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:
[Liu, Zhongyuan] 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.
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
摘要:
In this paper, we study the following critical elliptic problem with a variable exponent:
$$\left\{ {\matrix{{ - \Delta u = {u^{p + \epsilon a\left( x \right)}}} \hfill & {{\rm{in}}\,\,\Omega ,} \hfill \cr {u > 0} \hfill & {{\rm{in}}\,\,\Omega ,} \hfill \cr {u = 0} \hfill & {{\rm{on}}\,\partial \Omega ,} \hfill \cr } } \right.$$
where
$$a\left( x \right) \in {C^2}\left( {\overline \Omega } \right),\,p = {{N + 2} \over {N - 2}},\,\,\epsilon > 0$$
, and Ω is a smooth bounded domain in ℝN (N ≽ 4). We show that for ∊ small enough, there exists a family of bubble solutions concentrating at the negative stable critical point of the function a(x). This is a new perturbation to the critical elliptic equation in contrast to the usual subcritical or supercritical perturbation, and gives the first existence result for the critical elliptic problem with a variable exponent.
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.
期刊:
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年43(1):482-506 ISSN:1078-0947
通讯作者:
Angela Pistoia
作者机构:
[Chen, Haixia] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Pistoia, Angela] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Rome, Italy.;[Vaira, Giusi] Univ Bari Aldo Moro, Dipartimento Matemat, Bari, Italy.
通讯机构:
[Angela Pistoia] D;Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Italy
摘要:
We study a new family of metrics, weighted poset block metric, which generalizes the weighted coordinates poset metric introduced by Panek and Pinheiro (IEEE Trans Inf Theory 66(11):6823–6834, 2020) and the metric for linear error-block codes introduced by Feng et al. (Finite Fields Appl 12(4):638–652, 2006). This metric covers various metrics such as Hamming metric, Lee metric, poset metric, pomset metric, poset block metric, pomset block metric and so on. We give a complete description of the groups of linear isometries of these metric spaces in terms of a semi-direct product. Moreover, we obtain a Singleton type bound for codes equipped with weighted poset block metric and define MDS codes. When the poset is a chain, we study the relationship between MDS codes and perfect codes.
期刊:
Advances in Mathematics,2023年434:109320 ISSN:0001-8708
通讯作者:
Lim, MF
作者机构:
[Lei, Antonio] Univ Ottawa, Dept Math & Stat, 150 Louis Pasteur Pvt, Ottawa, ON K1N 6N5, Canada.;[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.;[Mueller, Katharina] Univ Laval, Dept Math & Stat, Pavill Alexandre Vachon,1045 Ave Med, Quebec City, PQ G1V 0A6, Canada.
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:
Anticyclotomic Iwasawa theory;Elliptic curves;Supersingular primes;Tate-Shafarevich groups
摘要:
Let p >= 5 be a prime number and E/Q an elliptic curve with good supersingular reduction at p. Under the generalized Heegner hypothesis, we investigate the p-primary subgroups of the Tate-Shafarevich groups of E over number fields contained inside the anticyclotomic Z(p)-extension of an imaginary quadratic field where p splits. (c) 2023 Elsevier Inc. All rights reserved.
期刊:
Advances in Mathematics,2023年431:109257 ISSN:0001-8708
通讯作者:
Lai, CK
作者机构:
[An, Lixiang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[An, Lixiang] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Lai, Chun-Kit] San Francisco State Univ, Dept Math, 1600 Holloway Ave, San Francisco, CA 94132 USA.
通讯机构:
[Lai, CK ] S;San Francisco State Univ, Dept Math, 1600 Holloway Ave, San Francisco, CA 94132 USA.
关键词:
Pro duct-form;Hadamard triples;Self-similar measures;Spectral measures
摘要:
In a previous work by Laba and Wang, it was proved that whenever there is a Hadamard triple (N, D, L), then the associated one-dimensional self-similar measure mu N,D generated by maps N-1(x + d) with d is an element of D, is a spectral measure. In this paper, we introduce pro duct-form digit sets for finitely many Hadamard triples (N, Ak, Lk) by putting each triple into different scales of N. Our main result is to prove that the associated self-similar measure mu N,D is a spectral measure. This result allows us to show that pro duct-form self-similar tiles are spectral sets as long as the tiles in the group ZN obey the Coven-Meyerowitz (T 1), (T 2) tiling condition. Moreover, we show that all self-similar tiles with N = p alpha q are spectral sets, answering a question by Fu, He and Lau in 2015. Finally, our results allow us to offer new singular spectral measures not generated by a single Hadamard triple. Such new examples allow us to classify all spectral self-similar measures generated by four equi-contraction maps, which will appear in a forthcoming paper. (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http:// creativecommons .org /licenses /by -nc /4 .0/).
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:
[Miao, S.] F;Faculty of Mathematics and Statistics, 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.
摘要:
This paper focuses on the existence of positive solutions for the following weakly coupled Schro center dot dinger system with supercritical growth except at the origin: {-Delta u(1) = mu(1)|u(1)|(p(r)-2)u(1) + beta|u(2)|(p(r)/2) |u(1)|(p(r)/2 -)2 u(1), x is an element of B-1(0), - Delta u(2) = mu(2)|u(2)|(p(r)-2)u(2) + beta|u(1)|(p(r)/2) |u(2)|(p(r)/2-2)u(2), x is an element of B1(0), where B-1(0) is an unit ball R-N with N >= 3, beta is an element of R is a coupling constant, mu(1), mu(2) is an element of R are constants, p(r) = 2* + r(alpha) with 2* = 2N/N-2 . Assuming that 0 < alpha < min{N/2 , N - 2}, we apply concentration-compactness idea to show that the problem has a positive solution provided that beta > 0 if N >= 5 and beta is an element of (0, beta(0)] boolean OR [beta(1), +infinity) for some positive constants beta(0) < beta(1) if N = 3, 4.
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 Physics,2023年64(1):011506 ISSN:0022-2488
作者机构:
[An, Xiaoming] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Peoples R China.;[Yang, Xian] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要:
In this paper, we show a connection between fractional Schrodinger equations with power-law nonlinearity and fractional Schrodinger equations with logarithm-law nonlinearity. We prove that ground state solutions of power-law fractional equations, as p & RARR; 2(+), converge to a ground state solution of logarithm-law fractional equations. In particular, we provide a new proof to the existence of a ground state of logarithm-law fractional Schrodinger equations.
摘要:
Symbol-pair codes are proposed to guard against pair-errors in symbol-pair read channels. The minimum symbol-pair distance is of significance in determining the error-correcting capability of a symbol-pair code. One of the central themes in symbol-pair coding theory is the constructions of symbol-pair codes with the largest possible minimum symbol-pair distance. Maximum distance separable (MDS) and almost maximum distance separable (AMDS) symbol-pair codes are optimal and sub-optimal regarding the Singleton bound, respectively. In this paper, six new classes of AMDS symbol-pair codes are explicitly constructed through repeated-root cyclic codes. Remarkably, one class of such codes has unbounded lengths and the minimum symbol-pair distance of another class can reach 13.(c) 2023 Elsevier B.V. All rights reserved.
期刊:
Journal of Mathematical Analysis and Applications,2023年:127609 ISSN:0022-247X
通讯作者:
Yong-qiang Yang
作者机构:
[Yan-fang Zhang] School of Science, Huzhou University, Huzhou, 313000, China;[Yong-qiang Yang] Department of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China
通讯机构:
[Yong-qiang Yang] D;Department of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China
关键词:
Self-affine sponge;Maximal power law;Component-counting measure
摘要:
Let (E,ρ) be a metric space and let hE(δ) be the cardinality of the set of δ-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 Sierpiński sponge, necessary and sufficient condition is given for the validity of the relation hE(δ)≍δ−dimBE, when δ→0. In this paper, we generalize the above result to self-affine sponges of Lalley-Gatzouras type; actually in this case, we show that there exists a Bernoulli measure μ such that for any cylinder W, it holds that hW(δ)≍μ(W)δ−dimBE, when δ→0.
期刊:
Machine Learning with Applications,2023年:100479 ISSN:2666-8270
作者机构:
[Xiongjun Zhang] School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China;[Jin Wu] School of Biological Sciences, The University of Hong Kong, Pokfulam, Hong Kong;[Michael K. Ng] Department of Mathematics, The University of Hong Kong, Pokfulam, Hong Kong
摘要:
In this paper, we study the problem of multilinear multitask learning (MLMTL), in which all tasks are stacked into a third-order tensor for consideration. In contrast to conventional multitask learning, MLMTL can explore inherent correlations among multiple tasks in a better manner by utilizing multilinear low rank structure. Existing approaches about MLMTL are mainly based on the sum of singular values for approximating low rank matrices obtained by matricizing the third-order tensor. However, these methods are suboptimal in the Tucker rank approximation. In order to elucidate intrinsic correlations among multiple tasks, we present a new approach by the use of transformed tensor nuclear norm (TTNN) constraint in the objective function. The main advantage of the proposed approach is that it can acquire a low transformed multi-rank structure in a transformed tensor by applying suitable unitary transformations which is helpful to determine principal components in grouping multiple tasks for describing their intrinsic correlations more precisely. Furthermore, we establish an excess risk bound of the minimizer of the proposed TTNN approach. Experimental results including synthetic problems and real-world images, show that the mean-square errors of the proposed method is lower than those of the existing methods for different number of tasks and training samples in MLMTL.
期刊:
INVERSE PROBLEMS AND IMAGING,2023年17(3):614-628 ISSN:1930-8337
通讯作者:
Yue Zhao
作者机构:
[Zhai, Jian] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China.;[Zhao, Yue] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构:
[Yue Zhao] S;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
摘要:
This paper is concerned with inverse source problems for the time harmonic elastic wave equations and Maxwell's equations with a single boundary measurement at a fixed frequency. We show the uniqueness and a Lipschitz type stability estimate under the assumption that the source function is piece wise constant on a domain which is made of a union of disjoint convex polyhedral subdomains.
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