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Geometric-like imaginarity: Quantification and state conversion

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science China(Physics,Mechanics & Astronomy) 2025年第2期Mechanics & Astronomy) .卷 17-26页

作者： Meng-Li Guo Bo Li Shao-Ming Fei school of science East China University of Technology school of Computer and Computing science Hangzhou City University school of mathematical sciences Capital Normal University

From the perspective of resource-theoretic approach, this study explores the quantification of imaginary in quantum physics. We propose a well defined measure of imaginarity, the geometric-like measure of imaginarity. Compared with the usual geometric imaginarity measure, this geometric-like measure of imaginarity exhibits smaller decay difference under quantum noisy channels and higher stability. As applications, we show that both the optimal probability of state transformations from a pure state to an arbitrary mixed state via real operations, and the maximal probability of stochastic-approximate state transformations from a pure state to an arbitrary mixed state via real operations with a given fidelity f, are given by the geometric-like measure of imaginarity.

关键词： quantum resource theory imaginarity geometric-like channels state transformations

An analytic proof of multivariate Polya-Carlson theorem

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Acta Mathematica Sinica,English Series 2025年

作者： Tian Long YU school of mathematical sciences Peking University

Polya-Carlson theorem asserts that if a power series with integer coefficients and convergence radius 1 can be extended holomorphically out of the unit disc, it must represent a rational function. In this note, we give a generalization of this result to multivariate case and give an application to rationality theorem about D-finite power series.

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Number rigid determinantal point processes induced by generalized Cantor sets

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Acta Mathematica Sinica,English Series 2025年

作者： Zhaofeng LIN Yanqi QIU Kai WANG school of Fundamental Physics and mathematical sciences HIAS University of Chinese Academy of Sciences school of mathematical sciences Fudan University

We consider the Ghosh-Peres number rigidity of translation-invariant determinantal point processes on the real line R, whose correlation kernels are induced by the Fourier transform of the indicators of generalized Cantor sets in the unit interval. Our main results show that for any givenθ∈(0, 1), there exists a generalized Cantor set with Lebesgue measure θ, such that the corresponding determinantal point process is Ghosh-Peres number rigid.

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Miyaoka-type inequalities for terminal threefolds with nef anti-canonical divisors

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science China Mathematics 2025年第1期68卷 1-18页

作者： Masataka Iwai Chen Jiang Haidong Liu Department of Mathematics Graduate School of ScienceOsaka UniversityOsaka 560-0043Japan Shanghai Center for mathematical sciences&school of mathematical sciences Fudan UniversityShanghai 200438China Department of mathematics Sun Yat-sen UniversityGuangzhou 510275China

In this paper,we study Miyaoka-type inequalities on Chern classes of terminal projective 3-folds with nef anti-canonical *** X be a terminal projective 3-fold such that-KX is *** show that if c1(X) · c2(X)≠0,then c1(X) · c2(X) ≥ 1/252;if further X is not rationally connected,then c1(X) · c2(X) ≥ 4/5 and this inequality is *** order to prove this,we give a partial classification of such varieties along with many *** also study the nonvanishing of c1(X)dim X-2 · c2(X) for terminal weak Fano varieties and prove a Miyaoka-Kawamata-type inequality.

关键词： terminal threefolds Miyaoka-type inequality boundedness

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Quantifying the Driving Effect of Colored Noise in Brownian Motors

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Chinese Physics Letters 2025年第1期42卷 88-92页

作者： Zhichao Zhang Yue Liu Congmin Wu Dahai He Department of Physics and Jiujiang Research Institute Xiamen University school of mathematical sciences Xiamen University

The colored noise disrupts the detailed balance, enabling directed transport in ratchet systems without additional driving forces. Despite a well-established understanding of the conditions for Brownian motors, quantification of the driving effect of colored noise and its connection to deviations from equilibrium remains unexplored. In this study, we examined the directed motion of an overdamped Brownian motor within an asymmetric traveling potential subjected to Ornstein–Uhlenbeck colored noise. We propose a scheme to quantify the driving effect of colored noise by defining an effective force based on the stopping velocity of the traveling potential where directed transport halts. Our results revealed a nonmonotonic dependence of the effective force on the noise correlation time and a monotonic dependence on the noise strength, corresponding to double and single current reversals, respectively. The nonmonotonicity of the current is attributed to the interplay between the fluctuating characteristics and the driving effects of colored noise.

关键词： Traction motors

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A SURVEY ON THE ISOPERIMETRIC PROBLEM IN RIEMANNIAN MANIFOLDS

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Acta Mathematica scientia 2025年第1期45卷 228-236页

作者：李嘉禹潘淑婧 school of mathematical sciences University of Science and Technology of China

This is a survey of the results in [14] regarding the isoperimetric problem in the Riemannian *** consider a mean curvature type flow in the Riemannian manifold endowed with a non-trivial conformal vector field,which was firstly introduced by Guan and Li [8] in space *** flow preserves the volume of the bounded domain enclosed by a star-shaped hypersurface and decreases the area of hypersurface under certain *** will prove the long time existence and convergence of the *** a result,the isoperimetric inequality for such a domain is established.

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Twist monomials of binary delta-matroids

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Acta Mathematica Sinica,English Series 2025年

作者： Qi YAN Xian'an JIN school of Mathematics and Statistics Lanzhou University school of mathematical sciences Xiamen University

Recently, we introduced the twist polynomials of delta-matroids and gave a characterization of even normal binary delta-matroids whose twist polynomials have only one term and posed a problem:what would happen for odd binary delta-matroids? In this paper, we show that a normal binary deltamatroid whose twist polynomials have only one term if and only if each connected component of the intersection graph of the delta-matroid is either a complete graph of odd order or a single vertex with a loop.

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Lyapunov optimizing measures and periodic measures for C2 expanding maps

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Acta Mathematica Sinica,English Series 2025年

作者： Wen HUANG Leiye XU Dawei YANG CAS Wu Wen-Tsun Key Laboratory of Mathematics School of Mathematical Sciences University of Science and Technology of China school of mathematical sciences Soochow University

We prove that there exists an open and dense subset U in the space of C2expanding selfmaps of the circle T such that the Lyapunov minimizing measures of any T ∈ U are uniquely supported on a periodic orbit. This answ...

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The P_(5)-saturation Game

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Acta Mathematicae Applicatae Sinica 2025年第1期41卷 295-304页

作者： Zhen HE Mei LU school of Mathematics and Statistics Beijing Jiaotong UniversityBeijing 100044China Department of mathematical sciences Tsinghua UniversityBeijing 100084China

Let F,G and H be three graphs with G■*** call G an F-saturated graph relative to H,if there is no copy of F in G but there is a copy of F in G+e for any e∈E(H)\E(G).The F-saturation game on host graph H consists of two players,named Max and Min,who alternately add edges of H to G such that each chosen edge avoids creating a copy of F in G,and the players continue to choose edges until G becomes F-saturated relative to *** wishes to maximize the length of the game,while Min wishes to minimize the *** sat_(g)(F,H)(***_(g)'(F,H))denote the number of edges chosen when Max(*** Min)starts the game and both players play *** this article,we show that sat_(g)(P_(5),K_(n))=sat_(g)'(P_(5),K_(n))=n+2 for n≥15,and satg(P_(5),K_(m,n)),sat_(g)'(P_(5),K_(m,n))lie in{m+n-[m+2/4];m+n-[m-3/4]}if n≥5/2m and m≥4,respectively.

关键词： saturation number saturation game host graph