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implying that the sequence of stopping times τ U is increasing.
where H n is an increasing sequence of stopping times with H0=0, and the mapping (t,x ↦v n ((t 1,x 1),⋯, t n,x n );t,x) is in C 1,2.
The objective of the animal population is to choose the sequence of stopping times (tau_{i}) ((1 le i le M)), so that the sum of the cumulative profit gain in each habitat (H_{i}) ((0 le i le M - 1)) and the terminal wealth gained at the goal of migration (H_{M}), namely the performance index (J_{tau} ) in (2), is maximized.
Define the sequence of stopping times begin{aligned} &tau_{1}=infbigllbrace tgeqslant 0 : x_{i}(t) geqslant2varepsilonbigrrbrace,qquad tau_{2k}=infbigllbrace t geqslanttau_{2k-1} : x_{i}(t)leqslant varepsilonbigrrbrace, &tau_{2k+1}=infbigllbrace tgeqslanttau_{2k} : x_{i}(t geqslant 2varepsilonbigrrbrace,quad k=1,2,ldots.
Defining a sequence of stopping times: begin{aligned}& tau_{1}=infbigl{ tgeq0: x t geq theta_{2}bigr},& tau_{2k}=infbigl{ tgeqsigma_{2k-1}: x(t)leq theta_{1} bigr}, qquadtau_{2k+1}=infbigl{ tgeq sigma_{2k}: x(t)geqtheta_{2} bigr},quad k=1,2,ldots.
Let us now define a sequence of stopping times begin{aligned}& tau_{1}=infbigl{ tgeqslant0 : x_{i}(t geqslant2 epsilonbigr},qquad tau_{2k}=infbigl{ tgeqslant tau_{2k-1} : x_{i}(t)leqslant epsilonbigr}, & tau_{2k+1}=infbigl{ tgeqslanttau_{2k} : x_{i}(t geqslant 2epsilonbigr},quad k=1,2,ldots.
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"Years later, I've ridden the same sequence of stops routinely," Mr. Lethem wrote in an e-mail.
Wearing one allows subway riders an easy, and discreet, way of checking the sequence of stops — it takes only a glance at your wrist.
In its simplest version, a Pedibus line is a sequence of stops starting from a child home, visiting a sequence of other children's home, and ending at the school.
In the United Kingdom, for example, postwar policy involved a sequence of "stop-go" moves by government for stabilization; unfortunately these often occurred too late and had unintended destabilizing effects.
In order to do so, we convert the raw GPS locations into a sequence of stops at places.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com