We present new, efficient algorithms for computations on separable matrix algebras over infinite fields. We provide a probabilistic method of the Monte Carlo type to find a generator for the centre of a given algebra A ⊆ Fm×m over an infinite field F. The number of operations used is within a logarithmic factor of the cost of solving m×m systems of linear equations. A Las Vegas algorithm is als...

We present new, e cient algorithms for computations on separable matrix algebras over in nite elds. We provide a probabilistic of the Monte Carlo type to nd a generator for the centre of a given algebra A Fm m over an in nite eld F using a number of operations that is within a logarithmic factor of the cost of solving m m systems of linear equations. A Las Vegas algorithm is also provided under...

We extend some classical results of Cowling and Meda to the noncommutative setting. Let (Tt)t>0 be a symmetric contraction semigroup on a noncommutative space Lp(M), and let the functions φ and ψ be regularly related. We prove that the semigroup (Tt)t>0 is φ-ultracontractive, i.e. ‖Ttx‖∞ ≤ Cφ(t)‖x‖1 for all x ∈ L1(M) and t > 0 if and only if its infinitesimal generator L has the Sobolev embeddi...

We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q∗ through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm converges at a geometric rate. By applying the concept to three different examples, namely, the ...

An MgB2 race track coil intended for demonstrating a down scaled pole of a 10 MW direct drive wind turbine generator has been designed. The coil consists of 10 double pancake coils stacked into a race track coil with a cross section of 84 mm x 80 mm. The length of the straight section is 0.5 m and the diameter of the end sections is 0.3 m. Expanded to a straight section of 3.1 m it will produce...

The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”grow-and-cut procedure”. We extend this concept to real numbers and call this the real congruence, which produces another class of random number...

We prove the existence of a poly(n,m)-time computable pseudorandom generator which “1/poly(n,m)-fools” DNFs with n variables and m terms, and has seed length O(log nm · log log nm). Previously, the best pseudorandom generator for depth-2 circuits had seed length O(log nm), and was due to Bazzi (FOCS 2007). It follows from our proof that a 1/m-biased distribution 1/poly(nm)-fools DNFs with m ter...

We use a power grid model with M generators and N consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers connected to a generator does not exceed i...

Let G = a 1 ,. .. , a n | a i a j a i · · · = a j a i a j. .. , i < j be an Artin group and let m ij = m ji be the length of each of the sides of the defining relation involving a i and a j. We show if all m ij ≥ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups a i , a j for which m ij < ∞.

Machine Interpreters M. Anton Ertl1; ;y, David Gregg2, Andreas Krall1, and Bernd Paysan3 1Institut f ur Computersprachen, Technische Universit at Wien, Argentinierstra e 8, A-1040 Wien, Austria 2Department of Computer Science, Trinity College, Dublin 2, Ireland 3Stockmannstr. 14, D-81477 M unchen, Germany SUMMARY In a virtual machine interpreter, the code for each virtual machine instruction...