15 papers
Strict Dirichlet Pólya Inequality for Simply Connected Planar Domains
Quanyu Tang, Zuoqin Wang
We establish the strict Dirichlet Pólya inequality on every bounded simply connected planar domain. The proof uses a unitary boundary transport formulation of the Helmholtz equatio…
Tilting Completion and Full-Rank Self-Orthogonal Modules
Wen Chang, Quanyu Tang
We give negative answers to two tilting-completion questions for finite-dimensional algebras. We construct two finite-dimensional basic connected quasi-hereditary -algeb…
The solution to Kadison's problem on orthonormal bases of unitaries for type factors
Yixin He, Quanyu Tang, Zongben Xu +1
In 1967, Kadison asked whether every type factor admits an orthonormal basis, with respect to its trace, consisting of unitaries. We resolve this problem in full ge…
Infinitely Many Components in Auslander--Reiten Quivers of Representation-Infinite Algebras over Perfect Fields
Wen Chang, Quanyu Tang
Let be a perfect field and let be a representation-infinite finite-dimensional -algebra. We prove that the Auslander--Reiten quiver of has infinitely many connected…
Strictly Convex Steklov-Isospectral Plane Domains
Tao Hu, Jiachen Shi, Quanyu Tang
We construct pairs of noncongruent bounded Euclidean plane domains with identical Steklov spectra, including multiplicities. This gives a negative answer to the planar Steklov anal…
Counterexamples to a higher-index Dirichlet eigenvalue-ratio conjecture
Yixin He, Quanyu Tang, Haiqi Zhang
Let denote the th Dirichlet Laplacian eigenvalue of a bounded planar domain , with eigenvalues counted with multiplicity. We disprove a conjectured higher-index exte…
Eventually greedy best Egyptian underapproximations of rational numbers via optimal control
Vjekoslav Kovač, Quanyu Tang
We prove that every positive rational number has eventually greedy best Egyptian underapproximations, both when repetitions of the denominators are allowed and when the denominator…
A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues
Yixin He, Yanyang Li, Quanyu Tang
We prove the Ashbaugh--Benguria conjecture for bounded domains with Lipschitz boundary in . More precisely, among all bounded Lipschitz domains of fixed volume, the ba…
The separable case of Kadison's problem on orthonormal bases of unitaries for type factors
Yixin He, Quanyu Tang, Teng Zhang
In 1967, Kadison asked ``does every type factor have an orthonormal (with respect to the trace) basis consisting of unitaries?'' Using a noncommutative Lyapunov the…
Almost Affine Invariance Over Prime Fields: Green Problem 90
Jie Ma, Quanyu Tang, Max Wenqiang Xu
Let with density 1/2. We call a set almost affine invariant under an affine transformation if \[|A \triangle ϕ(A)| =o(p).\] We determine tha…
Optimal universal growth for integral means of normalized logarithmic derivatives in the Carathéodory class
Yixin He, Quanyu Tang, Teng Zhang
We determine the optimal universal growth scale for the integral means of normalized logarithmic derivatives in the Carathéodory class. This resolves a problem of D.~K.~Thomas.
A sharp upper bound on the third adjacency eigenvalue of a graph
Quanyu Tang
For a graph of order , let be the eigenvalues of its adjacency matrix. We prove that every graph on vertices satisfies $$ λ_3(…
A Solution to a Problem of Rubel on Two-Parameter Normal Families of Entire Functions
Yixin He, Quanyu Tang, Teng Zhang
We construct an entire function such that the family of entire functions of \(z\) is normal on…
Sharp Schoenberg type inequalities and the de Bruin--Sharma problem
Quanyu Tang, Teng Zhang
In this paper, we confirm two conjectures proposed by Georgiev, Gómez-Serrano, Tao, and Wagner~\cite{GGTW25} on Schoenberg type inequalities of order , thereby providing a compl…
Schoenberg type inequalities
Quanyu Tang
In the geometry of polynomials, Schoenberg's conjecture, now a theorem, is a quadratic inequality between the zeros and critical points of a polynomial whose zeros have their centr…