Article
Mathematics, Applied
Mohammed Shehu Shagari, Qiu-Hong Shi, Saima Rashid, Usamot Idayat Foluke, Khadijah M. Abualnaja
Summary: This paper introduces a new concept of nonlinear contraction called r-hybrid psi-contraction and establishes fixed point results for such mappings in complete metric spaces. The presented ideas unify and extend well-known results in the literature, with special cases pointed out and analyzed. From an application perspective, the existence and uniqueness criteria of solutions to certain functional and integral equations are investigated, with nontrivial illustrative examples provided to demonstrate the generality and validity of the obtained results.
Article
Astronomy & Astrophysics
Samarth Kapoor, Shiroman Prakash
Summary: We study fixed points of scalar fields transforming into the bifundamental representation of O(N) x O(M) in 3-epsilon dimensions. We determine the complete beta function to order 1/N for arbitrary M in the limit where N is large but M is finite. We find a rich collection of large-N fixed points in d=3 and fixed points in d=3-epsilon that can be studied to all orders in epsilon over cap = N epsilon.
Article
Physics, Particles & Fields
Holger Gies, Kevin K. K. Tam, Jobst Ziebell
Summary: In this study, we explore the fixed-point structure of QED-like theories with a Pauli spin-field coupling. The research focuses on the fate of UV-stable fixed points in d=4 spacetime dimensions when generalized to lower or higher dimensions and for different fermion flavors N-f. The overall trend is that moving away from d=4 dimensions and increasing the flavor number tends to destabilize the non-Gaussian fixed points discovered in four dimensions. However, there is an exception - a non-Gaussian fixed point with finite Pauli spin-field coupling and vanishing gauge coupling, which remains stable in d=3 dimensions and for small flavor numbers. This finding has implications for the effective theories of layered condensed-matter systems.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Operations Research & Management Science
Liya Liu, Xiaolong Qin, Ravi P. Agarwal
Summary: This article investigates a descent-type iterative algorithm for finding a common element of fixed-point sets of nonexpansive mappings and zero-point sets of pseudomonotone mappings in Hilbert spaces. Necessary and sufficient conditions for strong convergence of the algorithm are derived with suitable assumptions, and numerical examples and applications in signal processing are provided to support the main results.
Article
Mathematics, Applied
Wolfgang Michael Grimm
Summary: A centroid- and covariance-invariant deterministic mapping of sets of discrete data points to nonlinear models is presented. The mapping algorithm is considered computationally fast and suitable for real-time parameter estimation. It also outperforms log-linear regression as it can handle nonpositive observations without any transformations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Kieu Phuong Chi, Erdal Karapinar, Tran Duc Thanh
Summary: This paper presents some results on the relationship between the convergence of nonlinear quasi-contractions and the convergence of their fixed point, extending existing literature on the topic, including the work of Nadler and Park. An illustrative example is provided to demonstrate the validity of the results.
Article
Engineering, Electrical & Electronic
Wenqiang Ji, Jianbin Qiu
Summary: This paper investigates the observer-based output feedback control of discrete-time nonlinear 2-D systems using Takagi-Sugeno (T-S) fuzzy-affine models. A piecewise fuzzy-affine observer is designed to estimate unmeasurable system states, and two enhanced observer-based piecewise OFC approaches are developed. Novel controller design results are proposed using piecewise quadratic Lyapunov functions (PQLFs) based on Young's matrix inequality. Simulation studies demonstrate the effectiveness of the developed approaches on a doubly indexed nonlinear process.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2022)
Article
Physics, Particles & Fields
Ryohei Kobayashi, Yasunori Lee, Ken Shiozaki, Yuya Tanizaki
Summary: In this study, the topological terms of (2+1)d sigma models and their consequences are examined, particularly focusing on the U(N)/U(1)(N) flag-manifold sigma model. It is found that certain Chern-Simons terms can convert skyrmions into fermions, challenging the initial expectation of the presence of a Hopf-like term.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Mathematics, Applied
Anton Freund
Summary: This paper proves the equivalence between Timothy Carlson's patterns of resemblance and Pi(1)(1)-comprehension.
SELECTA MATHEMATICA-NEW SERIES
(2022)
Article
Physics, Multidisciplinary
Zhenjiu Wang, Michael P. Zaletel, Roger S. K. Mong, Fakher F. Assaad
Summary: The study utilizes the half-filled zeroth Landau level in graphene as a regularization scheme to explore the physics of the SO(5) nonlinear sigma model subject to a Wess-Zumino-Witten topological term in 2 + 1 dimensions. The research shows an ordered phase within a specific parameter range, indicating the potential for deconfined quantum phase transitions between valence bond solids and antiferromagnets.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Particles & Fields
Riccardo Borsato, Sibylle Driezen
Summary: This study discusses the relationship between generalised fluxes and twists within the framework of Double Field Theory, analyzing the possibilities of turning on different types of fluxes and providing solution-generating techniques in supergravity. Additionally, the research uncovers canonical transformations of 2-dimensional sigma -models as a result of the study.
JOURNAL OF HIGH ENERGY PHYSICS
(2021)
Article
Physics, Multidisciplinary
Charlie Cresswell-Hogg, Daniel F. Litim
Summary: In the limit of many fermion flavors, the sextic Gross-Neveu theory in three dimensions exhibits a line of interacting UV fixed points with an exactly marginal sextic interaction. The conformal window of UV-complete theories, universal scaling dimensions, and phase diagram are determined using renormalization group methods. Massless theories occur naturally and mass generation occurs without discrete symmetry breaking. Striking similarities with critical scalar theories at large N are emphasized, along with implications from the perspective of conformal field theory and the AdS=CFT conjecture.
PHYSICAL REVIEW LETTERS
(2023)
Article
Computer Science, Interdisciplinary Applications
Weili Ma, Zengguang Xu, Junrui Chai, Cheng Cao, Yixuan Wang
Summary: This study focuses on estimating the representative elementary volume (REV) sizes of fractured rock masses, taking into account the linked trace length and fracture aperture in both linear and nonlinear flow regimes. Monte Carlo simulations were used to create discrete fracture network (DFN) models and calculate the permeability coefficient tensor K and non-Darcy coefficient tensor \beta. The findings reveal the consistency of computed K values for different flow regimes and suggest that the REV size determined by the \beta value exceeds that obtained using K for the same fracture network.
COMPUTERS AND GEOTECHNICS
(2023)
Article
Mathematics
Dur-e-Shehwar Sagheer, Zainab Rahman, Samina Batul, Ahmad Aloqaily, Nabil Mlaiki
Summary: This article presents the existence results of fuzzy fixed points of fuzzy mappings that satisfy certain contraction conditions using the platform of partial b-metric spaces. Some non-trivial examples are provided to authenticate the main results. The constructed results in this work will likely stimulate new research directions in fuzzy fixed-point theory and related hybrid models. Additionally, fixed-point results on multivalued mappings are established, showcasing an excellent application of main theorems on fuzzy mappings. The results of this article are extensions of many already existing results in the literature.
Article
Mathematics
Oscar Ortega-Moreno, Franz E. Schuster
Summary: It is shown that for any sufficiently regular even Minkowski valuation (I) which is homogeneous and intertwines rigid motions, there exists a neighborhood of the unit ball, where balls are the only solutions to the fixed-point problem Phi(2) K = cxK. This significantly generalizes results by Ivaki for projection bodies and suggests, via the Lutwak-Schneider class reduction technique, a new approach to Petty's conjectured projection inequality.
ADVANCES IN MATHEMATICS
(2021)
Article
Astronomy & Astrophysics
Nelson R. F. Braga, Octavio C. Junqueira
Summary: This study investigates the influence of rotation on the transition temperature of strongly interacting matter produced in non-central heavy ion collisions. By using a holographic description of an AdS black hole, the authors extend the analysis to the more realistic case where the matter spreads over a region around the rotational axis. The results show the coexistence of confined and deconfined phases and are consistent with the concept of local temperature in rotating frames developed by Tolman and Ehrenfest.
Article
Astronomy & Astrophysics
Bing Sun, Jiachen An, Zhoujian Cao
Summary: This paper investigates the effect of gravitational constant variation on the propagation of gravitational waves. By employing two analytical methods, the study finds that variations in the gravitational constant result in amplitude and phase corrections for gravitational waves, and the time variation of the gravitational constant can be constrained through the propagation of gravitational waves.
Article
Astronomy & Astrophysics
Abdellah Touati, Zaim Slimane
Summary: This letter presents the first study of Hawking radiation as a tunneling process within the framework of non-commutative gauge theory of gravity. The non-commutative Schwarzschild black hole is reconstructed using the Seiberg-Witten map and the star product. The emission spectrum of outgoing massless particles is computed using the quantum tunneling mechanism. The results reveal pure thermal radiation in the low-frequency scenario, but a deviation from pure thermal radiation in the high-frequency scenario due to energy conservation. It is also found that noncommutativity enhances the correlations between successively emitted particles.
Article
Astronomy & Astrophysics
Shahar Hod
Summary: The travel times of light signals between two antipodal points on a compact star's surface are calculated for two different trajectories. It is shown that, for highly dense stars, the longer trajectory along the surface may have a shorter travel time as measured by asymptotic observers. A critical value of the dimensionless density-area parameter is determined for constant density stars to distinguish cases where crossing through the star's center or following a semi-circular trajectory on the surface has a shorter travel time as measured by asymptotic observers.
