The Milnor–Totaro Theorem for Space Polygons

If denotes the curvature and the torsion of a closed, generic, and oriented polygonal space curve X in , then we show that _X (² + ²) ds = _X ds + _X | | ds > 4 if is positive. We also show that _X (² + ²) ds 2n if no four consecutive vertices lie in a plane and X has linking number n with a straight line. These extend theorems of Milnor and Totaro.     

Miller–Urey Revisited: When Lightning Strikes the Earth

A discharge is arced to different solutions containing the simple molecular species water, methanol, and ammonia. We show that the impact of the discharge at the discharge-solution interface produces a range of organic molecules, including amino acids and polymers containing carboxylate, amine, imine, and cyano groups. The classic Miller-Urey experiment, of which there are hundreds of variations, changing parameters such as gas composition, pressures, and voltage have been tested, involves the production of simple amino acids and other species in the gas phase in an arc discharge. This works emphasis is the production of various chemical species at a discharge-liquid interface. The analysis of the product is conducted by IR, UV–VIS, LC–MS and MALDI–MS. As a laboratory exercise or a demonstration, this simple derivation of the Miller-Urey experiment can be used in a variety of teaching settings, from high school through advanced undergraduate research classes to demonstrate the basic hypothesis of how life on Earth may have started.     

Microwave- and Ultrasound-Assisted Extraction of Cannabinoids and Terpenes from Cannabis Using Response Surface Methodology

Limited studies have explored different extraction techniques that improve cannabis extraction with scale-up potential. Ultrasound-assisted and microwave-assisted extraction were evaluated to maximize the yield and concentration of cannabinoids and terpenes. A central composite rotatable design was used to optimize independent factors (sample-to-solvent ratio, extraction time, extraction temperature, and duty cycle). The optimal conditions for ultrasound- and microwave-assisted extraction were the sample-to-solvent ratios of 1:15 and 1:14.4, respectively, for 30 min at 60 °C. Ultrasound-assisted extraction yielded 14.4% and 14.2% more oil and terpenes, respectively, compared with microwave-assisted extracts. Ultrasound-assisted extraction increased cannabinoid concentration from 13.2–39.2%. Considering reference ground samples, tetrahydrocannabinolic acid increased from 17.9 (g 100 g dry matter⁻¹) to 28.5 and 20 with extraction efficiencies of 159.2% and 111.4% for ultrasound-assisted and microwave-assisted extraction, respectively. Principal component analyses indicate that the first two principal components accounted for 96.6% of the total variance (PC1 = 93.2% and PC2 = 3.4%) for ultrasound-assisted extraction and 92.4% of the total variance (PC1 = 85.4% and PC2 = 7%) for microwave-assisted extraction. Sample-to-solvent ratios significantly (p < 0.05) influenced the secondary metabolite profiles and yields for ultrasound-assisted extracts, but not microwave-assisted extracts.     

Cold Ethanol Extraction of Cannabinoids and Terpenes from Cannabis Using Response Surface Methodology: Optimization and Comparative Study

Efficient cannabis biomass extraction can increase yield while reducing costs and minimizing waste. Cold ethanol extraction was evaluated to maximize yield and concentrations of cannabinoids and terpenes at different temperatures. Central composite rotatable design was used to optimize two independent factors: sample-to-solvent ratio (1:2.9 to 1:17.1) and extraction time (5.7 min–34.1 min). With response surface methodology, predicted optimal conditions at different extraction temperatures were a cannabis-to-ethanol ratio of 1:15 and a 10 min extraction time. With these conditions, yields (g 100 g dry matter⁻¹) were 18.2, 19.7, and 18.5 for −20 °C, −40 °C and room temperature, respectively. Compared to the reference ground sample, tetrahydrocannabinolic acid changed from 17.9 (g 100 g dry matter⁻¹) to 15, 17.5, and 18.3 with an extraction efficiency of 83.6%, 97.7%, 102.1% for −20 °C, −40 °C, and room temperature, respectively. Terpene content decreased by 54.1% and 32.2% for extraction at −20 °C and room temperature, respectively, compared to extraction at −40 °C. Principal component analysis showed that principal component 1 and principal component 2 account for 88% and 7.31% of total variance, respectively, although no significant differences in cold ethanol extraction at different temperatures were observed.     

Infrared multiphoton decomposition of highly excited t-butyl chloride-d9

The infrared multiphoton decomposition (IR MPD) of t-butyl chloride-d₉ as a function of pressure and fluence is reported. The major decomposition route was molecular elimination of DCl in accord with earlier pyrolysis studies. The effect of added gases (2-methyl propene-d₈, DCl and 2-methyl propene-h₈) on the MPD is presented. This study is a further example of the utility of a new method of analysis of MPD experiments. © 1994 John Wiley & Sons, Inc.