Study on Cross-Basin Ecological Compensation Mechanism and Compensation Standard

Water resources in China’s river basins are scarce, and the pollution that shrouds them is serious. Constant disputes have emerged between the upstream and downstream sectors due to the contamination of river basins. Moreover, China’s research on ecological compensation mechanisms and compensation standards is still immature at present. Thus, this study establishes a compensation model and introduces the compensation coefficient K, including the compensation coefficient K1 between the upstream and downstream governments and the compensation coefficient K2 between the upstream government and the central government. This paper adopts the Bargain Game Model and obtains the value of K2 through the decision-making process between the central government and the upstream local government. In addition, amendment to the final offer arbitration law is used to acquire the value of K1 by proving the existence and uniqueness of equilibrium. Then, this paper takes the Taohe River Basin as an example and combines the compensation model to analyze, using the simplified compensation function to determine the amount of emission pollution from upstream to downstream and the compensation that upstream should receive.

Stability Analysis of the Rhomboidal Restricted Six-Body Problem

We discuss the restricted rhomboidal six-body problem (RR6BP), which has four positive masses at the vertices of the rhombus, and the fifth mass is at the intersection of the two diagonals. These masses always move in rhomboidal CC with diagonals 2 a and 2 b . The sixth body, having a very small mass, does not influence the motion of the five masses, also called primaries. The masses of the primaries are m 1 = m 2 = m 0 = m and m 3 = m 4 = m ˜ . The masses m and m ˜ are written as functions of parameters a and b such that they always form a rhomboidal central configuration. The evolution of zero velocity curves is discussed for fixed values of positive masses. Using the first integral of motion, we derive the region of possible motion of test particle m 5 and identify the value of Jacobian constant C for different energy intervals at which these regions become disconnected. Using semianalytical techniques, we show the existence and uniqueness of equilibrium solutions on the axes and off the axes. We show that, for b ∈ 1 / 3 , 1.1394282249562009 , there always exist 12 equilibrium points. We also show that all 12 equilibrium points are unstable.

Thermodynamics of smooth models of pseudo–Anosov homeomorphisms

We develop a thermodynamic formalism for a smooth realization of pseudo-Anosov surface homeomorphisms. In this realization, the singularities of the pseudo-Anosov map are assumed to be fixed, and the trajectories are slowed down so the differential is the identity at these points. Using Young towers, we prove existence and uniqueness of equilibrium states for geometric t-potentials. This family of equilibrium states includes a unique SRB measure and a measure of maximal entropy, the latter of which has exponential decay of correlations and the central limit theorem.

Managing Congestion in Matching Markets

Problem definition: Participants in matching markets face search and screening costs when seeking a match. We study how platform design can reduce the effort required to find a suitable partner. Practical/academic relevance: The success of matching platforms requires designs that minimize search effort and facilitate efficient market clearing. Methodology: We study a game-theoretic model in which “applicants” and “employers” pay costs to search and screen. An important feature of our model is that both sides may waste effort: Some applications are never screened, and employers screen applicants who may have already matched. We prove existence and uniqueness of equilibrium and characterize welfare for participants on both sides of the market. Results: We identify that the market operates in one of two regimes: It is either screening-limited or application-limited. In screening-limited markets, employer welfare is low, and some employers choose not to participate. This occurs when application costs are low and there are enough employers that most applicants match, implying that many screened applicants are unavailable. In application-limited markets, applicants face a “tragedy of the commons” and send many applications that are never read. The resulting inefficiency is worst when there is a shortage of employers. We show that simple interventions—such as limiting the number of applications that an individual can send, making it more costly to apply, or setting an appropriate market-wide wage—can significantly improve the welfare of agents on one or both sides of the market. Managerial implications: Our results suggest that platforms cannot focus exclusively on attracting participants and making it easy to contact potential match partners. A good user experience requires that participants not waste effort considering possibilities that are unlikely to be available. The operational interventions we study alleviate congestion by ensuring that potential match partners are likely to be available.

BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension

In this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a BMO-neighborhood in strain space where there are no other equilibrium solutions.

Unique equilibrium states for some intermediate beta transformations

We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with [Formula: see text] having the property that the orbit of 0 is bounded away from 1.