Pseudo-Einstein and Q-flat metrics with eigenvalue estimates on CR-hypersurfaces

Let $M^{2n-1}$ be the smooth boundary of a bounded strongly pseudo-convex domain $\Omega$ in a complete Stein manifold $V^{2n}$. Then (1) For $n \ge 3$, $M^{2n-1}$ admits a pseudo-Eistein metric; (2) For $n \ge 2$, $M^{2n-1}$ admits a Fefferman metric of zero CR Q-curvature; and (3) for a compact strictly pseudoconvex CR embeddable 3-manifold $M^3$, its CR Paneitz operator $P$ is a closed operator

A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations

We extend a standard stochastic theory to study open quantum systems coupled to generic quantum environments including the three fundamental classes of noninteracting particles: bosons, fermions and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Staring from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hiearchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and exibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the presetn formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alterantively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.Comment: 31 pages, 2 figure

A New Cloud with IoT-Enabled Innovation and Skill Requirement of College English Teachers on Blended Teaching Model

The blended teaching model is a type of educational approach that combines traditional classroom-based instruction with online learning experiences. In this model, students are given access to digital content, resources, and tools, which they can use to supplement their in-person classroom instruction. The blended teaching model is also sometimes referred to as the hybrid learning model. IoT-SDNCT (IoT enabled SDN reinforcement learning with Cloud Technological Innovation and Skill Requirement of College English Teachers on Blended Teaching Model) is a proposed system that aims to revolutionize blended teaching models by leveraging the power of IoT, SDN, and cloud computing technologies. This system incorporates intelligent reinforcement learning algorithms and real-time data analysis to optimize the learning process and improve student engagement and outcomes. In the IoT-SDNCT system, IoT devices such as sensors and wearable technologies are deployed to collect real-time data on student engagement and performance. This data is then transmitted to an SDN controller, which dynamically manages the network infrastructure and optimizes learning pathways. The collected data is also stored and processed in cloud computing platforms, allowing for advanced analytics and personalized feedback for both students and teachers. The key contribution of IoT-SDNCT lies in its ability to adapt the learning process in real-time based on the collected data and intelligent algorithms. This adaptive learning approach enables personalized learning experiences, adjusts the difficulty level of learning tasks, and provides timely feedback to students. Moreover, it empowers teachers with valuable insights and analytics to enhance their teaching strategies and address individual student needs effectively. The proposed system addresses the technological innovation and skill requirements of college English teachers by integrating IoT, SDN, and cloud computing technologies. By utilizing IoT devices, SDN controllers, and cloud platforms, teachers can optimize their teaching methods and create dynamic and interactive learning environments. This not only enhances student engagement but also improves learning outcomes and fosters skill development in both teachers and students. The system's adaptive learning capabilities and real-time data analysis contribute to an enhanced learning experience, increased student engagement, and improved teaching effectiveness

Probing medium-induced jet splitting and energy loss in heavy-ion collisions

The nuclear modification of jet splitting in relativistic heavy-ion collisions at RHIC and the LHC energies is studied based on the higher twist formalism. Assuming coherent energy loss for the two splitted subjets, a non-monotonic jet energy dependence is found for the nuclear modification of jet splitting function: strongest modification at intermediate jet energies whereas weaker modification for larger or smaller jet energies. Combined with the smaller size and lower density of the QGP medium at RHIC than at the LHC, this explains the CMS-STAR groomed jet puzzle -- strong nuclear modification of the momentum sharing $z_g$ distribution at the LHC whereas no obvious modification of the $z_g$ distribution at RHIC. In contrast, the observed nuclear modification pattern of the groomed jet $z_g$ distribution cannot be explained solely by independent energy loss of the two subjets. Our result may be tested in future measurements of groomed jets with lower jet energies at the LHC and larger jet energies at RHIC, for different angular separations between the two subjets.Comment: 10 pages, 12 figure