## Search Theory: Some Recent DevelopmentsOn the solution of an optimal search problem with an exponential detection function. Covers one- and two-sided detection problems by furnishing continuous and discret time strategies; examines two-sided search strategies with solutions in hide and seek games in many discrete and continuous bounded |

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### Contents

Solution to an Optimal Search Problem | 7 |

A REVIEW OF RESULTS IN OPTIMAL SEARCH FOR MOVING TARGETS | 13 |

Optimal Searcher Path for a Moving Target | 27 |

CONTINUOUS SEARCH GAMES | 33 |

Search in Multidimensional Regions | 43 |

A DIFFERENTIAL EQUATIONS APPROACH | 55 |

The Differential Equations of Search Theory | 65 |

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Algebras algorithm allocation Alpern Appl Applications arcs assume assumption billiard boundary cell Chudnovsky consider constraint continuous continuous function Control Theory cost function defined denoted density detecting the target detection function detection search deterministic Differential Equations Differential Games domain dx dt dynamic systems e-covering e-Peano curve ergodic follows given graph immobile hider Kadane Koopman lateral range Lebesgue measure LEMMA linear search linear search problem Mangel Markov property Math Mathematics minimax mixed strategies models monster game oper optimal plans optimal search plan optimal search problem Poincaré recurrence theorem princess and monster probability of detecting random Ring Theory Ruckle satisfies search effort search equations search game search path search space search strategy search theory search trajectory searcher SIAM ſº solution solved stationary target stochastic sufficient conditions sweep width target location target motion theorem tion uniform distribution velocity Washburn York