The global B−LB-L symmetry in the flavor-unified SU(N){\rm SU}(N) theories

We study the origin of the global $B-L$ symmetry in a class of flavor-unified theories with gauge groups of ${\rm SU}(N\geq 6)$. In particular, we focus on the ${\rm SU}(8)$ theory which can minimally embed three-generational SM fermions non-trivially. A reformulation of the third law for the flavor sector proposed by Georgi is useful to manifest the underlying global symmetries. The 't Hooft anomaly matching and the generalized neutrality conditions for Higgs fields play the key roles in defining the $B-L$ symmetry. Based on the global $B-L$ symmetry, we count the Higgs fields that can develop the VEVs and the massless sterile neutrinos in the ${\rm SU}(8)$ theory. We also prove that a global $B-L$ symmetry can always be defined in any ${\rm SU}(N\geq 6)$ theory when it is spontaneously broken to the SM gauge symmetry.Comment: 34 pages, 11 table

Non-uniform Bid-scaling and Equilibria for Different Auctions: An Empirical Study

In recent years, the growing adoption of autobidding has motivated the study of auction design with value-maximizing auto-bidders. It is known that under mild assumptions, uniform bid-scaling is an optimal bidding strategy in truthful auctions, e.g., Vickrey-Clarke-Groves auction (VCG), and the price of anarchy for VCG is $2$. However, for other auction formats like First-Price Auction (FPA) and Generalized Second-Price auction (GSP), uniform bid-scaling may not be an optimal bidding strategy, and bidders have incentives to deviate to adopt strategies with non-uniform bid-scaling. Moreover, FPA can achieve optimal welfare if restricted to uniform bid-scaling, while its price of anarchy becomes $2$ when non-uniform bid-scaling strategies are allowed. All these price of anarchy results have been focused on welfare approximation in the worst-case scenarios. To complement theoretical understandings, we empirically study how different auction formats (FPA, GSP, VCG) with different levels of non-uniform bid-scaling perform in an autobidding world with a synthetic dataset for auctions. Our empirical findings include: * For both uniform bid-scaling and non-uniform bid-scaling, FPA is better than GSP and GSP is better than VCG in terms of both welfare and profit; * A higher level of non-uniform bid-scaling leads to lower welfare performance in both FPA and GSP, while different levels of non-uniform bid-scaling have no effect in VCG. Our methodology of synthetic data generation may be of independent interest

Thermal simulation modeling of a hydrostatic machine feed platform

Hydrostatic guideways are widely applied into precision and ultra-precision machine tools. Meanwhile, the oil film heat transfer causes thermal disturbance to the machine accuracy. Therefore, it is necessary to study the mechanism of the oil film heat transfer and the heat-transfer-reducing method to improve the machine accuracy. This paper describes a comprehensive thermal finite element (FE) simulation modeling method for the hydrostatic machine feed platform to study methods of reducing machine thermal errors. First of all, the generating heat power of viscous hydraulic oil flowing between parallel planes is calculated based on the Bernoulli equation. This calculation is then employed for the simulation load calculations for the closed hydrostatic guideways, which is adopted by the hydrostatic machine feed platform. Especially, in these load calculations, the changing of oil film thickness (resulted from external loads) and the changing of oil dynamic viscosity (influenced by its temperature) are taken into account. Based on these loads, thermal FE simulation modeling of the hydrostatic machine feed platform is completed to predict and analyze its thermal characteristics. The reliability of this simulation modeling method is verified by experiments. The studies demonstrate that the hydrostatic machine thermal error degree is determined by the oil film heat transfer scale, and this scale is mainly influenced by the relative oil supply temperature to ambient temperature (quantitative comparison of oil supply temperature and ambient temperature). Furthermore, the reduction of the absolute value of this relative oil supply temperature can reduce the oil film heat transfer scale and improve the machine accuracy

A differentiated multi-loops bath recirculation system for precision machine tools

Traditional bath recirculation cooler for precision machine tools always has the uniform and open-loop cooling strategy onto different heat generating parts. This causes redundant generated heat being transferred into the machine structure, and results in unsatisfactory thermal errors of precision machine tools. For the solution of this problem, this paper presents the differentiated multi-loops bath recirculation system. The developed system can accomplish differentiated and close-loop cooling strategies onto machine heat generating parts during its operation. Specially, in order to illustrate the advantages of this system, constant supply cooling powers strategy is presented with its applications onto a certain type of built-in motorized spindle. Consequently, advantages of the proposed strategy based on the differentiated multi-loops bath recirculation system are verified experimentally in the environment within consistent temperature (TR = 20 ± 0.3°C). Compared with room temperature tracing strategy based on the traditional bath recirculation cooler, the constant supply cooling powers strategy is verified to be advantageous in spindle temperature stabilization and thermal errors decrease