Article
Mathematics, Applied
Zhongkai Guo, Yong Xu, Weifeng Wang, Junhao Hu
Summary: This paper discusses the averaging principle for a class of stochastic differential equations with nonlinear terms satisfying only local Lipschitz and monotone conditions. Compared to classical conditions, the conditions in this paper are weaker, making the conclusions applicable to a wider range of SDEs.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Operations Research & Management Science
Feng Xue
Summary: Based on degenerate proximal point analysis, this study demonstrates that the Douglas-Rachford splitting can be reduced to a well-defined resolvent, but it generally fails to be a proximal mapping. This extends the recent findings of [Bauschke, Schaad and Wang. Math. Program. 2018;168:55-61] to a more general setting. The concepts and consequences related to maximal and cyclic monotonicity are also examined, which proves to be crucial for analyzing various operator splitting algorithms.
Article
Mathematics
Prasit Cholamjiak, Dang Van Hieu, Le Dung Muu
Summary: In this paper, two new inertial algorithms are introduced for solving a variational inclusion problem in a Hilbert space. These algorithms are constructed based on the resolvent of a maximally monotone operator and the inertial technique. They can work with or without a linesearch procedure and do not require prior knowledge of the Lipschitz constant of the operator. Theorems of weak convergence are established and the obtained results are applied to convex optimization problems, split feasibility problems, and composite monotone inclusions. Numerical results are reported to compare the performance of the new algorithms with others.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
(2022)
Article
Economics
Florian F. Gunsilius
Summary: This article introduces an empirical condition for nonparametric point identification in multivariate instrumental variable models with continuous endogenous variables using binary instruments. The condition verifies point identification in cases where traditional approaches cannot be applied. It demonstrates that nonlinear instrumental variable models with general heterogeneity can be point-identified with just a binary instrument, extending existing identification results that heavily restrict unobserved heterogeneity or require large instrument support. The main assumption is cyclic monotonicity of the first stage of the instrumental variable model, a multivariate generalization of the classical rank-invariance assumption for univariate models. Asymptotic convergence results for empirical observable distributions are derived to practically check the condition. Identification relies on a fixed-set convergence of cyclically monotone maps between quasi-concave functions.
JOURNAL OF ECONOMETRICS
(2023)
Article
Mathematics, Applied
Stefan Schiffer
Summary: This note investigates the complex constant rank condition for differential operators and its implications for coercive differential inequalities. Depending on the order of the operators, such inequalities can be viewed as generalizations of either Korn's inequality or Sobolev's inequality.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2024)
Article
Computer Science, Software Engineering
Sedi Bartz, Heinz H. Bauschke, Hung M. Phan, Xianfu Wang
Summary: This paper examines the monotonicity and convex analysis in the framework of multi-marginal optimal transport theory, extending classical theory into multi-marginal settings. It characterizes multi-marginal c-monotonicity and provides criteria for maximal monotonicity, while also expanding the decomposition of identity and quadratic functions into the multi-marginal context. Examples and applications are illustrated, along with pointing out open questions for further research.
MATHEMATICAL PROGRAMMING
(2021)
Article
Mathematics
Esra Kaya
Summary: This paper investigates the B-maximal operator on variable exponent Lebesgue spaces and establishes a necessary condition for its boundedness. It is proven that the B-maximal operator is unbounded when p(-) = 1, while the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator on the same space is demonstrated.
Article
Mathematics
Jan Chvalina, Michal Novak, Bedrich Smetana, David Stanek
Summary: The paper focuses on studying sequences of groups and hypergroups of linear differential operators, constructing hypercompositional structures, and exploring actions of differential operator groups on polynomial rings. The theoretical results are illustrated with examples from artificial neurons and infinite cyclic groups.
Article
Mathematics, Applied
Sergiusz Kuzel, Anna Rozanska
Summary: The aim of this work is to develop a functional calculus for simple maximal symmetric operators, based on the properties of self-adjoint extensions of Phillips symmetric operators. The obtained results are applied to describe non-cyclic vectors of backward shift operators.
ANNALS OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Aparajita Dasgupta, Vishvesh Kumar
Summary: This article proves the coincidence of the minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on Z(n)×T-n, and provides the domain in terms of a Sobolev space. It also demonstrates the equivalence of ellipticity and Fredholmness for pseudo-differential operators on Z(n) and computes the index of an elliptic pseudo-differential operator on Z(n).
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Sarah Eberle-Blick, Bastian Harrach
Summary: This paper focuses on reconstructing inclusions in elastic bodies using monotonicity methods and presents conditions for achieving a resolution in a given partition. These conditions consider both background error and measurement noise. The cases where the Lame parameters are either smaller or larger than the background Lame parameters are investigated, resulting in four different algorithms and corresponding resolution guarantees.
Article
Optics
Deyun Wei, Yi Shen
Summary: By utilizing the theory of super-differential operators, a new method for solving discrete CLCT has been proposed. This method appropriately decomposes the parameter matrix and uses coordinate multiplication operators and differential operators to represent each part of the decomposition. The use of operator theory not only makes the new discrete algorithm more accurate to the continuous transform, but also results in a discrete CLCT matrix with Fourier duality relation.
Article
Mathematics, Applied
Aymen Ammar, Aref Jeribi, Mayssa Zayed
Summary: The main objective of this paper is to introduce the concept of pseudospectrum for multivalued linear operators and establish several relations with the conventional spectrum. The paper starts by providing the definition and then focuses on characterizing, studying stability, and analyzing some properties of the pseudospectrum.
Article
Engineering, Aerospace
Xiaoyu Lang, Anton de Ruiter
Summary: This paper considers the use of orientation cellular space modules (OCSM) and rate cellular space modules (RCSM) for retired spacecraft attitude takeover control. By utilizing different sensors and control strategies, the OCSM and RCSM can provide effective attitude regulation and control.
Article
Mathematics
W. M. Schouten-Straatman, H. J. Hupkes
Summary: In this study, exponential dichotomies of functional differential equations of mixed type with infinite range discrete and/or continuous interactions are analyzed, building upon previous Fredholm theory. Different approaches for half line and full line cases are refined and constructed, with emphasis on degeneracy issues and alternative criteria based on the structure of the systems. Optimal results are obtained under specific conditions, illustrated with examples and counter-examples involving the Nagumo equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Samir Adly, Abderrahim Hantoute, Ba Khiet Le
SET-VALUED AND VARIATIONAL ANALYSIS
(2016)
Article
Operations Research & Management Science
Samir Adly, Ba Khiet Le
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2016)
Article
Operations Research & Management Science
Samir Adly, Ba Khiet Le
Article
Operations Research & Management Science
Samir Adly, Ba Khiet Le
OPTIMIZATION LETTERS
(2018)
Article
Mathematics, Applied
Samir Adly, Ba Khiet Le
APPLICABLE ANALYSIS
(2014)
Article
Automation & Control Systems
Samir Adly, Bernard Brogliato, Ba Khiet Le
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2013)
Article
Operations Research & Management Science
Samir Adly, Tahar Haddad, Ba Khiet Le
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2019)
Article
Operations Research & Management Science
Ba Khiet Le
Article
Mathematics, Applied
Ba Khiet Le
SET-VALUED AND VARIATIONAL ANALYSIS
(2020)
Article
Operations Research & Management Science
S. Adly, B. K. Le
Summary: This paper presents a new application of the Douglas-Rachford splitting method for finding a zero of the sum of two maximal monotone operators, where one operator implicitly depends on the state variable. The proposed algorithms are simpler and have better convergence rates compared to existing results, and can be implemented under general conditions. Numerical experiments demonstrate the convergence rate of the proposed algorithms.
OPTIMIZATION LETTERS
(2021)
Article
Mathematics
Ba Khiet Le
JOURNAL OF CONVEX ANALYSIS
(2020)
Article
Mathematics, Applied
Samir Adly, Ba Khiet Le
NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION
(2018)
Article
Operations Research & Management Science
Ba Khiet Le
PACIFIC JOURNAL OF OPTIMIZATION
(2017)
Article
Mathematics
Samir Adly, Bernard Brogliato, Ba Khiet Le
JOURNAL OF CONVEX ANALYSIS
(2016)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)