Let β be the middle-(1−2β) Cantor set with β ∈ (1/3, 1/2). We give all real numbers t with unique {−1, 0, 1}-code such that the intersections β ∩ ( β + t) are self-similar sets. For a given β ∈ (1/3, 1/2), a criterion is obtained to check whether or not a t ∈ [−1, 1] has the unique {−1, 0, 1}-code from both geometric and algebraic views. Mathematics Subject Classification: 28A80, 28A78

Introduction: Electrospun nanomembranes have been used for effective air filtration due to their potential for active surface modification. This study aims to synthesize polyurethane (PU) nanofiber membrane incorporated with different amounts of β-cyclodextrin (β-CD) to capture volatile organic compounds (VOCs) along with aerosol filtration from the air. Material and Methods: First, PU was sy...

The work aimed to improve the extraction efficiency of wheat bran polysaccharide by solid-state fermentation using bioactive fungus Isaria cicadae Miq. and identify structural properties fermented (IC-FWBP). fraction IC-FWBP was isolated with an yield 2.88% average molecular weight 3.31 × 106 Da. comprised mannose, glucose, galactose. methylation, nuclear magnetic resonance (NMR), Congo red ana...

Following recent interest in the qualitative analysis of some optimal control and shape optimisation problems, we provide this article a detailed study Robin boundary conditions PDE constrained calculus variations. Our main model consists an elliptic form −∆u β = f (x, u β) endowed with ∂ν +β(x)u 0. The variable is function β, which assumed to take values between 0 1 have fixed integral. Two ty...