Article
Mathematics
Xue Han, Huafeng Liu, Deyu Zhang
Summary: The paper proves the existence of positive real numbers N-1((0)) and N-2((0)) depending on c, d, alpha, beta, under certain conditions, the system of two Diophantine inequalities has solutions in prime variables.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Salma Iqbal, Naveed Yaqoob
Summary: This paper introduces a new concept called trapezoidal linear Diophantine fuzzy numbers (TrapLDFNs) in general. The concept of TrapLDFNs is introduced, and a ranking method for TrapLDFNs based on the circumcenter of centroids of TrapLDFN membership and non-membership functions is proposed.
Article
Mathematics, Interdisciplinary Applications
Congcong Qu, Juan Wang
Summary: This paper investigates the properties of a local diffeomorphism/diffeomorphism on a compact Riemannian manifold under the conditions of expansion/hyperbolicity of its invariant measure. The topological entropy and Hausdorff dimensions of the exceptional sets are studied for subsets with low entropy or dimension.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yan Feng, Bo Tan, Qing-Long Zhou
Summary: This study determines the Hausdorff dimensions of the sets E(beta) and U(beta), building on previous upper and lower bound estimations.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics
Igor Kukavica, Quinn Le
Summary: This paper investigates the quantitative uniqueness properties for a parabolic type equation, proving a strong unique continuation property and providing a pointwise observability estimate.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Victor Beresnevich, Lifan Guan, Antoine Marnat, Felipe Ramirez, Sanju Velani
Summary: The article discusses the set of Dirichlet improvable real numbers in different dimensions. In one dimension, it consists of badly approximable and singular numbers, while in higher dimensions, there exist continuum many Dirichlet improvable vectors that do not fall into these categories. The notion of intermediate Dirichlet improvable sets is introduced and its relationship with approximations by rational planes is proven. This extends a classical theorem and has implications for Diophantine sets.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Ashraf Al-Quran
Summary: This paper introduces the concept of T-spherical linear Diophantine fuzzy set (T-SLDFS) by combining the notions of T-spherical fuzzy set (T-SFS) and linear Diophantine fuzzy set (LDFS). The T-SLDFS is found to be more effective and dominant compared to T-SFS and LDFS. Various operations and properties of T-SLDFS are examined, along with the proposal of T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator for aggregating T-SLDFS data. Additionally, other operators such as T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) and T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) are presented.
Article
Mathematics
Gongrui Chen
Summary: When X is greater than N1/36+epsilon, the number of even integers n between N and N-X that cannot be expressed as n = p(1)(3) + . . . + p(8)(3) is a negligible fraction of X.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics
Philip T. Gressman, Shaoming Guo, Lillian B. Pierce, Joris Roos, Po-Lam Yung
Summary: The breakthrough work by Bourgain, Demeter, and Guth has shown the powerful results of decoupling inequalities in counting integral solutions to Diophantine equations. Furthermore, the study demonstrates the reversibility of this implication and its application in L-2n square function estimates and decoupling estimates for extension operators associated with non-degenerate curves in R-n. The proof is based on a combinatorial argument that relies on the idea that solutions to the equations are essentially permutations of each other.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Mathematics
Shanlin Huang, Gengsheng Wang, Ming Wang
Summary: The study explores parabolic type equations in multi-dimensional space with different operators H to determine the characteristics of stabilizable sets, showing differences between the classes of stabilizable sets and observable sets.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Energy & Fuels
Samayan Narayanamoorthy, J. V. Brainy, Raed A. Shalwala, Theyab R. Alsenani, Ali Ahmadian, Daekook Kang
Summary: The relevance of energy storage technology is highlighted due to the need for managing renewable resources, which are unpredictable and probabilistic. This study introduces the concept of linear diophantine hesitant fuzzy sets (LDHFS), combining linear diophantine fuzzy sets (LDFS) and dual hesitant fuzzy sets (DHFS), to provide decision makers with a flexible framework for analyzing numerous objects and options. The LDHF-SOWIA-MAIRCA model is used to assess the usefulness of LDHFS in selecting energy storage technology for India. The evaluation of five storage alternatives shows that BESS performs better based on technology, cost, environmental impact, performance, and social impact.
SUSTAINABLE ENERGY GRIDS & NETWORKS
(2023)
Article
Multidisciplinary Sciences
Saba Ayub, Muhammad Shabir, Muhammad Riaz, Muhammad Aslam, Ronnason Chinram
Summary: This paper introduces a novel mathematical approach, linear Diophantine fuzzy sets, which is valuable in decision-making problems involving fuzziness and uncertainty. The concept of linear Diophantine fuzzy relation (LDF-relation) is proposed to discuss symmetry between objects more flexibly. The analysis of algebraic structures derived from the collection of all LDF-relations demonstrates the significance of this approach in computational intelligence and modeling uncertainties in decision-making problems.
Article
Computer Science, Artificial Intelligence
Sait Gul, Ali Aydogdu
Summary: This study introduces the concept of linear Diophantine fuzzy set (LDFS) to address the limitations of fuzzy set extensions in multiple attribute decision making (MADM). Distance and entropy measures for LDFSs are developed and a MADM method extension for LDFS environment is proposed. The well-known TOPSIS method is extended to LDFS environment and applied in a healthcare management decision problem.
Article
Mathematics
Salma Iqbal, Naveed Yaqoob, Muhammad Gulistan
Summary: The research presents an interactive method for solving nonlinear fractional programming problems using the linear Diophantine fuzzy set notion. The method involves solving a max-min problem using Zimmermann's min operator method when the decision maker defines the degree of a level sets. By updating the degree of a, the decision maker can be solved from a set of a-cut optimal solutions based on the membership and non-membership functions. The approach demonstrates the reduction of a Diophantine fuzzy nonlinear programming problem to a crisp multi-objective nonlinear fractional programming problem, which can then be solved using any suitable algorithm.
Article
Mathematics
Simon Baker
Summary: In this paper, we present new lower bounds for the upper box dimension of alpha beta sets, and demonstrate that under certain conditions the upper box dimension is 1. Additionally, we use our dimension bounds to derive new results on affine embeddings of self-similar sets.
JOURNAL OF NUMBER THEORY
(2021)
