A series of previously conducted experiments pertaining to various chemicals and drugs uncover a natural linkage between the molecular structures and the bio-medical and pharmacological characteristics. The forgotten topological index computed for the molecular structures of various chemical compounds and drugs has proven significant in medical and pharmaceutical fields by predicting biological features of new chemical compounds and drugs. A topological index can be considered as the transformation of chemical structure into a real number. Dendrimers are highly-branched star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper, we determine forgotten topological indices of poly(propyl) ether imine, porphyrin, and zinc–porphyrin dendrimers.

A digital image watermarking algorithm using partial pivoting lower and upper triangular (PPLU) decomposition is proposed. In this method, a digital watermark image is factorised into lower triangular, upper triangular and permutation matrices by PPLU decomposition. The permutation matrix is used as the valid key matrix for authentication of the rightful ownership of the watermark image. The product of the lower and upper triangular matrices is embedded into particular sub‐bands of a cover image that is decomposed by wavelet transform using the singular value decomposition. The weightage‐based differential evolution algorithm is used to achieve the possible scaling factor for obtaining the maximum possible robustness against various image processing operations and pirate attacks. The authors experiments show that the proposed algorithm is highly reliable with better imperceptibility of the embedded image and computationally efficient compared with recently existed methods.

According to the research, many task scheduling approaches have been proposed like GA, ACO, etc., which have improved the performance of the cloud data centers concerning various scheduling parameters. The task scheduling problem is NP-hard, as the key reason is the number of solutions/combinations grows exponentially with the problem size, e.g., the number of tasks and the number of computing resources. Thus, it is always challenging to have complete optimal scheduling of the user tasks. In this research, we proposed an adaptive load-balanced task scheduling (ALTS) approach for cloud computing. The proposed task scheduling algorithm maps all incoming tasks to the available VMs in a load-balanced way to reduce the makespan, maximize resource utilization, and adaptively minimize the SLA violation. The performance of the proposed task scheduling algorithm is evaluated and compared with the state-of-the-art task scheduling ACO, GA, and GAACO approaches concerning average resource utilization (ARUR), Makespan, and SLA violation. The proposed approach has revealed significant improvements concerning the makespan, SLA violation, and resource utilization against the compared approaches.