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
In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).A...In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.展开更多
Two sections from the Silurian deposits in the Central Iran Micro and Turan Plates were measured and sampled. These deposits are mostly composed of submarine volcanic rocks, skeletal and non-skeletal limestone, shale ...Two sections from the Silurian deposits in the Central Iran Micro and Turan Plates were measured and sampled. These deposits are mostly composed of submarine volcanic rocks, skeletal and non-skeletal limestone, shale and sandstone that were deposited in low to high energy conditions （from tidal flat to deep open marine）. According to gradual deepening trend, wide lateral distribution of facies as well as absence of resedimentation deposits, a depositional model of a homoclinal ramp was proposed for these deposits. Field observations and facies distribution indicate that, two depositional sequences were recognized in both sections. These sections show similarities in facies and depositional sequence during the Early Silurian in the area. Although there are some opinions and evidences that demonstrated Paleo-Tethys rifting phase started at the Late Ordovician-Early Silurian, similarities suggest that the Turan and Iran Plates were not completely detached tectonic block during this time, and that their depositional conditions were affected by global sea level changes and tectonic events.展开更多
Much geological research has illustrated the transition of paleoenvironmental patterns during the Cenozoic from a planetary-wind-dominant type to a monsoon-dominant type, indicating the initiation of the East Asian mo...Much geological research has illustrated the transition of paleoenvironmental patterns during the Cenozoic from a planetary-wind-dominant type to a monsoon-dominant type, indicating the initiation of the East Asian monsoon and inland-type aridity. However, there is a dispute about the causes and mechanisms of the transition, especially about the impact of the Himalayan/Tibetan Plateau uplift and the Paratethys Sea retreat, Thirty numerical sensitivity experiments under different land-sea distributions and Himalayan/Tibetan Plateau topography conditions are performed here to simulate the evolution of climate belts with emphasis on changes in the rain band, and these are compared with the changes in the paleoenvironmental patterns during the Cenozoic recovered by geological records. The consistency between simulations and the geological evidence indicates that both the Tibetan Plateau uplift and the Paratethys Sea retreat play important roles in the formation of the monsoon-dominant environmental pattern. Furthermore, the simulations show the monsoon-dominant environmental pattern comes into being when the Himalayan/Tibetan Plateau reaches 1000-2000 m high and the Paratethys Sea retreats to the Turan Plate.展开更多
In this paper some new results for general orthogonal polynomials on infinite intervals are presented. In particular, an answer to Problem 54 of P. Turan[J. Approximation Theory, 29(1980),P.64] is given.
The Turán problem asks for the largest number of edges ex(n,H)in an n-vertex graph not containing a fixed forbidden subgraph H,which is one of the most important problems in extremal graph theory.However,the orde...The Turán problem asks for the largest number of edges ex(n,H)in an n-vertex graph not containing a fixed forbidden subgraph H,which is one of the most important problems in extremal graph theory.However,the order of magnitude of ex(n,H)for bipartite graphs is known only in a handful of cases.In particular,giving explicit constructions of extremal graphs is very challenging in this field.In this paper,we develop a polynomial resultant approach to the algebraic construction of explicit extremal graphs,which can efficiently decide whether a specified structure exists.A key insight in our approach is the multipolynomial resultant,which is a fundamental tool of computational algebraic geometry.Our main results include the matched lower bounds on the Turán number of 1-subdivision of K3,t1and the linear Turán number of the Berge theta hypergraph■_(3,t_(2))^(B).where t_(1)=25 and t_(2)=217.Moreover,the constant t1improves the random algebraic construction of Bukh and Conlon(2018)and makes the known estimation better on the smallest value of t1concerning a problem posed by Conlon et al.(2021)by reducing the value from a magnitude of 10^(56)to the number 25,while the constant t_(2)improves a result of He and Tait(2019).展开更多
The multicolor Ramsey number r_(k)(C_(4))is the smallest integer N such that any k-edge coloring of KN contains a monochromatic C_(4).The current best upper bound of r_(k)(C_(4))was obtained by Chung(1974)and independ...The multicolor Ramsey number r_(k)(C_(4))is the smallest integer N such that any k-edge coloring of KN contains a monochromatic C_(4).The current best upper bound of r_(k)(C_(4))was obtained by Chung(1974)and independently by Irving(1974),i.e.,r_(k)(C_(4))≤k^(2)+k+1 for all k≥2.There is no progress on the upper bound since then.In this paper,we improve the upper bound of r_(k)(C_(4))by showing that r_(k)(C_(4))≤k^(2)+k-1 for even k≥6.The improvement is based on the upper bound of the Turan number ex(n,C4),in which we mainly use the double counting method and many novel ideas from Firke,Kosek,Nash,and Williford[J.Combin.Theory,Ser.B 103(2013),327-336].展开更多
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.
基金supported by the National Natural Science Foundation of China(12371327)the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX0107).
文摘In this paper,we examine the functions a(n)and b(n),which respectively represent the number of cubic partitions and cubic partition pairs.Our work leads to the derivation of asymptotic formulas for both a(n)and b(n).Additionally,we establish the upper and lower bounds of these functions,factoring in the explicit error terms involved.Crucially,our findings reveal that a(n)and b(n)both satisfy several inequalities such as log-concavity,third-order Turan inequalities,and strict log-subadditivity.
基金the logistical and financial support given to this study by the Department of Geology of Ferdowsi University of Mashhad-Iran
文摘Two sections from the Silurian deposits in the Central Iran Micro and Turan Plates were measured and sampled. These deposits are mostly composed of submarine volcanic rocks, skeletal and non-skeletal limestone, shale and sandstone that were deposited in low to high energy conditions （from tidal flat to deep open marine）. According to gradual deepening trend, wide lateral distribution of facies as well as absence of resedimentation deposits, a depositional model of a homoclinal ramp was proposed for these deposits. Field observations and facies distribution indicate that, two depositional sequences were recognized in both sections. These sections show similarities in facies and depositional sequence during the Early Silurian in the area. Although there are some opinions and evidences that demonstrated Paleo-Tethys rifting phase started at the Late Ordovician-Early Silurian, similarities suggest that the Turan and Iran Plates were not completely detached tectonic block during this time, and that their depositional conditions were affected by global sea level changes and tectonic events.
基金This study was supported by the National Natural Science Foundation of China(Grant Nos.40125014 and 40231001)the Key Program of the Chinese Academy of Sciences KZCX3-SW-139.
文摘Much geological research has illustrated the transition of paleoenvironmental patterns during the Cenozoic from a planetary-wind-dominant type to a monsoon-dominant type, indicating the initiation of the East Asian monsoon and inland-type aridity. However, there is a dispute about the causes and mechanisms of the transition, especially about the impact of the Himalayan/Tibetan Plateau uplift and the Paratethys Sea retreat, Thirty numerical sensitivity experiments under different land-sea distributions and Himalayan/Tibetan Plateau topography conditions are performed here to simulate the evolution of climate belts with emphasis on changes in the rain band, and these are compared with the changes in the paleoenvironmental patterns during the Cenozoic recovered by geological records. The consistency between simulations and the geological evidence indicates that both the Tibetan Plateau uplift and the Paratethys Sea retreat play important roles in the formation of the monsoon-dominant environmental pattern. Furthermore, the simulations show the monsoon-dominant environmental pattern comes into being when the Himalayan/Tibetan Plateau reaches 1000-2000 m high and the Paratethys Sea retreats to the Turan Plate.
基金The Project Supported by National Natural Science Foundation of China
文摘In this paper some new results for general orthogonal polynomials on infinite intervals are presented. In particular, an answer to Problem 54 of P. Turan[J. Approximation Theory, 29(1980),P.64] is given.
基金supported by the Institute for Basic Science(IBS-R029-C4)supported by the National Key Research and Development Program of China(Grant No.2020YFA0712100)+1 种基金National Natural Science Foundation of China(Grant No.12231014)Beijing Scholars Program。
文摘The Turán problem asks for the largest number of edges ex(n,H)in an n-vertex graph not containing a fixed forbidden subgraph H,which is one of the most important problems in extremal graph theory.However,the order of magnitude of ex(n,H)for bipartite graphs is known only in a handful of cases.In particular,giving explicit constructions of extremal graphs is very challenging in this field.In this paper,we develop a polynomial resultant approach to the algebraic construction of explicit extremal graphs,which can efficiently decide whether a specified structure exists.A key insight in our approach is the multipolynomial resultant,which is a fundamental tool of computational algebraic geometry.Our main results include the matched lower bounds on the Turán number of 1-subdivision of K3,t1and the linear Turán number of the Berge theta hypergraph■_(3,t_(2))^(B).where t_(1)=25 and t_(2)=217.Moreover,the constant t1improves the random algebraic construction of Bukh and Conlon(2018)and makes the known estimation better on the smallest value of t1concerning a problem posed by Conlon et al.(2021)by reducing the value from a magnitude of 10^(56)to the number 25,while the constant t_(2)improves a result of He and Tait(2019).
基金supported by National Natural Science Foundation of China(No.12171088,12226401)Natural Science Foundation of Fujian Province(No.2022J02018).
文摘The multicolor Ramsey number r_(k)(C_(4))is the smallest integer N such that any k-edge coloring of KN contains a monochromatic C_(4).The current best upper bound of r_(k)(C_(4))was obtained by Chung(1974)and independently by Irving(1974),i.e.,r_(k)(C_(4))≤k^(2)+k+1 for all k≥2.There is no progress on the upper bound since then.In this paper,we improve the upper bound of r_(k)(C_(4))by showing that r_(k)(C_(4))≤k^(2)+k-1 for even k≥6.The improvement is based on the upper bound of the Turan number ex(n,C4),in which we mainly use the double counting method and many novel ideas from Firke,Kosek,Nash,and Williford[J.Combin.Theory,Ser.B 103(2013),327-336].
