期刊：
BMC PUBLIC HEALTH,2023年23(1):1-10 ISSN：1471-2458
通讯作者：
Wang, N.;Xu, T.
作者机构：
[Li, Lin] Natl Res Inst Family Planning, Clin Med Ctr, Beijing, Peoples R China.;[Xu, Tao; Chen, Feilong] Chinese Acad Med Sci, Inst Basic Med Sci, Dept Epidemiol & Biostat, Beijing, Peoples R China.;[Xu, Tao; Chen, Feilong] Peking Union Med Coll, Sch Basic Med, Beijing, Peoples R China.;[Wang, Ning; Gao, Yiyuan; Li, Xiaoyan] Natl Res Inst Family Planning, Ctr Hlth Qual, Beijing, Peoples R China.;[Diao, Xiyezi; Zhu, Silin] Cent China Normal Univ, Dept Stat, Wuhan, Hubei, Peoples R China.
通讯机构：
[Ning Wang] C;[Tao Xu] D;Center for Health Quality, National Research Institute for Family Planning, Beijing, China<&wdkj&>Department of Epidemiology and Biostatistics Institute of Basic Medical Sciences, Chinese Academy of Medical Sciences & School of Basic Medicine, Peking Union Medical College, Beijing, China
关键词：
The elderly;Calf circumference;Incontinence;Sarcopenia;Risk factor
作者机构：
[Yuan, Ganghua] Northeast Normal Univ, Sch Math & Stat, KLAS, Changchun 130024, Jilin, Peoples R China.;[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
作者机构：
[Qin, Hong; Xiao, Yao] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Peoples R China.;[Qin, Hong; Wang, Shiqi; Ning, Jianhui] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Jianhui Ning] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China
关键词：
Weighted uniform designs;sequential designs;weighted discrepancy;Gaussian process model
摘要：
Uniform designs seek to distribute design points uniformly in the experimental domain. Some discrepancies have been developed to measure the uniformity by treating all factors equally. It is reason-able when there exists no prior information about the system or when the potential model is completely unclear. However, in the sit-uation of sequential designs, experimental information, such as the importance of each factor, would be obtained from previous stage experiments. With this fact, the weighted L-2-discrepancy is more suit-able than the original discrepancy for choosing follow-up designs. In this paper, the sequentially weighted uniform design is proposed, which is obtained by minimizing the weighted L-2-discrepancy. The weights, indicating the relative importance of each factor, are esti-mated through a Bayesian hierarchical Gaussian process method based on serial experimental data. Results from several classic com-puter simulator examples, as well as a real application in circuit design, demonstrate that the performance of our new method sur-passes that of its counterparts.
作者：
Prasangika, K. D.;Tang, Wan;Yao, Zeng;Zuo, Guoxin
期刊：
Communications in Statistics - Theory and Methods,2023年52(5):1385-1399 ISSN：0361-0926
通讯作者：
Zuo, Guoxin(zuogx@mail.ccnu.edu.cn)
作者机构：
[Prasangika, K. D.] Univ Ruhuna, Dept Math, Matara, Sri Lanka.;[Tang, Wan] Tulane Univ, Dept Biostat & Data Sci, New Orleans, LA 70118 USA.;[Yao, Zeng; Zuo, Guoxin] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Guoxin Zuo] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, P.R. China
关键词：
Non parametric regression;local linear regression;double smoothing local linear regression;time series;asymptotic properties
期刊：
Finite Fields and Their Applications,2023年89:102223 ISSN：1071-5797
通讯作者：
Miao, Shujing(sjmiao2020@sina.com)
作者机构：
[Miao, Shujing; Wang, Junming; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Shujing Miao] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Cospectral graphs;Determined by generalized skew spectrum;Skew-adjacency matrix;Smith Normal Form
摘要：
Spectral characterization of graphs is an important topic in spectral graph theory. An oriented graph G(sigma) is obtained from a simple undirected graph G by assigning to every edge of G a direction so that G(sigma) becomes a directed graph. The skew-adjacency matrix of an oriented graph G(sigma) is a real skew-symmetric matrix S(G(sigma)) = (s(ij)), where s(ij) = -s(ji) = 1 if (i, j) is an arc; s(ij) = s(ji) = 0 otherwise. Let G(sigma) and H-tau be two oriented graphs whose skew-adjacency matrices are S(G(sigma)) and S(H-tau), respectively. We say G(sigma) is R-cospectral to H-tau if tJ - S(G(sigma)) and tJ - S(H-tau) have the same spectrum for any t is an element of R, where J is the all-ones matrix. An oriented graph G(sigma) is said to be determined by the generalized skew spectrum (DGSS for short), if any oriented graph which is R-cospectral to G(sigma) is isomorphic to G(sigma). Let W(G(sigma)) = [e, S(G(sigma))e, S-2(G(sigma))e, . . . , Sn-1(G(sigma))e] be the skew-walk-matrix of G(sigma), where e is the all-ones vector. A theorem of Qiu, Wang and Wang [9] states that if G(sigma) is a self-converse oriented graph and 2(-(sic)n/2(sic)) det W(G(sigma)) is odd and square-free, then G(sigma) is DGSS. In this paper, based on the Smith Normal Form of the skew-walk-matrix of G(sigma) we obtain our main result: Let q be a prime and G(sigma) be a self-converse oriented graph on n vertices with det W(G(sigma)) not equal 0. Assume that rank(q)(W(G(sigma))) = n - 1 if q is an odd prime, and rank(q)(W(G(sigma))) = (sic)n/2(sic) if q = 2. If Q is a regular rational orthogonal matrix satisfying Q(T)S(G(sigma))Q = S(H-tau) for some oriented graph H-tau, then the level of Q divides d(n)(W(G(sigma)))/q, where d(n)(W(G(sigma))) is the n-th invariant factor of q W(G(sigma)). Consequently, it leads to an easier way to prove Qiu, Wang and Wang's theorem above. (c) 2023 Elsevier Inc. All rights reserved.
期刊：
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2023年170:1-32 ISSN：0021-7824
通讯作者：
Guo, YJ
作者机构：
[Guo, Yujin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Guo, Yujin] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, YJ ] 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：
Bose-Einstein condensate;Rotational velocity;Nonexistence of vortices;Limit profiles
摘要：
As a continuation of [34], we consider ground states of rotating Bose-Einstein condensates with attractive interactions in non-radially harmonic traps V(x)=x12+Λ2x22, where 0<Λ≠1 and x=(x1,x2)∈R2. For any fixed rotational velocity 0≤Ω<Ω⁎:=2min{1,Λ}, it is known that ground states exist if and only if a<a⁎ for some critical constant 0<a⁎<∞, where a>0 denotes the product of the number of particles and the absolute value of the scattering length. We analyze the asymptotic expansions of ground states as a↗a⁎, which display the visible effect of Ω on ground states. As a consequence, we further prove that ground states do not have any vortex in the region R(a):={x∈R2:|x|≤C(a⁎−a)−112} as a↗a⁎ for some constant C>0, which is independent of 0<a<a⁎.
En continuant le travail [34], nous considérons les états fondamentaux des condensats de Bose-Einstein en rotation avec des interactions attractives dans des pièges non radialement harmoniques V(x)=x12+Λ2x22, où 0<Λ≠1 et x=(x1,x2)∈R2. Pour toute vitesse de rotation fixe 0≤Ω<Ω⁎:=2min{1,Λ}, il est connu que les états fondamentaux existent si et seulement si a<a⁎ pour certaine constante critique 0<a⁎<∞, où a>0 désigne le produit du nombre de particules et la valeur absolue de la longueur de dispersion. Nous analysons les développements asymptotiques des états fondamentaux quand a↗a⁎, ce qui montrent l'effet visible de Ω sur les états fondamentaux. Comme conséquence, nous prouvons que les états fondamentaux ne présentent aucun vortex dans la région R(a):={x∈R2:|x|≤C(a⁎−a)−112} quand a↗a⁎ pour une certaine constante C>0, qui est indépendante de 0<a<a⁎.
作者机构：
[Liu, Zhong Yuan] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China.;[Luo, Peng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Luo, Peng] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xie, Hua Fei] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.
通讯机构：
[Luo, P ] 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：
Single peak solutions;Schrödinger equation;variable exponent
摘要：
We study the following Schrödinger equation with variable exponent
$$ - \Delta u + u = {u^{p + \epsilon a(x)}},\,\,\,u > 0\,\,{\rm{in}}\,\,{\mathbb{R}^N},$$
where
$$\epsilon > 0,\,\,1 < p < {{N + 2} \over {N - 2}},\,\,a(x) \in {C^1}({\mathbb{R}^N}) \cap {L^\infty }({\mathbb{R}^N}),\,\,N \ge 3$$
Under certain assumptions on a vector field related to a(x), we use the Lyapunov–Schmidt reduction to show the existence of single peak solutions to the above problem. We also obtain local uniqueness and exact multiplicity results for this problem by the Pohozaev type identity.
关键词：
Infinitely many solutions;prescribed boundary mean curvature;finite reduction;local Pohozaev identities
摘要：
This paper deals with the following prescribed boundary mean curvature problem in
$${\mathbb{B}^N}$$
$$\left\{ {\matrix{{ - \Delta u = 0,\,u > 0,} \hfill & {y \in {\mathbb{B}^N},} \hfill \cr {{{\partial u} \over {\partial \nu }} + {{N - 2} \over 2}u = {{N - 2} \over 2}\tilde K(y){u^{{2^\sharp } - 1}},} \hfill & {y \in {\mathbb{S}^{N - 1}},} \hfill \cr } } \right.$$
where
$$\tilde K(y) = \tilde K(|{y^\prime }|,\tilde y)$$
is a bounded nonnegative function with
$$y = ({y^\prime },\tilde y) \in {\mathbb{R}^2} \times {\mathbb{R}^{N - 3}},\,\,{2^\sharp } = {{2(N - 1)} \over {N - 2}}$$
. Combining the finite-dimensional reduction method and local Pohozaev type of identities, we prove that if N ≥ 5 and
$$\tilde K(r,\tilde y)$$
has a stable critical point (r0,
$$({r_0},{\tilde y_0})$$
) with r0 > 0 and
$$\tilde K({r_0},{\tilde y_0}) > 0$$
, then the above problem has infinitely many solutions, whose energy can be made arbitrarily large. Here our result fill the gap that the above critical points may include the saddle points of
$$\tilde K(r,\tilde y)$$
.
作者机构：
[Long, Junhao; Dai, Yan; Chen, Pu; Lin, Yun; Yang, Juexi] Huazhong Univ Sci & Technol, Union Hosp, Tongji Med Coll, Dept Anesthesiol, Wuhan 430022, Peoples R China.;[Long, Junhao; Dai, Yan; Chen, Pu; Lin, Yun; Yang, Juexi] Huazhong Univ Sci & Technol, Union Hosp, Inst Anesthesia & Crit Care Med, Tongji Med Coll, Wuhan 430022, Peoples R China.;[Long, Junhao; Dai, Yan; Chen, Pu; Lin, Yun; Yang, Juexi] Huazhong Univ Sci & Technol, Key Lab Anesthesiol & Resuscitat, Minist Educ, Wuhan 430022, Peoples R China.;[Gu, Jinglan] Zhejiang Univ, Childrens Hosp, Natl Clin Res Ctr Child Hlth, Dept Nephrol,Sch Med, Hangzhou 310058, Peoples R China.;[Wu, Ming] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wu, Y ] H;[Wu, M ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Huazhong Univ Sci & Technol, Union Hosp, Tongji Med Coll, Dept Dermatol, Wuhan 430022, Peoples R China.
关键词：
Mendelian randomization (MR);causality;intestinal flora;inflammatory skin diseases;genome-wide association studies (GWAS)
摘要：
Emerging research underscores the substantial link between gut flora and various inflammatory skin diseases. We hypothesize that there exists a complex gut-skin axis, possibly affecting the progression of conditions such as eczema, acne, psoriasis, and rosacea. However, the precise nature of the causal connection between gut flora and skin diseases remains unestablished. In this study, we started by compiling summary data from genome-wide association studies (GWAS) featuring 211 unique gut microbiota and four types of skin conditions. We scrutinized these data across different taxonomic strata. Subsequently, we leveraged Mendelian randomization (MR) to ascertain if there is a causal link between gut microbiota and these skin conditions. We also performed a bidirectional MR analysis to identify the causality's direction. By utilizing Mendelian randomization, we identified 26 causal connections between the gut microbiome and four recognized inflammatory skin conditions, including 9 positive and 17 negative causal directions. Additional sensitivity analyses of these results revealed no evidence of pleiotropy or heterogeneity. Our MR analysis suggests a causal connection between gut microbiota and skin diseases, potentially providing groundbreaking perspectives for future mechanistic and clinical studies on microbiota-affected skin conditions.
期刊：
Journal of Mathematical Analysis and Applications,2023年527(1):127340 ISSN：0022-247X
通讯作者：
Zhang, MM
作者机构：
[Zhang, Min-Min; Zhang, MM; Lu, Jian-Feng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Min-Min; Zhang, MM; Lu, Jian-Feng] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Wang, Shi] Hu Bei Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Shi] Hu Bei Univ, Hubei Key Lab Appl Math, Wuhan 430079, Peoples R China.
通讯机构：
[Zhang, MM ] 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：
Let t >= 2 be an integer and p, q be two prime numbers, D =E-p circle plus (pq)l-1p Eq be a product-form digit set with l >= 1. Let mu t,D be the self-similar measure generated by the pair (t, D). It is known that Fu et al. [4,17] characterized the spectrality of mu t,D. In this paper, given a spectrum ? of mu t,D, we study some integers b such that b is also a spectrum of mu t,D. (c) 2023 Elsevier Inc. All rights reserved.
作者机构：
[Ye, Jianguo] Kashi Univ, Res Ctr Modern Math & Its Applicat, Sch Math & Stat, Kashi 844000, Peoples R China.;[Yan, Guozheng] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Guozheng Yan] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources. In the first part, we obtain the well-posedness of the direct scattering problem by the variational method. In the second part, we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity, and the shape of the external obstacle, however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
摘要：
The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we apply the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.
