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⁎.
期刊：
Calculus of Variations and Partial Differential Equations,2023年62(3):1-35 ISSN：0944-2669
通讯作者：
Peng Luo
作者机构：
[Luo, Peng; Zhou, Yang; Peng, Shuangjie] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Luo, Peng; Peng, Shuangjie] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Peng Luo] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
关键词：
35A01;35B25;35J20;35J60
摘要：
We revisit the well known prescribed scalar curvature problem
$$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=\big (1+\varepsilon K(x)\big )u^{2^*-1}, u(x)>0,~~ &{}{x\in \mathbb {R}^N},\\ u\in \mathcal {D}^{1,2}(\mathbb {R}^N),\\ \end{array}\right. } \end{aligned}$$
where
$$2^*=\frac{2N}{N-2}$$
,
$$N\ge 5$$
,
$$\varepsilon >0$$
and
$$K(x)\in C^1(\mathbb {R}^N)\cap L^{\infty }(\mathbb {R}^N)$$
. It is known that there are a number of results related to the existence of solutions concentrating at the isolated critical points of K(x). However, if K(x) has non-isolated critical points with different degenerate rates along different directions, whether there exist solutions concentrating at these points is still an open problem. We give a certain positive answer to this problem via applying a blow-up argument based on local Pohozaev identities and modified finite dimensional reduction method when the dimension of critical point set of K(x) ranges from 1 to
$$N-1$$
, which generalizes some results in Cao et al. (Calc Var Partial Differ Equ 15:403–419, 2002) and Li (J Differ Equ 120:319–410, 1995; Commun Pure Appl Math 49:541–597, 1996).
作者机构：
[Cui, Hengjian] Capital Normal Univ, Sch Math Sci, Beijing, Peoples R China.;[Liu, Yanyan] Wuhan Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Zhang, Jing] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan, Hubei, Peoples R China.;[Zhang, Jing] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Hubei, Peoples R China.
通讯机构：
[Jing Zhang; Jing Zhang Jing Zhang Jing Zhang] S;School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, Hubei, China
关键词：
conditional distance correlation;model-free screening;sure screening property;ultrahigh-dimensional survival data
摘要：
How to select the active variables that have significant impact on the event of interest is a very important and meaningful problem in the statistical analysis of ultrahigh-dimensional data. In many applications, researchers often know that a certain set of covariates are active variables from some previous investigations and experiences. With the knowledge of the important prior knowledge of active variables, we propose a model-free conditional screening procedure for ultrahigh dimensional survival data based on conditional distance correlation. The proposed procedure can effectively detect the hidden active variables that are jointly important but are weakly correlated with the response. Moreover, it performs well when covariates are strongly correlated with each other. We establish the sure screening property and the ranking consistency of the proposed method and conduct extensive simulation studies, which suggests that the proposed procedure works well for practical situations. Then, we illustrate the new approach through a real dataset from the diffuse large-B-cell lymphoma study S1.
期刊：
Journal of Pure and Applied Algebra,2023年227(7):107322 ISSN：0022-4049
通讯作者：
Chengkang Xu
作者机构：
[Guo, Hongyan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xu, Chengkang] Shangrao Normal Univ, Shangrao, Jiangxi, Peoples R China.
通讯机构：
[Chengkang Xu] S;Shangrao Normal University, Shangrao, Jiangxi, China
摘要：
This paper studies restricted modules of gap-p Virasoro algebra g(p) and their intrinsic connection to twisted modules of certain vertex algebras. We first establish an equivalence between the category of restricted g(p)-modules of level (l) under bar and the category of twisted modules of vertex algebra V-Np((l) under bar, 0), where N-p is a new Lie algebra, (l) under bar :=(l(0), 0, center dot center dot center dot, 0) is an element of C[p/2]+1, l(0) is an element of C is the action of the Virasoro center. Then we focus on the construction and classification of simple restricted g(p)-modules of level (l) under bar. More explicitly, we give a uniform construction of simple restricted g(p)-modules as induced modules. We present several equivalent characterizations of simple restricted g(p)-modules, as locally nilpotent (equivalently, locally finite) modules with respect to certain positive part of g(p). Moreover, simple restricted g(p)-modules of level (l) under bar are classified. They are either highest weight modules or simple induced modules. At the end, we exhibit several concrete examples of simple restricted g(p)-modules of level (l) under bar (including Whittaker modules). (c) 2023 Elsevier B.V. All rights reserved.
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：
Mathematical Methods in the Applied Sciences,2023年46(5):5099-5118 ISSN：0170-4214
通讯作者：
Hangzhou Hu<&wdkj&>Hangzhou Hu Hangzhou Hu Hangzhou Hu
作者机构：
[Hu, Hangzhou; Zhao, Dun] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China.;[Li, Yuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Hangzhou Hu; Hangzhou Hu Hangzhou Hu Hangzhou Hu] S;School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000 Gansu, China
关键词：
asymptotic behavior;ground states;NLS equations;periodic magnetic field;variational methods for second-order elliptic equations;XFEL Schrodinger equation
摘要：
We consider the following X‐ray free electron lasers Schrödinger equation (i∇−A)2u+V(x)u−μ|x|u=1|x|∗|u|2u−K(x)|u|q−2u,x∈ℝ3,$$ {\left(i\nabla -A\right)}&#x0005E;2u&#x0002B;V(x)u-\frac{\mu }{\mid x\mid }u&#x0003D;\left(\frac{1}{\mid x\mid}\ast {\left&#x0007C;u\right&#x0007C;}&#x0005E;2\right)u-K(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{q-2}u,x\in {\mathbb{R}}&#x0005E;3, $$ where A∈Lloc2(ℝ3,ℝ3)$$ A\in {L}_{loc}&#x0005E;2\left({\mathbb{R}}&#x0005E;3,{\mathbb{R}}&#x0005E;3\right) $$ denotes the magnetic potential such that the magnetic field B=curlA$$ B&#x0003D;\operatorname{curl}\kern0.4em A $$ is ℤ3$$ {\mathbb{Z}}&#x0005E;3 $$‐periodic, μ∈ℝ,K∈L∞ℝ3$$ \mu \in \mathbb{R},K\in {L}&#x0005E;{\infty}\left({\mathbb{R}}&#x0005E;3\right) $$ is ℤ3$$ {\mathbb{Z}}&#x0005E;3 $$ periodic and non‐negative, q∈(2,4)$$ q\in \left(2,4\right) $$. Using the variational method, based on a profile decomposition of the Cerami sequence in HA1ℝ3$$ {H}_A&#x0005E;1\left({\mathbb{R}}&#x0005E;3\right) $$, we obtain the existence of the ground state solution for suitable μ≥0$$ \mu \ge 0 $$. When μ<0$$ \mu &lt;0 $$ is small, we also obtain the non‐existence. Furthermore, we give a description of the asymptotic behavior of the ground states as μ→0+$$ \mu \to {0}&#x0005E;{&#x0002B;} $$.
摘要：
Cancer is a complex disease caused primarily by genetic variants. Reconstructing gene networks within tumors is essential for understanding the functional regulatory mechanisms of carcinogenesis. Advances in high-throughput sequencing technologies have provided tremendous opportunities for inferring gene networks via computational approaches. However, due to the heterogeneity of the same cancer type and the similarities between different cancer types, it remains a challenge to systematically investigate the commonalities and specificities between gene networks of different cancer types, which is a crucial step towards precision cancer diagnosis and treatment. In this study, we propose a new sparse regularized multi-layer decomposition graphical model to jointly estimate the gene networks of multiple cancer types. Our model can handle various types of gene expression data and decomposes each cancer-type-specific network into three components, i.e., globally shared, partially shared and cancer-type-unique components. By identifying the globally and partially shared gene network components, our model can explore the heterogeneous similarities between different cancer types, and our identified cancer-type-unique components can help to reveal the regulatory mechanisms unique to each cancer type. Extensive experiments on synthetic data illustrate the effectiveness of our model in joint estimation of multiple gene networks. We also apply our model to two real data sets to infer the gene networks of multiple cancer subtypes or cell lines. By analyzing our estimated globally shared, partially shared, and cancer-type-unique components, we identified a number of important genes associated with common and specific regulatory mechanisms across different cancer types.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of Research Network of Computational and Structural Biotechnology. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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：
[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.
期刊：
Journal of Mathematical Biology,2023年86(6):1-45 ISSN：0303-6812
通讯作者：
Huang, JC;Wang, H
作者机构：
[Zhang, Yuyue; Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;[Zhang, Yuyue; Huang, Jicai] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;[Wang, Hao] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.;[Wang, Hao] Univ Alberta, Interdisciplinary Lab Math Ecol & Epidemiol, Edmonton, AB T6G 2G1, Canada.
通讯机构：
[Wang, H ] U;[Huang, JC ] C;Cent China Normal Univ, Sch Math & Stat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Hubei, Peoples R China.;Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.
关键词：
Degenerate Bogdanov–Takens bifurcation;Generalist predator;Nilpotent cusp of codimension 4;Nilpotent focus of codimension 3;Predator–prey model;Specialist predator
摘要：
In this paper, we revisit a predator-prey model with specialist and generalist predators proposed by Hanski et al. (J Anim Ecol 60:353-367, 1991) , where the density of generalist predators is assumed to be a constant. It is shown that the model admits a nilpotent cusp of codimension 4 or a nilpotent focus of codimension 3 for different parameter values. As the parameters vary, the model can undergo cusp type (or focus type) degenerate Bogdanov-Takens bifurcations of codimension 4 (or 3). Our results indicate that generalist predation can induce more complex dynamical behaviors and bifurcation phenomena, such as three small-amplitude limit cycles enclosing one equilibrium, one or two large-amplitude limit cycles enclosing one or three equilibria, three limit cycles appearing in a Hopf bifurcation of codimension 3 and dying in a homoclinic bifurcation of codimension 3. In addition, we show that generalist predation stabilizes the limit cycle driven by specialist predators to a stable equilibrium, which clearly explains the famous Fennoscandia phenomenon.
期刊：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2023年22(1):304-317 ISSN：1534-0392
通讯作者：
Wu, S
作者机构：
[Wu, Shuang; Wu, S; Gao, Yongshuai; 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：
[Wu, S ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
