The object of the present paper was to study biharmonic maps on f-Kenmotsu manifolds and f-Kenmotsu manifolds with the Schouten–van Kampen connection. With the help of this connection, our results provided important insights related to harmonic and biharmonic maps.

This study explored the chemical composition and antimicrobial properties of Eucalyptus globulus essential oil. The oil was extracted by hydrodistillation, yielding a 0.23% concentration. Gas chromatography (GC) analysis revealed three primary constituents: 1,8-cineole (commonly known as eucalyptol) at 81.55%, D-limonene at 5.409%, and alpha-pinene at 4.107%, collectively comprising 91.067% of the oil. Additionally, two minor constituents, making up 1.196% and 1.017% of the oil composition, were detected but remain unidentified. The antimicrobial potential of the oil was assessed against two bacterial strains, highlighting its bioactive properties. Results indicated that Eucalyptus globulus essential oil exhibited strong inhibitory effects against Staphylococcus aureus, a Gram-positive bacterium known to cause various infections. It also showed moderate activity against Escherichia coli, a Gram-negative bacterium commonly found in the intestines but also associated with foodborne illness. These findings underscore the potential of Eucalyptus globulus oil as a natural antimicrobial agent, particularly for targeting Gram-positive bacteria like Staphylococcus aureus. The presence of 1,8-cineole as the predominant component is likely responsible for the oil's notable antimicrobial efficacy, suggesting possible applications in medicinal and preservation contexts.

Let $\psi:(M_{2k},\phi, g)\longrightarrow (N_{2k'},\phi', h)$ be a smooth map between almost anti-paraHermitian manifolds. The map $\psi$ induces the tangent map $\Psi:(TM,g^{BS})\longrightarrow (TN,h^{BS})$. In this paper, we deal with the harmonicity of a tangent map $\Psi$ and the biharmonicity of the identity map in the case where the tangent bundles $TM,TN$ are endowed with the Berger type deformed Sasaki metric $g^{BS}, h^{BS}$.

Image compression is crucial for multimedia applications with the aim of reduc ing storage and/or transmission costs, while preserving reliable visual quality. In this research, we propose a novel hybrid image compression technique based on staggering downsampling combined with discrete cosine transform (DCT). The proposed approach not only overlaps downsample images to reduce data re dundancy but also utilizes the energy compaction properties of DCT for efficient compression. The proposed method performance on benchmark grayscale im ages such as Lena, House, and other refernce images were evaluated by means of image quality assessment metrics, namely, peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), visual information fidelity (VIF); and com pression efficiency metrics: bitrate and compression ratio. The results clearly show that the proposed algorithm outperforms JPEG and Set partitioning in hi erarchical trees (SPIHT) + discrete wavelet transform (DWT) method, with the following results: PSNR of 45.02, MSSIM of 0.9856, VIF of 0.8271, Bitrate of 0.12 bpp and a Compression Ratio of 64.00 (i.e. a reduction of 64 times). The suggested hybrid image compression method optimizes bug multimedia stor age and transmission by minimizing storage space and bandwidth usage while maintaining image quality. It, therefore, achieves a balance between percep tual quality and compression efficiency, making it the best option for resource constrained applications such as remote sensing, embedded systems, video com pression, and medical image archival.