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Zhen Xia

Observed names: Xia, zhen, xia, zhen, 夏, 祯, 夏祯
ORCID: 0009-0008-3096-1810
Observed ORCID: 0009-0008-3096-1810
OpenAlex ID: A5113759464
二次特征 theta 函数的对数凹性:无穷幂增长族与极值情形(d=5) Log-concavity of theta functions of quadratic characters: an infinite family of power growth and the extremal case (d=5)
2026 · 夏祯, 包欣楠, et al. · Zenodo (CERN European Organization for Nuclear Research)
凸性而非对称:循环图与完全图ℓ1归一化谱半径最优化的机器验证理论 Convexity, Not Symmetry: A Machine-Verified Theory of ℓ1-Normalized Spectral Radius Optimization for Circulant and Complete Graphs
2026 · 夏祯, 包欣楠 · Zenodo (CERN European Organization for Nuclear Research)
\(K3^{[3]}\) 型六维流形中间次数的霍奇猜想:全体奇异 K3 曲面的情形 The Hodge Conjecture for the Middle Degree of Six-Dimensional \(K3^{[3]}\)-Type Manifolds: The Case of All Singular K3 Surfaces
2026 · 夏祯, 孙楠, et al. · Zenodo (CERN European Organization for Nuclear Research)
统一认知循环论:TRACE 与 PDCA 的深层同构 Towards a Unified Theory of the Cognitive Cycle: TRACE and PDCA as Instances of a Common Underlying Structure
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
H5 高维循环群两步覆盖系统:形式化理论 High-Dimensional Cyclic Group Two-Step Covering Systems: A Formal Theory
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
谱深渊自指方法论:当研究对象的结构在研究方法中再次出现 The Spectral Abyss Self-Referential Methodology: When the Structure of the Research Object Reappears in the Research Method
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
循环群等变霍奇问题:研究综述 Equivariant Hodge Problem for Cyclic Groups: A Research Survey
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
X16中间维数的有理霍奇猜想:一个非阿贝尔商簇正例 The Rational Hodge Conjecture in the Middle Degree for \(X_{16}\): A Non-Abelian Quotient Positive Case
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
最小闭环系统的维度锁定:循环图递归中 \(n=5\) 的唯一性 Dimensional Lock of Minimal Closed-Loop Systems: Uniqueness of \(n=5\) for Circulant Recursions
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
商六维簇 \(X_6\) 中间上同调的挠群精确值 \(N=526\) The Exact Torsion of the Middle Cohomology of the Quotient Sixfold \(X_6\): \(N=526\)
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
等变霍奇猜想的候选构型筛选:乘积-商、对角超曲面与 K3 及开放问题清单 Candidate Screening for the Equivariant Hodge Conjecture: Product-Quotient, Diagonal Hypersurfaces, and K3, with a List of Open Problems
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
\(X_6\) 中间次数的有理 Hodge 猜想:\(2+2r\) 维乘积闭链的张成 The Rational Hodge Conjecture in the Middle Degree for \(X_6\): Spanning by \(2+2r\) Product Cycles
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
商六维簇 \(X_6\) 的有理霍奇 (2,2) 类:一个显式维数公式 Rational Hodge (2,2) Classes on the Quotient Sixfold \(X_6\): An Explicit Dimension Formula
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
\(K3^{[3]}\)型簇的中间次数霍奇猜想:费马四次曲面的 Hilbert 三次概型 The Middle-Degree Hodge Conjecture for \(K3^{[3]}\)-Type Sixfolds: The Hilbert Cube of the Fermat Quartic
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
Navier–Stokes 立方点群在周期格 Fourier 截断上的谱间隙分类:谱间隙不是唯一瓶颈 Spectral Gaps of Cubic Point Groups on Periodic Fourier Truncations: Spectral Gap Is Not the Only Bottleneck
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
BSD C₅-AP24素数导体椭圆曲线的奇偶预测与开关分层——一项独立数值实证 Parity Predictions and a Switch Stratification for Prime-Conductor Elliptic Curves with \(N\equiv5\pmod{24}\): An Independent Numerical Verification
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
加权 K3 曲面上 5 阶纯非辛自同构的一个显式例子 An Explicit Example of an Order-5 Purely Non-Symplectic Automorphism on a Weighted K3 Surface
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
BSD 椭圆曲线格指数与 Sha 的数值关联:Atkin–Lehner 特征子格指数的观察 Numerical Correlation between Lattice Indices and Sha for Elliptic Curves: Atkin–Lehner Eigen-Sublattice Indices
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
Navier–Stokes \(C_5\) 对称 Galerkin 截断三维 Euler 方程:活性、级串结构与守恒量 \(C_5\) Symmetric Galerkin Truncation of 3D Euler Equations: Activity, Cascade Structure, and Conserved Quantities
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
Navier–Stokes 对称群谱系的结构理论:谱间隙跃迁、螺旋度瓶颈与临界对称性 Spectral Theory of Cubic Symmetry Groups: Spectral Gap Transitions, the Helicity Bottleneck, and Critical Symmetry
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
Redheffer 矩阵的 Smith 标准形:cokernel 结构、计算复杂性与 Mertens 函数的数值锚 Smith Normal Form of the Redheffer Matrix: Cokernel Structure, Computational Complexity, and Numerical Anchors for the Mertens Function
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
\( (F\times A_2'^{\,n-1}\times E)/C_5 \) 族的 codim 2 有理 Hodge 猜想:实分量正例、机制 A 与对角缺口 Rational Hodge Conjecture in Codimension 2 for the \((F\times A_2'^{\,n-1}\times E)/C_5\) Family: Real-Component Positives, Mechanism A, and the Diagonal Gap
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
Nair 三维杨–米尔斯质量隙不等式 \(\lambda\ge m\) 在固定模截断层级的严格化 Rigorousization of Nair's Mass-Gap Inequality \(\lambda\ge m\) for 3d Yang–Mills at Fixed Mode Cutoff
2026 · 夏祯 · Zenodo (CERN European Organization for Nuclear Research)
非乘积六维簇上的有理霍奇类:CM 域不兼容机制下的非平凡正例 Rational Hodge Classes on a Non-Product Sixfold: A Non-Trivial Positive Case via CM Field Incompatibility
2026 · 夏, 祯 · Zenodo (CERN European Organization for Nuclear Research)
Redheffer 扭转谱的谱半径——特征相消与多项式结构 Spectral Radius of the Twisted Redheffer Spectrum: Character Cancellation and Polynomial Structure
2026 · 夏, 祯 · Zenodo (CERN European Organization for Nuclear Research)
Works count: 56
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