We obtain exact, simple and very compact expressions for the linearization coefficients of products orthogonal polynomials; both conventional Clebsch-Gordan-type modified version. The are general depending only on three-term recursion relation linearizing polynomials. These more appropriate useful doing numerical calculations when compared to other exact formulas found in mathematics literature...

I Directed polymers A Why bother? II Hamiltonian and Randomness A Pure case B Let’s put randomness 1 Hamiltonian 2 Partition function 3 Averages C What to look for? D Size: disorder and thermal correlation 1 Free energy fluctuation 2 Our Aim 3 Digression: Self-averaging III Q.: Is disorder relevant? A Annealed average: low temperature problem B Moments of Z 1 Hamiltonian for moments 2 Bound sta...

A manifestly gauge invariant exact renormalization group for pure SU(N) Yang-Mills theory is proposed, allowing gauge invariant calculations, without any gauge fixing or ghosts. The necessary gauge invariant regularisation which implements the effective cutoff, is naturally incorporated by embedding the theory into a spontaneously broken SU(N |N) super-gauge theory. This guarantees finiteness t...

We show that finding orthogonal grid-embeddings of plane graphs (planar with fixed combinatorial embedding) with the minimum number of bends in the so-called Kandinsky model (which allows vertices of degree > 4) is NP-complete, thus solving a long-standing open problem. On the positive side, we give an efficient algorithm for several restricted variants, such as graphs of bounded branch width a...

A 1.5D terrain is an x-monotone polyline with n vertices. An imprecise 1.5D terrain is a 1.5D terrain with a y-interval at each vertex, rather than a fixed y-coordinate. A realization of an imprecise terrain is a sequence of n y-coordinates—one for each interval— such that each y-coordinate is within its corresponding interval. For certain applications in terrain analysis, it is important to be...

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 ...