A New Type Iterative Ridge Estimator: Applications and Performance EvaluationsRead the full article
Journal of Mathematics is a broad scope journal that publishes original research and review articles on all aspects of both pure and applied mathematics.
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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A Logistic Trigonometric Generalized Class of Distribution Characteristics, Applications, and Simulations
We propose a trigonometric generalizer/generator of distributions utilizing the quantile function of modified standard Cauchy distribution and construct a logistic-based new G-class disbursing cotangent function. Significant mathematical characteristics and special models are derived. New mathematical transformations and extended models are also proposed. A two-parameter model logistic cotangent Weibull (LCW) is developed and discussed in detail. The beauty and importance of the proposed model are that its hazard rate exhibits all monotone and non-monotone shapes while the density exhibits unimodal and bimodal (symmetrical, right-skewed, and decreasing) shapes. For parametric estimation, the maximum likelihood approach is used, and simulation analysis is performed to ensure that the estimates are asymptotic. The importance of the proposed trigonometric generalizer, G class, and model is proved via two applications focused on survival and failure datasets whose results attested the distinct better fit, wider flexibility, and greater capability than existing and well-known competing models. The authors thought that the suggested class and models would appeal to a broader audience of professionals working in reliability analysis, actuarial and financial sciences, and lifetime data and analysis.
Results on Implicit Fractional Pantograph Equations with Mittag-Leffler Kernel and Nonlocal Condition
In this study, the main focus is on an investigation of the sufficient conditions of existence and uniqueness of solution for two-classess of nonlinear implicit fractional pantograph equations with nonlocal conditions via Atangana–Baleanu–Riemann–Liouville (ABR) and Atangana–Baleanu–Caputo (ABC) fractional derivative with order . We introduce the properties of solutions as well as stability results for the proposed problem without using the semigroup property. In the beginning, we convert the given problems into equivalent fractional integral equations. Then, by employing some fixed-point theorems such as Krasnoselskii and Banach’s techniques, we examine the existence and uniqueness of solutions to proposed problems. Moreover, by using techniques of nonlinear functional analysis, we analyze Ulam–Hyers (UH) and generalized Ulam–Hyers (GUH) stability results. As an application, we provide some examples to illustrate the validity of our results.
Digital Hopf Spaces and Their Duals
In this article, we study the fundamental notions of digital Hopf and co-Hopf spaces based on pointed digital images. We show that a digital Hopf space, a digital associative Hopf space, a digital Hopf group, and a digital commutative Hopf space are unique up to digital homotopy type; that is, there is only one possible digital Hopf structure up to digital homotopy type on the underlying digital image. We also establish an equivalent condition for a digital image to be a digital Hopf space and investigate the difference between ordinary topological co-Hopf spaces and their digital counterparts by showing that any digital co-Hopf space is a digitally contractible space focusing on deep-learning methods in imaging science.
Fuzzy Intelligence in Physical Immersion Teaching System Based on Digital Simulation Technology
In order to improve the effect of physics teaching, this study combines digital simulation technology to construct a physical immersion teaching system to improve the effect of physics teaching in colleges and universities. Moreover, this study transforms abstract physical knowledge into recognizable digital physical images and realizes the idea of multifeature fusion through reasonable feature selection and the use of a classifier algorithm suitable for the subject of this paper. In addition, this study proposes a new algorithm based on the morphological features of geometric images, which combines the transformation detection method of cluster analysis to realize the intelligent processing of images. Finally, this study verifies the effectiveness of the physical immersion teaching system based on fuzzy intelligence and digital simulation technology through experimental research. The results show that the system can effectively improve the effect of physics teaching.
Numerical Analysis of Iterative Fractional Partial Integro-Differential Equations
Many nonlinear phenomena are modeled in terms of differential and integral equations. However, modeling nonlinear phenomena with fractional derivatives provides a better understanding of processes having memory effects. In this paper, we introduce an effective model of iterative fractional partial integro-differential equations (FPIDEs) with memory terms subject to initial conditions in a Banach space. The convergence, existence, uniqueness, and error analysis are introduced as new theorems. Moreover, an extension of the successive approximations method (SAM) is established to solve FPIDEs in sense of Caputo fractional derivative. Furthermore, new results of stability analysis of solution are also shown.
Quartic Functional Equation: Ulam-Type Stability in -Banach Space and Non-Archimedean -Normed Space
In this study, we use the alternative fixed-point approach and the direct method to examine the generalized Hyers–Ulam stability of the quartic functional equation with a fixed positive integer in the context of -Banach space. In non-Archimedean -normed space, we also verify Hyers–Ulam stability for the quartic functional equation stated. Many of the findings in the literature are improved and generalized by our findings.