Article
Mathematics, Applied
Preeti Dharmarha, Sonu Ram
Summary: In this paper, we prove the spectral mapping theorem for (m, n)-paranormal operators on separable Hilbert spaces, showing that Weyl's theorem also holds for such operators. Moreover, if T is algebraically (m, n)-paranormal, then both the spectral mapping theorem and Weyl's theorem are valid.
Article
Mathematics, Applied
Fabrizio Colombo, David P. Kimsey
Summary: In this paper, we prove the spectral theorem for normal operators on a Clifford module using the S-spectrum and establish the existence of a Borel functional calculus. Our results in functional analysis, operator theory, integration theory, and measure theory in a Clifford setting may be of independent interest. Our spectral theory is the natural spectral theory for the Dirac operator on manifolds in the non-self adjoint case, and our results provide a new notion of spectral theory and a Borel functional calculus for a class of n-tuples of operators on a real or complex Hilbert space.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Shankey Kumar
Summary: This article establishes a link between the classical Bohr radius, the arithmetic Bohr radius, and the multidimensional Bohr radius. By utilizing this relation, the article addresses raised questions regarding the multidimensional Bohr radius, including one raised by Defant et al. and an open problem. Additionally, the article presents improved estimates for the Bohr radii of holomorphic functions defined on Banach spaces.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Article
Multidisciplinary Sciences
Andrew Savinov, Andres Fernandez, Stanley Fields
Summary: The study maps the inhibitory activity of protein fragments and identifies factors that affect their inhibitory function, such as fragment length, cellular protein concentration, and protein-protein interactions. It demonstrates that inhibitory fragments likely act by titrating native protein interactions and highlights the importance of specific characteristics of the fragments for their inhibitory activity.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Mathematics
Natalia P. Bondarenko
Summary: The main goal of this paper is to propose an approach to solve inverse spectral problems for functional differential operators with involution by reducing the problem to the matrix form and solving the inverse problem for the matrix Sturm-Liouville operator. The obtained results show that the considered operators with involution can be uniquely specified by certain spectra of regular boundary value problems.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Fabrizio Colombo, Antonino De Martino, Stefano Pinton, Irene Sabadini
Summary: In this paper, the importance of holomorphic functions in operator theory and the use of the Cauchy formula to define operators is discussed. The Fueter-Sce-Qian extension theorem is introduced as a way to extend holomorphic functions to the hyperholomorphic setting. The extension procedure generates monogenic functions, and the associated monogenic functional calculus is described. Various factorizations of the extension operator are explored, resulting in different function spaces and associated functional calculi. The fine structure of the spectral theories on the S-spectrum is defined, including the harmonic and polyharmonic functions and calculi. The case of dimension five is studied in detail, as it determines the function spaces that appear in higher dimensions.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Clinical Neurology
Ellen Younger, Elizabeth G. Ellis, Nicholas Parsons, Patrizia Pantano, Silvia Tommasin, Karen Caeyenberghs, Julian Benito-Leon, Juan Pablo Romero, Juho Joutsa, Daniel T. Corp
Summary: This study found that structural and metabolic abnormalities in essential tremor (ET) are located in various regions of the brain, but these regions are connected to a common functional network. The cerebellum was identified as the hub of this network and showed similarities with the therapeutic network for ET. In addition, reduced functional connectivity in the cerebellar network was associated with tremor severity and cognitive functioning in ET patients.
Article
Quantum Science & Technology
Sho Kubota, Kei Saito, Yusuke Yoshie
Summary: This paper presents a new spectral mapping theorem for quantum walks, which is applicable to Grover walks utilizing a shift operator with a cube as the identity on finite graphs. One of the key differences compared to the conventional theorem is that lifting the eigenvalues of the induced self-adjoint matrix T to the unit circle provides most of the eigenvalues of the time evolution U.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Chemistry, Inorganic & Nuclear
Li Li, Li-Min Lu, Xian-Hao Zhao, De -Yuan Hu, Tian -Yu Tang, Yan-Lin Tang
Summary: In this study, the structure, vibration, and excited states of glucose and fructose molecules were calculated using density functional theory. The results showed that the structure of glucose molecule was more distorted, and the stretching vibration of C=O bond in fructose was stronger. The absorption peak of fructose belonged to the tail absorption band, while other peaks belonged to the far ultraviolet absorption band. The excitation mechanisms of different excited states were determined through electron-hole analysis. This study could provide theoretical support for drug development, biofuel preparation, and metal protection.
INORGANIC CHEMISTRY COMMUNICATIONS
(2022)
Article
Mathematics
Daniela M. Vieira
Summary: It is proven that if K subset of E and L subset of F are balanced compact determining subsets of separable Banach spaces with the approximation property, then the algebras of holomorphic germs H(K) and H(L) are topologically algebra isomorphic if, and only if, KP(E) and LP(F) (the polynomial convex hulls of K and L) are biholomorphically equivalent.
MATHEMATISCHE NACHRICHTEN
(2023)
Article
Mathematics, Applied
Chao Li, Xi Zhang, Qizhi Zhao
Summary: This paper generalizes the well-known Kodaira embedding theorem.
SCIENCE CHINA-MATHEMATICS
(2021)
Article
Mathematics
Chengjie Yu, Chuangyuan Zhang
Summary: By utilizing a general three circles theorem, this short note demonstrates the rigidity of the sharp Bezout estimate initially discovered by Gang Liu on nonnegatively curved Riemann surfaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Asli Deniz
Summary: This article proves that for several one-dimensional holomorphic families of holomorphic maps, there exists a local piece of a curve in the parameter plane that lands at a given parabolic parameter, similar to well-known results about the quadratic and exponential families. Under certain assumptions, this general result partially addresses the existence and landing questions of ray structures in the parameter planes for holomorphic families of transcendental entire maps.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Man-Chun Lee, Jeffrey Streets
Summary: This study proves that compact complex manifolds admitting metrics with negative Chern curvature operator either have a definite positive (1,1) form or are Kahler manifolds with ample canonical bundle. A complete classification is obtained for complex surfaces. The proofs rely on a global existence and convergence result for the pluriclosed flow.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics
Xiaojun Huang, Xieping Wang
Summary: The study focused on complex geodesics and complex Monge-Ampere equations on bounded strongly linearly convex domains in C-n. Uniqueness of complex geodesics with prescribed boundary value and direction was proven for domains with minimal regularity at the boundary. Building on this uniqueness and previously obtained results, a homogeneous complex Monge-Ampere equation with prescribed boundary singularity was solved, initially considered on smoothly bounded strongly convex domains in C-n by Bracci et al.
MATHEMATISCHE ANNALEN
(2022)
Article
Thermodynamics
Ennio Luciano, Jesus Oliva, Alvaro Sobrino, Javier Ballester
Summary: This work presents the first characterization study of a novel approach called pseudo-active instability control (PAIC), which offers the versatility of active control with simpler hardware requirements. Experimental results demonstrate the potential of this approach and reveal the acoustic interactions between the burner and the pilot line in influencing the limit cycle.
COMBUSTION SCIENCE AND TECHNOLOGY
(2022)
Article
Mathematics, Applied
J. Oliva-Maza
Summary: This paper studies the Lie group representations on Hilbert spaces in relation to operator ranges, discussing induced semigroup homomorphisms and group representations based on R- invariant operators. The continuity and smoothness of the representations are shown to depend on the R- invariance of the tangent map. Additionally, tautological representations of unitary or invertible operators are found to be neither group nor closed for a large set of nonclosed operator ranges, demonstrated through explicit counterexamples.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics
Jesus Oliva-Maza
Summary: Hardy kernels are a useful tool for defining integral operators on Hilbertian spaces. In this work, we use these kernels to study the range spaces of these operators as reproducing kernel Hilbert spaces, which have an algebraic L-1-structure. We obtain the reproducing kernels, which are also Hardy kernels in the case of L-2(R+). In the scenario of H-2(C+), the reproducing kernels are given by holomorphic extensions of Hardy kernels. Other results presented include theorems of Paley-Wiener type and a connection with one-sided Hilbert transforms.
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
(2023)
Article
Mathematics, Applied
Jesus Oliva-Maza, Mahamadi Warma
Summary: This article introduces families of generalized Black-Scholes equations involving Riemann-Liouville and Weyl space-fractional derivatives. It proves that these equations are well-posed in (L-1 - L-infinity)-interpolation spaces, with the involved elliptic-type operators generating holomorphic semigroups. The associated solutions are given explicit integral expressions. A new connection between bisectorial-like operators and sectorial operators in an abstract setting is also established, extending the scaling property of sectorial operators to a wider range of operators and functions.
JOURNAL OF EVOLUTION EQUATIONS
(2023)
Proceedings Paper
Engineering, Mechanical
Jesus Oliva, Ennio Luciano, Javier Ballester
PROCEEDINGS OF THE ASME TURBO EXPO: TURBOMACHINERY TECHNICAL CONFERENCE AND EXPOSITION, 2018, VOL 4B
(2018)
