Article
Statistics & Probability
Sungho Cho, Jeong Min Jeon, Dongwoo Kim, Kyusang Yu, Byeong U. U. Park
Summary: In this article, we develop semiparametric regression techniques for fitting partially linear additive models. These techniques are applicable to general Hilbert-space-valued responses. By using the powerful technique of additive regression, we are able to profile out the additive nonparametric components of the models and regressively analyze the nonadditive effects of covariates. We demonstrate the consistency and asymptotic Gaussianity of the estimators for the parametric components, as well as the convergence rate of the estimators for the nonparametric components, regardless of the dimension of the covariates. Numerical evidence and real data applications are presented to support the proposed method. Supplementary materials for this article are available online.
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
(2023)
Article
Mathematics, Applied
Jacek Bochnak, Wojciech Kucharz, Janos Kollar
Summary: This article studies the continuous map problem between real algebraic varieties and homogeneous spaces of linear real algebraic groups. It proves the conditions for approximating continuous maps using regular maps and provides applications and consequences of the results.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2022)
Article
Statistics & Probability
Jeong min Jeon, Young kyung Lee, Enno Mammen, Byeong U. Park
Summary: A new additive regression technique is developed for response variables in general Hilbert spaces. The method is based on smooth backfitting and utilizes local polynomial smoothing. The proposed approach overcomes limitations of existing methods and includes theoretical analysis, simulation study, and real data applications to demonstrate its efficiency.
Article
Mathematics, Applied
Hui Yan, Hongxing Wang, Kezheng Zuo, Yang Chen
Summary: This paper explores new characteristics and properties of weak group inverse and weak group matrix, including characterizing weak group inverse based on range space and null space, presenting different characterizations using projection and Bott-Duffin inverse, investigating relationships with other generalized inverses using core-EP decomposition, and obtaining new characterizations of weak group matrix.
Article
Mathematics
Zeyuan Song, Zuoren Sun
Summary: The central problem of this study is to represent any holomorphic and square integrable function on the Kepler manifold in the series form based on Fourier analysis. Three different domains on the Kepler manifold are considered and the weak pre-orthogonal adaptive Fourier decomposition (POAFD) is proposed. The weak maximal selection principle is shown to select the coefficient of the series, and a convergence theorem is proved to demonstrate the accuracy of the method.
Article
Statistics & Probability
Y. K. Lee, H. Hong, D. Kim, B. U. Park
Summary: This paper discusses a general method for improving the bias properties of nonparametric kernel regression estimators by constructing a semiparametric estimator that combines a parametric component and a nonparametric adjustment. The method is shown to consistently improve the bias of the local linear estimator, regardless of the choice of parametric model, for response variables in a general Hilbert space. An example with random density response variable is used to illustrate the method.
JOURNAL OF THE KOREAN STATISTICAL SOCIETY
(2021)
Article
Mathematics, Applied
Yonghong Yao, Olaniyi S. Iyiola, Yekini Shehu
Summary: In this paper, we propose a new subgradient extragradient method with double inertial extrapolation steps and self-adaptive step sizes for solving variational inequalities. We analyze the weak, strong, and linear convergence of the method. Numerical implementations show that our method is more efficient and effective compared to existing methods for solving variational inequalities.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
E. Garcia-Rio, R. Marino-Villar, M. E. Vazquez-Abal, R. Vazquez-Lorenzo
Summary: This study focuses on solitons for the two-loop renormalization group flow in four-dimensional gauge field theory, providing a classification of algebraic steady four-dimensional solitons.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2023)
Article
Statistics & Probability
Young Kyung Lee, Enno Mammen, Byeong U. Park
Summary: We discuss a method to improve local linear additive regression for response variables in a general separable Hilbert space. Our methodology is applicable to both non-additive and additive regression functions. We present relevant theory in this flexible framework and demonstrate the benefits of the proposed technique through a real data application.
JOURNAL OF NONPARAMETRIC STATISTICS
(2023)
Article
Mathematics, Applied
Chaochao Sun, Yuanbo Liu
Summary: We construct the Pontryagin dual of the multiplicative group of positive rational numbers. Then we study its topological generators and representations.
Article
Mathematics, Applied
Wei Qu, Tao Qian, Haichou Li, Kehe Zhu
Summary: This study explores the best kernel approximation problem for analytic functions on the unit disk D in the reproducing kernel Hilbert space H, proving the existence of the best kernel approximation for weighted Bergman spaces with standard weights.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Xiaolin Zhou, Gang Cai, Prasit Cholamjiak, Suparat Kesornprom
Summary: This paper investigates a generalized proximal method with a new step size update for solving the variational inequality problem in Hilbert spaces. Weak convergence of the proposed scheme is proven under certain assumptions on the operators and parameters, with an additional R-linear convergence rate when the operator is strongly monotone. Numerical experiments are conducted to demonstrate the efficacy of the proposed iterative algorithm, and it is noted that several existing methods in the literature are special cases of the proposed method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics
Frederic Bayart
Summary: This article provides a sufficient condition for a composition operator with positive characteristic to be compact on the Hardy space of Dirichlet series.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2023)
Article
Mathematics
Stephen Dilworth, Gustavo Garrigos, Eugenio Hernandez, Denka Kutzarova, Vladimir Temlyakov
Summary: New results on Lebesgue-type inequalities for the Weak Chebyshev Greedy Algorithm in uniformly smooth Banach spaces are presented, with improved bounds for dictionaries satisfying a new property. These results are applied to derive optimal bounds in two natural examples of sequence spaces, achieving optimality specifically in the case of the multivariate Haar system in L-p with 1 < p <= 2 under the Littlewood-Paley norm.
JOURNAL OF FUNCTIONAL ANALYSIS
(2021)
Article
Mathematics, Applied
Changho Keem, Yun-Hwan Kim
Summary: In this paper, we prove that the Hilbert scheme of smooth curves is non-empty in certain cases with low genus, and it is irreducible.
JOURNAL OF ALGEBRA AND ITS APPLICATIONS
(2022)
Article
Mathematics
Mikhail Borovoi, Yves Cornulier
COMPTES RENDUS MATHEMATIQUE
(2015)
Article
Mathematics
Mikhail Borovoi
JOURNAL OF ALGEBRA
(2015)
Article
Mathematics
Mikhail Borovoi, Zachi Evenor
JOURNAL OF ALGEBRA
(2016)
Article
Mathematics
Mikhail Borovoi, Cyril Demarche
COMMENTARII MATHEMATICI HELVETICI
(2013)
Article
Mathematics
M. Borovoi, J. -L. Colliot-Thelene, A. N. Skorobogatov
DUKE MATHEMATICAL JOURNAL
(2008)
Article
Mathematics
Mikhail Borovoi, Boris Kunyavskii, Nicole Lemire, Zinovy Reichstein
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2014)
Article
Mathematics
Mikhail Borovoi, Joost van Hamel
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
(2009)
Article
Mathematics
Mikhail Borovoi, Cristian D. Gonzalez-Aviles
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
(2014)
Article
Mathematics
Mikhail Borovoi, Nikita Semenov, Maksim Zhykhovich
Summary: The paper establishes a Hasse principle for binary direct summands of the Chow motive of a smooth projective quadric Q over a number field F, and shows that these summands are twists of Rost motives. Furthermore, a complete motivic decomposition of Q is described in the case when F has at most one real embedding.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics
Mikhail Borovoi
TRANSFORMATION GROUPS
(2020)
Article
Mathematics
M. Borovoi, D. A. Timashev
Summary: This study computed the first Galois cohomology set H-1(Double-struck capital R;G) for a connected semisimple group G over the field of real numbers, using a method proposed by Onishchik and Vinberg, and represented it in terms of Kac labelings of the affine Dynkin diagram of G.
TRANSFORMATION GROUPS
(2021)
Article
Mathematics, Applied
Mikhail Borovoi, Tomer M. Schlank
MOSCOW MATHEMATICAL JOURNAL
(2012)
Article
Mathematics
Mikhail Borovoi, Zinovy Reichstein
ALGEBRA & NUMBER THEORY
(2011)
Article
Mathematics
M Borovoi, J van Hamel
COMPTES RENDUS MATHEMATIQUE
(2006)