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We prove a strong form of finite rigidity for pants graphs of spheres. Specifically, for any n ≥ 4, we construct a finite subgraph X n of the pants graph P(S 0,n ) of the n-punctured sphere S 0,n with the following property. Any simplicial embedding of X n into any pants graph P(S 0,m ) of a punctured sphere is induced by an embedding S 0,n → S 0,m . arXiv:1303.3873v3 [math.GT]

A laboratory experiment utilizing locally available Indian Gooseberry (Phyllanthus emblica Linn.) extract as a bioreagent to determine iron(III) is described with the goal of providing students with hands-on experience in spectrophotometry and green chemistry. Spectrophotometry was used to measure the concentration of the complex formed between iron(III) and gallic acid, an active compound found in Indian Gooseberry extract. Excellent results from the quantitative analysis of iron(III) in water were achieved. In this case, the bioreagent was used to replace the conventional hazardous chemicals that are usually employed as chromogenic reagents. The use of Indian Gooseberry extract is simple, inexpensive, and environmentally friendly. This experiment is appropriate for use as a simple spectrophotometric protocol for undergraduate teaching in an analytical-or generalchemistry laboratory.

A green, simple, and rapid synthesis of gold nanoparticles using plant extract, Cryptolepis buchanani Roem. and Schult, and their applications are first described in this paper. The formation of gold nanoparticles was visually observed by the appearance of a ruby red color, which was further indicated by an absorption peak at 530 nm in UV-Vis spectroscopy. Optimization of reaction parameters for the gold nanoparticles was also investigated. Various analytical techniques were employed as part of the process of characterizing the resulting gold nanoparticles. Fourier transform infrared (FTIR) analysis revealed that the phenol compounds present in the extract were responsible for gold(III) reduction and stabilization of gold nanoparticles. Transmission electron microscopy (TEM) analysis showed that the gold nanoparticles were spherical in shape with an average diameter of 11 nm. Powder X-ray diffraction (XRD) pattern indicated that the green synthesis approach produced highly crystalline, face-centered cubic gold nanoparticles. Energy-dispersive X-ray spectroscopy (EDS) measurements confirmed the presence of elemental gold in the prepared nanoparticles. The negative zeta potential value of gold nanoparticles was found to be -30.28 mV. The green synthesized gold nanoparticles expressed effective antibacterial activity against Staphylococcus aureus, methicillin-resistant Staphylococcus aureus, and Acinetobacter baumannii and exhibited an excellent catalytic property in terms of its reduction ability of methylene blue.

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