Restricted modules and associated vertex algebras of extended Heisenberg-Virasoro algebra

In this paper, a family of infinite dimensional Lie algebras $\tilde{\mathcal{L}}$ is introduced and investigated, called the extended Heisenberg-Virasoro algebra,denoted by $\tilde{\mathcal{L}}$. These Lie algebras are related to the $N=2$ superconformal algebra and the Bershadsky-Polyakov algebra. We study restricted modules and associated vertex algebras of the Lie algebra $\tilde{\mathcal{L}}$. More precisely, we construct its associated vertex (operator) algebras $V_{\tilde{\mathcal{L}}}(\ell_{123},0)$, and show that the category of vertex algebra $V_{\tilde{\mathcal{L}}}(\ell_{123},0)$-modules is equivalent to the category of restricted $\tilde{\mathcal{L}}$-modules of level $\ell_{123}$.Then we give uniform constructions of simple restricted $\tilde{\mathcal{L}}$-modules. Also, we present several equivalent characterizations of simple restricted modules over $\tilde{\mathcal{L}}$.Comment: 22 page

The Research of The Pricing Strategy of New Market Entrants Entering Market

First of all, based on the summary of the development of SaaS, this paper takes the free trial strategy as the entry point, and takes the market share and market price as the decision points, the strategy model of market new entrants’ optimal pricing and the market entry strategy model are discussed under the two dimensions of space and time. On the model side, the hotelling-based model expands the strategy of free strategy, supplier and consumer sustainable expectations-oriented pricing strategies. New entrants with low product quality consider from a short-term perspective to enter at high prices, relying on free strategies to accumulate market share, and provide space for subsequent price cuts. New entrants with high product quality enter at low prices, increase conversion rate through free trials, and stabilize the market with brand effect

Stability and bifurcation analysis of Westwood+ TCP congestion control model in mobile cloud computing networks

In this paper, we first build up a Westwood+ TCP congestion control model with communication delay in mobile cloud computing networks. We then study the dynamics of this model by analyzing the distribution ranges of eigenvalues of its characteristic equation. Taking communication delay as the bifurcation parameter, we derive the linear stability criteria depending on communication delay. Furthermore, we study the direction of Hopf bifurcation as well as the stability of periodic solution for the Westwood+ TCP congestion control model with communication delay. We find that the Hopf bifurcation occurs when the communication delay passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by the normal form theory and the center manifold theorem. Finally, numerical simulation is done to verify the theoretical results

The Mechanism of Crowd Stampede Based on Case Statistics through SNA Method

Stampede is a concern of urban pubic security management. The current academic research focus is the identification of risk factors of trampling accidents and determination of correlation patterns and accident-causing mechanisms among stampede elements in order to effectively obtain the influencing factors of stampede and clarify the transmission routes of stampede risk factors. Previous index cases were scrutinized and analyzed in 78 typical stampedes from 2010 - 2019 based on "pedestrian-equipment-environment-management" framework, and 17 influencing factors of stampede by adopting a conceptual coding method were obscured. Then, the degree centrality, intermediate centrality and respective weights of the influencing factors were calculated based on the social network analysis (SNA) method. The influencing level of the factors was signified, and the transmission mechanism of risk in the system network was determined. The results reveal that the degree centrality and weight with conspicuous features of over-density of crowds, pedestrian swarming and falling, and insufficient on-site transactions contribute the most. This finding indicates that these factors play a relatively major role in the stampede system. Furthermore, the intermediate centrality of insufficient on-site transactions is the top factor, meaning that this factor has a strong controlling force in the incident system and considerably influences other factors. This study shows that the SNA method is feasible in analyzing the mechanism of stampede incidents, simultaneously addressing the shortcomings of the linear statistical model of factors and providing theoretical support for comprehensive control of crowd risk

A New Two-Dimensional Functional Material with Desirable Bandgap and Ultrahigh Carrier Mobility

Two-dimensional (2D) semiconductors with direct and modest bandgap and ultrahigh carrier mobility are highly desired functional materials for nanoelectronic applications. Herein, we predict that monolayer CaP3 is a new 2D functional material that possesses not only a direct bandgap of 1.15 eV (based on HSE06 computation), and also a very high electron mobility up to 19930 cm2 V-1 s-1, comparable to that of monolayer phosphorene. More remarkably, contrary to the bilayer phosphorene which possesses dramatically reduced carrier mobility compared to its monolayer counterpart, CaP3 bilayer possesses even higher electron mobility (22380 cm2 V-1 s-1) than its monolayer counterpart. The bandgap of 2D CaP3 can be tuned over a wide range from 1.15 to 0.37 eV (HSE06 values) through controlling the number of stacked CaP3 layers. Besides novel electronic properties, 2D CaP3 also exhibits optical absorption over the entire visible-light range. The combined novel electronic, charge mobility, and optical properties render 2D CaP3 an exciting functional material for future nanoelectronic and optoelectronic applications