This paper is concerned with the Hyers–Ulam stability of the first-order linear differential equation x′ − ax = 0, where a is a non-zero real number. The main purpose is to find an explicit solution x(t) of x′−ax = 0 satisfying |φ(t)−x(t)| ≤ ε/|a| for all t ∈ R under the assumption that a differentiable function φ(t) satisfies |φ′(t)− aφ(t)| ≤ ε for all t ∈ R. In addition, the precise behavior ...

In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution usually has an infinite variance. Therefore, we are especially interested in such degree distributions. In addition, we analyze the clustering coefficient for ...

In this study we propose a new method to design Pseudo-QMF prototype filters to implement Near Perfect Reconstruction (NPR) cosine-modulated filter banks. The method is based on the eigenfilter approach, that is simple to implement, but, nevertheless, is very efficient in designing high attenuation prototype filters. The method also allows to design complex coefficient prototypes that can be us...

The tire-road friction coefficient is critical information for conventional vehicle safety control systems. Most previous studies in tire-road friction estimation have only considered either longitudinal or lateral vehicle dynamics which tends to cause significant underestimation of the actual tire-road friction coefficient. In this paper, the parameters, including the tireroad friction coeffic...

The paper considers five fraction-free (FF) tests to determine whether a complex or a real polynomial has all its zeros inside the unit-circle. A FF test for complex polynomial is applicable to both complex and real polynomials where the FF property means that when it is applied to Gaussian or real integer coefficients, it can be completed over the respective ring of integers, i.e., it is Gauss...

abstract introduction: dyes are among the most hazardous chemicals in industrial wastesdue to their toxicity for aquaculture, reduction of light permeability, and in turn development of disorders in photosynthesis process. the current study aimed to investigate the efficiency of coral in removing red reactive 198 from textile dye wastewater was investigated. materials & methods: in this experim...