The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction
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Journal of Mathematics is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.
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Chief Editor, Professor Jen-Chih Yao, is currently based at Zhejiang Normal University in China. His current research includes dynamic programming, mathematical programming, and operations research.
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More articlesSome Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space
Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in Sobolev space . We obtain the sufficient and necessary conditions for IWS and IGS to be frames. By applying these conditions, we also derive the characterizations of IWS and IGS to be frames. Finally, we discuss the perturbation theorem of irregular wavelet frames (IWFs) and irregular Gabor frames (IGFs). We also provided some examples to support our results.
Subgradient Extragradient Method for Finite Lipschitzian Demicontractions and Variational Inequality Problems in a Hilbert Space
In this research, the modified subgradient extragradient method and -mapping generated by a finite family of finite Lipschitzian demicontractions are introduced. Then, a strong convergence theorem for finding a common element of the common fixed point set of finite Lipschitzian demicontraction mappings and the common solution set of variational inequality problems is established. Furthermore, numerical examples are given to support the main theorem.
Modern Approach in Pattern Recognition Using Circular Fermatean Fuzzy Similarity Measure for Decision Making with Practical Applications
The circular Fermatean fuzzy (CFF) set is an advancement of the Fermatean fuzzy (FF) set and the interval-valued Fermatean fuzzy (IVFF) set which deals with uncertainty. The CFF set is represented as a circle of radius ranging from 0 to with the center at the degree of association (DA) and degree of nonassociation (DNA). If multiple people are involved in making decisions, the CFF set, as an alternative to the FF and IVFF sets, can deal with ambiguity more effectively by encircling the decision values within a circle rather than taking an average. Using algorithms, a pattern can be observed computationally or visually. Machine learning algorithm utilizes pattern recognition as an instrument for identifying patterns and also similarity measure (SM) is a beneficial pattern recognition tool used to classify items, discover variations, and make future predictions for decision making. In this work, we introduce the CFF cosine and Dice similarity measures (CFFDMs and CFFSMs), and their properties are studied. Unlike traditional approaches of decision making, which emphasize a single number, the proposed CFFSMs observe the pattern over the circular region to help in dealing with uncertainty more effectively. We introduce an innovative decision-making method in the FF setting. Available bank loans and applicants’ eligibility levels are represented as CFF set using their FF criteria and are taken as loan patterns and customer eligibility patterns. The loan is allocated to the applicant by measuring the CFFCSM and CFFDSM between the two patterns. Also, laptops are suggested to the customers by measuring the similarity between specification pattern and requirement pattern. The correctness and consistency of the proposed models are ensured by comparison analysis and graphical simulations of the input and similarity CFFNs.
A Solution Matrix by IEVP under the Central Principle Submatrix Constraints
The real matrix is called centrosymmetric matrix if where is permutation matrix with ones on cross diagonal (bottom left to top right) and zeroes elsewhere. In this article, the solvability conditions for left and right inverse eigenvalue problem (which is special case of inverse eigenvalue problem) under the submatrix constraint for generalized centrosymmetric matrices are derived, and the general solution is also given. In addition, we provide a feasible algorithm for computing the general solution, which is proved by a numerical example.
Global Well-Posedness and Convergence Results to a 3D Regularized Boussinesq System in Sobolev Spaces
We consider a regularized periodic three-dimensional Boussinesq system. For a mean free initial temperature, we use the coupling between the velocity and temperature to close the energy estimates independently of time. This allows proving the existence of a global in time unique weak solution. Also, we establish that this solution depends continuously on the initial data. Moreover, we prove that this solution converges to a Leray-Hopf weak solution of the three-dimensional Boussinesq system as the regularizing parameter vanishes.
A New Statistical Approach Based on the Access of Electricity Application with Some Modified Control Charts
This article introduces a new probability model based on reflected parameter called the reflected Pareto (RP) distribution. The key properties of the RP model are investigated. A simulation study of the RP model is conducted to evaluate the performances of its estimators. A real-life application is considered to examine the performance of proposed model. The different criteria are discussed numerically as well as graphically to show the flexibility of the RP model. The exponential weighted moving average control charts based on the maximum likelihood and modified maximum likelihood estimators for the shape parameter of the RP distribution are obtained. Detailed simulation results of proposed charts are performed to examine and analyze the performance of these charts with three in-control average run length values and two sample sizes. Finally, the application of the proposed control charts is shown by considering a real-life data set.