Article
Mathematics
Julian Bailey
Summary: The article introduces classes of weights for which certain operators are bounded on weighted Lebesgue spaces. It also proves the boundedness of Lv-Riesz potentials and examines different generalized forms of Schrodinger operators. Finally, necessary conditions for weights to satisfy in order for certain operators to be bounded are investigated.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Li Yang, Pengtao Li
Summary: In this paper, we establish the quantitative weighted boundedness of Littlewood-Paley functions generated by fractional heat semigroups related with the Schrodinger operators, using the regularity estimate of the fractional heat kernel related with L.
JOURNAL OF FUNCTION SPACES
(2023)
Article
Mathematics, Applied
B. Bongioanni, E. Harboure, P. Quijano
Summary: In this work, we investigate the boundedness of Riesz transforms associated with the Schrodinger operator and the additional conditions required on the potential. We explore the boundedness of first and second order Riesz transforms and their effects on regularity spaces.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Baptiste Devyver, Emmanuel Russ
Summary: In this paper, we study the Hardy spaces on complete Riemannian manifolds and establish the equivalence between the Hardy spaces of exact 1-differential forms and the closure in Lp. This result holds when the Ricci curvature has quadratic decay and the volume growth is strictly faster than quadratic, and it applies particularly to manifolds with a finite number of Euclidean ends.
Article
Mathematics
Rafik Imekraz, El Maati Ouhabaz
Summary: In this work, the classical Bernstein inequality is extended to a more general setting involving various types of operators on Riemannian manifolds or domains. The L-p Bernstein inequalities are proved, along with a novel reverse inequality that is applicable even for compact manifolds. The relationship between L-p Bernstein inequality and the boundedness of the Riesz transform on L-p is highlighted, with the development of new techniques for reformulating the Bernstein inequalities.
MATHEMATISCHE ANNALEN
(2022)
Article
Mathematics, Applied
Julian Bailey, Andrew J. Morris, Maria Carmen Reguera
Summary: This study demonstrates that the Riesz transform corresponding to a specific Schrodinger operator in spaces with totally irregular measures is not bounded in the L-2 space, even with the presence of potentials. New exponential decay estimates for the kernel of the Riesz transform were obtained, along with Holder regularity estimates at local scales determined by the critical radius function of the potential.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Thomas Cometx
Summary: The study focuses on the Littlewood-Paley-Stein functions associated with Hodge-de Rham and Schrodinger operators on Riemannian manifolds. Boundedness on L-p for p in some interval is proven under conditions on the Ricci curvature, while a link is made to the Riesz Transform. A criterion is provided to obtain the boundedness of the vertical Littlewood-Paley-Stein function associated with Schrodinger operators on L-p for p > 2.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Mathematics
Jinghao Huang, Fedor Sukochev, Dmitriy Zanin
Summary: This article investigates the distribution function of martingale transforms in a probability space and provides a sharp estimate, complementing and extending classical results from previous research.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Daniel Spector, Cody B. Stockdale
Summary: We have shown the existence of an absolute constant C > 0 that satisfies a particular inequality involving the Riesz transform on Double-struck capital Rn. This result provides a new proof for dimensional estimates and can be applied to a wider class of Calderon-Zygmund operators.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2021)
Article
Mathematics, Applied
Yingzhan Wang
Summary: This paper studies the general orthogonal Radon transform R-j, k(p) and its existence conditions on Lebesgue spaces. The paper also explores the relation formulas between the transform and fractional integrals, as well as Semyanistyi integrals. Several explicit inversion formulas are obtained when the function is restricted to the range of j-plane transforms.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Physics, Mathematical
Salem Ben Said, Selma Negzaoui
Summary: This article investigates a large family of Flett potentials, which includes some classical cases that have been studied before. The explicit inversion formula of Flett potentials is obtained using a tool generated by a Poisson type semigroup and signed Borel measures. The article also proves the almost everywhere convergence of a convolution operator. The research in this article is of great significance for understanding and applying Flett potentials.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
M. Perrin, F. Gruy
Summary: This study extends the Riesz transform to higher order Riesz transforms and proposes an integral transform method for function transformation. By computing the Fourier multiplier, a recursive algorithm for the coefficients of the transformed kernel is obtained, and experimental results are presented.
QUARTERLY OF APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
J. J. Betancor, M. De Leon-Contreras
Summary: This paper establishes the L-p-boundedness properties for variation, oscillation, and jump operators associated with Riesz transforms and Poisson semigroups related to Laguerre polynomial expansions.
ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics
Juan Luis Garcia Guirao, Mobashir Iqbal, Zia Bashir, Tabasam Rashid
Summary: This paper focuses on fuzzy order bounded linear operators between two fuzzy Riesz spaces and defines lattice operations to make the set of all bounded linear operators as a fuzzy Riesz space. It also studies the separation property in fuzzy order dual as a special case and discusses the relation between fuzzy order dual and topological dual of a locally convex solid fuzzy Riesz space.
Article
Mathematics, Applied
Alberto Debernardi, Nir Lev
Summary: We prove the existence of a Riesz basis of exponential functions in the space L-2(Omega) for any centrally symmetric convex polytope Q in R-d, where all faces of Q in all dimensions are also centrally symmetric. This result is new for any dimension d greater than one.
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2022)
Article
Nanoscience & Nanotechnology
Zichen Zhang, Matthias Passlack, Gregory Pitner, Cheng-Hsuan Kuo, Scott T. Ueda, James Huang, Harshil Kashyap, Victor Wang, Jacob Spiegelman, Kai-Tak Lam, Yu-Chia Liang, San Lin Liew, Chen-Feng Hsu, Andrew C. Kummel, Prabhakar Bandaru
Summary: A low-temperature AlOx process was used to deposit high nucleation density oxide layers on carbon materials, enabling the growth of sub-nanometer gate oxides. Electrical measurements and simulations demonstrated the feasibility of using this low-temperature AlOx process for gate oxides on carbon nanotubes, showing potential for carbon-based electronic device applications.
ACS APPLIED MATERIALS & INTERFACES
(2022)
Article
Engineering, Electrical & Electronic
Zuopu Zhou, Leming Jiao, Jiuren Zhou, Qiwen Kong, Sheng Luo, Chen Sun, Zijie Zheng, Xiaolin Wang, Dong Zhang, Gan Liu, Gengchiau Liang, Xiao Gong
Summary: The researchers have developed a comprehensive ferroelectric tunnel junction (FTJ) model that considers dynamic and multi-domain switching behaviors. By combining the Time-Dependent Landau-Ginzburg equations and the Non-Equilibrium Green Function, they were able to successfully reproduce experimental results and predict the dynamic and multi-state switching of FTJ. This model shows promise for applications in high-density data storage and analog computing.
IEEE ELECTRON DEVICE LETTERS
(2022)
Article
Mathematics, Applied
Kai Yang, Chongchun Zeng, Xiaoyi Zhang
Summary: This article examines the focusing energy critical nonlinear Schrodinger equation with inverse square potential in dimensions 3, 4, and 5. The characteristics of solutions on the energy surface of the ground state are described and proved. It is shown that solutions with kinetic energy less than that of the ground state must converge to the ground state, while solutions with greater kinetic energy will blow up in finite time.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Statistics & Probability
Xiaoyi Zhang
Summary: This study deals with the problem of optimal benefit distribution and asset allocation for a DC pension plan during its decumulation phase. Taking into account the influence of inflation, the plan aims to reduce fluctuations of benefit and terminal wealth by investing in a financial market.
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
(2022)
Editorial Material
Nanoscience & Nanotechnology
Steven Lukman, Lu Ding, Lei Xu, Ye Tao, Anders C. Riis-Jensen, Gang Zhang, Qingyang Steve Wu, Ming Yang, Sheng Luo, Chuanghan Hsu, Liangzi Yao, Gengchiau Liang, Hsin Lin, Yong-Wei Zhang, Kristian S. Thygesen, Qi Jie Wang, Yuanping Feng, Jinghua Teng
NATURE NANOTECHNOLOGY
(2022)
Article
Psychiatry
Tao Zhou, Xiaoyi Zhang, Shuming Fan, Zeming Deng, Can Jiao
Summary: This study found that childhood neighborhood cohesion predicts cognitive function among elderly people through the mediating roles of childhood friendship, depression, and social activity engagement.
FRONTIERS IN PSYCHIATRY
(2022)
Article
Fisheries
Xiao Yi Zhang, Xin Yao, Fan Zhou, Cheng Zhong Yang, Yang Liu
Summary: During a parasitological survey of goldfish in China, two myxosporeans were collected and identified as a new species named Thelohanellus pseudonikolskii n. sp and the known species Myxobolus koi, respectively.
AQUACULTURE REPORTS
(2022)
Article
Pediatrics
Xiaoyi Zhang, Zhoudao Dai, Collins Opoku Antwi, Jun Ren
Summary: Research using the Mental Health Test (MHT) has shown that left-behind children (LBC) experience a slight but significant decline in mental health over time, especially for left-behind boys (LBBs). The mental health of LBC in junior high and elementary school has shown a stable and significant deterioration. Furthermore, LBC with neither parent present have a significantly worse mental health status compared to those with one parent present.
Article
Chemistry, Multidisciplinary
Jiahui Liu, Ziheng Li, Honglin Li, Yichu Zhang, Chunxu Yang, Xinchen Wang, Han Liang, Jiacheng Song, Xiaoyi Zhang, Haoteng Sun, Yanbin Zhang
Summary: In this study, hexagonal prism-shaped ZnO with exposed (002) and (200) planes was synthesized and its characteristic adsorption species and photocurrent spectrum mechanism were investigated through experimental and theoretical simulations. The results showed that hexagonal prism-shaped ZnO can be used for gas-sensitive detection by consuming adsorbed oxygen or using the photocurrent spectrum to detect reduced gas molecules.
JOURNAL OF PHYSICS AND CHEMISTRY OF SOLIDS
(2022)
Article
Mathematics
Kai Yang, Xiaoyi Zhang
Summary: This article investigates the focusing energy critical nonlinear wave equation with inverse square potential in dimensions 3, 4, and 5. The characteristics of solutions on the energy surface of the ground state are analyzed. It is proven that solutions with kinetic energy lower than that of the ground state either scatter to zero or belong to the stable/unstable manifold of the ground state and converge exponentially to the ground state in the energy space as t -> infinity or t -> -infinity. When the kinetic energy is greater than that of the ground state, all solutions with finite mass blow up in finite time in dimensions 3 and 4. In dimension 5, a finite mass solution can either have a finite lifespan or lie on the stable/unstable manifolds of the ground state. The proof relies on detailed spectral analysis of the linearized operator, local invariant manifold theory, and global Virial analysis.
MATHEMATISCHE ZEITSCHRIFT
(2022)
Article
Materials Science, Multidisciplinary
Baofang Cai, Yihan He, Yue Xin, Zhengping Yuan, Xue Zhang, Zhifeng Zhu, Gengchiau Liang
Summary: The conventional computing method based on the von Neumann architecture faces challenges of high energy consumption and limited data exchange bandwidth. Neuromorphic computing and stochastic computing have emerged as promising alternatives due to their potential for energy-efficient and high-performance computing. Among the various unconventional computing technologies, MTJs have shown remarkable efficiency and similarity to biological nervous systems, making them a suitable candidate for implementing unconventional computing architectures.
APPLIED PHYSICS A-MATERIALS SCIENCE & PROCESSING
(2023)
Article
Health Care Sciences & Services
Jingchun Liu, Xiaoyi Zhang, Haoyu Wang, Xiaohu Zuo, Li Hong
Summary: Purine metabolism is an important branch of metabolic reprogramming in cancer research. In this study, a prognostic signature consisting of nine genes related to purine metabolism was identified in ovarian cancer. The signature can distinguish prognostic risk and immune landscape of patients, and provide personalized drug options. A composite nomogram combining risk scores with clinical characteristics was created for more accurate and individualized prediction of prognosis.
JOURNAL OF PERSONALIZED MEDICINE
(2023)
Article
Engineering, Electrical & Electronic
Sheng Luo, Yihan He, Baofang Cai, Xiao Gong, Gengchiau Liang
Summary: A probabilistic bit (p-bit) is a random binary bitstream producer with tunable probability, and it is the crucial component of probabilistic computing circuitry. By utilizing the randomness induced by thermal noise-induced lattice vibration in the ferroelectric (FE) material, we propose p-bits based on stochastic ferroelectric FET (FeFET). The domain dynamic is found to be essential for the stochasticity of FE p-bits, as the domain coupling suppresses dipole fluctuation. Our proposed FE p-bits possess both extremely low hardware cost and scalability for p-bit circuitry, making it a promising candidate for PC.
IEEE ELECTRON DEVICE LETTERS
(2023)
Article
Mathematics, Applied
Kai Yang, Xiaoyi Zhang
Summary: We study the Cauchy problem for the focusing energy-critical nonlinear Schrodinger equation with an inverse square potential in dimensions d = 4, 5, 6. We prove that if the supremum of the kinetic energy of a solution over its maximal lifespan is less than the kinetic energy of the ground state, then the solution exists globally in time and scatters in both time directions. We develop the long-term kinetic energy decoupling associated with the appearance of the inverse square potential. No radial assumption is made on the initial data. This extends the result in [22] by the first author to the non-radial case.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2023)
Article
Radiology, Nuclear Medicine & Medical Imaging
Tongtong Jia, Bin Zhang, Xiaoyi Zhang, Xin Xu, Shibiao Sang, Shengming Deng
Summary: We reported a rare case of thymic Rosai-Dorfman disease (RDD) that initially presented with chest pain and did not show typical painless neck lymphadenopathy throughout the disease course. RDD should be considered as a possible diagnosis for young patients with thymic masses.