L.A. Shepp has posed aild analyzed the problem of optimal random drawinp with Jut replacement from an urn containing predetermined numbers of plus and minus balls. ;Here Shepp’s results are extended by improving the bounds on value; of penturbeu urns, deriving an exact algorithm for the urn values and computing the stopping boundary for urns of u-, tn 200 balls.

A k-uniform, d-regular instance of Exact Cover is a family of m sets Fn,d,k = {Sj ⊆ {1, . . . , n}}, where each subset has size k and each 1 ≤ i ≤ n is contained in d of the Sj . It is satisfiable if there is a subset T ⊆ {1, . . . , n} such that |T ∩ Sj | = 1 for all j. Alternately, we can consider it a d-regular instance of Positive 1-in-k SAT, i.e., a Boolean formula with m clauses and n var...

The Dial-A-Ride Problem (DARP) has often been used to organize transport of elderly and handicapped people, assuming that these people can book their transport in advance. But the DARP can also be used to organize usual passenger or goods transportation in real online scenarios with time window constraints. This paper presents an efficient exact algorithm with significantly reduced calculation ...

We derive the exact time-evolution for a general quantum system under the influence of a bosonic bath that causes pure phase noise and demonstrate that for a Gaussian initial state of the bath, the exact result can be obtained also within a perturbative time-local master equation approach already in second order of the system–bath coupling strength. We reveal that this equivalence holds if the ...

A field theoretical realization of topological gravity is discussed in the semirigid geometry context. In particular, its topological nature is given by the relation between deRham cohomology and equivariant BRST cohomology and the fact that all but one of the physical operators are BRST-exact. The puncture equation and the dilaton equation of pure topological gravity are reproduced, following ...

Let $K={\mathbb Q}(\alpha)$ be a number field generated by complex root $\alpha$ of monic irreducible polynomial $f(x)=x^{18}-m$, $m\neq \mp 1$, is square free rational integer. We prove that if $ m \equiv 2$ or $3 {\rm(mod }{ 4})$ and $m\not\equiv 1 9})$, then the $K$ monogenic. If $m\equiv not

Let $K$ be a pure number field generated by complex root of monic irreducible polynomial $F(x)=x^{60}-m\in \mathbb{Z}[x]$, with $m\neq \pm1$ square free integer. In this paper, we study the monogeneity $K$. We prove that if $m\not\equiv 1\md{4}$, \mp 1 \md{9} $ and $\overline{m}\not\in\{\mp 1,\mp 7\} \md{25}$, then is monogenic. But $m\equiv \mp1 \md{9}$, or 1\md{25}$, not Our results are illus...

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools. JEL G13

Using the ‘Riemann Problem with zeros’ method, Ward has constructed exact solutions to a (2 + 1)–dimensional integrable Chiral Model, which exhibit solitons with nontrivial scattering. We give a correspondence between what we conjecture to be all pure soliton solutions and certain holomorphic vector bundles on a compact surface. AMS Classification numbers Primary: 35Q51 Secondary: 58F07

An exact solution is found describing the collision of a class of axisymmetric pp-waves. They are impulsive in character and their coordinate singularities become point curvature singularities at the boundaries of the interaction region. The solution is conformally flat. Concrete examples are given, involving an ultrarelativistic black hole against a burst of pure radiation or two colliding bea...