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The density matrix of an arbitrary pure state of a system consisting of two spin‐1/2 particles is derived from the Pauli spin angular momentum operators. Mixed singlet and triplet states are then formed from linear combinations of pure states and their corresponding density matrices constructed. Singlet and triplet states are exemplified by the spin isomers parahydrogen and orthohydrogen, respectively. Partial mixing is illustrated with the example of bilinear spin–spin coupling. Various properties of the density matrices of pure and mixed states are discussed, including idempotence, factoring, and spin correlation.

Identifying soil microbial feedbacks to increasing temperatures and moisture alterations is critical for predicting how terrestrial ecosystems will respond to climate change. We performed a 5-year field experiment manipulating warming, watering and their combination in a semiarid temperate steppe in northern China. Warming stimulated the abundance of genes responsible for degrading recalcitrant soil organic matter (SOM) and reduced SOM content by 13%. Watering, and warming plus watering also increased the abundance of recalcitrant SOM catabolism pathways, but concurrently promoted plant growth and increased labile SOM content, which somewhat offset SOM loss. The treatments also increased microbial biomass, community complexity and metabolic potential for nitrogen and sulfur assimilation. Both microbial and plant community composition shifted with the treatment conditions, and the sample-to-sample compositional variations of the two communities (pairwise β-diversity distances) were significantly correlated. In particular, microbial community composition was substantially correlated with the dominant plant species (~0.54 Spearman correlation coefficient), much more than with measured soil indices, affirming a tight coupling between both biological communities. Collectively, our study revealed the direction and underlying mechanisms of microbial feedbacks to warming and suggested that semiarid regions of northern steppes could act as a net carbon source under increased temperatures, unless precipitation increases concurrently.

Identifying soil microbial feedbacks to increasing temperatures and moisture alterations is critical for predicting how terrestrial ecosystems will respond to climate change. We performed a 5-year field experiment manipulating warming, watering and their combination in a semiarid temperate steppe in northern China. Warming stimulated the abundance of genes responsible for degrading recalcitrant soil organic matter (SOM) and reduced SOM content by 13%. Watering, and warming plus watering also increased the abundance of recalcitrant SOM catabolism pathways, but concurrently promoted plant growth and increased labile SOM content, which somewhat offset SOM loss. The treatments also increased microbial biomass, community complexity and metabolic potential for nitrogen and sulfur assimilation. Both microbial and plant community composition shifted with the treatment conditions, and the sample-to-sample compositional variations of the two communities (pairwise ß-diversity distances) were significantly correlated. In particular, microbial community composition was substantially correlated with the dominant plant species (~0.54 Spearman correlation coefficient), much more than with measured soil indices, affirming a tight coupling between both biological communities. Collectively, our study revealed the direction and underlying mechanisms of microbial feedbacks to warming and suggested that semiarid regions of northern steppes could act as a net carbon source under increased temperatures, unless precipitation increases concurrently.

Dynamic two-dimensional ¹H and ¹³C NMR studies of the conformationally restricted amide N-(1-naphthoyl)-cis-2,6-dimethylpiperidine reveal correlated rotation about the aryl–CO and amide bonds. The naphthalene and piperidine rings are tightly meshed and their rotation is virtually entirely (>99%) concerted, as evidenced by separate NMR measurement of the much slower rates of rotation about the individual aryl–CO and amide bonds. A disrotatory cogwheeling mechanism for the concerted rotation is proposed. Copyright © 2000 John Wiley & Sons, Ltd.

Overall system latency—the elapsed time from input human motion until the immediate consequences of that input are available in the display—is one of the most frequently cited shortcoming of current virtual environment (VE) technology. Given that spatial displacement trackers are employed to monitor head and hand position and orientation in many VE applications, the dynamic response intrinsic to these devices is an unavoidable contributor to overall system latency. In this paper, we describe a testbed and method for measurement of tracker dynamic response that use a motorized rotary swing arm to sinusoidally displace the VE sensor at a number of frequencies spanning the bandwidth of volitional human movement. During the tests, actual swing arm angle and VE sensor reports are collected and time stamped. By calibrating the time stamping technique, the tracker's internal transduction and processing time are separated from data transfer and host computer software execution latencies. We have used this test-bed to examine several VE sensors—most recently to compare latency, gain, and noise characteristics of two commercially available electromagnetic trackers: Ascension Technology Corp.'s Flock of Birds™ and Polhemus Inc.'s Fastrak™.

Slow dynamic processes are usually investigated via magnetization transfer methods in which chemical exchange occurs during a mixing interval in the absence of an rf field (effective field along z) or in the presence of a very strong rf field ω1=γB1 (effective field along x). The longitudinal or transverse magnetizations associated with the exchanging spins I and S are coupled by chemical exchange and the time-dependent behavior after some initial perturbation is governed by the two eigenvalues of the relaxation matrix. These experiments may be viewed as limiting cases of a general scenario which uses a tilted rf field to effect magnetization transfer. To illustrate the principles of magnetization transfer phenomena in the presence of continuous radiofrequency fields, an experiment is described which locks the I and S magnetizations at intermediate angles in the x–z plane. At the 45° angle, the coupling of the locked states due to chemical exchange vanishes. Single exponential decay of the magnetization is a function of the angle θ and leads to a steady state governed by saturation and magnetization transfer factors. The experiment is demonstrated with a study of amide bond rotation in N,N-dimethylacetamide. ©1999 John Wiley & Sons, Inc. Concepts Magn Reson 11: 89–95, 1999

Saturation-transfer or lineshape measurements of kinetics of proton exchange show that HZof ethyl acetimidate in 46% H2SO4or ethyl N-methylformimidate in 40% H2SO4exchanges faster than HE, and HEof protonated 2-iminotetrahydrofuran exchanges faster than HZ, as expected on the basis of the stabilities of the stereoisomeric imidate esters. In contrast, amide exchange is too fast to measure in aqueous H2SO4, but can be measured in 100% H2SO4, where HEand HZexchange at equal rates. Also, there is intramolecular exchange occurring at this same rate. These results are interpreted as evidence for exchange in amides via the N-protonated intermediate, whose lifetime in H2SO4is sufficiently long to permit the protons on nitrogen to become equivalent. By comparing OH exchange with NH exchange, it is concluded that N-protonation is the rate-limiting step. Even though this is a thermodynamically favorable proton transfer in H2SO4, its rate constant is significantly lower than the diffusion-controlled limit. The contrasts between imidate esters and amides and between dilute solutions and H2SO4are discussed.