1)copies of P_(ι)and k_(2)copies of S_(ι-1).In 2022,[Graphs Combin.,2022,38(3):Paper No.84,16 pp.] raised a conjecture about the Turan number of k_(1)P_(2ι)∪k_(2)S_(2ι-1).In this paper,we determine the Turan numbers of P_(ι)∪kS_(ι-1)and k_(1)P_(2ι)∪k_(2)S_(2ι-1)for n appropriately large,which implies the above conjecture.The corresponding extremal graphs are also completely characterized.展开更多
文摘Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the progressive degeneration of upper and lower motor neurons in the brainstem and spinal cord,leading to muscle weakness,paralysis,and respiratory failure (Morgan and Orrell,2016).
文摘We have found through calculations that the differences between the closest supposed prime numbers other than 2 and 3 defined in the articles are: 2;4: and 6. For those whose difference is equal to 6, we showed their origin then we classified them into two categories according to their classes, we showed in which context two prime numbers which differ from 6 are called sexy and in what context they are said real sexy prime. For those whose difference is equal to 4, we showed their origin then we showed that two prime numbers which differ from 4, that is to say two cousin prime numbers, are successive. We made an observation on the supposed prime numbers then we established two pairs of equations from this observation and deduced the origin of the Mersenne number and that of the Fermat number.
文摘A simple recursive algorithm to generate the set of natural numbers, based on Mersenne numbers: M<sub>N</sub> = 2<sup>N</sup> – 1, is used to count the number of prime numbers within the precise Mersenne natural number intervals: [0;M<sub>N</sub>]. This permits the formulation of an extended twin prime conjecture. Moreover, it is found that the prime numbers subsets contained in Mersenne intervals have cardinalities strongly correlated with the corresponding Mersenne numbers.
文摘This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
基金supported by the National Natural Science Foundation of China(Grant Nos.32000377,32172037,and 32472211)the Biological Breeding-National Science and Technology Major Project,China(Grant No.2023ZD04068)+2 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.KJQN202103)the open funds of the State Key Laboratory of Crop Genetics&Germplasm Enhancement and Utilization,China(Grant No.ZW202401)the Cyrus Tang Innovation Center for Crop Seed Industry,China.
文摘Rice grain yield is primarily determined by three key agronomic traits:panicle number,grain number per panicle,and grain weight(GW).However,the inherent tradeoffs among these yield components remain a persistent challenge in rice breeding programs.Notably,compared with GW,brown rice weight(BRW)provides a more direct metric associated with actual grain yield potential.In this study,we conducted a two-year replicated genome-wide association study to elucidate the genetic architecture of BRW and identify new loci regulating GW.Among seven consistently detected loci across experimental replicates,four were not co-localized with previously reported genes associated with BRW or GW traits.BRW1.1,one of the four newly identified loci,was found to encode a novel RNA-binding protein.Functional characterization revealed that BRW1.1 acts as a negative regulator of BRW,potentially through modulating mRNA translation processes.Intriguingly,through integrated analysis of mutant phenotypes and haplotype variations,we demonstrated that BRW1.1 mediates the physiological tradeoff between GW and panicle number.This study not only delineates the genetic determinants of BRW but also identifies BRW1.1 as a promising molecular target for breaking the yield component tradeoff in precision rice breeding.
基金supported by the National Research Program for Key Issues in Air Pollution Control in China(No.DQGG202137)the National Natural Science Foundation of China(No.42277429)。
文摘The COVID-19 lockdown was a typical example of extreme emission reduction,providing an opportunity to study the impact of lockdown measures on air pollution.Particle number concentrations(PNC)originate from direct emissions or through new particle formation events.However,their variations during the lockdown period are under investigation.This study focuses on Luohe,a city on the southern edge of the North China Plain,analyzing the changes in PNC and its sources before,during,and after the COVID-19 lockdown.From March 25^(th)to May 31^(st),2022,real-time PNC measurements were conducted using a Scanning Mobility Particle Sizer for particle size.Results showed an 11.2%decrease in PNC during the lockdown compared to pre-lockdown and a 3.6%decrease compared to post-lockdown,indicating reduced local emissions and weakened regional transportation during the lockdown.Positive Matrix Factorization analysis identified six sources contributing to the total PNC,including photochemical nucleation,aged photochemical nucleation,gasoline vehicle emissions,diesel vehicle emissions,coal and biomass combustion,and secondary aerosols.The significant changes in source emissions indicate a substantially reduced traffic volume after the implementation of lockdown measures(2644.8#/cm^(3),2202.2#/cm^(3),2792.7#/cm^(3)).Concurrently,photochemical nucleation(310.1#/cm^(3),306.3#/cm^(3),393.1#/cm^(3))and photochemical nucleation aging(592.8#/cm^(3),744.1#/cm^(3),810.7#/cm^(3))exhibited increasing trends,while coal/biomass combustion(1656.6#/cm^(3),1586.2#/cm^(3),980.0#/cm^(3))and secondary sources(999.4#/cm^(3),791.1#/cm^(3),804.1#/cm^(3))showed decreasing trends.In summary,the contributions of traffic emissions to PNC highlight the potential for targeted traffic management strategies to improve urban air quality.
文摘This work is devoted to the theory of prime numbers. Firstly it introduced the concept of matrix primes, which can help to generate a sequence of prime numbers. Then it proposed a number of theorems, which together with theorem of Dirichlet, Siegel and Euler allow to prove the infinity of twin primes.
文摘This study describes how one can construct sets of composite natural numbers as tensorial products of the vectors created with the natural powers of prime numbers.
文摘The application of the Euclidean division theorem for the positive integers allowed us to establish a set which contains all the prime numbers and this set we called it set of supposedly prime numbers and we noted it E<sub>sp</sub>. We subsequently established from the previous set the set of non-prime numbers (the set of numbers belonging to this set and which are not prime) denoted E<sub>np</sub>. We then extracted from the set of supposedly prime numbers the numbers which are not prime and the set of remaining number constitutes the set of prime numbers denoted E<sub>p</sub>. We have deduced from the previous set, the set of prime numbers between two natural numbers. We have explained during our demonstrations the origin of the twin prime numbers and the structure of the chain of prime numbers.
基金Supported by the NNSF of China(10001016) SF for the Prominent Youth of Henan Province
文摘The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.
基金Supported by the National Natural Science Foundation of China(11671060).
文摘In this article, we consider the structured condition numbers for LDU, factorization by using the modified matrix-vector approach and the differential calculus, which can be represented by sets of parameters. By setting the specific norms and weight parameters, we present the expressions of the structured normwise, mixed, componentwise condition numbers and the corresponding results for unstructured ones. In addition, we investigate the statistical estimation of condition numbers of LDU factorization using the probabilistic spectral norm estimator and the small-sample statistical condition estimation method, and devise three algorithms. Finally, we compare the structured condition numbers with the corresponding unstructured ones in numerical experiments.
基金funded by the National Natural Science Foundation of China(grant no.32270238 and 31870311).
文摘Subtropical evergreen broad-leaved trees are usually vulnerable to freezing stress,while hexaploid wild Camellia oleifera shows strong freezing tolerance.As a valuable genetic resource of woody oil crop C.oleifera,wild C.oleifera can serve as a case for studying the molecular bases of adaptive evolution to freezing stress.Here,47 wild C.oleifera from 11 natural distribution sites in China and 4 relative species of C.oleifera were selected for genome sequencing.“Min Temperature of Coldest Month”(BIO6)had the highest comprehensive contribution to wild C.oleifera distribution.The population genetic structure of wild C.oleifera could be divided into two groups:in cold winter(BIO6≤0℃)and warm winter(BIO6>0℃)areas.Wild C.oleifera in cold winter areas might have experienced stronger selection pressures and population bottlenecks with lower N_(e) than those in warm winter areas.155 singlenucleotide polymorphisms(SNPs)were significantly correlated with the key bioclimatic variables(106 SNPs significantly correlated with BIO6).Twenty key SNPs and 15 key copy number variation regions(CNVRs)were found with genotype differentiation>50%between the two groups of wild C.oleifera.Key SNPs in cis-regulatory elements might affect the expression of key genes associated with freezing tolerance,and they were also found within a CNVR suggesting interactions between them.Some key CNVRs in the exon regions were closely related to the differentially expressed genes under freezing stress.The findings suggest that rich SNPs and CNVRs in polyploid trees may contribute to the adaptive evolution to freezing stress.
基金Project supported by the National Natural Science Foundation of China(Nos.12471367 and12361076)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Nos.NJZY19186,NJZY22036,and NJZY23003)。
文摘We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing it.For a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical methods.This analysis aims to illustrate the discrepancies among various low-dissipative numerical algorithms.Furthermore,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable algorithms.To verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.
基金supported by NSFC(Nos.12161141003,11931006)supported by NSFC(Nos.11801520,12171436,12271489)supported by NSFC(No.11601527)。
文摘For k given graphs H_(1),...,H_(k) with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors,then there exists some i with 1≤i≤k such that K_(N) has a subgraph in color i isomorphic to H_(i).Let C_(m) be a cycle of length m and K_(1,n) a star of order n+1.In this paper,we systematically introduce the latest research progress on star-quadrilateral Ramsey numbers and provide an overview of Ramsey numbers concerning quadrilaterals,including multicolor cases.
文摘TENORM Regulation in the United States of America post-West Virginia vs.EPA Spenser Lynn,Charles Wilson,Emily Caffrey1(1.University of Alabama at Birmingham,School of Health Professions,Clinical and Diagnostic Sciences,Health Physics Program,1720 University Blvd,Birmingham,AL 35294)Abstract:The regulation of technologically enhanced naturally occurring radioactive materials(TENORM)in the United States of America consists of fragmentary rules split between the federal and state governments.
基金supported by the National Natural Science Foundation of China(Grant No.11671145)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).
文摘In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].
基金Supported by Changsha Natural Science Foundation(No.kq2208001)the Key Project Funded by Hunan Provincial Department of Education(No.21A0590)。
文摘Determining the crossing number of a given graph is NP-complete. The cycle of length m is denoted by Cm = v1v2…vmv1. G^((1))_(m) (m ≥ 5) is the graph obtained from Cm by adding two edges v1v3 and vlvl+2 (3 ≤ l ≤ m−2), G^((2))m (m ≥ 4) is the graph obtained from Cm by adding two edges v1v3 and v2v4. The famous Zarankiewicz’s conjecture on the crossing number of the complete bipartite graph Km,n states that cr(Km,n)=Z(m,n)=[m/2][m-1/2][n/2[n-1/2].Based on Zarankiewicz’s conjecture, a natural problem is to study the change in the crossingnumber of the graphs obtained from the complete bipartite graph by adding certain edge sets.If Zarankiewicz’s conjecture is true, this paper proves that cr(G^((1))_(m)+Kn)=Z(m,n)+2[n/2] and cr(G^((2))_(m)+Kn)=Z(m,n)+n.
文摘The Turan number of a graph H,denoted by ex(n,H),is the maximum number of edges in any graph on n vertices containing no H as a subgraph.Let P_(ι)denote the path onιvertices,S_(ι-1)denote the star onιvertices and k_(1)P_(ι)∪k_(2)S_(ι-1)denote the path-star forest with disjoint union of k_(1)copies of P_(ι)and k_(2)copies of S_(ι-1).In 2022,[Graphs Combin.,2022,38(3):Paper No.84,16 pp.] raised a conjecture about the Turan number of k_(1)P_(2ι)∪k_(2)S_(2ι-1).In this paper,we determine the Turan numbers of P_(ι)∪kS_(ι-1)and k_(1)P_(2ι)∪k_(2)S_(2ι-1)for n appropriately large,which implies the above conjecture.The corresponding extremal graphs are also completely characterized.
