the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

Finite and Infinite Sets. Countability. Proof Techniques (Chapter 1, Sections 1.4, 1.5) Finite sets finite number of elements can be counted Infinite sets infinite number of elements Equinumerous sets: Sets A and B are equinumerous if there is a bijection f : A → B E.G.: A = {1,2,3}, B = {a,b,c} Countably infinite sets: A set is countably infinite if it is equinumerous with N (the set of natura...

This special issue of ‘Hyperbolic Problems: Theory and Computation’ presents selected papers from the presentations given in the mini-symposium entitled ‘Recent Progress in Hyperbolic Problems: Theory and Computation’ at the International Conference on Applied Mathematics, Modeling and Computational Science (AMMCS 2013), taking place inWaterloo, Ontario, Canada from August 26 to 30, 2013. Hyper...

simply check whether all coefficients 1 2 , ,..., n i i i c F  are zero. The problem becomes non-trivial when the polynomial is given in an implicit form, e.g. as determinant of a matrix with polynomial entries. One can compute the determinant polynomial to express it in the above form. However, the size of the polynomial can grow exponentially in this process and so this algorithm is exponent...

We provide an introduction to Fredholm theory and discuss using the Fredholm determinant to compute pure-point spectra.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x Chapter

The routinely made assumptions for simulating solid materials are briefly summarized, since they need to be critically assessed when new aspects become important, such as excited states, finite temperature, time-dependence, etc. The significantly higher computer power combined with improved experimental data open new areas for interdisciplinary research, for which new ideas and concepts are nee...

Consider the DFA on the right. It has a particular defined start state. However, we could start it from any of its states. If the original DFA was named M , define Mq to be the DFA with its start state changed to state q. Then the language Lq, is the one accepted if you start at q. For example, in this picture, L3 is (a+b)∗, and L6 is the same. Also, L2 and L5 are both b∗a(a+b)∗. Finally, L7 is...

We generalize the notion of slice introduced in our earlier paper [6]. A slice of a distributed computation with respect to a global predicate is the smallest computation that contains all consistent cuts of the original computation that satisfy the predicate. We prove that slice exists for all global predicates. We also establish that it is, in general, NP-complete to compute the slice. An opt...

Submitted to the Department of Physics in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Physics and to the Department of Electrical Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degrees of Bachelor of Science in Electrical Engineering and Computer Science and Master of Engineering in Electrical Engineering and Computer Sci...