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This article investigates the geometric and topologic of warped product submanifolds in Riemannian warped product Qεm×R{{\mathbb{Q}}}_{\varepsilon }^{m}\times {\mathbb{R}}. In this respect, we obtain the first Chen inequality that involves extrinsic invariants like the length of the warping functions and the mean curvature. This inequality involves two intrinsic invariants (sectional curvature and δ\delta -invariant). In addition, an integral bound is provided for the Bochner operator formula of compact warped product submanifolds in terms of the Ricci curvature gradient. We aim to apply this theory to many structures and obtain Dirichlet eigenvalues for problem applications. Some new results regarding the vanishing mean curvature are presented as a partial solution, and this can be considered for the well-known problem given by Chern.

Background and Aim: Antibiotic resistance in Klebsiella pneumoniae, especially extended-spectrum beta-lactamase (ESBL) producers, has become a global public health problem. This study aimed to estimate the prevalence of multidrug resistance (MDR) and ESBL-producing K. pneumoniae in wastewater from dairy farms. Materials and Methods: This study was conducted on dairy farms in East Java Province from June to October 2022. In total, 342 dairy farm wastewater samples were isolated on buffered peptone water media from six cities/regencies with the highest dairy cattle population in East Java. Samples were identified using MacConkey agar media, Gram-staining,eosin-methylene blue agar, and biochemical tests. In total, 14.32% (49/342) samples contained K. pneumoniae. Positive isolates were tested for antibiotic sensitivity. Klebsiella pneumoniae resistant to beta-lactam was confirmed using the double-disk synergy test to confirm the presence of ESBL-producing bacteria. Results: The percentage of antibiotic resistance in K. pneumoniae was 98% resistance to ampicillin, 67.3% to cefotaxime, 46.9% to tetracycline, 49% to ciprofloxacin, 98% to streptomycin, 14.3% to sulfamethoxazole–trimethoprim, and 83.7% to chloramphenicol. The prevalence of MDR in K. pneumoniae was 12.57% (43/342), with the highest prevalence in the five classes of antibiotics at 41.86% (18/43), and the prevalence of ESBL-producing K. pneumoniae was 5.55% (19/342), with the highest prevalence in the districts of Blitar and Pasuruan at 26.31% (5/19). Conclusion: Although the prevalence of ESBL-producing K. pneumoniae in wastewater samples from dairy farms was low, caution is recommended because they can be a reservoir for ESBL.

The prime objective of the approach is to give geometric classifications of kk-almost Ricci solitons associated with paracontact manifolds. Let M2n+1(φ,ξ,η,g){M}^{2n+1}\left(\varphi ,\xi ,\eta ,g) be a paracontact metric manifold, and if a KK-paracontact metric gg represents a kk-almost Ricci soliton (g,V,k,λ)\left(g,V,k,\lambda ) and the potential vector field VV is Jacobi field along the Reeb vector field ξ\xi , then either k=λ−2nk=\lambda -2n, or gg is a kk-Ricci soliton. Next, we consider KK-paracontact manifold as a kk-almost Ricci soliton with the potential vector field VV is infinitesimal paracontact transformation or collinear with ξ\xi . We have proved that if a paracontact metric as a kk-almost Ricci soliton associated with the non-zero potential vector field VV is collinear with ξ\xi and the Ricci operator QQ commutes with paracontact structure φ\varphi , then it is Einstein of constant scalar curvature equals to −2n(2n+1)-2n\left(2n+1). Finally, we have deduced that a para-Sasakian manifold admitting a gradient kk-almost Ricci soliton is Einstein of constant scalar curvature equals to −2n(2n+1)-2n\left(2n+1).

We prove that if an η\eta -Einstein para-Kenmotsu manifold admits a conformal η\eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η\eta -Ricci soliton is Einstein if its potential vector field VV is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η\eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η\eta -Ricci soliton and satisfy our results. We also have studied conformal η\eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

Utilizing NMR (1H-NMR and 13C-NMR), FT-IR, UV-Visible, and quantum chemical approaches by using the DFT technique, experiments on 2-phenylthioanline were carried out. The B3LYP method and the 6-311++G(d,p) basis set were used to optimize the molecular structure and vibrational modes. The ideal binding parameters match up well with the experimental binding parameters. VEDA successfully finished the assignments concerning the distribution of potential energy. The GIAO method was used to calculate shifts in the 1H-NMR and 13C-NMR, and the outcomes were compared to experimental spectra. The TDDFT approach and the CPCM solvent model were used to examine electronic properties such as UV-Vis (in the gas phase, methanol, Acetone, and DCM), and the results were compared to experimental UV-Vis spectra. The HOMO/LUMO energy values provide sufficient proof of such. Molecular docking and dynamic simulations were carried out with a 2HI4 protein target and gave the best result among the three proteins. [ABSTRACT FROM AUTHOR]

We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional sl (2 , R) and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentzian–Sasakian Hom-Lie algebras are investigated. If v is a contact 1-form, conditions under which the Ricci curvature tensor is v-parallel are given. Ricci solitons for Lorentzian–Sasakian Hom-Lie algebras are also studied. It is shown that a Ricci soliton vector field ζ is conformal whenever the Lorentzian–Sasakian Hom-Lie algebra is Ricci semisymmetric. To illustrate the use of the theory, a two-parameter family of three-dimensional Lorentzian–Sasakian Hom-Lie algebras which are not Lie algebras is given and their Ricci solitons are computed. [ABSTRACT FROM AUTHOR]

The concept of wormholes is still hypothetical in physics but attractive among researchers. In this work, motivated by the important effect of f (R , T) gravity theory, we seek the existence of wormhole solutions. We consider the field equations that can be derived from two different choices of matter Lagrangian density and utilize them to find the possibility of having some wormhole geometry. This procedure is based on the specific choice of an equation-of-state that obeys a certain physical requirement on the matter stress-energy [S. Kar and D. Sahdev, Restricted class of traversable wormholes with traceless matter, Phys. Rev. D 52 (1995) 2030]. For this purpose, the functional form of the redshift function is taken into consideration, and the possible existence of wormhole solutions is proven. Finally, the work examines the energy conditions and shows that violations of null energy conditions hold throughout spacetime. [ABSTRACT FROM AUTHOR]