The sharp estimate of nodal sets for Dirichlet Laplace eigenfunctions in polytopes

Let $P$ be a bounded $n$-dimensional Lipschitz polytope, and let $\varphi_{\lambda}$ be a Dirichlet Laplace eigenfunction in $P$ corresponding to the eigenvalue $\lambda$. We show that the $(n-1)$-dimensional Hausdorff measure of the nodal set of $\varphi_{\lambda}$ does not exceed $C(P)\sqrt{\lambda}$. Our result extends the previous ones in quaisconvex domains (including $C^1$ and convex domains) to general polytopes that are not necessarily quasiconvex.Comment: 20 page

Study on nonlinear dynamic of ball bearing-offset disk rotor system with whirling-swing coupling vibration

A dynamic model of ball bearing-offset disk rotor system with whirling-swing coupling vibration is presented, in which the rotor disk offset position and the swing vibration of disk are concerned. In the model of ball bearing, the bearing radial clearance, nonlinear Hertzian contact force and the varying compliance (VC) vibration are considered. Numerical methods are used to obtain the nonlinear dynamic response of the system under different disk offset values for considering the disk swing vibration or not. Effects of bearing radial clearance variation on the dynamic performance of the system under different rotor offset values are investigated. It is shown that the nonlinear dynamic of the offset disk rotor system enhances obviously when rotor disk swing vibration is considered. As rotor disk offset increasing, the sensitivity of critical speed to variation of the bearing radial clearance improves

Research on the Construction of Agro-Ecological Park Under the Background of Smart Agriculture - Take Zengcheng Chuangxian Smart Agriculture Model Park as an Example

[EN] In the process of agricultural modernization in China, smart. agriculture is the new direction of rural development, and scientific development of agroecological parks is an important starting point to promote agricultural transformation and upgrading, as well as an effective way to promote rural revitalization. At present, the application of smart agriculture in agricultural ecological parks in China is still in the experimental stage, and the pilots have been carried out in various regions, but most of them are almost stagnant at the level of agricultural production, failing to maximize the use of smart agricultural resources to build agroecological parks. This paper analyzes the case of Zengcheng Chuangxian Smart Agriculture Model Park on the basis of describing its current development and the existing problems after the introduction of smart agriculture, and puts forward relevant suggestions.Chen, J.; Cai, Y.; Gaoge, Y.; Lv, H. (2022). Research on the Construction of Agro-Ecological Park Under the Background of Smart Agriculture - Take Zengcheng Chuangxian Smart Agriculture Model Park as an Example. En 4th International Conference on Advanced Research Methods and Analytics (CARMA 2022). Editorial Universitat Politècnica de València. 283-283. http://hdl.handle.net/10251/18976228328

Are categories’ cores more isomorphic than their peripheries?

Isomorphism holds that, ideally, a single meaning is expressed by a single form. However, despite long-standing support, the theoretical viability of the isomorphic principle has been called into question. There is widespread recognition that the coexistence of (near-) synonymous expressions—variation—is actually very common in language. In this study, we explore a possible path toward reconciling the theoretical notion of isomorphism with the observable fact of variation. To this end, we adopt an analogy to tool use inspired by Zipf (1949). Tools largely monopolize their core functional domains (e.g., for cutting, knives are overwhelmingly preferred over screwdrivers) but compete over more peripheral functions (for puncturing, knives and screwdrivers have more equal chances of selection). In the same way, we hypothesize forms can code a prototypically organized network of senses, whereby they largely monopolize the core but are more likely to come into competition with other forms in the periphery. To test this hypothesis, a case study is conducted on variation in the use of two prepositions: at and with. For each, a semantic core and periphery are established. Using a corpus consisting of parallel translations of the same source text, it is then tested whether translators are more likely to converge on the same preposition to express one of that preposition’s core senses than to express one of its peripheral senses. This is the pattern one would expect if isomorphic pressure is stronger for semantic cores than for peripheries. The results are promising but inconclusive. They confirm that the sense most prone to competition is arguably the most peripheral but also reveal a surprisingly high level of competition for the spatial core use of at

A Distributed Model Predictive Control Approach for Optimal Coordination of Multiple Thermal Zones in a Large Open Space

Model Predictive Control (MPC) based approaches have recently seen a significant increase in applications to the supervisory control of building heating, ventilation and air-conditioning (HVAC) systems, thanks to their ability to incorporate weather, occupancy, and utility price information in the optimization of heating/cooling strategy while satisfying the physical constraints of HVAC equipment. Many of the proposed MPC solution approaches are centralized ones that often have difficulty in dealing with large-scale building clusters or even a single building consisting of multiple thermal zones due to the high computational cost caused by the large number of decision variables and the overhead in information gathering and distribution. This paper investigates a decomposition technique based on a variant of the Alternating Direction Method of Multipliers (ADMM) that can significantly reduce the computational and communication costs of centralized solutions, and more importantly, facilitates a plug-and-play implementation. The proposed Distributed Model Predictive Control (DMPC) framework takes advantage of parallel computation and collaborations among multiple agents, each of which is assigned to address a smaller dimensional optimization problem. The proposed method is general in that it can accommodate some fairly general types of couplings in agent dynamics as well as in the cost function; therefore it can be used for a broad class of HVAC optimal operation problems. A case study on one of the Purdue Living Labs is carried out to demonstrate the effectiveness of the proposed method. The Living Lab considered is an open office space served by one central air handling unit (AHU) with multiple diffusers whose openings can be controlled individually. The office space is partitioned into multiple thermal zones with individual thermostat controls. In view of significant thermal couplings due to direct air exchange and noticeable load gradient between zones, a multiple thermal zone coordination problem is formulated with the objective of optimally scheduling the different thermostat setpoints for energy minimization and comfort delivery while satisfying actuation constraints. Preliminary results show that the proposed method successfully converges to the optimal solution for the problem concerned in this case study. The optimal solutions demonstrate significant opportunities of inter-zonal coordination and energy savings potentials