Watermarking provides an efficient mechanism for copyright protection of digital media by embedding information in the object to identify the owner. This paper proposed a watermarking technique that can successfully embed a grey-scale image in a 3D mesh object. In our proposed technique, each three vertices of the 3D object can hide one pixel from the secret image. The experimental results showed that the proposed technique has better visual quality on both the watermarked object and the extracted secret image.

A new study aims to clarify the analytical and mathematical dimensions of the tangent hyperbolic fluid through the plate and cone with useful uses in technical devices like the handling of biomass pyrolysis and viscometer. The presence of chemical process and mixed convection in the natural characteristics of liquid is taken into account. By implementing the homotopy analysis approach, the achieved coupling system is inspected. The influence of the flow control variables on the related profiles is evaluated quantitatively and qualitatively in order to get a full understanding of the current pagination. Through the deep study, it is calculated that convective thermal and surface drag factor for the plate is greater in magnitude than for the cone. The superiority is also observed for the plate in the thermal field relative to that in the cone. The results shows that the heat transfer improves as Hartmann number (M) and Brownian motion factor (Nt) increase but it decreases with an increase of thermophoresis factor (Nb). Also it can be found that effect of drag coefficient is more pronounced or higher for cone as compared to plate.

The aim of this paper is to present the degree of semi-preopenness, semi-precontinuity, and semi-preirresoluteness for functions in (L, M)-fuzzy pretopology with the help of implication operation and (L, M)-fuzzy semi-preopen operator introduced by [Ghareeb A., L-fuzzy semi-preopen operator in L-fuzzy topological spaces, Neural Comput. & Appl., 2012, 21, 87-92]. Further, we generalize the properties of semi-preopenness, semi-precontinuity and semi-preirresoluteness to (L, M)-fuzzy pretopological setting relying on graded concepts. Also, we discuss their relationships with the corresponding degrees of semiprecompactness, semi-preconnectedness and semi-preseparation axioms.

This paper presents a new representation of α-openness, α-continuity, α-irresoluteness, and α-compactness based on L-fuzzy α-open operators introduced by Nannan and Ruiying [1] and implication operation. The proposed representation extends the properties of α-openness, α-continuity, α-irresoluteness, and α-compactness to the setting of L-fuzzy pretopological spaces based on graded concepts. Moreover, we introduce and establish the relationships among the new concepts.

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in $RL$-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise $RL$-fuzzy semicontinuous and pairwise $RL$-fuzzy irresolute functions are extended and discussed based on the $(i,j)$-$RL$-semiopen gradation. Further, pairwise $RL$-fuzzy semi-compactness of an L-fuzzy set in $RL$-fuzzy bitopological spaces are given and characterized. As $RL$-fuzzy bitopology is a generalization of L-bitopology, $RL$-bitopology, L-fuzzy bitopology, and $RL$-fuzzy topology, the results of our paper are more general.