期刊：
Journal of Mathematical Analysis and Applications,2024年529(1):127609 ISSN：0022-247X
通讯作者：
Yang, YQ
作者机构：
[Zhang, Yan-fang] Huzhou Univ, Sch Sci, Huzhou 313000, Peoples R China.;[Yang, Yong-qiang] Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Yang, YQ ] C;Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
关键词：
Self-affine sponge;Maximal power law;Component-counting measure
摘要：
Let (E, ) be a metric space and let hE (5) be the cardinality of the set of 5-connected components of E. In literature, in case of that E is a self-conformal set satisfying the open set condition or E is a self-affine Sierpinski sponge, necessary and sufficient condition is given for the validity of the relation hE(5) x 5- dimB E, when 5 & RARR; 0. In this paper, we generalize the above result to self-affine sponges of LalleyGatzouras type; actually in this case, we show that there exists a Bernoulli measure & mu; such that for any cylinder W, it holds that hW (5) x & mu;(W )5- dimB E, when 5 & RARR; 0.& COPY; 2023 Elsevier Inc. All rights reserved.
关键词：
Compressible Navier-Stokes-Allen-Cahn system;Strong/classical solutions;Density-dependent viscosity;Large initial data
摘要：
This paper is concerned with a one-dimensional isentropic compressible Navier-Stokes-Allen-Cahn system with density-dependent viscosity, which models the motion of a mixture of two viscous compressible fluids. The case when the pressure $ p(\rho) = \rho^\gamma $, the viscosity $ \nu(\rho, \chi) = \rho^\alpha $, the interface thickness $ \delta(\rho) = \rho^\beta $ and the relaxation time function $ a(\rho, \chi, \chi_y) = \rho^\lambda $ is considered, where $ \rho $ and $ \chi $ are the density and the phase variable, respectively, and $ \gamma, \alpha, \beta, \lambda\in\mathbb{R} $ are parameters. Under some suitable assumptions on the parameters $ \gamma , \alpha, \beta, \lambda $ and the initial data, we prove the global existence and large-time behavior of nonvacuum strong and classical solutions to its Cauchy problem with large initial data. This appears to be the first global existence result on the Cauchy problem of the compressible Navier-Stokes-Allen-Cahn system with density-dependent viscosity and large data.
摘要：
This paper focuses on the existence of positive solutions for the following weakly coupled Schrödinger system with supercritical growth except at the origin: $ \begin{equation*} \left\{ \begin{array}{ll} -\Delta u_1 = \mu_1|u_{1}|^{p(r) - 2}u_1 + \beta|u_{2}|^{\frac{p(r)}{2}}|u_1|^{\frac{p(r)}{2}-2}u_{1}, & x\in B_1(0), \\ -\Delta u_2 = \mu_2|u_{2}|^{p(r) - 2}u_{2} + \beta|u_{1}|^{\frac{p(r)}{2}}|u_2|^{\frac{p(r)}{2}-2}u_{2}, & x\in B_1(0), \end{array} \right. \end{equation*} $ where $ B_1(0) $ is an unit ball $ {\mathbb{R}^N} $ with $ N\ge 3 $, $ \beta\in\mathbb{R} $ is a coupling constant, $ \mu_1,\mu_2\in {\mathbb R} $ are constants, $ p(r) = 2^* + r^{\alpha} $ with $ 2^* = \frac{2N}{N-2} $. Assuming that $ 0<{\alpha}<\min\{\frac{N}{2},N-2\} $, we apply concentration-compactness idea to show that the problem has a positive solution provided that $ \beta>0 $ if $ N\ge 5 $ and $ \beta\in(0,\beta_0]\cup[\beta_1,+\infty) $ for some positive constants $ \beta_0<\beta_1 $ if $ N = 3,4 $.
期刊：
Journal of Inverse and Ill-posed Problems,2024年 ISSN：0928-0219
通讯作者：
Xiang, JL
作者机构：
[Xiang, Jianli; Xiang, JL] China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.;[Yan, Guozheng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Guozheng] Hubei Key Lab Math Phys, Wuhan, Peoples R China.
通讯机构：
[Xiang, JL ] C;China Three Gorges Univ, Coll Sci, Three Gorges Math Res Ctr, Yichang 443002, Peoples R China.
关键词：
Modified linear sampling method;variational method;interior transmission problem;partially coated dielectric
摘要：
Consider time-harmonic electromagnetic wave scattering by an infinitely long, cylindrical, orthotropic dielectric partially coated with a very thin layer of a highly conductive material, which can be modeled by a transmission problem with mixed boundary conditions. Having established the well-posedness of the direct and interior transmission problem by the variational method under certain conditions, we make use of the classical linear sampling method to reconstruct the shape of the obstacle. Then, based on a modification of the general data-to-pattern operator G, we propose a novel and simple method to justify the modified linear sampling method.
摘要：
In this paper, we suggest an empirical likelihood -based test for the autoregressive coefficient of an integer -valued AR(1) model, i.e., INAR(1). We derive the limit distributions of the resulting test statistic under both null and alternative hypotheses. It turns out that regardless of whether the INAR process is stable or unstable, the statistic is always chi -squared distributed asymptotically under the null hypothesis, and as a result, it can offer unified inferences for the autoregressive coefficient. The performance of its finite sample is also demonstrated using simulations and an empirical example.
摘要：
A graph G has a
$${\mathcal {P}}_{\geqslant k}$$
-factor if G has a spanning subgraph H such that every component of H is a path of order at least k. A graph G is
$${\mathcal {P}}_{\geqslant k}$$
-factor deleted if
$$G-e$$
has a
$${\mathcal {P}}_{\geqslant k}$$
-factor for each edge e of G. In this paper, we give two necessary and sufficient conditions defining a
$${\mathcal {P}}_{\geqslant 2}$$
-factor deleted graph and a
$${\mathcal {P}}_{\geqslant 3}$$
-factor deleted graph, respectively. Based on the result of
$${\mathcal {P}}_{\geqslant 2}$$
-factor deleted graphs, we establish respectively a lower bound on the size and a lower bound on the spectral radius to ensure whether or not a graph is
$${\mathcal {P}}_{\geqslant 2}$$
-factor deleted. Furthermore, by constructing extremal graphs, we show that all the above bounds are best possible.
摘要：
Linear complementary dual (LCD) codes can provide an optimum linear coding solution for the two-user binary adder channel. LCD codes also can be used to against side-channel attacks and fault non-invasive attacks. Let dLCD(n,k) denote the maximum value of d for which a binary [n,k,d] LCD code exists. In \cite{BS21}, Bouyuklieva conjectured that dLCD(n+1,k)=dLCD(n,k) or dLCD(n,k)+1 for any lenth n and dimension k >= 2. In this paper, we first prove Bouyuklieva's conjecture \cite{BS21} by constructing a binary [n,k,d-1] LCD codes from a binary [n+1,k,d] LCDo,e code, when d >= 3 and k >= 2. Then we provide a distance lower bound for binary LCD codes by expanded codes, and use this bound and some methods such as puncturing, shortening, expanding and extension, we construct some new binary LCD codes. Finally, we improve some previously known values of d(LCD)(n,k) of lengths 38 <= n <= 40 and dimensions 9 <= k <= 15. We also obtain some values of d(LCD)(n,k) with 41 <= n <= 50 and 6 <= k <= n-6.
期刊：
Journal of Mathematical Analysis and Applications,2024年530(1):127636 ISSN：0022-247X
通讯作者：
Duan, R
作者机构：
[Duan, Ran; Chang, Shengchuang] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Duan, R ] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Navier-Stokes-quantum equations;Rayleigh-Taylor instability;Hadamard sense
摘要：
Consider the linear and nonlinear Rayleigh-Taylor instability of the three-dimensional incompressible viscous Navier-Stokes-Quantum equations. For linearized problem, we determine the critical number.cprecisely. Then, we construct a linear growth solution by a modified variational method for k <.k(c). In addition, we show that.cis infinite for a special steady state <(rho)over bar>, which implies that quantum potential inhibit the instability instead of cutting it off. Based on this unstable linear solution and the priori estimates of the smooth solution to the perturbed problem, we establish the nonlinear instability of the density and the velocities in the sense of Hadamard. Compared with the related study on Navier-Stokes-Korteweg equations (Zhang (2022) [41]), we do not ask the capillarity coefficient to be small. (c) 2023 Elsevier Inc. All rights reserved.
摘要：
Let
$$A\in M_2({\mathbb {Z}})$$
be an expanding integer matrix and
$$D=\{d_1={\textbf{0}},d_2,d_3\}\subset {\mathbb {Z}}^2$$
. It follows from Hutchinson (Indiana Univ Math J 30:713–747, 1981) that the generalized Sierpinski self-affine set
$${\textbf{T}}(A,D)$$
is the unique compact set determined by the pair (A,D) satisfing the set-valued equation
$$A{\textbf{T}}(A,D)=\bigcup _{i=1}^3({\textbf{T}}(A,D)+d_i)$$
. In this paper, we show that Fuglede’s conjecture holds on
$${\textbf{T}}(A,D)$$
, which states that
$${\textbf{T}}(A,D)$$
is a spectral set if and only if
$${\textbf{T}}(A,D)$$
is a translational tile. For the classical Sierpinski self-affine set
$${\textbf{T}}(A,D_{c})$$
with
$$D_{\text {c}}=\{(0,0)^t,(1,0)^t, (0,1)^t\}$$
, a finer characterization of tiling set is given. As an application, we find that the classical Sierpinski self-affine tile
$${\textbf{T}}(A,D_{\text {c}})$$
is suitable for Kolountzakis’ conjecture on product domain. This enriches the results that are now known.
期刊：
Nonlinear Analysis: Real World Applications,2024年77:104046 ISSN：1468-1218
通讯作者：
Wang, YT
作者机构：
[Ma, Xuan] Wuhan Text Univ, Res Ctr Nonlinear Sci, Sch Math & Phys Sci, Wuhan 430200, Peoples R China.;[Wang, Yating] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Yating] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, YT ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
The dynamics of a rarefied gas in a finite channel with the same temperatures and opposite velocities is a fundamental problem in kinetic theory. The relative motion of the planar boundaries can induce a non-equilibrium state which is referred to as the Couette flow. In this paper, we demonstrate that the unsteady Couette flow for the Boltzmann equation in 3D finite channel time asymptotically converges to the 1D steady state constructed in Duan et al. (2022), we also prove the exponential time decay rate as a byproduct. The validity of the analysis is established for all hard potentials.
摘要：
The Alon–Tarsi number was defined by Jensen and Toft (Graph coloring problems, Wiley, New York, 1995). The Alon–Tarsi number AT(G) of a graph G is the smallest integer k such that G has an orientation D with maximum outdegree
$$k-1$$
and the number of even circulation is not equal to that of odd circulations in D. It is known that
$$\chi (G)\le \chi _l(G)\le AT(G)$$
for any graph G, where
$$\chi (G)$$
and
$$\chi _l(G)$$
are the chromatic number and the list chromatic number of G. Denote by
$$H_1 \square H_2$$
and
$$H_1\bowtie H_2$$
the Cartesian product and the semi-strong product of two graphs
$$H_1$$
and
$$H_2$$
, respectively. Kaul and Mudrock (Electron J Combin 26(1):P1.3, 2019) proved that
$$AT(C_{2k+1}\square P_n)=3$$
. Li, Shao, Petrov and Gordeev (Eur J Combin 103697, 2023) proved that
$$AT(C_n\square C_{2k})=3$$
and
$$AT(C_{2m+1}\square C_{2n+1})=4$$
. Petrov and Gordeev (Mosc. J. Comb. Number Theory 10(4):271–279, 2022) proved that
$$AT(K_n\square C_{2k})=n$$
. Note that the semi-strong product is noncommutative. In this paper, we determine
$$AT(P_m \bowtie P_n)$$
,
$$AT(C_m \bowtie C_{2n})$$
,
$$AT(C_m \bowtie P_n)$$
and
$$AT(P_m \bowtie C_{n})$$
. We also prove that
$$5\le AT(C_m \bowtie C_{2n+1})\le 6$$
.
期刊：
Journal of Functional Analysis,2024年286(3):110243 ISSN：0022-1236
通讯作者：
Guo, YJ;Li, Y
作者机构：
[Guo, Yujin; Luo, Yong] Cent China Normal Univ, Sch Math & Stat, Minist Educ, POB 71010, Wuhan 430079, Peoples R China.;[Guo, Yujin] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, POB 71010, Wuhan 430079, Peoples R China.;[Li, Yan] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Luo, Yong] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Y ; Guo, YJ ] C;Cent China Normal Univ, Sch Math & Stat, Minist Educ, POB 71010, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, POB 71010, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.
摘要：
This paper is concerned with ground states of attractive Bose gases confined in an anharmonic trap V(x) = omega(vertical bar x vertical bar(2)+ k vertical bar x vertical bar(4)) rotating at the velocity Omega > 0, where omega > 0 denotes the trapping frequency, and k > 0 represents the strength of the quartic term. It is known that for any Omega > 0, ground states exist in such traps if and only if 0 < a < a*, where a*:= parallel to Q parallel to(2)(2) and Q > 0 is the unique positive solution of Delta Q - Q + Q(3)= 0 in R-2. By analyzing the refined energies and expansions of ground states, we prove that there exists a constant C > 0, independent of 0 < a < a*, such that ground states do not have any vortex in the region R(a) := {x is an element of R-2 : vertical bar x vertical bar <= C(a* - a)(-1-6 beta 20)} as a NE arrow a*, for the case where omega= 3 Omega(2)/4, k = 1/6, and Omega = C-0(a*- a)(-beta) varies for some beta is an element of[0, 1/6) and C-0 > 0. (c) 2023 Elsevier Inc. All rights reserved.
作者机构：
[Zhou, Zihan; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhou, Zihan; Li, Shuchao] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Sun, Wanting] Shandong Univ, Data Sci Inst, Jinan 250100, Peoples R China.;[Wei, Wei] Shanghai Univ Engn Sci, Ctr Intelligent Comp & Appl Stat, Sch Math Phys & Stat, Shanghai 201620, Peoples R China.;[Zhang, Minjie; Zhang, MJ] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.
通讯机构：
[Zhang, MJ ] H;Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.
关键词：
Signed mixed graph;Eisenstein matrix;Spectral radius
摘要：
A mixed graph M-G is obtained from a simple graph G by orienting an edge subset of G. A signed mixed graph is a mixed graph with arcs and edges signed + or -. The unit Eisenstein matrix (epsilon-matrix for short) of a signed mixed graph was recently introduced by Wissing and van Dam [32]. This novel matrix is indexed by the vertices of the signed mixed graph, and the entry corresponding to a positive arc from u to v is equal to omega = 1+i root 3/2 (and its symmetric entry is (omega) over bar = 1-i root 3/2); the entry corresponding to a negative arc is equal to -omega (and its symmetric entry is -(omega) over bar); the entry corresponding to a positive edge is equal to 1; the entry corresponding to a negative edge is equal to -1; and 0 otherwise. In this paper, we study the spectral properties of this epsilon-matrix. We characterize all the signed mixed graphs whose eigenvalues are contained in (-alpha, alpha) for alpha is an element of {root 2, root 3, root 2} .(c) 2023 Elsevier B.V. All rights reserved.
作者机构：
[Huang, Jing] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou, Peoples R China.;[Geng, Xianya] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan, Peoples R China.;[Zhou, Zihan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Zhou, Zihan] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
通讯机构：
[Zhou, ZH ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan, Peoples R China.
摘要：
Identifying the graph with maximum or minimum spectral radius among a given class of graphs is a central problem in extremal spectral graph theory, known as the Brualdi- Solheid problem. For a graph G = (V-G, E-G), a subset S subset of V-G is called a maximum dissociation set if the induced subgraph G[S] does not contain P-3 as its subgraph, and the subset has maximum cardinality. The dissociation number of G is the number of vertices in a maximum dissociation set of G. In this paper, we first characterize all the connected graphs (resp. bipartite graphs, trees) having maximum spectral radius among connected graphs (resp. bipartite graphs, trees) with given order and dissociation number. Secondly, we show that the connected n-vertex graph with dissociation number phi having minimum spectral radius is a tree, where phi >= [2/3n] . Finally, we determine the graphs having minimum spectral radius with fixed order n and dissociation number phi is an element of {2, [2n/3], n - 1, n - 2}.(c) 2023 Elsevier B.V. All rights reserved.
作者：
He, Ying;Wang, Yan;Yang, Jerry Zhijian;Yin, Hongshuang
期刊：
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2024年14(1):79-103 ISSN：2079-7362
通讯作者：
Wang, Y
作者机构：
[Yang, Jerry Zhijian; Yin, Hongshuang; He, Ying] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[He, Ying] Yanqi Lake Beijing Inst Math Sci & Applicat, Beijing 101408, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Yan] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Global Science Press;EAJAM;East Asian Journal on Applied Mathematics;Nonlinear Dirac equation;uniformly accurate;finite difference method;time-splitting method;exponential integrator.
摘要：
Numerical methods for the nonlinear Dirac equation (NDE) in the massless nonrelativistic regime are considered. In this regime, the equation contains a small dimensionless parameter $0 <\varepsilon≤ 1,$ and its solution is highly oscillatory in time. We present and analyze traditional numerical schemes for the NDE, including finite difference methods, time-splitting methods and exponential integrators. Error analysis indicates that all these methods require an $\varepsilon$-dependent time-step size to achieve an optimal convergence order. Utilizing an operator splitting technique, we propose a uniformly accurate (UA) scheme. The scheme enables first-order convergence in time for all $\varepsilon ∈ (0, 1]$ without restrictions on time-step size. Error estimates for the UA scheme are rigorously established and numerical results confirm the properties of the method.
期刊：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2024年56(2):2149-2170 ISSN：0036-1410
通讯作者：
Zhao, Y
作者机构：
[Li, Peijun] Acad Math & Syst Sci, Chinese Acad Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China.;[Li, Peijun] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China.;[Zhao, Yue; Yao, Xiaohua; Zhao, Y] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhao, Yue; Yao, Xiaohua; Zhao, Y] Cent China Normal Univ, Key Lab NAA MOE, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab NAA MOE, Wuhan 430079, Peoples R China.
摘要：
This paper addresses the meromorphic continuation of the outgoing resolvent associated with Schrodinger-type operators in three dimensions. The first part focuses on the classical Schrodinger-type operator involving unbounded potentials. The absence of nonzero real poles for the outgoing resolvent is investigated. The second part examines the fractional Schrodinger operator, including both bounded and unbounded potentials. The analysis relies on a resolvent identity that establishes a connection between the resolvents of the fractional Schrodinger operator and its classical counterpart.
期刊：
ELECTRONIC JOURNAL OF COMBINATORICS,2024年31(1) ISSN：1077-8926
通讯作者：
Li, SC
作者机构：
[Lei, Xingyu; Li, Shuchao; Li, SC] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, SC ] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
For a given graph F, we say that a graph G is F -free if it does not contain F as a subgraph. A graph is color -critical if it contains an edge whose deletion reduces its chromatic number. Let Kr+ (a1, a2,... , ar) be the graph obtained from complete r -partite graph with parts of sizes a1 2, a2, ... , ar, by adding an edge to the first part. In this paper, we focus on the spectral extrema of disjoint colorcritical graphs. For fixed t, a1, ... , ar (r 2) and large enough n, we characterize the unique n -vertex tKr+ (a1, ... , ar)-free graph having the largest spectral radius. Moreover, let F1, ... , Ft be t disjoint color -critical graphs with the same chromatic number. We identify the unique n -vertex Uti=1 Fi-free graph having the largest spectral radius for sufficiently large n. Consequently, we generalize the main results obtained by Ni, Wang and Kang
期刊：
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY,2024年176(2):287-308 ISSN：0305-0041
通讯作者：
Lim, MF
作者机构：
[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan, Hubei, Peoples R China.;[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Lim, MF ] C;Cent China Normal Univ, Sch Math & Stat, 152 Luoyu Rd, Wuhan, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, 152 Luoyu Rd, Wuhan 430079, Hubei, Peoples R China.
关键词：
11R23;11G05;11S25
摘要：
This paper is concerned with the study of the fine Selmer group of an abelian variety over a $\mathbb{Z}_{p}$-extension which is not necessarily cyclotomic. It has been conjectured that these fine Selmer groups are always torsion over $\mathbb{Z}_{p}[[ \Gamma ]]$, where $\Gamma$ is the Galois group of the $\mathbb{Z}_{p}$-extension in question. In this paper, we shall provide several strong evidences towards this conjecture. Namely, we show that the conjectural torsionness is consistent with the pseudo-nullity conjecture of Coates–Sujatha. We also show that if the conjecture is known for the cyclotomic $\mathbb{Z}_{p}$-extension, then it holds for almost all $\mathbb{Z}_{p}$-extensions. We then carry out a similar study for the fine Selmer group of an elliptic modular form. When the modular forms are ordinary and come from a Hida family, we relate the torsionness of the fine Selmer groups of the specialization. This latter result allows us to show that the conjectural torsionness in certain cases is consistent with the growth number conjecture of Mazur. Finally, we end with some speculations on the torsionness of fine Selmer groups over an arbitrary p-adic Lie extension.
期刊：
Communications in Statistics - Theory and Methods,2024年 ISSN：0361-0926
通讯作者：
Jing, L
作者机构：
[Ouyang, Yang] Natl Inst Cultural Dev, Wuhan, Peoples R China.;[Jing, Luo; Zhimeng, Xu; Jing, L] South Cent Minzu Univ, Dept Math & Stat, Wuhan 430074, Peoples R China.;[Jing, Luo; Jing, L] Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Peoples R China.;[Jing, Luo; Jing, L] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.;[Qiuping, Wang] Zhaoqing Univ, Sch Math & Stat, Zhaoqing, Peoples R China.
通讯机构：
[Jing, L ] S;South Cent Minzu Univ, Dept Math & Stat, Wuhan 430074, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
The Bradley-Terry model is a common model for analyzing paired comparison data. Under differential private mechanism, there is a lack of asymptotic properties for the parameter estimator of parameters in this model. In this article, we show that the moment estimators of the parameters based on the differential private degree sequence with Laplace noise is uniformly consistent and asymptotically normal. Simulations are provided to illustrate asymptotic results.
