In this paper, we consider a generalization of Horadam sequence {w n } which is defined by the recurrence relation w n = χ (n)w n-1 + cw n-2 , where χ (n) = a if n is even, χ (n) = b if n is odd with arbitrary initial conditions w 0 , w 1 and nonzero real numbers a, b and c. As a special case, by taking the initial conditions 0, 1 and 2, b we define the sequences {u n } and {v n }, respectively. The main purpose of this study is to derive some basic properties of the sequences {u n }, {v n } and {w n } by using a matrix approach.

High-dimensional data poses unique challenges in outlier detection process. Most of the existing algorithms fail to properly address the issues stemming from a large number of features. In particular, outlier detection algorithms perform poorly on data set of small size with a large number of features. In this paper, we propose a novel outlier detection algorithm based on principal component analysis and kernel density estimation. The proposed method is designed to address the challenges of dealing with high-dimensional data by projecting the original data onto a smaller space and using the innate structure of the data to calculate anomaly scores for each data point. Numerical experiments on synthetic and real-life data show that our method performs well on highdimensional data. In particular, the proposed method outperforms the benchmark methods as measured by the F 1 -score. Our method also produces better-than-average execution times compared to the benchmark methods.

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Inspired by the applications in electromagnetic nanomaterials processing in enclosures and hybrid fuel cell technologies, a mathematical model is presented to analyze the mixed convective flow of electrically conducting nanofluids ([Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]) inside a square enclosure saturated with porous medium under an inclined magnetic field. The Tiwari–Das model, along with the viscosity, thermal conductivity, and effective Prandtl number correlations, is considered in this study. The impacts of Joule heating, viscous dissipation, and internal heat absorption/generation are taken into consideration. Strongly nonlinear conservation equations, which govern the heat transfer and momentum inside the cavity with associated initial and boundary conditions, are rendered dimensionless with appropriate transformations. The marker-and-cell technique is deployed to solve the non-dimensional initial-boundary value problem. Validations with a previous study are included. A detailed parametric study is carried out to evaluate the influences of the emerging parameters on the transport phenomena. When [Formula: see text]-[Formula: see text] nanoparticles are suspended into [Formula: see text] base-fluid, the average heat transfer rate of [Formula: see text]-[Formula: see text] nanoliquid is increased by [Formula: see text] compared with the case where nanoparticles are absent. When [Formula: see text]-[Formula: see text] nanoparticles are suspended into [Formula: see text] base-fluid, the average heat transfer rate of [Formula: see text]-[Formula: see text] nanofluid is increased by [Formula: see text] compared with the case where nanoparticles are absent. Furthermore, when the heat source is present, the average heat transfer rate of [Formula: see text]-[Formula: see text] nanofluid is [Formula: see text] higher than that in the case of [Formula: see text]-[Formula: see text] nanofluid.

Enterprise Network (EN) has increasingly gained popularity in academia. Over the past few decades, a substantial amount of EN studies have been published in China. Drawing upon a sample of 603 papers retrieved from the Chinese Social Sciences Citation Index database (CSSCI) between 1998 and 2020, this study aims to delve into the status quo, knowledge base, research focus, and evolutionary trends of EN research in China. A multifaceted bibliometric analysis was performed using CiteSpace. The findings mainly indicate that the research on EN in China has a clear development context, and the research content gradually changes from macro to micro. In addition to foreign Social Network theories, the research results of domestic scholars have become the basic knowledge in this field. The research includes these topics: the conceptualization of EN, EN as indicators of enterprise development, EN’s impact on start-ups, mechanisms of EN’s effect and governance of EN. The potential direction for future research has been identified as the integration between EN and other forms of networks, and the structure of EN.