...This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, with the goal of choosing the lifespan parameter τ sufficiently small so that all the phase functions...

... to eliminate the error term in the parametrix. For the proof of the Main Lemma, estimates for Q and the material derivative as well as its spatial derivatives are derived. The chapter finds a solution to Equation (1069) with good transport properties by solving it via a Transport equation...

... with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful “Main Lemma”—used here to construct nonzero solutions...

... to the global frame constructed in Proposition 3.26. To recover α from q, the chapter derives a transport equation for α where q is on the RHS. It then derives as Teukolsky–Starobinsky identity a parabolic equation for α. The chapter also improves bootstrap assumptions for α. Theorem M2 Theorem M3 decay...

... of the granary, the market, and long-distance transport; food preparation, the realm of the kitchen; food consumption, the realm of the meal and, in many instances also, the realm of the table; and finally food disposal, the realm of the dustbin or refuse deposit and, par excellence, the realm of archaeology...

... linear programming relaxation pure assignment strong duality weak duality minimax theorem wage Becker copula discrete choice hedonic model principal–agent Walrasian Wasserstein Becker–Coase optimal transport Monge–Kantorovich problem optimal assignment worker assignment primal problem...

...This chapter focuses on Germany's adaptation of centralized controls of European raw materials, industry, and transport. German economic controls aim to utilize all resources of occupied Europe, manpower, raw materials, machines and machine tools, railroads and other vehicles, industrial capacities...

... displacement function elliptic element hyperbolic element semisimple element d dγ mγ X γ ⊂ X z a Z γ z γ Z0 γ Hessian parallel transport element ψa aTX' z⊥ a tγ g0 γ g0 z k K γ t γ t⊥ γ K0 γ pa ⊥ γ γ ⊥ γ za ⊥ γ Za ⊥ 0 γ z⊥ γ NX γ X pγ ργ Toponogov φf t df dx dy r f...

... bombings Madrid Spain subway attacks McClain Noah Molotch Harvey Moscow subway attacks profiling Spain subways terrorism terrorists Tokyo subway attacks color code alert system Fosher Kerry labor unions Metropolitan Transit Authority MTA Transport Workers Union Local 100 unions U S...

...Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation...

... suction with respect to coal and iron, and concludes with an analysis of the transport revolution during the period. industry innovation invention labor land mechanization organic economy power steam engine textiles Allen Robert price wood Austria Belgium England France Germany income...

...This chapter discusses how domestic market integration in Spain was much slower than it's integration with the international economy over the long run, and its progress was regionally extremely diverse. Poor transport technology and bad roads did not help matters and provide some of the background...

... geography did not lend itself easily to the technologically available means of improving transport either on water or land. However, the extent to which unfavorable transport conditions contributed to Spain's overall predicament and restricted market integration is poorly understood. Castile geography...

... field in space, the lifespan parameter, and the parameter used to make sure the phase functions are high frequency. In addition to the High–High term, the chapter considers the Transport term, which becomes large when a short lifespan is chosen. It also shows how the Transport term could be made to have...

.... The first transport derivative always costs a factor Ξeᵥ½ in the estimates, and each spatial derivative costs a factor of Ξ until the total order of differentiation exceeds L, at which point one obtains a larger cost of Nsuperscript 1/LΞ...

... Xiusuperscript l. These terms are the High–Low Interaction term, the main High–High terms, the remainder of the High–High terms, and the Transport term. For each of these factors, the parametrix expansion for the divergence equation is used. The error...

...This chapter examines the role of energy in the economic growth of ancient Greece, with particular emphasis on the impact of the cost of transportation. It first considers the different sources of energy in the Greek city-states, including heat generated by the sun, wood, and charcoal, before...

...This introductory chapter provides an overview of the book's main themes. This book discusses the problem of optimal transport (OT), which can be best exemplified by the problem of assigning workers to jobs: given the distribution of a population of workers with heterogeneous skills, and given...

... assignment Kantorovich linear programming relaxation permutation doubly stochastic matrix linear programming Kronecker product vectorization marginal probability distributions Monge–Kantorovich problem linear programming optimal transport We still consider the problem of assigning workers to jobs...

... minimization problem. The chapter discusses how to perform this computation in practice. Hotelling power diagram Voronoi tessellation optimal assignment tâtonnement discrete choice extreme point matching surplus worker assignment optimal assignment optimal transport computational geometry...