Journal of Mathematical Study
type: channel
description: Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics. JMS is edited by a group of leading researchers and aims to become a premier mathematical journal.
publisher: Global Science Press
language: en
publication name: Journal of Mathematical Study
issn: 2096-9856
items: A Note on the Global Existence for the Strong Solution of the Stochastic Three-Dimensional Axially Symmetric Euler Equations
items: Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application
items: A Regularity Result for the Incompressible Elastodynamics with a Free Interface
items: On a Class of Degenerate Nonlinear Elliptic Equations in Weighted Sobolev Spaces
items: Common Fixed Point Results for a Pair of Generalized Nonlinear Mappings in Complete Metric Spaces
items: Some $p$-Adic Hardy Operators and Their Commutators
items: Non-Traveling Wave Solutions of (3+1)-Dimensional Variable Coefficients BLMP Equation with a Compound Technology
items: A Note on the Determinant of a Special Class of $Q$-Walk Matrices
items: Characterizations of Umbilical Hypersurfaces by Partially Overdetermined Problems in Space Forms
items: An Alternative Proof for the Upper Bound of Curvature Integral on Manifolds with Lower Sectional Curvature Bound
items: On Conical Asymptotically Flat Manifolds
items: Moduli Spaces of Metrics with Lower or Pinched Curvature Bounds and Their Compactifications
items: Rigidity for Einstein Manifolds under Bounded Covering Geometry
items: Pair-of-Pants Decompositions of 4-Manifolds Diffeomorphic to General Type Hypersurfaces
items: Volume Gap Theorems for Ricci Nonnegative Metrics and Einstein Metrics
items: Affine Isoperimetric Type Inequalities for Static Convex Domains in Hyperbolic Space
items: Monotone Sequences of Metric Spaces with Compact Limits
items: Examples of Ricci Solitons
items: Ricci Curvature and Fundamental Groups of Effective Regular Sets
items: Quasi-Convex Subsets and the Farthest Direction in Alexandrov Spaces with Lower Curvature Bound
items: $L^4$-Bound of the Transverse Ricci Curvature under the Sasaki-Ricci Flow
items: Preface: Special Issues in Honor of Professors Xiaochun Rong
items: A Brief Introduction on Prof. Rong’s Mathematical Work
items: Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem
items: On the Computational Problems of Upper Convex Densities for Self-Similar Sets with the Open Set Condition
items: Normalized Solutions for a Kirchhoff Equation with Potential in $\mathbb{R}^3$
items: Fitting Heavy-Tailed Distributions to Mortality Indexes for Longevity Risk Forecasts
items: Endpoint Estimates for an Oscillatory Multiplier Associated with Wave Equations on the Torus
items: B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence
items: The Category Types of Extensions of a Tambara-Yamagami Category

A Note on the Global Existence for the Strong Solution of the Stochastic Three-Dimensional Axially Symmetric Euler Equations
type: item
description: This paper establishes the global existence of the pathwise solutions for the stochastic 3-D incompressible Euler equations with the axially symmetric initial data and axially symmetric additive noise.
subject: Articles
  topic: section
creator: Lihuai Du
creator: Jinbo Geng
creator: Haoyong Zhou
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 407
ending page: 416
doi: 10.4208/jms.v58n3.25.09

Generalized Estimation of Numerical Radius for the off-Diagonal 2×2 Operator Matrices and Its Application
type: item
description: We give some generalized upper bounds for the numerical radius of off-diagonal 2×2 operator matrices. These inequalities are mainly based on the extension Buzano inequality and the generalized Young inequality. And our bounds refine and generalize the existing related upper bounds. Moreover, the conclusion is applied to the non-monic operator polynomials and gives a new bound for the eigenvalues of these operator polynomials.
subject: Articles
  topic: section
creator: Muqile Gao
creator: Deyu Wu
creator: Alatancang Chen
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 323
ending page: 337
doi: 10.4208/jms.v58n3.25.05

A Regularity Result for the Incompressible Elastodynamics with a Free Interface
type: item
description: We consider the incompressible inviscid elastodynamics equations with a free surface and establish the regularity of solutions for elastic system. Compared with the previous result on this free boundary problem [ Gu X and Wang F, Well-posedness of the free boundary problem in incompressible elastodynamics under the mixed type stability condition, J. Math. Anal. Appl., 2020, 482(1): 123529] in space $H^3,$ we are able to establish the regularity in space $H^{2.5+δ}.$ It is achieved by reformulating the system into the Lagrangian formulation, presenting the uniform estimates for the pressure, the tangential estimates for the system, as well as the divergence and curl estimates.
subject: Articles
  topic: section
creator: Binqiang Xie
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 338
ending page: 361
doi: 10.4208/jms.v58n3.25.06

On a Class of Degenerate Nonlinear Elliptic Equations in Weighted Sobolev Spaces
type: item
description: In this paper we are interested in the existence of solutions for Dirichlet problem associated to the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces $W^{1,p}_ 0 (Ω,ω).$
subject: Articles
  topic: section
creator: Albo Carlos Cavalheiro
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 362
ending page: 379
doi: 10.4208/jms.v58n3.25.07

Common Fixed Point Results for a Pair of Generalized Nonlinear Mappings in Complete Metric Spaces
type: item
description: In this paper, under the asymptotically regular condition, we investigate the existence of a unique common fixed point for a pair of generalized nonlinear mappings in the framework of complete metric spaces. Additionally, we extend our analysis to the case involving two control functions. Our work generalizes some results in recent papers.
subject: Articles
  topic: section
creator: Chao Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 314
ending page: 322
doi: 10.4208/jms.v58n3.25.04

Some $p$-Adic Hardy Operators and Their Commutators
type: item
description: In this paper, we will study the sharp estimates of $p$-adic weighted Hardy operator on central and noncentral weighted $p$-adic Morrey spaces. Moreover, we can obtain the sharp bound of generalized $p$-adic Hardy operator. In addition, the commutator that is generated by the generalized $p$-adic Hardy operator and the central BMO function is also bounded on $p$-adic Morrey spaces.
subject: Articles
  topic: section
creator: Xizheng Zhang
creator: Xiang Li
creator: Dunyan Yan
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 380
ending page: 406
doi: 10.4208/jms.v58n3.25.08

Non-Traveling Wave Solutions of (3+1)-Dimensional Variable Coefficients BLMP Equation with a Compound Technology
type: item
description: We investigate non-traveling wave solutions of the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation with time-dependent coefficients, which describes the propagation of waves in incompressible fluids. We creatively combine the extended three-wave method with the generalized variable separation method and successfully obtain sixty exact non-traveling solutions including kink-like solutions, singular solitary wave-like solutions, periodic solitary wave-like solutions, periodic kink-like solutions, periodic cross-kink-like waves, homoclinic breather wave-like solutions and so on. The variable coefficients and arbitrary functions in the obtained solutions are easy to exhibit abundant soliton structures, which may be of great significance for explaining some practical physical phenomena. By contour plots, 2D plots, and 3D plots, we analyze the dynamic characteristics of periodic cross-kink-like solution, singular solitary wave-like solution, homoclinic breather wave-like solution. Additionally, we show changes of solutions under different tails to illustrate the influence of tails on solutions.
subject: Articles
  topic: section
creator: Xiaoxiao Zheng
creator: Yuanqing Xu
creator: Lingling Zhao
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 253
ending page: 274
doi: 10.4208/jms.v58n3.25.01

A Note on the Determinant of a Special Class of $Q$-Walk Matrices
type: item
description: For a graph $G$ of order $n,$ its $Q$-walk matrix is defined by $W_Q(G) = [e,Qe,···,Q^{n−1}e],$ where $Q$ is the signless Laplacian matrix of $G$ and $e$ denotes the all-one column vector. Let $G \circ P_k$ represent the rooted product graph of $G$ and a path $P_k.$ In this note, we establish the relationship between determinants of $W_Q(G)$ and $W_Q(G \circ P_k )$ for $k=2,3.$
subject: Articles
  topic: section
creator: Guixian Tian
creator: Junxing Wu
creator: Shuyu Cui
creator: Huilu Sun
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 275
ending page: 285
doi: 10.4208/jms.v58n3.25.02

Characterizations of Umbilical Hypersurfaces by Partially Overdetermined Problems in Space Forms
type: item
description: In this paper, we characterize the rigidity of umbilical hypersurfaces by a Serrin-type partially overdetermined problem in space forms, which generalizes the similar results in Euclidean half-space and Euclidean half-ball. Guo-Xia first obtained these rigidity results when the Robin boundary condition on the support hypersurface is homogeneous, at this time the target umbilical hypersurface has orthogonal contact angle with the support. However, in this paper we can obtain any contact angle $θ ∈ (0,π)$ by changing the Robin boundary condition to be inhomogeneous.
subject: Articles
  topic: section
creator: Yangsen Xie
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-16
publication date: 2025-09-16
starting page: 286
ending page: 313
doi: 10.4208/jms.v58n3.25.03

An Alternative Proof for the Upper Bound of Curvature Integral on Manifolds with Lower Sectional Curvature Bound
type: item
description: Petrunin proved that the integral of scalar curvature in a unit ball is bounded from above in terms of the dimension of the manifold and the lower bound of the sectional curvature. In this paper, we give an alternative proof for this result. The main difference between this proof and Petrunin’s original proof is that we construct a stratified finite covering and apply it directly to the given manifold, rather than arguing by contradiction for a sequence of manifolds, which satisfy some technical lifting properties.
subject: Articles
  topic: section
subject: Scalar curvature
  topic: keywords
subject: sectional curvature
  topic: keywords
subject: $L^1$-norm
  topic: keywords
subject: Alexandrov space
  topic: keywords
subject: stratification
  topic: keywords
subject: covering.
  topic: keywords
subject: 53B20
  topic: subjects
subject: 53C21
  topic: subjects
creator: Nan Li
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 164
ending page: 174
doi: 10.4208/jms.v58n2.25.03

On Conical Asymptotically Flat Manifolds
type: item
description: We prove a conjecture of Petrunin and Tuschmann on the non-existence of asymptotically flat 4-manifolds asymptotic to the half plane. We also survey recent progress and questions concerning gravitational instantons, which serve as our motivation for studying this question.
subject: Articles
  topic: section
subject: Asymptotically flat
  topic: keywords
subject: collapsing
  topic: keywords
subject: gravitational instanton.
  topic: keywords
subject: 53C21
  topic: subjects
subject: 53C23
  topic: subjects
creator: Mingyang Li
creator: Song Sun
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 188
ending page: 210
doi: 10.4208/jms.v58n2.25.05

Moduli Spaces of Metrics with Lower or Pinched Curvature Bounds and Their Compactifications
type: item
description: We present a metric approach to the study of moduli spaces of metrics with certain curvature bounds and suitable other geometric constraints, and their compactifications. This is accompanied by a deeper discussion of related results, questions and problems in the realm of positive and positively pinched sectional as well as Ricci curvature. Regarding the latter two topics, we place special emphasis on corresponding works and contributions of Rong X and his collaborators.
subject: Articles
  topic: section
subject: Moduli spaces
  topic: keywords
subject: metrics
  topic: keywords
subject: lower curvature bounds
  topic: keywords
subject: pinching.
  topic: keywords
subject: 53C20
  topic: subjects
creator: Wilderich Tuschmann
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 175
ending page: 187
doi: 10.4208/jms.v58n2.25.04

Rigidity for Einstein Manifolds under Bounded Covering Geometry
type: item
description: In this note, we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. ${\rm Ric}_g =λg$ for some real number $λ.$ (2) A compact Einstein manifold with a non-vanishing and almost maximal volume entropy is hyperbolic. (3) A compact Einstein manifold admitting a uniform local rewinding almost maximal volume is isometric to a space form.
subject: Articles
  topic: section
subject: Einstein
  topic: keywords
subject: rigidity
  topic: keywords
subject: almost nonnegative Ricci curvature
  topic: keywords
subject: bounded covering geometry
  topic: keywords
subject: space forms.
  topic: keywords
subject: 53C23
  topic: subjects
subject: 53C21
  topic: subjects
subject: 53C20
  topic: subjects
subject: 53C24
  topic: subjects
creator: Cuifang Si
creator: Shicheng Xu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 145
ending page: 163
doi: 10.4208/jms.v58n2.25.02

Pair-of-Pants Decompositions of 4-Manifolds Diffeomorphic to General Type Hypersurfaces
type: item
description: In this paper, we show that a smooth 4-manifold diffeomorphic to a complex hypersurface in $\mathbb{CP}^3$ of degree $d≥5$ can be decomposed as the union of $d(d−4)^2$ copies of 4-dimensional pair-of-pants and certain subsets of ${\rm K3}$ surfaces.
subject: Articles
  topic: section
subject: Pair-of-pants decompositions
  topic: keywords
subject: general type hypersurfaces.
  topic: keywords
subject: 53C56
  topic: subjects
subject: 14T05
  topic: subjects
creator: Yuguang Zhang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 211
ending page: 252
doi: 10.4208/jms.v58n2.25.06

Volume Gap Theorems for Ricci Nonnegative Metrics and Einstein Metrics
type: item
description: In this note, we prove some gap theorems of asymptotic volume ratio for Ricci nonnegative metrics, and gap theorems of volume for Einstein metrics.
subject: Articles
  topic: section
subject: Asymptotic volume ratio
  topic: keywords
subject: Ricci curvature
  topic: keywords
subject: Einstein metrics.
  topic: keywords
subject: 53C21
  topic: subjects
creator: Xiuxiong Chen
creator: Conghan Dong
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-26
publication date: 2025-06-26
starting page: 133
ending page: 144
doi: 10.4208/jms.v58n2.25.01

Affine Isoperimetric Type Inequalities for Static Convex Domains in Hyperbolic Space
type: item
description: In this paper, the notion of hyperbolic ellipsoids in hyperbolic space is introduced. Using a natural orthogonal projection from hyperbolic space to Euclidean space, we establish affine isoperimetric type inequalities for static convex domains in hyperbolic space. Moreover, equality of such inequalities is characterized by these hyperbolic ellipsoids.
subject: Articles
  topic: section
subject: Static convex
  topic: keywords
subject: Blaschke-Santalό inequality
  topic: keywords
subject: affine isoperimetric inequality
  topic: keywords
subject: orthogonal projection
  topic: keywords
subject: hyperbolic space.
  topic: keywords
subject: 52A40
  topic: subjects
subject: 53C24
  topic: subjects
subject: 53A15
  topic: subjects
creator: Yingxiang Hu
creator: Haizhong Li
creator: Yao Wan
creator: Botong Xu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 62
ending page: 81
doi: 10.4208/jms.v58n1.25.04

Monotone Sequences of Metric Spaces with Compact Limits
type: item
description: In this paper, we consider a fixed metric space (possibly an oriented Riemannian manifold with boundary) with an increasing sequence of distance functions and a uniform upper bound on diameter. When the fixed space endowed with the point-wise limit of these distances is compact, then there is uniform and Gromov-Hausdorff (GH) convergence to this space. When the fixed metric space also has an integral current structure of uniformly bounded total mass (as is true for an oriented Riemannian manifold with boundary that has a uniform bound on total volume), we prove volume preserving intrinsic flat convergence to a subset of the GH limit whose closure is the whole GH limit. We provide a review of all notions and have a list of open questions at the end.
subject: Articles
  topic: section
subject: Metric spaces
  topic: keywords
subject: Riemannian
  topic: keywords
subject: Gromov-Hausdorff
  topic: keywords
subject: intrinsic flat.
  topic: keywords
subject: 53C24
  topic: subjects
creator: Raquel Perales
creator: Christina Sormani
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 96
ending page: 132
doi: 10.4208/jms.v58n1.25.06

Examples of Ricci Solitons
type: item
description: In this survey paper, we discuss various examples of Ricci solitons and their constructions. Some open questions related to the rigidity and classification of Ricci solitons will be also discussed through those examples.
subject: Articles
  topic: section
subject: Ricci flow
  topic: keywords
subject: Ricci soliton
  topic: keywords
subject: ancient solution
  topic: keywords
subject: singularity model.
  topic: keywords
subject: 53E20
  topic: subjects
subject: 53C20
  topic: subjects
subject: 53C25
  topic: subjects
subject: 58J05
  topic: subjects
creator: Ziyi Zhao
creator: Xiaohua Zhu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 82
ending page: 95
doi: 10.4208/jms.v58n1.25.05

Ricci Curvature and Fundamental Groups of Effective Regular Sets
type: item
description: For a Gromov-Hausdorff convergent sequence of closed manifolds $M^n_i\xrightarrow{GH} X$ with ${\rm Ric}\ge -(n-1)$, ${\rm diam}(M_i) ≤ D,$ and ${\rm vol}(M_i) ≥ v > 0,$ we study the relation between $π_1(M_i)$ and $X.$ It was known before that there is a surjective homomorphism $ϕ_i : π_1(M_i) → π_1(X)$ by the work of Pan-Wei. In this paper, we construct a surjective homomorphism from the interior of the effective regular set in $X$ back to $M_i,$ that is, $ψ_i :π_1(\mathcal{R}^◦_{ϵ,δ} )→π_1(M_i).$ These surjective homomorphisms $ϕ_i$ and $ψ_i$ are natural in the sense that their composition $ϕ_i◦ψ_i$ is exactly the homomorphism induced by the inclusion map $R^◦_{ ϵ,δ}\hookrightarrow X.$
subject: Articles
  topic: section
subject: Ricci curvature
  topic: keywords
subject: fundamental groups
  topic: keywords
subject: Gromov-Hausdorff convergence.
  topic: keywords
subject: 53C21
  topic: subjects
subject: 53C23
  topic: subjects
creator: Jiayin Pan
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 3
ending page: 21
doi: 10.4208/jms.v58n1.25.01

Quasi-Convex Subsets and the Farthest Direction in Alexandrov Spaces with Lower Curvature Bound
type: item
description: Let $F$ be a closed subset in a finite dimensional Alexandrov space $X$ with lower curvature bound. This paper shows that $F$ is quasi-convex if and only if, for any two distinct points $p,r∈F,$ if there is a direction at $p$ which is more than $\frac{π}{2}$ away from $⇑^r_p$ (the set of all directions from $p$ to $r$), then the farthest direction to $⇑^r_p$ at $p$ is tangent to $F.$ This implies that $F$ is quasi-convex if and only if the gradient curve starting from $r$ of the distance function to $p$ lies in $F.$ As an application, we obtain that the fixed point set of an isometry on $X$ is quasi-convex.
subject: Articles
  topic: section
subject: Quasi-convex subset
  topic: keywords
subject: Alexandrov space
  topic: keywords
subject: extremal subset
  topic: keywords
subject: gradient curve.
  topic: keywords
subject: 53C20
  topic: subjects
subject: 51F99
  topic: subjects
creator: Xiaole Su
creator: Hongwei Sun
creator: Yusheng Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 22
ending page: 37
doi: 10.4208/jms.v58n1.25.02

$L^4$-Bound of the Transverse Ricci Curvature under the Sasaki-Ricci Flow
type: item
description: In this paper, we show that the uniform $L^4$-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular transverse Fano Sasakian $(2n+1)$-manifold $M.$ Then we are able to study the structure of the limit space. As consequences, when $M$ is of dimension five and the space of leaves of the characteristic foliation is of type I, any solution of the Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold Sasaki-Ricci soliton and is trivial one if $M$ is transverse $K$-stable. Note that when the characteristic foliation is of type II, the same estimates hold along the conic Sasaki-Ricci flow.
subject: Articles
  topic: section
subject: Sasaki-Ricci flow
  topic: keywords
subject: Sasaki-Ricci soliton
  topic: keywords
subject: transverse Fano Sasakian manifold
  topic: keywords
subject: transverse Sasaki-Futaki invariant
  topic: keywords
subject: transverse $K$-stable
  topic: keywords
subject: Foliation singularities.
  topic: keywords
subject: 53E50
  topic: subjects
subject: 53C25
  topic: subjects
subject: 53C12
  topic: subjects
subject: 14E30
  topic: subjects
creator: Shu-Cheng Chang
creator: Yingbo Han
creator: Chien Lin
creator: Chin-Tung Wu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 38
ending page: 61
doi: 10.4208/jms.v58n1.25.03

Preface: Special Issues in Honor of Professors Xiaochun Rong
type: item
subject: Articles
  topic: section
subject:
  topic: subjects
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: i
ending page: i
doi: 10.4208/jms.v58n1.25.preface

A Brief Introduction on Prof. Rong’s Mathematical Work
type: item
description: Xiaochun Rong was born on June 17th, 1954. He graduated from Beijing Normal College (now Capital Normal University) in 1982, and received his Ph.D. from Stony Brook University in 1990. Rong was a Sloan Research Fellow in 1996-1998, and an NSF research grant awardee in 1994-2013. He has been a distinguished professor at Rutgers University in New Brunswick since 2008. Rong was a 2002 ICM invited speaker, and a 2017 Fellow of the American Mathematical Society.
subject: Articles
  topic: section
subject:
  topic: subjects
creator: Yusheng Wang
creator: Shicheng Xu
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-03-31
publication date: 2025-03-31
starting page: 1
ending page: 2
doi: 10.4208/jms.v58n1.25.00

Analytic Insights into an Adapted Algorithm for the Score-Based Secretary Problem
type: item
description: In this paper, we study some basic analytic properties of a sequence of functions $\{S^{\mu,σ}_n\}$ that is directly derived in an adaptive algorithm originating from the classical score-based secretary problem. More specifically, we show that: 1. the uniqueness of maximum points of the function sequence $\{S^{\mu,σ}_n\};$ 2. the maximum point sequence of $\{S^{\mu,σ}_n\}$ monotone increases to infinity as $n$ tends to infinity. All of the proofs are elementary but nontrivial.
subject: Articles
  topic: section
subject: Secretary problem
  topic: keywords
subject: adaptive algorithm
  topic: keywords
subject: expected score
  topic: keywords
subject: uniqueness of maximum points.
  topic: keywords
subject: 26A06
  topic: subjects
subject: 49K05
  topic: subjects
creator: Giangvuthanh Nguyen
creator: Xiang Xu
creator: Yanxiang Zhao
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 476
ending page: 485
doi: 10.4208/jms.v57n4.24.05

On the Computational Problems of Upper Convex Densities for Self-Similar Sets with the Open Set Condition
type: item
description: Let $E$ be a self-similar set satisfying the open set condition. Zhou and Feng posed an open problem in 2004 as follows: let $x ∈ E,$ under what conditions is there a set $U_x$ containing $x$ with $|U_x| > 0$ such that $\overline{D}^s_C(E,x) = \frac{\mathcal{H}^s(E \cap U_x)}{|U_x|^s}?$ The aim of this paper is to present a solution of this problem. Under the assumption that there exists a nonempty convex open set $V$ containing $E$ and satisfying the requirement of the open set condition, it is proved that if $x ∈ E$ and the upper convex density of $E$ at $x$ equals 1, then there exists a convex set $U_x$ containing $x$ with $|U_x| > 0$ such that $\overline{D}^s_C(E,x) =\frac{\mathcal{H}^s (E∩U_x)}{|U_x|^s}.$ Finally, as an application of this result, an equivalent condition for $E_0 = E$ is given, where $E_0 =\{x∈E|\overline{D}^s_C(E,x)=1\}.$
subject: Articles
  topic: section
subject: Hausdorff measure
  topic: keywords
subject: self-similar set
  topic: keywords
subject: open set condition
  topic: keywords
subject: upper convex density.
  topic: keywords
subject: 28A78
  topic: subjects
subject: 28A80
  topic: subjects
creator: Jiandong Yin
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 499
ending page: 508
doi: 10.4208/jms.v57n4.24.07

Normalized Solutions for a Kirchhoff Equation with Potential in $\mathbb{R}^3$
type: item
description: In this paper, for given mass $c>0,$ we study the existence of normalized solutions to the following nonlinear Kirchhoff equation $$\begin{cases} (a+b\int_{\mathbb{R}^3}[|\nabla u|^2+V(x)u^2]dx)[-\Delta u+V(x)u]=\lambda u+\mu|u|^{q-2}u+|u|^{p-2}u, \ \ \ {\rm in}\ \ \mathbb{R}^3, \\ \int_{\mathbb{R}^3}|u|^2dx=c^2, \end{cases}$$where $a>0, b>0, λ∈\mathbb{R},$ $5<q< p<6,$ $\mu>0$ and $V$ is a continuous non-positive function vanishing at infinity. Under some mild assumptions on $V,$ we prove the existence of a mountain pass normalized solution via the minimax principle.
subject: Articles
  topic: section
subject: Kirchhoff equation
  topic: keywords
subject: normalized solutions
  topic: keywords
subject: minimax principle.
  topic: keywords
subject: 35C15
  topic: subjects
subject: 35Q51
  topic: subjects
creator: Yuan Xu
creator: Yongyi Lan
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 509
ending page: 527
doi: 10.4208/jms.v57n4.24.08

Fitting Heavy-Tailed Distributions to Mortality Indexes for Longevity Risk Forecasts
type: item
description: Modeling and predicting mortality rates are crucial for managing and mitigating longevity risk in pension funds. To address the impacts of extreme mortality events in forecasting, researchers suggest directly fitting a heavy-tailed distribution to the residuals in modeling mortality indexes. Since the true mortality indexes are unobserved, this fitting relies on the estimated mortality indexes containing measurement errors, leading to estimation biases in standard inferences within the actuarial literature. In this paper, the empirical characteristic function (ECF) technique is employed to fit heavy-tailed distributions to the time series residuals of mortality indexes and normal distributions to the measurement errors. Through a simulation study, we empirically validate the consistency of our proposed method and demonstrate the importance and challenges associated with making inferences in the presence of measurement errors. Upon analyzing publicly available mortality datasets, we observe instances where mortality indexes may follow highly heavy-tailed distributions, even exhibiting an infinite mean. This complexity adds a layer of difficulty to the statistical inference for mortality models.
subject: Articles
  topic: section
subject: Characteristic function
  topic: keywords
subject: Lee-Carter model
  topic: keywords
subject: mortality rates
  topic: keywords
subject: unit root model.
  topic: keywords
subject: 62M10
  topic: subjects
subject: 62P05
  topic: subjects
creator: Longyu Chen
creator: Tsz Chai Fung
creator: Yinhuan Li
creator: Liang Peng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 486
ending page: 498
doi: 10.4208/jms.v57n4.24.06

Endpoint Estimates for an Oscillatory Multiplier Associated with Wave Equations on the Torus
type: item
description: In this paper, we establish the endpoint estimate for an oscillatory multiplier associated with wave equations on the torus, which extends the results of Fan and Sun. In addition, we obtain a more general result for sublinear operators on compact measure spaces.
subject: Articles
  topic: section
subject: Oscillatory multiplier
  topic: keywords
subject: wave equation
  topic: keywords
subject: compact measure spaces.
  topic: keywords
subject: 42B15
  topic: subjects
subject: 42B25
  topic: subjects
subject: 42B99
  topic: subjects
creator: Ziyao Liu
creator: Dashan Fan
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 528
ending page: 538
doi: 10.4208/jms.v57n4.24.09

B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence
type: item
description: In this paper, we first give the concept of B-statistical uniform integrability with respect to Cesàro matrix (B-CUI), which is weaker than Cesàro uniform integrability. Then we establish some B-statistical convergence theorems for random sequence under the condition of B-CUI, which generalizes the outcomes of some known results. Finally, for some special kinds of triangular array or pairwise independent sequences of random variables, similar results are also derived without conditions of B-CUI.
subject: Articles
  topic: section
subject: B-statistical uniform integral
  topic: keywords
subject: Cesàro matrix
  topic: keywords
subject: martingale difference
  topic: keywords
subject: $\mathfrak{L}_p$ convergence.
  topic: keywords
subject: 60F25
  topic: subjects
creator: Mengru Chen
creator: Weicai Peng
creator: Zhongzhi Wang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 446
ending page: 459
doi: 10.4208/jms.v57n4.24.03

The Category Types of Extensions of a Tambara-Yamagami Category
type: item
description: In this paper, we study the group extension of a Tambara-Yamagami category which has Frobenius-Perron dimension $2pq,$ where $p,q$ are prime numbers. We prove that there are two possible category types when $p\ne q,$ and five possible category types when $p=q.$
subject: Articles
  topic: section
subject: Fusion category
  topic: keywords
subject: extension
  topic: keywords
subject: Tambara-Yamagami category
  topic: keywords
subject: category type.
  topic: keywords
subject: 18M20
  topic: subjects
subject: 16T05
  topic: subjects
creator: Kai Wang
creator: Jingcheng Dong
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2024-12-13
publication date: 2024-12-13
starting page: 437
ending page: 445
doi: 10.4208/jms.v57n4.24.02