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On the Divisor Problem with Congruence Conditions: 《数学进展》2025年第1期1-17,共17页JIA Lirui ZHAI Wenguang CAI Tianxin; supported by the Talent Fund of Beijing Jiaotong University(No.2020RC012);NSFC(No.11871295),supported by NSFC(No.11971476),supported by NSFC(No.12071421)。; Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2))...; 关键词：divisor problem sign change congruence condition

A KAM theorem for 2-dimensional nonlinear Schrodinger equations with forcing terms and(2p+1)-nonlinearities: 《Frontiers of Mathematics in China》2024年第2期75-100,共26页Shuaishuai XUE; In this paper,we prove an infinite dimensional KAM theorem and apply it to study 2-dimensional nonlinear Schrodinger equations with different large forcing terms and(2p+1)-nonlinearities iu_(t)-Δu+φ_(1)(ω_(1)+t)u+...; 关键词：Schrodinger equation reducible KAM tori small divisor quasi-periodic solution

Normal Crossings Singularities for Symplectic Topology:Structures: 《Acta Mathematica Sinica,English Series》2024年第1期107-160,共54页Mohammad FARAJZADEH-TEHRANI Mark MCLEAN Aleksey ZINGER; Supported by NSF grants DMS-2003340(F.Tehrani);DMS-1811861(Mclean);DMS-1901979(Zinger)。; Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological...; 关键词：Normal crossings divisor Chern class Logarithmic tangent bundle

Manin’s conjecture for a class of singular cubic hypersurfaces被引量：1: 《Frontiers of Mathematics in China》2022年第6期1089-1132,共44页Wenguang ZHAI; supported by the National Natural Science Foundation of China(Grant No.11971476).; Letℓ≥2 be a fixed positive integer and Q(y)be a positive definite quadratic form inℓvariables with integral coefficients.The aim of this paper is to count rational points of bounded height on the cubic hypersurface d...; 关键词：Manin’s conjecture quadratic form asymptotic formula divisor problem exponential sum

本刊英文版2022年65卷第10期(1997–2218)摘要: 《中国科学：数学》2022年第10期I0001-I0004,共4页; W-translated Schubert divisors and transversal intersections Dong Seon Hwang, Hwayoung Lee, Jae-Hyouk Lee & Changzheng Li Abstract We study the toric degeneration of Weyl group translated Schubert divisors of a partia...; 关键词：INTERSECTION DIVISOR TRANSVERSAL

Divisibility Properties of Power Matrices Associated with Arithmetic Functions on a Divisor Chain: 《Algebra Colloquium》2022年第3期527-540,共14页Long Chen Zongbing Lin Qianrong Tan; supported partially by Doctoral Research Initiation FundProjectof PanzhihuaUniversity(bkqj2019050).; Let a,b and n be positive integers withn≥2,f be an integer-valued arithmetic function,and the set S={x_(1),…,x_(n)}of n distinct positive integers be a divisor chain such that x_(1)|x_(2)|⋯|x_(n).We first show that ...; 关键词：divisor chain integer-valued arithmetic function integer matrix DIVISIBILITY

Analytic Invariant Curves for an Iterative Equation Related to Ricker-type Second-order Equation: 《Acta Mathematica Sinica,English Series》2021年第7期1041-1052,共12页Hou Yu ZHAO Michal FECKAN; the National Natural Science Foundation of China(Grant Nos.11671061,11971081);the Natural Science Foundation of Chongqing(Grant No.cstc2020jcyj-msxm X0857);Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN201800502,KJQN201900525);Foundation of youth talent of Chongqing Normal University(02030307-00039),the(Grant Nos.VEGA-MS 1/0358/20,VEGA-SAV 2/0127/20);the Slovak Research and Development Agency under the contract(Grant No.APVV-18-0308)。; In this paper,we consider the existence of analytic invariant curves of an iterative equation f(f(x))=xea-x-f(x)which arises from Ricker-type second-order equation.By reducing the equation with the Schr?der transforma...; 关键词：Difference equation invariant curves analytic solution small divisor

Moduli Space of Quasi-Polarized K3 Surfaces of Degree 6 and 8: 《Chinese Annals of Mathematics,Series B》2021年第3期427-450,共24页Zhiyuan LI Zhiyu TIAN; supported by the National Natural Science Foundation of China(Nos.11771076,11731004,118771155,831013,11890662);National Kay Research and Development Program of China(No.2020YFA0713200);Shanghai Education Commission(No.17SG01).; In this paper,the authors study the moduli space of quasi-polarized complex K3 surfaces of degree 6 and 8 via geometric invariant theory.The general members in such moduli spaces are complete intersections in projecti...; 关键词：K3 surfaces GIT Noether-Lefschetz divisor Looijenga compactification

What the Volume of Matrices Says?: 《Advances in Linear Algebra & Matrix Theory》2020年第4期53-69,共17页Balasubramani Prema Rangasamy; We know matrices and their transposes and we also know flip matrices. In my previous paper Matrices-One Review, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would ...; 关键词：MATRICES Matrix Addition Matrix Subtraction Matrix Division Dividend Matrix Divisor Matrix Quotient Matrix Remainder Matrix Fraction Division

Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves被引量：1: 《Chinese Journal of Electronics》2020年第1期97-105,共9页YOU Lin YANG Yilin GAO Shuhong; supported by the Key Program of the Nature Science Foundation of Zhejiang Province of China(No.LZ17F020002);the National Natural Science Foundation of China(No.61772166); In an(hyper)elliptic curve cryp to sys tem,the most important operation or the most time-consuming operation is the divisor scalar multiplication which consists of a sequence of doubling(of divisor)and addition(of two...; 关键词：Genus-3 hyperelliptic curve cryptosys tem Divisor scalar multiplication Divisor doubling Divisor halving.

DIVISOR