Results 81 to 90 of about 649,170 (367)

On positive definite solutions of the matrix equation $ X-\sum_{i = 1}^{m}A_{i}^{\ast}X^{-p_{i}}A_{i} = Q $

AIMS Mathematics
In this paper, we used the outstanding properties of the Thompson metric to conclusively demonstrate the existence of a unique positive definite solution for the nonlinear matrix equation $ X-\sum_{i = 1}^{m}A_{i}^{\ast}X^{-p_{i}}A_{i} = Q $ without any ...
Changzhou Li , Chao Yuan , Shiliang Chen
doaj   +1 more source

Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation X=Q+A∗(X^−C)−1A

Abstract and Applied Analysis, 2013
We consider the nonlinear matrix equation X=Q+A∗(X^−C)−1A, where Q is positive definite, C is positive semidefinite, and X^ is the block diagonal matrix defined by X^=diag(X,X,…,X).
Dongjie Gao
doaj   +1 more source

Pure states proof of the Matrix-valued P\'olya Positivstellensatz

, 2023
Let $\Sigma$ denote the linear form $x_1 + \cdots + x_n$. By a classical Positivstellensatz of P\'olya, if a real form $f$ is strictly positive on the standard simplex, then $\Sigma^m f$ has strictly positive coefficients for some nonnegative integer $m$.
Tan, Colin
core  

Correlation Between Fecal Microbiota and Corticosteroid Responsiveness in Primary Immune Thrombocytopenia: an Exploratory Study

Advanced Science, EarlyView.
This study uses gut microbiome data to predict corticosteroid response in patients with immune thrombocytopenia (ITP). Fecal samples from 212 patients with ITP are sequenced. Six machine‐learning algorithms are used to train predictive models. The support vector machine‐based model integrated clinical data and selected microbial species, diversities ...
Feng‐Qi Liu, Zhuo‐Yu An, Li‐Juan Cui, Meng‐Yu Xiao, Ye‐Jun Wu, Wei Li, Bang‐Shuo Zhang, Li Yu, Jia Feng, Zhuo‐Gang Liu, Ru Feng, Zhong‐Xing Jiang, Rui‐Bin Huang, Hong‐Mei Jing, Jin‐Hai Ren, Xiao‐Yu Zhu, Yun‐Feng Cheng, Yu‐Hua Li, He‐Bing Zhou, Da Gao, Yi Liu, Fan Yu, Xin Wang, Jian‐Lin Qiao, Dai‐Hong Hu, Lu‐Lu Wang, Meng‐Tong Zang, Qi Chen, Qing‐Yuan Qu, Jian‐Ying Zhou, Meng‐Lin Li, Yu‐Xiu Chen, Qiu‐Sha Huang, Hai‐Xia Fu, Yue‐Ying Li, Qian‐Fei Wang, Xiao‐Jun Huang, Xiao‐hui Zhang, the Cooperative ITP Working Group   +38 more
wiley   +1 more source

The common Re-nonnegative definite and Re-positive definite solutions to the matrix equations $ A_1XA_1^\ast = C_1 $ and $ A_2XA_2^\ast = C_2 $

AIMS Mathematics, 2022
In this paper, we consider the common Re-nonnegative definite (Re-nnd) and Re-positive definite (Re-pd) solutions to a pair of linear matrix equations $ A_1XA_1^\ast = C_1, \ A_2XA_2^\ast = C_2 $ and present some necessary and sufficient conditions for ...
Yinlan Chen, Lina Liu
doaj   +1 more source

On the matrix version of new extended Gauss, Appell and Lauricella hypergeometric functions [PDF]

arXiv, 2021
Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric matrix function, confluent hypergeometric matrix function, Appell matrix function and Lauricella matrix function of ...
arxiv  

Diagonality Measures of Hermitian Positive-Definite Matrices with Application to the Approximate Joint Diagonalization Problem

, 2016
In this paper, we introduce properly-invariant diagonality measures of Hermitian positive-definite matrices. These diagonality measures are defined as distances or divergences between a given positive-definite matrix and its diagonal part.
Alyani, Khaled, Congedo, Marco, Moakher, Maher   +2 more
core   +2 more sources

In Situ Control of Reactive Mesogens Alignment During 3D Printing by Two‐Photon Lithography

Advanced Science, EarlyView.
Manipulating material properties at the microscale is crucial for 3D printing of smart microdevices. Two‐photon lithography directly patterns molecular alignment in liquid crystal resists. The polymerization reaction wavefront along the writing path induces an easy‐axis for the mesogenic moieties.
Tiziana Ritacco, Alfredo Mazzulla, Michele Giocondo, Gabriella Cipparrone, Pasquale Pagliusi   +4 more
wiley   +1 more source

Viridicatol from the Deep‐Sea‐Derived Fungus Alleviates Bone Loss by Targeting the Wnt/SHN3 Pathway

Advanced Science, EarlyView.
Viridicatol (VDC), isolated from the deep‐sea‐derived fungus, enhances osteogenesis in vitro and in vivo by targeting Wnt/SHN3 signaling pathway. It can be delivered via engineered nanovesicles to mitigate bone loss of osteoporosis, fracture repair, and osteogenesis imperfecta.
Chun‐Lan Xie, Shang‐Hui Ye, Yu‐Ting Yue, Bao‐Hong Shi, Jing‐Ping Xu, Lian‐Jie Li, Zheng‐Biao Zou, Matthew B. Greenblatt, Na Li, Xian‐Wen Yang, Ren Xu   +10 more
wiley   +1 more source

Channel matrix, measurement matrix and collapsed matrix in teleportation [PDF]

arXiv, 2014
In this paper, two kinds of coefficient matrixes (channel matrix, measurement matrix)associated with the pure state for teleportation are presented, the general relation among channel matrix, measurement matrix and collapsed matrix is obtained. In addition, a criterion for teleportation that the number of coefficient of an unknown state is determined ...
arxiv