When the ground state hyperfine splitting of alkali metal vapor atoms is well optically resolved, the spin coherence on one hyperfine sublevel can be generated directly or indirectly by pumping the same or the other sublevel respectively. We experimentally studied the pump power dependence of the field response of a Bell-Bloom magnetometer for the two pumping schemes in a paraffin coated 87 Rb vapor cell. We find that although the maximum field response is achieved by combining the two pumping schemes, indirect pumping alone can do nearly as good while being much simpler to operate. We have achieved a sensitivity of 100 fT/Hz 1/2 with a single indirect pump at room temperature.
<abstract><p>This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To effectively reduce communication costs and control updates, we propose an event-triggered protocol based on stochastic sampling. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Using the event-triggered strategy, we present sufficient conditions to ensure mean square consensus. Finally, we provide a numerical example demonstrating the effectiveness of the theoretical results.</p></abstract>
Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry and dense spatial arrangements. As a result, these compounds hold great potential for applications in materials science, catalytic chemistry, and other related fields. The Kirchhoff index of a graph G is defined as the sum of resistive distances between any two vertices in G. This article focuses on studying a type of tetrafunctional compound with a linear crossed square chain shape. The Kirchhoff index and degree Kirchhoff index of this compound are calculated, and a detailed analysis and discussion is conducted. The calculation formula for the Kirchhoff index is obtained based on the relationship between the Kirchhoff index and Laplace eigenvalue, and the number of spanning trees is derived for linear crossed quadrangular chains. The obtained formula is validated using Ohm’s law and Cayley’s theorem. Asymptotically, the ratio of Kirchhoff index to Wiener index approaches one-fourth. Additionally, the expression for the degree Kirchhoff index of the linear crossed quadrangular chain is obtained through the relationship between the degree Kirchhoff index and the regular Laplace eigenvalue and matrix decomposition theorem.
Digital finance is considered an important driving force for improving the level of population agglomeration. This article matches the data of Peking University's digital inclusive finance with information on regional population agglomeration to study the relationship between the development of digital finance and population agglomeration. The regression results of the instrumental variable method show that the development of digital finance can promote population agglomeration at a significant level of 1%, and a series of robustness tests further support this finding. In addition, this article finds that the breadth of coverage in the digital finance index has a greater impact on population agglomeration, and the heterogeneity analysis of regions shows that the promotion of digital finance development on population agglomeration is more evident in western regions. This has reference significance for promoting the even distribution of the national population.
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