We prove an upper bound on computing advice for a language A in the class of languages acceptable in deterministic polynomial time with logarithmic advice, A 2 P=log), relative to A itself. We then provide conditions under which advice for a language A 2 P=log can be computed in PF(A), and conditions for the existence of a set A in P=log without advice in PF(A). We show that paddable languages ...

A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete category. It includes each finite-dimensional Lie group, each locally-compact group that has a compact quotient group modulo its identity compo...

We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given to notably addition of a...

The objective of this paper was to study and optimize the concrete paving operations taking place in the reconstruction project of Interstate 74 using simulation. To achieve this objective, field data were collected during construction, and were then used to determine adequate probabilistic density functions for the activities duration and to validate a developed simulation model. Upon validati...

background: the purpose of this study was to assess the vasopressin effect on operation time and the need for electrocauterization frequency and ovarian reserve during laparoscopic stripping of ovarian endometriomas. methods: this was a randomized prospective clinical trial, in which twenty patients between 18-35 years with unilateral endometriomas were randomly divided in two groups of cases a...

We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials n!m! and also derive asymptotic formulas for the number of solutions of various congruences with factorials. For example, we prove that the products of two factorials n!m! with max{n,m} < p1/2+ε are uniformly distributed modulo ...

We discuss three problems of the following kind: given a set A ⊆ Fp of n := |A| residues modulo a prime p, how are the absolute values |SA(z)| of the corresponding exponential sums SA(z) := ∑ a∈A e 2πi p ; z ∈ Fp distributed in the interval [0, n]?

We prove a higher dimensional generalization of Gross and Zagier’s theorem on the factorization of differences of singular moduli. Their result is proved by giving a counting formula for the number of isomorphisms between elliptic curves with complex multiplication by two different imaginary quadratic fields K and K′, when the curves are reduced modulo a supersingular prime and its powers. Equi...

A system of vertical wells was evaluated for its potential to add moisture into landfilled waste. Leachate (and groundwater) was added through 78 vertical wells installed at three different depths. The results of injection tests performed over a 17month duration are presented in this paper. A total of 17,700 m of leachate and groundwater were injected over ____hours of operation time. No signif...

Given a permutation π, the application of prefix reversal f (i) to π reverses the order of the first i elements of π. The problem of sorting by prefix reversals (also known as pancake flipping), made famous by Gates and Papadimitriou (Discrete Math., 27 (1979), pp. 47–57), asks for the minimum number of prefix reversals required to sort the elements of a given permutation. In this paper we stud...