作者机构：
[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Lim, MF; Lim, Meng Fai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Lim, MF ] 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：
even K-groups;class groups;Kummer's criterion
期刊：
Calculus of Variations and Partial Differential Equations,2023年62(7):1-31 ISSN：0944-2669
通讯作者：
Guo, YJ
作者机构：
[Guo, Yujin] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, POB 71010, Wuhan 430079, Peoples R China.;[Li, Yan; Liu, Qiang] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Lu, Lu] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Peoples R China.
通讯机构：
[Guo, YJ ] C;Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, POB 71010, Wuhan 430079, Peoples R China.
摘要：
We study ground states of attractive Bose gases, which are confined in a harmonic trap
$$V(x)=x_1^2+\Lambda x_2^2$$
(
$$\Lambda \ge 1$$
) rotating at the velocity
$$\Omega $$
. For any
$$0\le \Omega <\Omega ^*:=2$$
, where
$$\Omega ^*$$
is called a critical rotational velocity, it is well known that ground states exist if and only if
$$ a<a^*$$
for some critical constant
$$0<a^*<\infty $$
, where
$$a>0$$
denotes the product for the number of particles times the absolute value of the scattering length. In this paper, we consider the critical rotating case, where the rotational velocity
$$\Omega =\Omega ^*$$
, to study the existence and non-existence of ground states with respect to
$$a>0$$
. As imposed in Remark 2.2 of Lewin et al. (Blow-up profile of rotating 2D focusing bose gases. macroscopic limits of quantum systems, Springer, Berlin, 2018), we also analyze the limiting behavior of ground states as
$$a\nearrow a^*$$
for the case where
$$\Omega =\Omega _{a}:=\Omega ^*\sqrt{1-C_0(a^*-a)^m}\nearrow \Omega ^*$$
,
$$0\le m<\frac{1}{2}$$
and
$$0<C_0<1$$
.
期刊：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,2023年31(05):2350037 ISSN：0218-348X
通讯作者：
Yi, SF
作者机构：
[Pan, Yuewei] GuiZhou Normal Univ, Sch Math Sci, Guiyang 550001, Guizhou, Peoples R China.;[Yi, Shanfeng; Yi, SF] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Yi, SF ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
Let Sigma(infinity)(i=1) c(i)R(i)(x) be the Rademacher series, where {R-i(x)}(i=1)(infinity) is the classical Rademacher function system and {c(i)}(i=1)(infinity) is an arbitrary real number sequence. In this paper, we first show that the value range of the Rademacher series at any subinterval of [0, 1] is R boolean OR {+/- 8} when {c(i)}(1)(infinity) is an element of l(2)\l(1). This result provides us with the basic facts that when {c(i)}(1)(infinity) is an element of l(2)\l(1), the Rademacher series cannot converge to an approximate continuous function, and there is no approximate limit at any point of [0,1]. Further, when {c(i)}(1)(infinity) is an element of l(2)\l(1), we show various dimensions of the level set of Rademacher series on any subinterval of [0, 1]. Finally, we give the relationship between the box dimension and the coefficient of Rademacher series when {ci}(1)(infinity) is an element of l(1), and the exact values of box dimension, packing dimension and Hausdorff dimension are obtained in some special cases.
期刊：
Journal of Fixed Point Theory and Applications,2023年25(1):1-22 ISSN：1661-7738
通讯作者：
Tao Yang
作者机构：
[Luo, Xiao] Hefei Univ Technol, Sch Math, Hefei 230009, Peoples R China.;[Yang, Tao] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China.;[Yang, Tao] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Tao Yang] D;Department of Mathematics, Zhejiang Normal University, Jinhua, People’s Republic of China<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China
摘要：
We consider ground states of three-dimensional dipolar Bose–Einstein condensate, which can be described equivalently by positive
$$L^2$$
-constraint critical points of the Gross–Pitaevskii energy functional involving mass-subcritical perturbation. When the physical parameters describing the strength of nonlinearities lie in a defined regime, the corresponding energy functional is unbounded on the
$$L^2$$
-spheres, so we turn to study a suitable local minimization problem and prove the existence of ground states. Furthermore, we show that any ground state is a local minimizer and it is stable under the Cauchy flow, which indicates that the mass-subcritical perturbation stabilizes the system that is initially unstable. Finally, by refining the upper bound of the ground state energy, we provide a precise description of the asymptotic behavior of the ground states as the mass vanishes.
摘要：
This paper investigates the sparse beta model with l(1) penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis.
作者机构：
[Fan, Aihua] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fan, Aihua] Univ Picardie, LAMFA, UMR 7352, CNRS, F-80039 Amiens, France.;[Meyer, Yves] Univ Paris Saclay, CNRS, ENS Cachan, CMLA, F-91190 Paris, France.
通讯机构：
[Aihua Fan] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China<&wdkj&>LAMFA, CNRS UMR 7352, University of Picardie, Amiens, France
摘要：
The random trigonometric series
$$\sum\nolimits_{n = 1}^\infty {{\rho _n}\cos \left( {nt + {\omega _n}} \right)} $$
on the circle
$$\mathbb{T}$$
are studied under the conditions ∑∣ρn∣2 = ∞ and ρn → 0, where {ωn} are independent and uniformly distributed random variables on
$$\mathbb{T}$$
. They are almost surely not Fourier-Stieltjes series but determine pseudo-functions. This leads us to develop the theory of trigonometric multiplicative chaos, which produces a class of random measures. The kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly computed. The behavior of the partial sums of the above series is proved to be multifractal. Our theory holds on the torus
$${\mathbb{T}^d}$$
of dimension d ⩾ 1.
期刊：
Journal of Functional Analysis,2023年284(10):109882 ISSN：0022-1236
作者机构：
[Chen, Haixia] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Medina, Maria] Univ Autonoma Madrid, Dept Matemat, Ciudad Univ Cantoblanco, Madrid 28049, Spain.;[Pistoia, Angela] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via Scarpa 16, I-00161 Rome, Italy.
摘要：
We consider the elliptic system -Delta u(i) = u(i)(3)+ Sigma(q+1)(j=1 j not equal i) beta(ij)u(i)u(j)(2) in R-4, i = 1, ..., q + 1, when alpha := beta(ij) and beta := beta(i(q+1)) = beta((q+1)j) for any i, j = 1, ... , q. If beta < 0 and |beta| is small enough we build solutions such that each component u(1), . . . , u(q) blows-up at the vertices of q polygons placed in different great circles which are linked to each other, and the last component u(q+1) looks like the radial positive solution of the single equation. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org /licenses/by-nc-nd /4 .0/).
期刊：
Mathematical Methods in the Applied Sciences,2023年46(4):3429-3444 ISSN：0170-4214
通讯作者：
Shuang Li<&wdkj&>Shuang Li Shuang Li Shuang Li
作者机构：
[Li, Shuang] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China.;[Li, Yong] Yangtze Univ, Sch Informat & Math, Jingzhou, Peoples R China.;[Zhang, Xinan] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Shuang Li; Shuang Li Shuang Li Shuang Li] C;College of Mathematics and Information Science, Henan Normal University, Xinxiang, China
关键词：
Lévy noise;persistence in the mean;predator–prey;stochastic perturbation
摘要：
An eco-epidemiological system with Levy noise and white noise is proposed. In this prey-predator system, assume that the predator population is infected by disease and divided into two classes: susceptible predator and infected predator. The existence of global positive solution is derived. Threshold conditions of extinction and persistence in the mean for prey and predator population are given by Ito's formula and comparison theorem for stochastic model. The long-time behavior of this random system is also discussed by constructing suitable Lyapunov function, which shows the relationship between the solution of stochastic system and the equilibria of corresponding deterministic system. Finally, these results are verified by numerical simulation. Our results illustrate whether Levy noise and white noise are both unfavorable to the population size of species.
期刊：
International Journal of Energy Research,2023年2023 ISSN：0363-907X
作者机构：
[Cheng, Fei] Zhejiang Huayun Informat Technol Co Ltd, Hangzhou, Peoples R China.;[Wei, Cong] Zhejiang Univ Finance & Econ, Sch Econ, Hangzhou, Peoples R China.;[Wei, Cong] Springfield Coll, Springfield, MA USA.;[Tang, Tian; Kong, Jiayang] Cent China Normal Univ, Sch Econ & Business Adm, Wuhan, Peoples R China.;[Tang, Tian; Kong, Jiayang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
摘要：
In recent years, the Chinese Central Government has put great emphasis on the marine economy, since it has been a new driving force of the national economic development. Yet, the relationship between marine economic development and energy efficiency remains unknown. In this paper, we investigate whether marine economic development affected energy efficiency. We focused on the Zhoushan Archipelago, the first National New Area for marine economic development in China. We applied panel data approach to construct the counterfactual of Zhoushan Archipelago. We compared Zhoushan and its counterfactual, the synthetic Zhoushan, and viewed the difference between them, after the Zhoushan Archipelago New Area, as the impact of marine economic development on energy efficiency. We found that compared with its counterfactual, the real Zhoushan had a more substantial improvement in energy efficiency after the National New Area construction. We estimated that the construction of the National New Area for Marine Economy increased energy efficiency by about 10 percentage points. We also applied the bootstrapping technique to illustrate the significance of the estimated results. The results suggest that the Zhoushan Archipelago New Area construction had a statistically significant impact on energy efficiency. In addition, we conducted two tests, including leave-one-out tests and permutation tests, to check the robustness of estimated results, which also serve as an illustration of significance of the estimated results from an alternative empirical perspective. The results from these two tests are similar to each other, both indicating that the Zhoushan Archipelago New Area construction had a statistically significant positive impact on energy efficiency. Overall, our results suggest that marine economic development had a sizable improvement in energy efficiency.
期刊：
Journal of Functional Analysis,2023年285(2):109945 ISSN：0022-1236
通讯作者：
Liangjun Weng
作者机构：
[Liu, Lei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Liu, Lei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Wang, Guofang] Albert Ludwigs Univ Freiburg, Math Inst, D-79104 Freiburg, Germany.;[Weng, Liangjun] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China.
通讯机构：
[Liangjun Weng] S;School of Mathematical Sciences, Anhui University, Hefei, 230601, PR China
关键词：
Relative isoperimetric inequality;Michael-Simon and Allard inequality;ABP method;Free boundary
摘要：
In this paper, we mainly consider the relative isoperimetric inequalities for minimal submanifolds with free boundary. We first generalize ideas of restricted normal cones introduced by Choe-Ghomi-Ritore in [10] and obtain an optimal area estimate for generalized restricted normal cones. This area estimate, together with the ABP method of Cabre in [5], provides a new proof of the relative isoperimetric inequality obtained by Choe-Ghomi-Ritore in [11]. Furthermore, we use this estimate and the idea of Brendle in his recent work [3] to obtain a relative isoperimetric inequality for minimal submanifolds with free boundary on a convex support surface in Rn+m, which is optimal and gives an affirmative answer to an open problem proposed by Choe in [9], Open Problem 12.6, when the codimension m <= 2. (c) 2023 Elsevier Inc. All rights reserved.
作者机构：
[Chen, Shuang] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Chen, Shuang] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.;[Duan, Jinqiao] IIT, Dept Appl Math, Dept Phys, Chicago, IL 60616 USA.;[Duan, Jinqiao] Great Bay Univ, Sch Sci, Dept Math, Dongguan 523000, Guangdong, Peoples R China.;[Duan, Jinqiao] Huazhong Univ Sci & Technol, Ctr Math Sci, Wuhan 430074, Hubei, Peoples R China.
通讯机构：
[Duan, JQ ] I;IIT, Dept Appl Math, Dept Phys, Chicago, IL 60616 USA.
关键词：
Perturbation theory;Bifurcation;Stability;Ginzburg-Landau equation;FitzHugh-Nagumo system;Hyperbolic Burgers-Fisher model
摘要：
We study the spectra for a class of differential operators with asymptotically constant coefficients. These operators widely arise as the linearizations of nonlinear partial differential equations about patterns or nonlinear waves. We present a unified framework to prove the perturbation results on the related spectra. The proof is based on exponential dichotomies and the Brouwer degree theory. As applications, we employ the developed theory to study the stability of quasi-periodic solutions of the Ginzburg-Landau equation, fold-Hopf bifurcating periodic solutions of reaction-diffusion systems coupled with ordinary differential equations, and periodic annulus of the hyperbolic Burgers-Fisher model.& COPY; 2023 Elsevier B.V. All rights reserved.
期刊：
Journal of Mathematical Physics,2023年64(5):051508 ISSN：0022-2488
通讯作者：
Wang, LS
作者机构：
[Tang, Zhongwei] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China.;[Wang, Lushun] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China.;[Xie, Huafei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, LS ] Z;Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China.
摘要：
This paper is devoted to a class of singularly perturbed nonlinear Schrodinger systems defined on a smooth bounded domain in R-N(N = 2,3). We use the Lyapunov-Schmidt reduction method to construct synchronized vector solutions with multiple spikes both on the boundary and in the interior of the domain. For each vector solution that has been constructed, we point out that the interior spikes locate near sphere packing points in the domain, and the boundary spikes locate near the critical points of the mean curvature function related to the boundary of the domain.
期刊：
NAGOYA MATHEMATICAL JOURNAL,2023年250:533-548 ISSN：0027-7630
通讯作者：
JIAN LIU
作者机构：
[Liu, Jian] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[JIAN LIU] S;School of Mathematics and Statistics Central China Normal University Wuhan 430079 China
关键词：
annihilator of the singularity category;cohomological annihilator;generation time;Jacobian ideal;Koszul object
摘要：
Let R be a commutative Noetherian ring. We prove that if R is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the annihilator of the singularity category of R coincides with the Jacobian ideal of R up to radical. We establish a relationship between the annihilator of the singularity category of R and the cohomological annihilator of R under some mild assumptions. Finally, we give an upper bound for the dimension of the singularity category of an equicharacteristic excellent local ring with isolated singularity. This extends a result of Dao and Takahashi to non-Cohen-Macaulay rings.
作者机构：
[Lu, Zheng-Yi; Ai, Wen-Hui; Lu, ZY] Hunan Normal Univ, Sch Math & Stat, Minist Educ, Key Lab Comp & Stochast Math, Changsha 410081, Hunan, Peoples R China.;[Zhou, Ting] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Lu, ZY ] H;Hunan Normal Univ, Sch Math & Stat, Minist Educ, Key Lab Comp & Stochast Math, Changsha 410081, Hunan, Peoples R China.
摘要：
Let. be a symmetric measure of Lebesgue type, i.e., rho = 1/2 (mu X delta(0) + delta(0) x mu), where the component measure mu is the Lebesguemeasure supported on [t, t + 1] for t is an element of Q\{- 1/2} and delta(0) is the Dirac measure at 0. We prove that rho is a spectral measure if and only if t is an element of 1/2Z. In this case, L-2(rho) has a unique orthonormal basis of the form {e(2 pi i(lambda x-lambda y)) : lambda is an element of Lambda(0) }, where Lambda(0) is the spectrum of the Lebesgue measure supported on [-t - 1,-t]boolean OR[t, t + 1]. Our result answers some questions raised by Lai, Liu and Prince [ JFA, 2021].
作者机构：
[Hu, Xiaoli] School of Artificial Intelligence, Jianghan University, Wuhan, Hubei 430056, People's Republic of China;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of American;School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China;[Jing, Naihuan] Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of American<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China
通讯机构：
[Xiaoli Hu] S;[Naihuan Jing] D;Department of Mathematics, North Carolina State University, Raleigh, NC 27695, United States of American<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, People's Republic of China<&wdkj&>School of Artificial Intelligence, Jianghan University, Wuhan, Hubei 430056, People's Republic of China
摘要：
Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an in-depth investigation using the methodologies of sampling coordinates of observables and convex functions to refine the uncertainty relations in both the product form of two observables and summation form of multiple observables.
摘要：
In this article, we consider the following Schrodinger-Poisson problem: {-epsilon(2)Delta u + V(y)u + Phi(y)u = vertical bar u vertical bar(p-1)u, y is an element of R-3, -Delta Phi(y) = u(2), y is an element of R-3, where epsilon > 0 is a small parameter, 1 < p < 5, and V(y) is a potential function. We construct multi-peak solution concentrating at the critical points of V(y) through the Lyapunov-Schmidt reduction method. Moreover, by using blow-up analysis and local Pohozaev identities, we prove that the multi-peak solution we construct is non-degenerate. To our knowledge, it seems be the first non-degeneracy result on the Schodinger-Poisson system.
作者机构：
[Qin, Hong; Zou, Na; Qin, H] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Peoples R China.;[Qin, Hong; Qin, H] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Chatterjee, Kashinath] Visva Bharati Univ, Dept Stat, Santini Ketan, W Bengal, India.;[Chatterjee, Kashinath] Augusta Univ, Med Coll Georgia, Dept Biostatist & Data Sci, Populat Hlth Sci, Augusta, GA USA.
通讯机构：
[Qin, H ] Z;Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
关键词：
Average Lee discrepancy;average Lee-moment;uniformity;lower bound;62K15;62K10;62K99
摘要：
In this paper, we proposed the average Lee discrepancy to measure the uniformity of designs and studied its connection with the standard optimality measures used in the context of design of experiments. Lower bounds to such measure are provided as a benchmark to obtain uniform designs. We also defined the minimum average Lee-moment aberration criterion used to compare and screen the optimal design, and some lower bounds to such criterion are also provided.
作者机构：
[Dong, Yan-fei; Chen, Wang-xue] Jishou Univ, Dept Math & Stat, Jishou 416000, Peoples R China.;[Xie, Min-yu] Cent China Normal Univ, Dept Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wang-xue Chen] D;Department of Mathematics and Statistics, Jishou University, Jishou, China
关键词：
location-scale parameters;best linear unbiased estimator;moving extremes ranked set sampling
摘要：
In the current paper, the best linear unbiased estimators (BLUEs) of location and scale parameters from location-scale family will be respectively proposed in cases when one parameter is known and when both are unknown under moving extremes ranked set sampling (MERSS). Explicit mathematical expressions of these estimators and their variances are derived. Their relative efficiencies with respect to the minimum variance unbiased estimators (MVUEs) under simple random sampling (SRS) are compared for the cases of some usual distributions. The numerical results show that the BLUEs under MERSS are significantly more efficient than the MVUEs under SRS.
